The Lorna Prieta, California, Earthquake 

of October 17, 1989-Main-Shock Characteristics 

PAUL SPUDICH, Editor 

EARTHQUAKE OCCURRENCE 

WILLIAM H. BAKUN and WILLIAM H. PRESCOTT, Coordinators 

U.S. GEOLOGICAL SURVEY PROFESSIONAL PAPER 1550-A 

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1996 
DEPARTMENT OF THE INTERIOR 

BRUCE BABBITT, Secretary 

U.S. GEOLOGICAL SURVEY 

Gordon P. Eaton, Director 

Any use of trade, product, or firm names in this publication 

is for descriptive purposes only and does not imply endorsement 

by the U.S. Government 

Manuscript approved for publication, July 13, 1995 

Text and illustrations edited by George A. Havach 

Library of Congress catalog-card No. 92-32287 

For sale by the 

U.S. Geological Survey 

Information Services 

Box 25286 

Denver 'Federal Center 

Denver, CO 80225 
CONTENTS 

Rupture history of the earthquake from high- frequenc y 

strong-motion data ................................................... 

By Gregory C. Beroza 

Source characteristics of the earthquake from global digital 

Comparison of L and L2 norms in a teleseismic-waveform 

inversion for the rupture history of the earthquake ------------- 

By Stephen H. Hartzell, Gordon S. Stewart, and Carlos Mendoza 

Frequency-domain inversion for the rupture characteristics 

during the earthquake, using strong-motion data and 

geodetic observations - .............................................. 

By Stephen Horton, John G. Anderson, and Andres J. Mendez 

Broadband study of the source characteristics of the earthquake --- 

By Hiroo Kanamori and Kenji Satake 

Geodetic measurements of coseismic horizontal deformation ------ 

By Michael Lisowski, Mark H. Murray, and Jerry L. Svarc 

Elevation changes associated with the earthquake and their use 

to infer fault-slip geometry ......................................... 

By Grant A. Marshall and Ross S. Stein 

Main-shock and very early aftershock activity ........................ 

By Karen C. McNally, Gerald W. Simila, and Judy G. Brown 

Downdip geometry of the Loma Prieta rupture from teleseismicwaveform inversion ................................................. 

By John L. NAbZlek 

Mechanical modeling of a fault-fold system, with application 

Are rupture models consistent with geodetic measurements? ------- 

By Jamison H. Steidl and Ralph J. Archuleta 

Page 

A1 
Long-period surface-wave observations of the earthquake ---------- 

By Aaron A. Velasco, Thome Lay, and Jiajun Zhang 

Source parameters of the earthquake, determined by using 

longmperiod seismic waves ......................................... 

By Aaron A. Velasco, Thome Lay, and Jiajun Zhang 

Strong-motion and broadband teleseismic analysis of the 

earthquake for rupture-process modeling and hazard 

assessment -------------.----------------------------------------------- 

By David J. Wald, Donald V. Helmberger, and Thomas H. Heaton 

Coseismic displacements measured with the Global Positioning 

System -----------------.----------------------------------------------- 

By Chesley R. Williams and Paul Segall 

Estimation of the rupture velocity of the main shock from the 

Love-wave group velocity .......................................... 

By Francis T. Wu 

Use of stress-drop models to interpret GeodeliteIGlobal 

Positioning System and leveling measurements at 

Loma prieta----------------------------------------------------------- 

By Mingdong Wu and John W. Rudnicki 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAKE OCCURRENCE 

CONTENTS 

MAIN-SHOCK CHARACTERISTICS 

SYNOPSIS 

By Paul Spudich, 

U.S. Geological Survey 

Page 

A1 

1 

2 

2 

3 

3 

4 

4 

4 

4 

5 

5 

5 

6 

6 

SUMMARY OF SOURCE 

CHARACTERISTICS 

The October 17, 1989, Loma Prieta, Calif., earthquake 

(0004:15.2 G.m.t. October 18; lat 37.036' N., long 

121.883' W.; 19-km depth) had a local magnitude (M,,) 

of about 6.7, a surface-wave magnitude (Mr) of 7.1, a 

seismic moment of 2.2~10~~ N-m to 3.5x1019 N-m, a 

source duration of 6 to 15 s, and an average stress drop of 

at least 50 bars. Slip occurred on a dipping fault surface 

about 35 km long and was largely confined to a depth of 

about 7 to 20 km. The slip vector had a large vertical 

component, and slip was distributed in two main regions 

situated northwest and southeast of the hypocenter. This 

slip distribution caused about half of the earthquake's energy to be focused toward the urbanized San Francisco 

Bay region, while the other half was focused toward the 

southeast. Had the rupture initiated at the southeast end of 

the aftershock zone, shaking in the bay region would have 

been both longer and stronger. These source parameters 

suggest that the earthquake was not a typical shallow San 

Andreas-type event but a deeper event on a different fault 

with a recurrence interval of many hundreds of years. 

Therefore, the potential for a damaging shallow event on 

the San Andreas fault in the Santa Cruz Mountains may 

still exist. 

INTRODUCTION 

The source mechanism of the earthquake is one of the 

best determinations ever obtained, owing to the epicenter's 

location within a region with good geodetic control and 

numerous strong-motion accelerometers. In addition, the 

earthquake was large enough to be well recorded by globally distributed seismometers, though not so large as to 

clip on many global stations. Thus, we have been afforded 

an unusual opportunity to study earthquake-source mechanics and to cross-calibrate the source parameters (such 

as earthquake magnitude, seismic moment, fault location 

and extent, slip distribution, and associated stress change) 

determined by inversion of local geodetic data, teleseismic 

long-period surface waves and body waves, regional surface waves, and local strong-motion accelerations. 

The papers in this chapter address and attempt to resolve questions raised in earlier initial analyses of the 

earthquake. Many of these initial analyses were published 

in the ~ul~, August, and September 1990 issues of Geophysical Research Letters and in the October 1991 issue 

of the Bulletin of the Seismological Society of America. 

Although this introduction does not pretend to be a comprehensive review of the source process of the earthquake, 

I attempt to summarize the main findings of this chapter 

and place them in the context of previously unresolved 

questions. 

Several papers in this chapter document original data 

collection in greater detail than previously presented elsewhere. Lisowski documents and corrects the geodetic data 

set in the epicentral region previously analyzed by 

Lisowski and others (1990), which consists of position 

measurements using the Global Positioning System 

(GPS), distance measurements using a laser Geodolite, 
A2 MAIN-SHOCK CHARACTERISTICS 

and position changes measured using very long baseline 

interferometry. Marshall and Stein document the elevation differences observed in the epicentral region and used 

by Marshall and others (1991). Williams and Segall document an important new geodetic data set; they found that 

the California Department of Transportation (Caltrans) had 

conducted a GPS survey in the epicentral region during 

February and March 1989. Williams and Segall reoccupied eight of the Caltrans stations with GPS receivers in 

March 1990. Owing to the short timespan between these 

GPS surveys, they have been able to obtain estimates of 

coseismic displacements that are less affected by 

interseismic deformations than the data obtained by 

Lisowski (this chapter), Marshall and Stein (this chapter), 

or Snay and others (1991). 

Many of the tremendous number of seismic data obtained from the earthquake are not documented in this 

chapter, except that McNally and others present a unique 

set of epicentral digital-accelerometer recordings of the 

main shock and early aftershocks. These recordings show 

the largest peak accelerations measured during the main 

shock. Borcherdt (1994) provides references to other local main-shock strong-motion data. The best guide to the 

global digital-data set is the station list reported by Morelli 

(1994), and additional pointers and indications of data 

quality are provided by the first paper of Velasco and 

others (this chapter). 

Parts of some of the papers in this chapter have appeared elsewhere. Beroza expands on the report by Beroza 

(1991) by including a complete parametrization of his preferred finite-fault rupture model; a comparison of this 

model with those of Hartzell and others (1991), Steidl and 

others (1991), and Wald and others (1991); and a calculation of the long-period displacements that his model predicts in the epicentral region. Lisowski documents the 

data more thoroughly and finds an improved best-fitting 

fault plane over that of Lisowski and others (1990). 

Marshall and Stein document their data more completely, 

reanalyzing their leveling data to account for the covariances of the section elevation differences; they also consider the effect of low-velocity surface layers and 

low-velocity wedges between the Sargent and San Andrea~ faults. Wald and others review the rupture model 

that they previously constructed (Wald and others, 199 l), 

and examine several aspects of the use of such inversions 

for determining seismic hazards. They demonstrate that 

the smoothed rupture model derived from inversion of 

teleseismic body waves can be used to predict local strong 

ground motions fairly well. They use their preferred rupture model to predict ground motions throughout the 

epicentral region, and they estimate the regional strong' 

ground motions that would result from a Loma Prietatype event occurring at shallow depth on a vertical San 

Andreas fault. 

SOURCE PARAMETERS 

MAGNITUDE, MOMENT, AND DURATION 

From a compilation of global data, the International 

Seismological Center (1989) determined a surface-wave 

magnitude (My) of 7.1, which agrees with the initial assessment in the monthly "Preliminary Determination of 

Epicenters" published by the U.S. National Earthquake 

Information Center. The local magnitude (Mr) was reported by McNally and others (1990) as 6.88k0.44, based 

on 32 records, including several recordings on WoodAnderson seismographs in southern California. Uhrhammer 

and Bolt (1991) reported ML=6.7k0.09, based on 20 recordings within 105-km epicentral distance. These two 

estimates agree within their error bounds, and the discrepancy results from the use of different station sets and 

averaging methods. Both investigations used synthetic 

Wood-Anderson records derived from strong-motion 

accelerograms, and so the magnitudes inferred from individual stations are biased by known directivity effects and 

other amplification factors, such as the likely mantle reflected shear wave that boosted ground motions in San 

Francisco and Oakland (Somerville and Yoshimura, 1990). 

The seismic moments and source durations inferred from 

local geodetic data, teleseismic body and surface waves, 

and local strong-motion records largely agree. The seismic moment reported in this chapter ranges from 2.2~10~~ 

N-m (1 ~-m=10~ dyne-cm) to 3.5x1019 N-m, and the 

source duration from 6 to 15 s (table I), with all investigators agreeing that most of the slip occurred within the 

first 10 s (table 1). The discrepancies appear to result 

from assumptions of the modeling procedures and variations in data selection. The general agreement of the estimates of seismic moment and source duration is significant 

because it tends to refute the hypothesis of Wallace and 

others (199 1) that the total source duration was 18 to 30 s 

and may have involved deep, slow slip. They proposed 

this hypothesis because several earlier studies of longperiod surface waves and free oscillations, including those 

by Dziewonski and others (1990), Romanowicz and LyonCaen (1990), Zhang and Lay (1990), and Jordan (1991), 

yielded source-duration estimates of 20 to 44 s and centroid depths of about 20 km (see second paper by Velasco 

and others, this chapter). These depths and durations differ significantly from those inferred from the aftershock 

distribution and from geodetic and strong-motion models 

of the earthquake source. Velasco and others show that a 

shorter duration can be obtained from surface waves if 

higher resolution Earth velocity and attenuation models 

are used in the analysis. They believe that the source parameters inferred from surface-wave observations are consistent with those derived from body waves and that there 

is no evidence for slow, deep slip. Kanamori and Satake 
SYNOPSIS A3 

Table 1.-Determination of seismic moment and duration of the earthquake 

[Data types: btb, broadband teleseismic body waves; g, Geodolite, Global Positioning System; 1, leveling; la, local accelerograms; lpb, long-period body waves; 

Ips, long-period surface waves] 

Seismic Investigators Data Duration moment (this chapter) YPe (1019 N-~) (s) 

Beroza ........................... Is 

Choy and Boatwright --------- btb 

Hartzell and others ------------ btb 

Horton and others ------------- g, 1, la 

Kanamori and Satake ---------- lpb, Ips 

Lisowski and others----------- g 

Marshall and Stein------------- 1 

Nabelek ......................... ~P'J 

Velasco and others------------- IPS 

Wald and others ---------------- la, lpb 

Wu and Rudnicki -------------- g, 1 

'Starting 1.8 s after the origin time of Dietz and Ellsworth (1990). 

285 percent of seismic moment occurs in the first 7 to 10 s. 

(this chapter) also note a similarity of the moments derived from teleseismic body waves and 256-s-period surface waves, which they interpret as indicating no slow 

slip at the source. 

EXTENT AND LOCATION OF FAULTING 

LOCATION OF THE FAULT SURFACE 

An early controversy over the location of the faulting at 

depth, caused by a discrepancy between the slip surfaces 

inferred from geodetic measurements and aftershocks, has 

largely been resolved. On the basis of line-length changes, 

GPS data, and leveling data, Lisowski and others (1991) 

and Marshall and others (1991) obtained preliminary bestfitting fault planes that were displaced by several kilometers from the fault surface defined by aftershocks (Dietz 

and Ellsworth, 1990). This discrepancy has been extensively studied, and several assumptions of the preliminary 

geodetic modeling have been identified that would cause 

the geodetically inferred fault plane to be located systematically too shallow. 

The assumption of uniform slip on a rectangular fault 

plane is tested by Horton and others (this chapter), who 

invert the leveling data and obtain a smoothly varying 

slip distribution on a fault plane coincident with the aftershocks. The resulting data misfit is comparable to that of 

Marshall and others (199 1). 

The assumption of a laterally homogeneous, elastic Earth 

is tested by several authors. Steidl and Archuleta (this 

chapter) point out that slip on a fault plane coincident 

with the aftershock plane in a laterally homogeneous medium causes almost no motion of the geodetic monument 

on Loma Prieta. They claim that Lisowski and others 

(1990) were forced to offset their fault plane from the 

aftershocks, and that Snay and others (1991) were forced 

to introduce a bend into their fault surface, in order to 

match the observed displacement of Loma Prieta peak. 

This claim is consistent with the observation by Lisowski 

and others (1990) that the geodetic data most poorly fitted 

by their preliminary model come from the stations around 

Loma Prieta peak. Steidl and Archuleta show that if the 

geodetic observations involving Loma Prieta peak are excluded from the data set, then the surface deformations 

predicted by the slip model of Steidl and others (1991), in 

which the fault plane coincides with the aftershock zone, 

fit the remaining observations as well as do the deformations predicted by the slip model of Lisowski and others 

(1990). Eberhart-Phillips and Stuart (1992) showed that 

the low-rigidity material known to be present between the 

San Andreas and Zayante faults substantially alters the 

surface deformations caused by buried faults, especially 

around Loma Prieta, relative to the surface deformations 

predicted in a layered half-space. They show that to fit 

the observed displacements (which include the effect of 

the low-rigidity wedge) by using a half-space model, the 

fault would have to be shallower and to the southwest of 

its true position, as Lisowski and others (1990) and 

Marshall and others (1991) located it. 

The effects of the assumption of statistical independence of the geodetic data were estimated by ~rnadfittir 

and others (1992), who tested the effects of the assumed 

diagonal error-covariance matrices used by Lisowski and 

others (1990) and Marshall and others (199 1). ~rnadfittir 

and others found that if the off-diagonal terms of the error-covariance matrix were included in the misfit statistics for the leveling data, then their inversion method could 

find a best-fitting fault plane which coincided with the 

aftershock plane and fitted the leveling data slightly better than did Marshall and others' offset fault plane. Essentially, the difference between their approaches is that 

~rnadfittir and others used as data the height differences 

between adjacent bench marks, which is the quantity measured in leveling, whereas Marshall and others used as 

data the differences between preearthquake and 

postearthquake bench-mark elevations. knadfittir and others' suggestions also apply to the work of Wu and Rudnicki 

(this chapter), who use Marshall and others' data. 

~rnadfittir and others found that omission of the off-diagonal elements of the error-covariance matrix does not 

bias Lisowski and others' (1990) fault location appreciably, although by a more systematic search of model space 

~rnadfittir and others found a best-fitting fault plane closer 

to the aftershock plane than that found by Lisowski and 
A4 MAIN-SHOCK CHARACTERISTICS 

others (1990). Williams and others (1993) confirmed that 

a fault plane coincident with the aftershock zone is consistent with the Caltrans GPS measurements. Marshall and 

Stein (this chapter), incorporating the suggestions of 

~rnadottir and others (1992) and Eberhart-Phillips and 

Stuart (1992), confirm that the leveling data can be fitted 

by slip on a fault plane nearly coincident with the aftershock zone. They note, however, that the use of ~rnadottir 

and others' method achieves this coincidence by seriously 

downweighting the relatively few bench marks in the areas of greatest elevation change. 

EXTENT OF THE FAULT SURFACE 

The extent of fault rupture is best defined by modeling 

strong-motion data. This work assumes that the fault plane 

coincides with the aftershock zone. Beroza (this chapter) 

plots his slip distribution along with that of Hartzell and 

others (1991), Steidl and others (1991), and Wald and 

others (this chapter) on an identical scale, and all these 

models, as well as that of Horton and others (this chapter), agree that most of the slip occurred at a depth of 7 to 

20 km. In the horizontal direction, rupture was confined 

to a zone within 20 km of the hypocenter. Beroza (this 

chapter), Horton and others (this chapter), and Wald and 

others (this chapter) discuss the differences between the 

various strong-motion slip models. Long-period body- and 

surface-wave studies are largely consistent with the extent of faulting observed in strong-motion studies, although 

the spatial resolution of these long-period studies is poor. 

Nibglek (this chapter) notes that only the depth distribution of slip can be resolved well from long-period-bodywave studies; the horizontal propagation of rupture in this 

event is unresolvable if source mechanisms and time functions are unconstrained. He also points out that Hartzell 

and others could obtain a slip distribution from long-period body waves by assuming a mechanism, rupture velocity, and a slip time function at each point on the fault 

surface. Judging by the resemblance between Hartzell and 

others' slip distribution and the strong-motion slip distributions, those assumptions appear to have been appropriate. Kanamori and Satake (this chapter) derive a 35-km 

upper bound on rupture length from long-period body and 

surface waves, which they note is anomalously short for 

an event with a moment magnitude of 6.9. 

The fault-length estimates from geodetic studies are 

probably biased slightly high by an assumption of uniform slip or stress drop over the fault surface. These studies, however, yield fault lengths similar to or slightly larger 

than those obtained in seismic studies: 32.4 krn (Snay and 

others, 1991), 37 km (Lisowski and others, this chapter), 

31 to 37 km (Marshall and Stein, this chapter), and 40 to 

44 km (Wu and Rudnicki. this chapter). 

If most of the slip in the main shock was confined to a 

depth greater than 7 km, then the surface cracks observed 

in the Summit Ridge area and Foothills thrust belt (Ponti 

and Wells, 1991) may have resulted from folding of 

surficial sedimentary layers overlying a tectonically offset basement, although other mechanisms, such as 

landsliding, may be possible. Reches and Zoback (this 

chapter) examine a model of horizontal elastic layers 

draped over a faulted basement. They show how terrnination of the rupture at depth leads to extension southwest 

of the tip of the buried rupture and compression northeast 

of the tip; they correlate these zones of extension and 

compression with the surface cracks observed in the Summit Ridge area and Foothills thrust belt. In their mechanical model, a vertical zone of increased shear stress develops 

that they correlate with the shallow aftershock zone, although their shear-failure criterion neglects the preexisting stress field. Though not accounting for regions of 

compression or dilation directly, the mechanical model of 

Eberhart-Phillips and Stuart (1992) may similarly explain 

the surface cracks. 

SLIP DISTRIBUTION AND MECHANISM 

One of the most surprising observations about the slip 

distribution is as yet unexplained from a mechanical standpoint. The teleseismic observations of Hartzell and others 

(1991), the strong-motion observations of Steidl and others (1991), Beroza (this chapter), and Wald and others 

(this volume), and the leveling data of Marshall and Stein 

(this volume) are all consistent with the conclusion that 

most slip in the earthquake occurred in two regions, situated northwest and southeast of the hypocenter, and that 

slip in the southeasterly region was predominantly strike 

slip, whereas slip in the northwesterly region had a considerable thrust component. Most investigators reported 

little slip at the hypocenter; there is as yet no satisfactory 

explanation for the cause of this variation in rake. The 

slip models of Steidl and others (1991) and Beroza (this 

chapter) show the largest variations in rake. Beroza's 

model probably represents an upper bound on the variation in rake because he constructs models with less rake 

rotation that fit his data nearly as well as does his preferred model. It seems quite well established, however, 

that slip to the northwest of the hypocenter had a considerably larger thrust component than slip to the southeast. 

In general, the average slip direction in strong-motion 

source models agrees well with the mechanism of initial 

slip at the hypocenter, determined by Oppenheimer (1990) 

to be oblique slip. 

DYNAMIC BEHAVIOR OF THE SOURCE 

RUPTURE INITIATION 

Wald and others (this chapter) observe that during the 

first 1.8 s after Dietz and Ellsworth (1990)'s origin time, 
SYNOPSIS A5 

the earthquake appeared to be a rather small (M-5), slowly 

growing event. After 1.8 s, however, the energy radiated 

by the source grew enormously, and this later energy was 

large enough to trigger local strong-motion instruments. 

Similar behavior was noted in the initiation of the 1979 

Imperial Valley, Calif., earthquake (Hartzell and Heaton, 

1983) and the 1987 Superstition Hills, Calif., earthquake 

(Wald and others, 1990). These observations are critical 

to the question whether large earthquakes start as small 

earthquakes that grow out of control. A careful analysis 

of the initiation of these events may provide a critical test 

of the feasibility of earthquake prediction. 

RUPTURE VELOCITY AND RISE TIME 

Although most investigators agree on the slip distribution of the earthquake, they differ significantly regarding 

the temporal evolution of the source. The inversions of 

Steidl and others (1991), Beroza (this chapter), and Wald 

and others (this chapter) all assume that slip at any point 

on the fault can happen only during a relatively brief time 

window (~2-s duration). The initiation and termination of 

this time window are controlled by an assumed rupture 

velocity. Steidl and others obtained an average rupture 

velocity of 3.0 km/s and a velocity of 3.4 kds for propagation to the southeast, Beroza obtains a rupture velocity 

of 2.7 to 3.1 km/s, and Wald and others obtain a rupture 

velocity of 2.5 kds. Each model assumes that rupture 

propagates to the northwest and southeast simultaneously. 

Horton and others (this chapter) use a frequency-domain 

inversion technique that allows much greater freedom in 

the rupture behavior; their rupture model shows rupture to 

the northwest initiating after rupture to the southeast. 

Moreover, they obtain a higher rupture velocity of 3.5 to 

5 kds. Because of restrictions on the parametrizations in 

the other studies, it would be impossible for them to obtain this solution. Horton and others' solution must therefore be regarded as preliminary because they use a small 

data set, and, in particular, the timing of northwest-propagating rupture in their model depends strongly on the assumed timing of the accelerogram at station SAR. The net 

effect, however, is that the thrust component of the earthquake follows the strike-slip component, consistent with 

the teleseismic observations of Romanowicz and LyonCaen (1990) and NAbElek (this chapter), who observe a 

predominance of thrust faulting at a late stage of the rupture. These observations, however, do not prove that thrusting occurred late in the rupture process. In fact, they imply 

a curious scenario of initial oblique slip at the hypocenter 

(Oppenheimer, 1990), followed by strike-slip faulting to 

the southeast, then by oblique faulting to the northwest. 

The various source models of the earthquake differ radically in the slip duration estimated for each point on the 

fault. Steidl and others (1991) obtained a slip duration 

(rise time) of 1.0 s, Beroza (this chapter) 0.3 s, and Wald 

and others (this chapter) approximately 1.0 s, although 

Horton and others (this chapter) obtain a rise time of 1.75 

s at the point of maximum slip. These varying results 

have fundamentally different implications for the mechanics of earthquake rupture (Heaton, 1990). 

STRESS DROP, FRACTURE ENERGY, AND 

RECURRENCE INTERVAL 

The inferred stress drop and fracture energy of the earthquake generally support a long recurrence interval (much 

more than 100 yr) for this event, on the basis of the notion that high stress drops and fracture energies correlate 

with stronger faults having longer recurrence intervals. 

Kanamori and Satake (this chapter) note that the rupture 

length of the earthquake is anomalously short relative to 

those of other earthquakes with similar seismic moments. 

A short rupture length implies a high stress drop. Kanamori 

and Satake's calculation of a 50-bar static-stress drop is 

consistent with Choy and Boatwright's (this chapter) estimate of a dynamic-stress drop of 51 bars. Houston (1990) 

noted that the earthquake's stress drop is rather high for 

an interplate event and is more similar to that of intraplate 

events; she furthermore observed, on the basis of correlation with other events, that a high stress-drop implies a 

long recurrence interval. From their geodetic model, Wu 

and Rudnicki (this chapter) calculate a static-stress drop 

of 20 to 26 bars, which also is probably a lower bound on 

the stress drop, owing to their high estimates of fault length 

(table 1). They also estimate a maximum energy-release 

rate (fracture energy) of more than 5.5~10~ ~/m~, which 

they consider to be in the upper range of observed fracture energies, implying a strong fault and a long recurrence interval. All of these stress-drop estimates are 

averages over a presumed-large fault surface. Taking into 

account the actual double-peaked slip distribution of the 

earthquake, Wald and others (this chapter) estimate stress 

drops of 218 bars for the northwest slip patch and 136 

bars for the southeast slip patch. These stress drops further support the notion that the fault segments that slipped 

in the earthquake were relatively strong. Additional support for this idea comes from Michael and Eberhart-Phillips 

(1991), who found that the two regions of high slip in the 

strong-motion models are correlated with regions of high 

P-wave velocity obtained from inversions of earthquake 

arrival-time data. 

STRONG-MOTION GEODESY 

Several of the papers in this chapter (for example, 

Beroza, Horton and others, and Steidl and Archuleta) are 

notable in showing that the boundary between geodesy 
A6 MAIN-SHOCK CHARACTERISTICS 

and seismology is blurring, with interesting implications 

for earthquake engineering. These papers predict coseismic 

static surface deformations from slip models derived from 

strong-motion accelerograms, using established 

seismologic methods. It has been recognized that permanent ground offsets can be recovered from digital-accelerometer recordings of ground motions (Anderson and others, 

1986). Beroza obtains static displacements of 10 to 20 cm 

from integration of a digital accelerogram of the earthquake recorded near San Jose, Calif., and he shows that 

his slip model predicts such displacements. In the future, 

the behavior of fault slip over periods of 1 s to a few days 

will probably be observable by a combination of strongmotion accelerometers and GPS instruments. Heaton and 

Hartzell(199 1) noted that from an engineering standpoint, 

the large static displacements that occur within the first 

few seconds of an earthquake may have serious consequences for current base-isolated structures because the 

isolators typically are not designed to accommodate excursions as large as those observed. 

IMPLICATIONS FOR SEISMIC 

HAZARDS 

Taken together, these results suggest that the earthquake 

was not the typical shallow strike-slip San Andreas event 

anticipated by the Working Group on California Earthquake Probabilities (1988). Beroza (this chapter) points 

out that the great depth of slip suggests that the earthquake occurred on a fault distinct from the San Andreas 

fault, and that the San Andreas fault itself may have acted 

as an obstacle to rupture in this event. He cites the work 

of Segall and Lisowski (1990), who showed that the movement of Loma Prieta in 1989 was quite different from that 

in 1906, further distinguishing the 1989 Loma Prieta earthquake from typical San Andreas events. Certainly, the 

considerable thrust component of slip in 1989 differed 

considerably from that in 1906. Therefore, Beroza states 

that the seismic hazard in the Santa Cruz Mountains may 

still be high, owing to the possibility of a shallow San 

Andreas event there. Wald and others (this volume), who 

estimate ground motions for an event on the shallow San 

Andreas fault, show that such an event might cause stronger shaking in the Santa Cruz Mountains than those caused 

by the 1989 Loma Prieta earthquake, simply because of 

its shallower depth. 

The earthquake source could have caused considerably 

more damage, had its rupture behavior not been so mercifully brief and simple, and had it been shallower. Kanamori 

and Satake (this chapter) show that the duration of the 

earthquake was considerably shorter than that of the 1988 

Armenia earthquake, despite their similar magnitudes. In 

addition, shaking in the densely urbanized regions of the 

San Francisco Bay region could have been either significantly stronger or weaker under equally likely rupture scenarios. The bilateral rupture propagation in the earthquake 

focused a significant fraction of the seismic energy toward the less urbanized southeastward direction; rupture 

initiation at the southeast end of the causative fault would 

have increased the intensity of shaking around the bay, 

whereas rupture initiation at the northwest end of the causative fault would have focused more shaking toward 

Hollister, Calif., and less toward the bay. 

REFERENCES CITED 

Anderson, J.G., Bodin, Paul, Brune, J.N., Prince, Jorge, Singh, S.K., 

Quaas, Roberto, and Onate, Mario, 1986, Strong ground motion 

from the Michoacan, Mexico, earthquake: Science, v. 233, no. 4768, 

p. 1043-1049. 

Arnadottir, Thora, Segall, Paul, and Matthews, M.V., 1992, Resolving 

the discrepancy between geodetic and seismic fault models for the 

1989 Loma Prieta, California, earthquake: Seismological Society of 

America Bulletin, v. 82, no. 5, p. 2248-2255. 

Beroza, G.C., 1991, Near-source modeling of the Loma Prieta earthquake: Evidence for heterogeneous slip and implications for earthquake hazards: Seismological Society of America Bulletin, v. 81, 

no. 5, p. 1603-1621. 

Borcherdt, R.D., ed., 1994, The Loma Prieta, California, earthquake of 

October 17, 1989-strong ground motions: U.S. Geological Survey 

Professional Paper 1551-A, 272 p. 

Choy, G.L., and Boatwright, John, 1990, Source characteristics of the 

Loma Prieta, California, earthquake of October 18, 1989 from global digital seismic data: Geophysical Research Letters, v. 17, no. 8, 

p. 1183-1 186. 

Dietz, L.K., and Ellsworth, W.E., 1990, The October 17, 1989, Loma 

Prieta, California, earthquake and its aftershocks; geometry of the 

sequence from high-resolution locations: Geophysical Research Letters, v. 17, no. 9, p. 1417-1420. 

Dziewonski, A.M., Ekstrom, Goran, Woodhouse, J.H., and Zwart, 

Gretchen, 1990, Centroid moment tensor solutions for OctoberDecember 1989: Physics of the Earth and Planetary Interiors, v. 62, 

no. 3-4, p. 194-207. 

Eberhart-Phillips, D.M., and Stuart, W.D., 1992, Material heterogeneity 

simplifies the picture; Loma Prieta: Seismological Society of 

America Bulletin, v. 82, no. 4, p. 1964-1968. 

Hartzell, S.H., and Heaton, T.H., 1983, Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of 

the 1979 Imperial Valley, California, earthquake: Seismological 

Society of America Bulletin, v. 73, no. 6, pt. A, p. 1553-1583. 

Hartzell, S.H., Stewart, G.S., and Mendoza, Carlos, 1991, Comparison 

of L and L2 norms in a teleseismic waveform inversion for the slip 

history of the Loma Prieta, California, earthquake: Seismological 

Society of America Bulletin, v. 8 1, no. 5, p. 15 18-1539. 

Heaton, T.H., 1990, Evidence for and implications of self-healing pulses 

of slip in earthquake rupture: Physics of the Earth and Planetary 

Interiors, v. 64, no. 1, p. 1-20. 

Heaton, T.H., and Hartzell, S.H., 1991, Near field ground motions in 

large earthquakes and base-isolated structures [abs.]: Seismological 

Research Letters, v. 62, no. 1, p. 49. 

Houston, Heidi, 1990, A comparison of broadband source spectra, seismic energies, and stress drops of the 1989 Loma Prieta and 1988 

Armenian earthquakes: Geophysical Research Letters, v. 17, no. 9, 

p. 1413-1416. 
SYNOPSIS A7 

International Seismological Centre Bulletin, 1989: v. 26, no. 1, p. 109. 

Jordan, T.H., 1991, Far-field detection of slow precursors to fast seismic ruptures: Geophysical Research Letters, v. 18, no. 11, p. 2019- 

2022. 

Kanamori, Hiroo, and Satake, Kenji, 1990, Broadband study of the 1989 

Loma Prieta earthquake: Geophysical Research Letters, v. 17, no. 

8, p. 1179-1182. 

Lisowski, Michael, Prescott, W.H., Savage, J.C., and Johnston, M.J.S., 

1990, Geodetic estimate of coseismic slip during the 1989 Loma 

Prieta, California, earthquake: Geophysical Research Letters, v. 17, 

no. 9, p. 1437-1440. 

Marshall, G.A., Stein, R.S., and Thatcher, Wayne, 1991, Faulting geometry and slip from co-seismic elevation changes; the 18 October 

1989, Loma Prieta, California, earthquake: Seismological Society 

of America Bulletin, v. 81, no. 5, p. 1660-1693. 

McNally, K.C., Yellin, Joseph, Protti-Quesada, Marino, Simila, G.W., 

Malavassi, Eduardo, Schillinger, Walter, Terdiman, Richard, and 

Zhang, Zhi, 1990, The local magnitude of the 18 October 1989 

Santa Cruz Mountains earthquake is ML=6.9: Geophysical Research 

Letters, v. 17, no. 10, p. 1781-1784. 

Michael, A.J., and Eberhart-Phillips, D.M., 1991, Relations among fault 

behavior, subsurface geology, and three-dimensional velocity models: Science, v. 253, no. 5020, p. 651-654. 

Morelli, Andrea, 1994, 1994 status report of the Federation of Digital 

Seismographic Networks: Annali di Geofisica, v. 37, no. 5, p. 1037- 

1112. 

Ponti, D.J., and Wells, R.E., 1991, Off-fault ground ruptures in the 

Santa Cruz Mountains, California; ridge-top spreading versus tectonic extension during the 1989 Loma Prieta earthquake: Seismological Society of America Bulletin, v. 81, no. 5, p. 1480-1510. 

Romanowicz, B.A., and Lyon-Caen, Helene, 1990, The Lorna Prieta 

earthquake of October 18, 1989; results of teleseismic mantle and 

body-wave inversion: Geophysical Research Letters, v. 17, no. 8, p. 

1191-1 194. 

Oppenheimer, D.H., 1990, Aftershock slip behavior of the 1989 Loma 

Prieta, California earthquake: Geophysical Research Letters, v. 17, 

no. 8, p. 1199-1202. 

Segall, Paul, and Lisowski, Michael, 1990, Surface displacement in the 

1906 San Francisco and 1989 Loma Prieta earthquakes: Science, v. 

250, no. 4985, p. 1241-1244. 

Snay, R.A., Neugebauer, H.C., and Prescott, W.H., 1991, Horizontal 

deformation associated with the Loma Prieta earthquake: Seismological Society of America Bulletin, v. 81, no. 5, p. 1647-1659. 

Somerville, P.G., and Yoshimura, Joanne, 1990, The influence of critical Moho reflections on strong ground motions recorded in San 

Francisco and Oakland during the 1989 Loma Prieta earthquake: 

Geophysical Research Letters, v. 17, no. 8, p. 1203-1206. 

Steidl, J.H., Archuleta, R.J., and Hartzell, S.H., 1991, Rupture history 

of the 1989 Loma Prieta, California, earthquake: Seismological Society of America Bulletin, v. 81, no. 5, p. 1573-1602. 

Uhrhamrner, R.A., and Bolt, B.A., 1991, The seismic magnitude of the 

1989 Loma Prieta main shock determined from strong-motion 

records: Seismological Society of America Bulletin, v. 81, no. 5, p. 

1511-1517. 

Wald, D.J., Helmberger, D.V., and Hartzell, S.H., 1990, Rupture process of the 1987 Superstition Hills earthquake from the inversion of 

strong-motion data: Seismological Society of America Bulletin, v. 

80, no. 5, p. 1079-1098. 

Wald, D.J., Helmberger, D.V., and Heaton, T.H., 1991, Rupture model 

of the 1989 Loma Prieta earthquake from the inversion of strongmotion and broadband teleseismic data: Seismological Society of 

America Bulletin, v. 81, no. 5, p. 1540-1572. 

Wallace, T.C., Velasco, A.A., Zhang, Jiajun, and Lay, Thorne, 1991, A 

broadband seismological investigation of the 1989 Loma Prieta, 

California, earthquake; evidence for deep slow slip?: Seismological 

Society of America Bulletin, v. 81, no. 5, p. 1622-1646. 

Williams, C.R., ~rnaddttir, Thora, and Segall, Paul, 1993, Coseismic 

deformation and dislocation models of the 1989 Lorna Prieta earthquake derived form Global Positioning System measurements: Journal of Geophysical Research, v. 98, no. B3, p. 4567-4578. 

Working Group on California Earthquake Probabilities, 1988, 

Probabilities of large earthquakes occurring in California on the 

San Andreas Fault: U.S. Geological Survey Open-File Report 88- 

398, 62 p. 

Zhang, Jiajun, and Lay, Thorne, 1990, Source parameters of the 1989 

~oma Prieta earthquake determined from long-period Rayleigh 

waves: Geophysical Research Letters, v. 17, no. 8, p. 1195- 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAKEOCCURRENCE 

MAIN-SHOCK CHARACTERISTICS 

RUPTURE HISTORY OF THE EARTHQUAKE 

FROM HIGH-FREQUENCY STRONG-MOTION DATA 

CONTENTS 

By Gregory C. Beroza, 

Stanford University 

Page 

A9 

9 

10 

12 

14 

23 

24 

26 

27 

29 

30 

3 1 

3 1 

3 1 

ABSTRACT 

I have derived a rupture model for the 1989 Loma Prieta 

earthquake, using data from 20 strong-motion instruments 

that recorded the main shock in the near-source region. 

The earthquake ruptured bilaterally at approximately 80 

percent of the local shear-wave velocity over a total distance of slightly more than 30 km, from 13 km northwest 

to 20 km southeast of the hypocenter. Slip over the rupture surface was highly irregular in both amplitude and 

direction. Slip amplitude at the hypocenter and immediately updip was only about 1 m. There were two main 

areas of high slip: one centered 7 km northwest of the 

hypocenter at a depth of 14 km and the other centered 6 

km southeast of the hypocenter at a depth of 12 km. Peak 

slip amplitudes on both of these high-slip areas exceeded 

4.5 m. A surprising aspect of this rupture model is that 

the rake ranges from predominantly strike slip to the southeast to predominately reverse slip to the northwest. Despite this variation in rake, the equivalent point-source 

moment tensor matches that found from teleseismic observations. A correlation exists between areas of high slip 

and areas of low aftershock activity. A simple explanation is that areas of high slip are areas of high strength, 

which slip only during infrequent large events. Other areas of the fault are weaker and may slip both seismically 

and aseismically. Most of the slip in the earthquake occurred at 9- to 16-km depth on a structure that dips southwest and runs underneath the surface trace of the San 

Andreas fault at 8- to 10-km depth. This observation complicates the assessment of seismic hazard on the southern 

Santa Cruz Mountains section of the San Andreas fault. 

INTRODUCTION 

In this paper, I present a rupture model of the earthquake, compare this model with other published extendedsource models of the main shock, and discuss its 

implications for earthquake-source mechanics and seismic hazard. The main shock occurred at OO:O4: 15.2 G.m.t. 

on October 18, 1989, at lat 37.040' N., long 121.880Â W., 

at 17-km depth (Dietz and Ellsworth, 1990), southwest of 

the southern Santa Cruz Mountains section of the San 

Andreas fault. Aftershocks extended bilaterally from the 

hypocenter for a distance of approximately 50 km, filling 

a region that had previously shown relatively little microearthquake activity (U.S. Geological Survey staff, 

1990). The locations of aftershocks with respect to the 

hypocenter suggest that the rupture propagated bilaterally 

along strike and unilaterally updip. Below about 10-krn 

depth, the aftershocks define a plane dipping 65'-70' SW. 

(Dietz and Ellsworth, 1990) that, if continued to the surface, would crop out near the surface trace of the Sargent 

fault. Above 10 km depth, however, where the fault is 

approximately beneath the surface trace of the San Andreas fault, the aftershock distribution is more diffuse and 

does not define a single plane (Dietz and Ellsworth, 1990). 

At the south end of the aftershock zone, the fault surface 

defined by aftershocks grades into a vertical fault plane 

beneath the surface trace of the San Andreas fault. The 

local magnitude (Mr) of 6.9 for the earthquake (McNally 

and others, 1990) is consistent with estimates of the scalar seismic moment of 1.7~10~~ to 3.4~10~~ N-m (for 

example, Kanamori and Satake, 1990), which yield an 

estimate of Mw=6.9 (Hanks and Kanamori, 1979). 
A10 MAIN-SHOCK CHARACTERISTICS 

The 1989 Loma Prieta earthquake has been the subject 

of numerous studies that used teleseismic records to determine the source parameters (Barker and Salzberg, 1990; 

Choy and Boatwright, 1990; Kanamori and Satake, 1990; 

Langston and others, 1990; Ndbelek, 1990; Romanowicz 

and Lyon-Caen, 1990; Ruff and Tichelaar, 1990; Zhang 

and Lay, 1990). All of these studies are quite consistent 

and indicate oblique slip on a fault dipping approximately 

70' and striking approximately 130'. These results, in 

turn, agree well with the average dip and strike based on 

well-located aftershocks recorded by the densely spaced, 

high-gain stations of the U.S. Geological Survey (USGS)'s 

northern California seismic network (Calnet) (Dietz and 

Ellsworth, 1990). The teleseismically determined rake is 

approximately 135' (for example, Zhang and Lay, 1990), 

consistent with a constant-slip model of the earthquake 

with 1.6 m of strike slip and 1.2 m of dip slip determined 

from analysis of geodetic data (Lisowski and others, 1990). 

Near-source strong-motion data can greatly increase 

the resolution of details of the rupture process. In this 

paper, I analyze strong-motion data from the near-source 

region of the main shock. I fit the near-source data by 

modeling the earthquake with spatially varying slip on an 

extended planar fault. I find that the region of high slip in 

the earthquake is quite compact, with a rupture length of 

slightly more than 30 km. There is evidence of complexity in the rupture process, with slip amplitude exceeding 5 

m locally and slip direction varying strongly and systematically from northwest to southeast. Finally, because most 

slip occurred below 10-km depth, the coincidence of longterm forecasts of an earthquake on the San Andreas fault 

in the southern Santa Cruz Mountains (Working Group on 

California Earthquake Probabilities, 1988) with the occurrence of the 1989 Loma Prieta earthquake may have 

been fortuitous. A possible interpretation of my results is 

that the earthquake began at 18-km depth on a fault distinct from the San Andreas, ruptured updip along that 

fault, and terminated -10-km depth when it reached a 

vertical San Andreas fault, which acted as an obstacle to 

further rupture propagation. 

STRONG-MOTION DATA 

The earthquake occurred in a region that is densely 

instrumented with strong-motion accelerographs. Because 

strong-motion instruments record data onscale in the nearsource region, where the Green's functions for different 

segments of the fault vary widely, these data can resolve 

detailed aspects of the rupture process that are unresolvable 

using data from the teleseismic far field, where most of 

the variation in the Green's functions for different segments of the fault is simply due to a difference in phase 

(Aki and Richards, 1980, v. 2, p. 804-805). The abundance of high-quality data in the near-source region of the 

earthquake provides one of the best opportunities to date 

to study the rupture process of a large event. 

Near-source data were collected on film-recording, analog strong-motion instruments operated by the USGS 

(Maley and others, 1989) and the California Division of 

Mines and Geology (CDMG) (Shakal and others, 1989), 

and on digital instruments deployed in the epicentral region before the main shock by the University of California, Santa Cruz (UCSC) (Simila and others, 1990). Many 

of these instruments use absolute time from radio station 

WWVB code. The locations of stations used in the analysis are shown in figure 1 and listed in table 1. 

The acceleration data were obtained after instrument 

correction and resampling at a uniform interval. The data 

were processed by filtering with a two-pole, zero-phase 

Butterworth filter with low- and high-cut corner frequencies at 0.33 and 2.0 Hz. The high-frequency corner represents the limit at which the seismograms could be modeled 

deterministically, and the low-frequency limit was constrained by the requirement in the high-frequency, nearsource approximation that the receivers be several 

wavelengths from the nearest segment of the fault (Spudich 

and Frazer, 1984). Finally, the horizontal components of 

motion were rotated into a coordinate system with the xaxis parallel to the strike of the fault (130' clockwise 

from north), the z-axis pointing downward, and the y-axis 

forming a right-handed system (220' clockwise from 

north). 

The aftershock zone and the distribution of strong-motion stations deployed by the CDMG, USGS, and UCSC 

that recorded the main shock are shown in figure 1. Data 

from the 20 stations (solid triangles, fig. 1) were used; 

other nearby stations (open triangles) were excluded either because the instruments are not free-field sites (for 

example, sta. WATS), the source-receiver distances are 

too large (most stations), or the local site geology makes 

it difficult to predict waveforms (for example, sta. SCA). 

The fault-perpendicular (220') and fault-parallel (130') 

components of displacement in the frequency band 0.2-5 

Hz for the 20 stations used in the inversion are plotted in 

figure 2. ' 

Because some of the UCSC stations were not secured 

to the ground, they may have moved during the earthquake and thus not faithfully recorded true ground acceleration. One UCSC station could be checked because it 

was deployed very near a CDMG station (SCZ, fig. 1) on 

the UCSC campus. Except for a difference in the orientation of the sensors, the two seismograms agree quite 

closely. Another station (LGP) of more concern, located 

at the Los Gatos Presentation Center, had the highest peak 

acceleration of any of the stations and may have moved 

during the earthquake. The closest CDMG station is at the 

Lexington Dam (LEX). As plotted in figure 2, the 220' 

component of motion is quite similar at these two stations, whereas the 130Â°componen of motion differs con- 
RUPTURE HISTORY OF THE EARTHQUAKE FROM HIGH-FREQUENCY STRONG-MOTION DATA A1 1 

siderably. This is attributable to the fact that the 130' 

component of motion should be nearly nodal for each 

station, and so the waveforms are not expected to be similar. The resemblance of the station LGP data to the station LEX data, and the successful prediction of the ground 

motion at station LGP by the rupture model, indicate that 

any motion of the instrument with respect to the ground 

probably did not affect the data greatly. Owing to the 

important locations of the UCSC stations, I have included 

them in the analysis. The important features of the rupture 

model, however, are not determined solely by these data. 

By examining the gross features of the displacement 

data, we can anticipate some aspects of the inversion results. As shown in figure 2, the duration of strong shaking 

is less than 10 s at all stations, indicating that the strong 

ground motion is generated by a much smaller source 

than the -50-km-long aftershock zone would suggest. The 

displacements at station COR (fig. I), which is directly 

updip from the hypocenter, and at other stations near the 

center of the aftershock zone (BRN, CAP) are relatively 

small, indicating that slip in the hypocentral region and 

directly updip is relatively low. In contrast, displacements 

at stations to the northwest (LGP, LEX, STG) are much 

larger. These data are affected primarily by slip on the 

fault northwest of the hypocenter, indicating that slip in 

this region is higher than in the hypocentral region. Similarly, the displacements at stations to the southeast (Gilroy 

array, GHB, HDA) are large, indicating that the southFigure 1.-Epicentral region of the earthquake, showing locations of aftershocks (x's), 

mapped surface traces of major faults (heavy lines), and strong-motion stations (triangles). 

Solid triangles, 20 strong-motion stations used in the inversion; open triangles, other 

stations not used because they were too far from epicenter, had obvious effects due to 

unmodeled velocity structure, or were not free-field sites. 
A12 MAIN-SHOCK CHARACTERISTICS 

Table 1 .-Strong-motion stations used in the analysis 

[Organizations: CDMG, California Division of Mines and Geology; UCSC, University of California, Santa Cruz; USGS, U.S. Geological Survey] 

Code Number Organization Location 

ADD 1652 USGS Anderson Dam, downstream. 

BRN --- UCSC 5001 Branciforte Ct., Santa Cruz. 

CAP 47125 CDMG Capitola Fire Station. 

CLD 57504 CDMG Coyote Lake Dam. 

COR 57007 CDMG Corralitos. 

Gl 47379 CDMG Gilroy array station 1. 

G2 47380 CDMG Gilroy array station 2. 

G3 47381 CDMG Gilroy array station 3. 

G4 57382 CDMG Gilroy array station 4. 

G6 57383 CDMG Gilroy array station 6. 

GHB 57476 CDMG Gilroy historical building. 

HCH 1575 USGS Hollister City Hall. 

HDA 1656 USGS Hollister Airport. 

HSP 47524 CDMG South and Pine Streets, Hollister. 

LEX 57180 CDMG Lexington Dam. 

LGP --- UCSC Los Gatos Presentation Center. 

S CZ 58 135 CDMG UCSC campus. 

SJS 57563 CDMG Santa Theresa HLills, San Jose. 

STG 58065 CDMG Aloha Avenue, Saratoga. 

WHO --- UCSC 738 Cable Court, Santa Cruz. 

eastern segment of the rupture zone also had high slip as 

well. Note that stations HDA and GO2 through GO4 are 

all soft-soil sites, and if substantial site amplification occurred, there might be a bias toward higher slip on the 

southeastern segment of the fault. 

Absolute-timing information was available for many of 

the stations from radio station WWVB code; however, to 

account for lateral variations in the velocity structure, apparent trigger times at all stations were adjusted so that 

the initial S wave from the hypocenter arrived at the time 

predicted by the laterally homogeneous model. For stations with absolute-timing information, the average correction to the origin time was about +2 s, too large to be 

attributable to lateral variations in velocity structure. This 

discrepancy indicates that the earthquake began with a 

subevent too small to trigger the strong-motion instruments but large enough to register on the sensitive, highgain stations that were used to determine the: hypocenter. 

Similar behavior was noted in both the 1979 Imperial 

Valley, Calif., earthquake (Hartzell and Heaton, 1983) and 

the 1987 Superstition Hills, Calif., earthquakie (Wald and 

others, 1990). Understanding such earthquake nucleation 

is a critical problem that is difficult to study with triggered, strong-motion data; however, the advent of continuously recording, broadband, high-dynamic range digital 

networks will help in this effort. 

The data were modeled by varying the rupture time and 

slip amplitude from a simple assumed starting model, using the tomographic backprojection technique of Olson 

(1987) adopted to a sparse system with inequality and 

smoothness constraints (Beroza and Spudich, 1988). The 

data are linearly related to variations in slip amplitude 

and nonlinearly related to variations in rupture time, and 

so a linearization was used, and the inversion process was 

repeated until the solution converged. 

To increase the stability of the solution inequality constraints were applied to both the strike-slip (constrained 

to be right lateral) and dip-slip (constrained to be reverse) 

components of motion. These inequality constraints were 

enforced by a penalty function (Beroza and Spudich, 1988). 

Smoothness constraints were applied to the slip-amplitude and rupture-time calculations (Hartzell and Heaton, 

1983; Beroza and Spudich, 1988). 

MODEL PARAMETRIZATION 

The fault plane used in the analysis (see section above 

entitled "Introduction") extends from 20 km northwest to 

20 km southeast of the hypocenter. The dipping fault plane 

intersects the hypocenter at a depth of 18 km, with a 

strike of 130' and a dip of 70' SW. The modeled extent 

of the rupture zone in the updip direction from the hypocenter is 14 km, corresponding to depths from 18 km to 

slightly less than 5 km. A 1-krn grid spacing is used in 

both the updip and along-strike directions, and the model 

is specified as a triplet of strike-slip amplitude, dip-slip 

amplitude, and rupture time. In this parametrization, the 

rake is a derived quantity because the strike-slip and dipslip components of the slip vector are allowed to vary 

independently. 

The velocity model used to calculate the Green's functions is a piecewise linear-velocity-gradient approximation to the one-dimensional velocity model of Dietz and 

Ellsworth (1990) based on their analysis of Loma Prieta 

aftershocks (table 2). Because their model indicates a difference in the velocity of the uppermost layers across the 

San Andreas fault, a slightly different model was used on 

the northeast and southwest sides of the fault. 

Theoretical seismograms and partial derivatives with 

respect to model parameters were calculated by using a 

high-frequency, near-source approximation (Spudich and 

Frazer, 1984), in which the effects of lateral heterogeneity can be incorporated if the velocity model is sufficiently well known (Cormier and Beroza, 1987), although 

I have not attempted to do so in this study. 

This parametrization of the rupture process allows each 

segment of the fault to slip once when the rupture front 

passes with a spatially variable amplitude. The slip velocity is assumed to decay after rupture as the inverse square 

root of time (-IJ2, as in crack models of earthquake rupture, and the rise time is assumed to be a uniform 0.3 s 

everywhere on the fault. A short rise time, which is required by the data, suggests that the duration of slip at 

any point on the fault is not controlled by the distance to 

the edge of the fault (Beroza and Spudich, 1988; Heaton, 

1990), as is usually assumed (for example, Day, 1982). 
RUPTURE HISTORY OF THE EARTHQUAKE FROM HIGH-FREQUENCY STRONG-MOTION DATA A 13 

The combination of such short rise times and very large vary, regions of the fault that did not undergo high slip 

displacements indicates that the particle acceleration across could have much longer rise times; however, the areas of 

the fault plane is quite high. If rise time were allowed to high slip are the most problematic. An alternative explaCOR 11 \ I 

HSP 

Figure 2.-Fault-perpendicular (220' clockwise from north) (A) and fault-parallel (130' clockwise from north) (B) components of displacement at 20 

strong-motion stations used in inversion, calculated by integrating corrected accelerograms twice to displacement and bandpass filtering between 0.2 

and 5 Hz (this passband is used for display only). Note that displacements at stations near hypocenter are smaller than at stations to northwest or 

southeast. Inset shows locations of stations (see fig. 1 for explanation). 
A 14 MAIN-SHOCK CHARACTERISTICS 

nation is that the true slip-time function decays more RESULTS 

quickly than ^\I2. Such a slip history could accommodate 

a longer rise time. Resolution of the observation of short Because this is a linearized inversion, I attempted to 

rise times, which imply a high dynamic stress drop, with converge to a solution from a wide range of starting modthe low earthquake stress drops inferred by other methods els. I found no evidence for variations in the rupture veis an important problem in earthquake-source mechanics. locity large enough to be considered resolvable. Because 

B 

s 

SCZ STG 

BRN 

" - "" 

COR 

1 HDA Ã ft 

10 s 

Figure 2.-Continued. 

v SJS 

s 

ADD 
RUPTURE HISTORY OF THE EARTHQUAKE FROM HIGH-FREQUENCY STRONG-MOTION DATA A 15 

Table 2.-Parameters used in the velocity model 

[a, P-wave velocity; 3, 5-wave velocity; p, density] 

Depth (km) a (kmls) p (kmls) p (kg/m3) 

Northeast of fault 

Southwest of fault 

0.0 3.42 197 2,500 

1.1 4.58 2.64 2,700 

9 1 6.26 3.61 2,700 

245 6.95 401 2,800 

the data can be fitted nearly as well without variations in 

rupture velocity, the rupture velocity was held at a fixed 

fraction of the local shear-wave velocity, and an inversion 

was performed for the strike-slip and dip-slip amplitudes. 

The preferred rupture model has a rupture velocity of 80 

percent of the local shear-wave velocity, which amounts 

to 3.1 kmls at the hypocentral depth and 2.7 kmls at 6-km 

depth. Much lower or higher rupture velocities substantially degraded the fit to the data. 

A rescaled version of the rupture velocity model obtained by the inversion (Beroza, 1991) is shown in figure 

3. The hypocenter is located at 18-km depth, 0 km along 

strike. The top of the assumed fault plane is at 4.8-km 

depth (14 krn updip from the hypocenter). Slip amplitude 

ranges from 0 to more than 5 m, with a total seismic 

moment in this rescaled model of 2.3~10~~ N-m, in agreement with the teleseismically and geodetically determined 

range 1.7~10~~-3.4~10~~ N-m. The various slip amplitudes and rupture times in the rescaled model are listed in 

table 3. 

The model shown in figure 3 and the fit to the data 

shown in figure 4 are the results of rescaling the slip 

amplitudes determined from a least-squares inversion. 

Before rescaling, the seismic moment was calculated to 

be 1.3x1019 N-m. The slip amplitudes were rescaled to 

account for a systematic underprediction of amplitudes by 

the least squares inversion procedure. 

-20 ALONG-STRIKE DISTANCE, IN KILOMETERS 2 0 

0 20 100 200 300 400 500 

SLIP AMPLITUDE, IN CENTIMETERS 

Figure 3.-Rupture model of earthquake. Bottom of fault plane is at 18-km depth, and t6p at 4.8-km depth. 

A, Rupture time at 0.5-s intervals. Rupture front spreads outward from hypocenter (at 0 km along strike and 

0 km updip) at a constant 80 percent of local shear-wave velocity. B, Amplitude of slip vector. Slip in 

hypocentral region and updip from hypocenter is relatively low. Note two high-slip areas at 12- and 14-km 

depth; most slip occurs at 9- to 16-km depth. 
MAIN-SHOCK CHARACTERISTICS 

Table 3.-Rupture model of the earthquake 

[Columns correspond to different distances along dip; step size, 1 km. The first column is the deepest, and the second 

column corresponds to the depth of the hypocenter. Rows correspond to different distances along strike; step size, 0.5 km. 

The first row is at the northwest end of the model fault, and the 41st row corresponds to the location of the hypocenter. 

Positive values are right-lateral and reverse slip] 

Rupture time (s) 
RUPTURE HISTORY OF THE EARTHQUAKE FROM HIGH-FREQUENCY STRONG-MOTION DATA 

Table 3.-Rupture model of the earthquakeÃ‘Continue 

Rupture time (s)Ã‘Continue 

Strike-slip amplitude (m) 
MAIN-SHOCK CHARACTERISTICS 

Table 3.-Rupture model of the earthquake-Continued 

Strike-slip amplitude (m)-Continued 

Dip-slip amplitude (m) 
RUPTURE HISTORY OF THE EARTHQUAKE FROM HIGH-FREQUENCY STRONG-MOTION DATA 

Table 3.-Rupture model of the earthquakeÃ‘Continue 

Dip-slip amplitude (m)-Continued 

There are several possible explanations for this amplitude discrepancy, including too short a rise time, a lower 

average rupture velocity than assumed, and unmodeled 

slip occurring after the rupture front passed. The discrepancy could not be accounted for by changing the assumed 

rupture velocity, as discussed above. Similarly, inverting 

the data using a rise time much longer than the assumed 

0.3 s degrades the fit to the data. Finally, allowing the 

rupture time to be a free parameter results in rupture models that still have the same discrepancy. 

I believe that the primary source of the amplitude discrepancy is most likely the inability of the theoretical 

Green's functions to match the phase of the true Green's 

functions precisely. In the presence of such errors in phase, 

the least-squares misfit to the data will be smaller if the 

amplitudes of the predicted waveforms are smaller than 
A20 MAIN-SHOCK CHARACTERISTICS 

those of the observed waveforms, biasing the solution toward lower slip values and a lower seismic moment. To 

correct for this bias, I adopt the median ratio of peak 

amplitudes for the y component of motion in the observed 

versus predicted seismograms to rescale the slip model. 

The resulting ratio of 1.8 eliminates the waveform-amplitude misfit and scales the seismic moment to 2.3~10~~ Nm, a result consistent with that determined in other studies. 

A more satisfactory way to address this problem in future 

studies would be to use aftershock recordings to calibrate 

site and path effects. 

Deconvolved displacements, obtained by integrating the 

corrected accelerograms, bandpass filtering between 0.33 

and 2 Hz, and deconvolving the assumed slip-velocity 

function, are compared with the observed data in figure 4. 

The 220' component of motion at stations near the fault 

trace, or on the northwest-southeast extension of the fault 

trace, is predicted quite well by the rupture model; this 

WHO - 

Ã‘Ã‘Ã‘^/V\A^\/^\/^/\ 

scz v--- - 

CAP 

LEX CLD - 

LGP ADD 

COR 

HDA 

G6 

G4 

SJS 

- 

GHB 

Figure 4.-Fit to fault-perpendicular (220' clockwise from north) (A) and fault-parallel (130' clockwise 

from north) (B) components of deconvolved displacement at 20 strong-motion stations used in inversion (see 

fig. 1 for locations). Upper curve, predicted seismogram; lower curve, observed seismogram. 220Â component of displacement was used to scale rupture model so that median peak amplitudes in predicted seismograms fit median peak amplitude in observed seismograms. 
RUPTURE HISTORY OF THE EARTHQUAKE FROM HIGH-FREQUENCY STRONG-MOTION DATA A2 1 

component of motion at these stations is dominated by SH 

waves. In contrast, the 130' component of motion at these 

stations is rather poorly fitted by the rupture model (for 

example, the 130' component of motion at sta. COR, fig. 

I), a result attributable to the fact that this component 

consists largely of P-SV waves and is nearly nodal for an 

idealized planar fault. Irregularities in fault geometry and 

lateral heterogeneity in the velocity structure are the probable causes of these discrepancies (Cormier and Beroza, 

1987; Beroza and Spudich, 1988). Stations far removed 

from the fault are not predicted to be nodal, and the model 

does a much better job of fitting these data. 

The slip amplitude in the hypocentral region was found 

to be approximately 1 m; immediately updip from the 

hypocenter it is even less. This result is consistent with 

the observation that the station at Corralitos (COR, fig. 1) 

recorded relatively small slip amplitudes, despite its location nearly directly updip from the hypocenter. I find two 

main areas of concentrated slip (fig. 35). One area is centered 7 km northwest of the hypocenter at 14-krn depth, 

with a peak slip of 4.5 m, and is responsible for the large 

amplitudes observed at stations northwest of the hypocenter. The other area, located 12 km southeast of the 

hypocenter at 12-km depth, with a peak amplitude of 5.9 I 

* --dl+-- 

BRN STG 

CAP COR 

HCH Ã‘Ã‘^V HDA GO1 Ã‘\A/VÃ‘- 

A 

HSP 

Figure 4.-Continued 
MAIN-SHOCK CHARACTERISTICS 

ALONG-STRIKE DISTANCE, IN KILOMETERS 

SLIP AMPLITUDE, IN CENTIMETERS 

ALONG-STRIKE DISTANCE, IN KILOMETERS 

Figure 5.-Slip amplitudes (A-C) and rake (D) in rupture model of earthquake. A, Right-lateral component 

of slip vector. Note that most slip occurs southeast of hypocenter (at 0 km along strike and 0 km updip). B, 

Reverse dip-slip component of slip vector. Note that most slip occurs northwest of hypocenter. C, Total slip. 

D, Local orientation (rake) and relative length of slip vector (motion of hanging wall). 
RUPTURE HISTORY OF THE EARTHQUAKE FROM HIGH-FREQUENCY STRONG-MOTION DATA A23 

m, is responsible for the large amplitudes observed at 

stations southeast of the hypocenter. Several other highslip areas on the southeastern section of the fault are less 

well constrained, owing to the station distribution. 

The overall extent of the high-slip area in this model is 

from about 13 krn northwest of the hypocenter, near the 

intersection of the surface traces of the Sargent and San 

Andreas faults, to 20 km southeast of the hypocenter. 

This area is considerably smaller than the extent of the 

aftershock zone, which is approximately 50 km. Nearly 

all the slip occurred at 9- to 16-km depth. Substantial slip 

is thus confined to an area of about 230 krn2, quite small 

for an Mr=6.9 event. 

With few exceptions (for example, Romanowicz and 

Lyon-Caen, 1990), slip in the 1989 Loma Prieta earthquake has previously been modeled as oblique, with a 

constant rake. I allowed the rake to vary in the rupture 

model by separately estimating variations in the dip-slip 

and strike-slip amplitudes. The distributions of right-latera1 strike slip, reverse slip, and total slip are plotted in 

figures 5A, 55, and 5C, respectively, and the local orientation (rake) and relative length of the slip vector in figure 5D. Slip near the hypocenter is oblique, but to the 

northwest it is dominated by the dip-slip component, and 

to the southeast by the strike-slip component. The peak 

reverse-slip amplitude is 4.4 m, in the high-slip area northwest of the hypocenter (fig. 3B) where the strike-slip amplitude is less than 1 m. The peak strike-slip amplitude is 

5.9 m in the high-slip area southeast of the hypocenter 

(fig. 3B), where dip slip is low. Farther to the southeast, 

slip is purely right lateral. Although I find a strong spatial 

partitioning of slip, the proportions of the total strike-slip 

and dip-slip moments are the same in this model as in the 

teleseismic and geodetic models. This consistency is derived rather than imposed because no teleseismic data and 

no constraint on the point-source moment tensor are used 

in the modeling. 

The partitioning of total slip into strike-slip and dipslip components is a surprising result, and it would be 

useful to determine whether such variations are required 

by the data. To do so, I devised a simple norm that minimizes the deviation of the slip vector from a constant 

assumed direction. If s is the estimated slip vector and so 

is the assumed slip vector, then the norm to be minimized 

while fitting the data is given by a(~-s)~( s-so), where 

the superscript T denotes the vector transpose and the 

factor a determines the importance assigned to fitting the 

assumed rake. By modeling the data with different values 

of a, the variations in rake required to fit the data can be 

determined. 

In applying this procedure, I assumed the relative proportions of the slip vector to be 1.6 m of strike slip and 

1.2 m of dip slip. The data do not strongly constrain the 

slip on the northwest end of the fault zone to be predominantly dip slip, and oblique slip in the assumed direction 

will fit the data nearly as well on this segment of the 

fault. Southeast of the hypocenter, however, oblique slip 

will seriously degrade the fit to the data because at many 

stations to the southeast, the contribution of reverse slip 

to the seismograms is opposite in sign to that for strike 

slip and opposite to that observed. 

COMPARISON WITH OTHER STUDIES 

Four extended-source models of the earthquake have 

previously been published (Beroza, 199 1 ; Hartzell and others, 1991; Steidl and others, 1991; Wald and others, 1991). 

Although many of the data are common to these four 

studies, several differences in the analyses can lead to 

varying results, including different frequency bands, data 

selection (for example, velocity versus displacement seismograms), station corrections, model parametrizations, 

matrix-inversion methods, and solution methods for the 

forward problem. I now briefly review the assumptions used 

in each study in comparison with those used in this paper. 

Beroza (1991) used the horizontal components of displacement in the frequency band 0.33-2 Hz for 20 of the 

closest strong-motion stations. The parametrization of the 

rupture history allowed each point of the fault to slip only 

once, with a constant slip-velocity function (tell2 singularity) and duration (0.3 s) of slip after rupture. The inversion was performed by using a tomographic backprojection 

technique that approximates a least-squares inversion with 

inequality constraints on the slip direction and smoothness constraints on the perturbations to slip amplitude and 

rupture time. The forward problem was solved by using 

geometric-ray theory in a time-dependent Kirchoff formulation (Spudich and Frazer, 1984). This method has 

some advantages over more computationally intensive, 

complete-seismogram methods in that it eliminates the 

need for a subfault formulation, but it is applicable only 

at frequencies high enough that near-field contributions 

are unimportant. 

Steidl and others (1991) modeled strong-motion velocity records from 20 near-source stations filtered over the 

frequency band 0.05-1 Hz. In their parametrization of the 

rupture history, they divided the fault plane into subfaults 

and allowed each subfault to slip once with variable slip 

amplitude and rupture time, using a constant slip velocity 

function (isosceles triangle) of 1-s duration. The inversion was performed with inequality and smoothness constraints. The forward problem was solved by using a 

complete-seismogram method. 

Hartzell and others (1991) used teleseismic P waves 

from 24 stations and SH body waves from 16 stations in 

the Global Seismic Network at frequencies above 1 Hz 

and great-circle distances of 30'-90'. In their parametrization of the rupture history, they divided the fault into 

RUPTURE HISTORY OF THE EARTHQUAKE FROM HIGH-FREQUENCY STRONG-MOTION DATA A25 

can be determined. This point varies from station to station, with a substantially lower frequency of validity for 

several stations; however, because it is difficult to predict 

when this breakdown will occur, it is better to be conservative in choosing the lower-frequency limit. 

It would be desirable to include lower-frequency data 

in future inversions. One impediment is that nearly all the 

stations are analog, and so the low-frequency information 

is difficult to recover. It is surprising how much of the 

signa -1 is lost in this way. The same complete seismo- lem. 

grams shown in figure 7 are plotted in figure 8, high-pass 

filtered at 0.25 Hz, which is a typical lower limit for 

displacement derived from analog strong-motion records. 

The other seismograms, which are not high-pass filtered, 

indicate how much signal is lost in the digitization. Potential slow or smooth components of the earthquake 

rupture that generate no strong high-frequency waves 

would be much more easily visible at lower frequencies. 

Accurate digital accelerographs could alleviate this prob100 200 300 400 

SLIP AMPLITUDE, IN CENTIMETERS 

I 1 1 J 

-3 0 -1 0 10 30 

0 400 

SLIP AMPLITUDE, IN CENTIMETERS 

ALONG-STRIKE DISTANCE, IN KILOMETERS 

Figure 6.-Amplitude of total slip in extended-source models of earthquake. Star, hypocenter. A, Model of 

Beroza (1991). B, Combined strong-motion teleseismic model of Wald and others (1991). C, Ly model of 

Hartzell and others (1991). D, Model of Steidl and others (1991). 
A26 MAIN-SHOCK CHARACTERISTICS 

COMPARISON WITH LONG-PERIOD NEAR- pass filter at 1 Hz and a high-pass filter at 0.0 

SOURCE DATA two seismograms are compared in figure 9. 

1 Hz. The 

Although only high-frequency seismograms were used 

to calculate the rupture model, the availability of digital 

strong-motion records of the 1989 Loma Prieta earthquake 

allows a comparison of my rupture model with observations at much longer periods. For this purpose, complete 

seismograms were calculated, using the DWFE method, 

for the displacement data from the accelerograph at the 

station in the Santa Theresa Hills (SJS, fig. 1). These 

seismograms were then filtered with a zero-phase, lowThe agreement is fairly good on all three components, 

suggesting that the parametrization and assumptions used 

here are capable of representing most of the slip in the 

earthquake. The apparent static offset on the 130' and 

vertical (z) components match the observed seismograms 

quite well, but the 220' component is somewhat 

overpredicted by the rupture model. The most obvious 

disagreement between the two seismograms is a tendency 

for the large displacement pulse to be somewhat broader 

in the observed waveforms than in the predicted seismo0 200 400 

SLIP AMPLITUDE, IN CENTIMETERS 

ALONG-STRIKE DISTANCE, IN KILOMETERS 

Figure 6.-Continued 
RUPTURE HISTORY OF THE EARTHQUAKE FROM HIGH-FREQUENCY STRONG-MOTION DATA A27 

grams. This difference could have several causes, including a lower rupture velocity, rupture propagation farther 

to the northwest, or a longer rise time. The generally good 

agreement between the predicted and observed seismograms at long periods for this station suggests that the 

rescaled model correctly recovers the seismic moment of 

the earthquake and that the parametrization of the rupture 

process is consistent with the data even at very long 

periods. 

Such long-period near-source data can provide valuable 

constraints on the rupture history and are not as sensitive 

to path and site effects as high-frequency data. If the digitization is accurate enough, the strong-motion data can 

also record the static offset. Measuring static displacements in this way would provide important information 

and be free of the reference-frame problems that plague 

most geodetic measurements. 

EXTENT OF COSEISMIC RUPTURE AND THE 

POTENTIAL FOR FUTURE EARTHQUAKES 

Coseismic faulting extended over slightly more than 

half of the 50-km-long aftershock zone, from about 13 

scz BRN 

WHO SJS 

TIME, IN SECONDS 

Figure 7.-Theoretical seismograms calculated by using discrete-wavenumberlfinite-element method (upper 

curve) in comparison with ray-theoretical seismograms (lower curve) for 130Â° 220Â° and vertical (2) components of displacement over frequency band 0.33-2 Hz at five strong-motion stations (see fig. 1 for locations). 
A28 MAIN-SHOCK CHARACTERISTICS , 

km northwest to 20 km southeast of the hypocenter. To 

the northwest, rupture reached the intersection of the San 

Andreas and Sargent faults. To the southeast, rupture extended into the region where the fault plane delineated by 

aftershocks warps into a vertical fault (Dietz and Ellsworth, 

1990). 

The geometry of the Loma Prieta fault plane and the 

depth of faulting make it difficult definitively to associate 

the 1989 Loma Prieta earthquake with the San Andreas 

fault. All we can say is that rupture propagated upward 

from the hypocenter until it reached a point about 10 krn 

below the surface trace of the San Andreas fault. Slip at 

shallower depths is much lower in all the extended-source 

models, and the aftershock distribution becomes diffuse. 

If the San Andreas fault is vertical in this area, as suggested by the sparse seismicity before the earthquake 

(Olson, 1990), then the earthquake may have ruptured a 

fault distinct from the San Andreas and terminated at the 

lower reaches of the San Andreas fault. The San Andreas 

fault may even have acted as an obstacle to rupture during 

the earthquake. The location and geometry of slip in the 

earthquake cast doubt on long-term forecasts of the 1989 

scz 

SJS 

BRN 

WHO 

130' 

l~l~l~lnl~l 

0 10 20 

TIME, IN SECONDS 

LGP 

Figure 8.-Theoretical seismograms calculated using discrete-wavenumberlfinite-element method for 130' 

and 220' components of displacement, unfiltered (solid line) and highpass filtered at 0.25 Hz (dashed 

curve), at five strong-motion stations (see fig. 1 for locations), showing how high-frequency displacement 

records recovered from analog accelerograrns represent only a small fraction of ground motion recorded at 

longer periods. 
RUPTURE HISTORY OF THE EARTHQUAKE FROM HIGH-FREQUENCY STRONG-MOTION DATA A29 

Loma Prieta earthquake based on estimates of shallow 

slip on the San Andreas fault in previous earthquakes. 

Additional doubts about any long-term forecast of the 

earthquake are raised by the work of Segall and Lisowski 

(1990) who demonstrated that the motion of Loma Prieta 

(fig. 1) in the 1906 San Francisco earthquake was completely unlike that in 1989. Their analysis indicated that 

much more strike slip occurred in the southern Santa Cruz 

Mountains during the 1906 earthquake than during the 

1989 earthquake and that much of the slip in 1906 was 

shallow. Because most slip in the 1989 earthquake occurred below 10-km depth, this earthquake cannot be considered a repeat of the 1906 earthquake in the southern 

Santa Cruz Mountains, even if both earthquakes occurred 

on the same fault. 

The results of this study and of that by Segall and 

Lisowski (1990) suggest that the coincidence of long-term 

forecasts of a large earthquake on the southern Santa Cruz 

Mountains section of the San Andreas fault (Lindh, 1983; 

Sykes and Nishenko, 1984; Thatcher and Lisowski, 1987; 

Working Group on California Earthquake Probabilities, 

1988) with the occurrence of the 1989 Loma Prieta earthquake may have been only fortuitous. The potential for 

future earthquakes on this segment of the San Andreas 

fault is estimated to be extremely low (Working Group on 

California Earthquake Probabilities, 1990); however, the 

results presented in this paper suggest th 

seismic hazard remains uncertain and 

is widely appreciated. 

HETEROGENEOUS FAULTING AND 

AFTERSHOCKS 

0 10 20 

TIME, IN SECONDS 

Figure 9.-Theoretical seismograms calculated by using the discretewavenumberlfinite-element method (upper curve) in comparison with 

observed seismograms (lower curve) for 130Â° 220Â° and vertical (z) 

components of displacement over frequency band 0.01-1.0 Hz at station 

SJS (fig. 1). Vertical component has been inverted so that positive values correspond to upward motion. Horizontal lines, zero displacement 

level. 

Well-located aftershocks from the USGS (Oppenheimer, 

1989), as well as large early aftershocks (Simila and others, 1990), are projected onto the assumed fault plane 

along the fault-normal vector in figure 10. There is a distinct correlation between areas of high slip during the 

main shock and areas of low aftershock activity. The strongest concentration of aftershocks to the northwest is situated just beyond the end of the high-slip area at the 

intersection of the San Andreas and Sargent fault traces, 

about 15 km along strike. Included in this group are the 

large, early aftershocks located by Simila and others 

(1990). The area of very low slip directly updip from and 

southeast of the hypocenter shows a considerable amount 

of aftershock activity. The two patches of very high slip 

occurred on parts of the fault that showed very little aftershock activity. Also, very few aftershocks occurred in the 

hypocentral region. 

The tendency for high-slip areas during earthquakes to 

be deficient in aftershocks relative to adjacent areas of the 

fault, which has been noted by several investigators (for 

example, Hartzell and Mendoza, 1988; Beroza and 

Spudich, 1988; Houston and Engdahl, 1989) is important 

in understanding the cause of rupture heterogeneity. Two 

possible explanations for heterogeneous rupture are that 

the heterogeneity is controlled by fault-zone heterogeneity 

or by the dynamics of a fault with uniform properties. 

In the fault-zone-heterogeneity model, high-slip areas 

in the main shock are areas of enhanced strength, either 

because of variations in material properties or because of 

complexities in the fault-zone geometry (Kanamori, 198 1). 

These areas are too strong to rupture except during large 

earthquakes, accounting for the observation that high-slip 

areas show little seismicity during both the aftershock 
A30 MAIN-SHOCK CHARACTERISTICS 

sequence and the interseismic period (for example, Houston and Engdahl, 1989; Schwartz and others, 1989). 

In the alternative model, high-slip areas are not due to 

changes in material properties. Horowitz and Ruina (1989) 

showed how complex rupture behavior is possible with a 

spatially homogeneous fault. In their model, a wide range 

of slip behavior results from a homogeneous fault governed by a state-variable friction law (Dieterich, 1979). In 

such a model, it is unclear how aftershocks would be 

related to main-shock slip; however, aftershocks and earthquakes during the interseismic period may be controlled 

in the same way. If so, then variations in seismicity 

may result from the same fault-constitutive behavior 

responsible for the spatial variations in main-shock slip. 

Thus, it may be impossible to differentiate between the 

two models by comparing the distribution of main-shock 

slip with the distribution of seismicity. 

The most promising approach to differentiating between 

these models may be to use independent data to infer 

variations in fault-zone properties at depth. High-slip areas during the 1989 Loma Prieta earthquake correlate fairly 

well with areas of high seismic velocities within the fault 

zone, as determined by Eberhart-Phillips and others (1990) 

and Lees. (1990). If rupture variations during many earthquakes were systematically correlated with such fault-zone 

heterogeneity, it would argue persuasively for a causal 

relationship. 

VARIATIONS IN SLIP DIRECTION 

In the rupture model of the 1989 Loma Prieta earthquake, slip ranges from nearly pure strike slip at the southeast end of the rupture zone to nearly pure reverse slip at 

the northwest end. Such a strong variation in slip direction over a short distance of about 20 krn is a surprising 

result. As discussed above in the section entitled "Results," slip northwest of the hypocenter could be modeled 

as oblique without substantially degrading the fit to the 

data, but it was much more difficult to introduce a substantial reverse-slip component to slip southeast of the 

hypocenter. Variations in rake during rupture have been 

observed during other earthquakes, such as the 1979 Imperial Valley, Calif., earthquake (Olson and Apsel, 1982), 

but not on such a large scale. If this rupture model is 

correct, there ought to be supporting evidence in other 

data sets. 

Broadband teleseismic studies may provide additional 

constraints, but apparently the data can be fitted quite 

well with a point source of oblique slip. Geodetic data 

could provide an independent check on the rupture model, 

and other studies (Marshall and others, 1991; see Williams and others, this chapter) support a variation in rake 

similar to the one found here. Support for this variation 

might also be found in the focal mechanisms of aftershocks analyzed by Oppenheimer (1990). Although there 

is a great diversity of mechanisms, he reported that events 

northwest of the hypocenter tend to have oblique mechanisms, whereas those southeast of the hypocenter tend to 

have purely strike-slip mechanisms (Oppenheimer, 1990). 

Beroza and Zoback (1993) tested whether aftershocks relieve the main-shock-induced stress change implied by 

rupture model and found that they do not. Thus, the use 

of aftershock mechanisms may neither confirm nor deny a 

strong variation in rake. 

A source of potential bias in the estimate of rake is the 

inadequacy of the theoretical Green's functions. If the 

2 0 

ALONG-STRIKE DISTANCE, IN KILOMETERS 

SLIP AMPLITUDE, IN CENTIMETERS 

Figure 10.-Distribution of well-located aftershocks of MSl.0 that occurred during October 1989 superimposed on assumed fault plane in rupture model (see fig. 3B), showing correlation between high-slip areas 

and areas of low aftershock activity. Note abundant aftershock activity in low-slip areas both updip and 

northwest of hypocenter (at 0 km along strike and 0 km updip). 
RUPTURE HISTORY OF THE EARTHQUAKE FROM HIGH-FREQUENCY STRONG-MOTION DATA A3 1 

polarity of the predicted waves differs substantially from Schwartz, Paul Segall, Paul Spudich, and David Wald prothe true polarity, spurious variations in rake might be ob- vided helpful comments and discussions. Steve ~artiell, 

served. One approach to addressing this problem is to Jamie Steidl, and Dave Wald kindly provided their rupmodel the effects of known lateral variations in velocity ture models plotted at a common scale for figure 6. Bill 

structure (Eberhart-Phillips and others, 1990; Lees, 1990) Ellsworth provided the carefully processed digital 

on the predicted waveforms by combining dynamic ray accelerograms from stations SJS used in figure 8 and sugtracing with the high-frequency, near-source approxima- gested comparing my model with the data at low frequention (Cormier and Beroza, 1987). Another approach is to cies. Marino Protti-Quesada and Walter Schillinger 

model the ground motion of aftershocks, for which focal provided data from the UCSC accelerographs. Thanks are 

mechanisms are well known (Oppenheimer, 1990). Use also due to the USGS, CDMG, and UCSC for having the 

of these techniques should allow this issue to be addressed foresight to deploy strong-motion instrumentation in the 

in the future. study area. 

CONCLUSIONS 

Coseismic faulting extended over slightly more than 

half of the 50-km-long aftershock zone, from about 13 

km northwest to 20 km southeast of the hypocenter. To 

the northwest, rupture reached the intersection of the San 

Andreas and Sargent faults. The southeast end of rupture 

extends to the region where the fault plane delineated by 

aftershocks warps into a vertical fault. Nearly all of the 

slip occurs below 10-km depth, and rupture in the updip 

direction may have been terminated by a vertical San Andrea~ fault. The depth and location of slip on a dipping 

fault that terminates -10 km below the surface trace of 

the San Andreas fault suggest that forecasts of an M=7 

earthquake on the San Andreas fault in the southern Santa 

Cruz Mountains based on estimates of shallow slip in 

previous earthquakes may not be relevant for the 1989 

Loma Prieta earthquake and that the seismic hazard on 

this segment of the San Andreas fault remains uncertain. 

We find two areas of very high slip: one approximately 

7 km northwest of the hypocenter at 12-km depth and 

another 6 km southeast of the hypocenter at 14-km depth, 

with peak slip amplitudes of 4.5 and 5.9 m, respectively. 

These high-slip areas are observed to have a relative paucity of aftershocks, whereas regions of low slip within the 

rupture zone have a relative abundance of aftershocks. 

This observation, together with the correlation of areas of 

high slip with areas of anomalous seismic velocity, suggests that rupture heterogeneity is caused by strength heterogeneity in the fault zone. 

There is a surprisingly rapid and strong variation in slip 

direction from nearly pure strike slip southeast of the hypocenter to nearly pure dip slip to the northwest over a 

very short distance of -15 km. This substantial change 

in rake is corroborated by recently published geodetic 

models. 

ACKNOWLEDGMENTS 

This research was supported by U.S. National Science 

Foundation grant EAR-9011456. Tom Hanks, David 

REFERENCES CITED 

Aki, Keiiti, and Richards, P.G. 1980, Quantitative seismology; theory 

and methods: San Francisco, W.H. Freeman, 2 v. 

Archuleta, R.J., 1984, A faulting model for the 1979 Imperial Valley, 

California, earthquake: Journal of Geophysical Research, v. 89, no. 

B6, p. 4559-4585. 

Barker, J.S., and Salzberg, D.H. 1990, Long-period and broad-band 

teleseismic body-wave modeling of the October 18, 1989 Loma 

Prieta earthquake: Geophysical Research Letters, v. 17, no. 9, p. 

1409-1412. 

Beroza, G.C., 1991, Near-source modeling of the Loma Prieta earthquake; evidence for heterogeneous slip and implications for earthquake hazard: Seismological Society of America Bulletin, v. 81, 

no. 5, p. 1603-1621. 

Beroza, G.C., and Spudich, Paul, 1988, Linearized inversion for fault 

rupture behavior; application to the 1984 Morgan Hill, California, 

earthquake: Journal of Geophysical Research, v. 93, no. B6, p. 

6275-6296. 

Beroza, G.C., and Zoback, M.D., 1993, Mechanism diversity of the 

Loma Prieta aftershocks and the mechanics of mainshock-aftershock interaction, Science, v. 259, no. 5092, p. 210-213. 

Choy, G.L., and Boatwright, John, 1990, Source characteristics of the 

Loma Prieta, California, earthquake of October 18, 1989 from global digital seismic data: Geophysical Research Letters, v. 17, no. 8, 

p. 1183-1186. 

Cormier, V.F., and Beroza, G.C., 1987, Calculation of strong ground 

motion due to an extended source in a laterally varying structure: 

Seismological Society of America Bulletin, v. 77, no. 1, p. 1-13. 

Day, S.M., 1982, Three-dimensional finite difference simulation of fault 

dynamics: rectangular faults with fixed rupture velocity: Seismological Society of America Bulletin, v. 72, no. 3, p. 705-727. 

Dieterich, J.H., 1979, Modeling of rock friction; 1, Experimental results 

and constitutive equations: Journal of Geophysical Research, v. 84, 

no. B5, p. 2161-2168. 

Dietz, L.D., and Ellsworth, W.L., 1990, The October 17, 1989, Lorna 

Prieta, California, earthquake and its aftershocks; geometry of the 

sequence from high-resolution locations: Geophysical Research Letters, v. 17, no. 9, p. 1417-1420. 

Eberhart-Phillips, D.M., Labson, V.F., Stanley, W.D., Michael, A.J., 

and Rodriguez, B.D., 1990, Preliminary velocity and resistivity 

models of the Loma Prieta earthquake region: Geophysical Research Letters, v. 17, no. 8, p. 1235-1238. 

Hanks, T.C., and Kanamori, Hiroo, 1979, A moment magnitude scale: 

Journal of Geophysical Research, v. 84, no. B5, p. 2348-2350. 

Hartzell, S.H., and Heaton, T.H., 1983, Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of 

the 1979 Imperial Valley, California, earthquake: Seismological 
A32 MAIN-SHOCK CHARACTERISTICS 

Society of America Bulletin, v. 73, no. 6, pt. A, p. 1553-1583. 

Hartzell, S.H., Stewart, G.S., and Mendoza, Carlos, 1991, Comparison 

of L and L2 norms in a teleseismic waveform inversion for the slip 

history of the Loma Prieta, California, earthquake: Seismological 

Society of America Bulletin, v. 81, no. 5, p. 1518-1539. 

Heaton, T.H., 1990, Evidence for and implications of self-healing pulses 

of slip in earthquake ruptures: Physics of the Earth and Planetary 

Interiors, v. 64, no. 1, p. 1-20. 

Horowitz, F.G., and Ruina, Andy, 1989, Slip patterns in a spatially 

homogeneous fault model: Journal of Geophysical Research, v. 94, 

no. B8, p. 10279-10298. 

Houston, Heidi, and Engdahl, E.R., 1989, A comparison of the spatiotemporal distribution of moment release for the 1986 Andreanof 

Islands earthquake with relocated seismicity: Geophysical Research 

Letters, v. 16, no. 12, p. 1421-1424. 

Kanamori, Hiroo, 1981, The nature of seismicity patterns before large 

earthquakes, in Simpson, D.W., and Richards, P.G., eds., Earthquake prediction; an international review (Maurice Ewing Series, v. 

4): Washington, D.C., American Geophysical Union, p. 1-19. 

Kanamori, Hiroo, and Satake, Kenji, 1990, Broadband study of the 1989 

Loma Prieta earthquake: Geophysical Research Letters, v. 17, no. 

8, p. 1179-1 182. 

Langston, C.A., Furlong, K.P., Vogfjord, K.S., Clouser, R.H., and 

Ammon, C.J., 1990, Analysis of teleseismic body waves radiated 

from the Loma Prieta earthquake: Geophysical Research Letters, v. 

17, no. 9, p. 1405-1408. 

Lees, J.M., 1990, Tomographic P-wave velocity images of the Loma 

Prieta earthquake asperity: Geophysical Research Letters, v. 17, no. 

9, p. 1433-1436. 

Lindh, A.G., 1983, Preliminary assessment of long-term probabilities 

for large earthquakes along selected fault segments of the San Andreas fault system in California: U.S. Geological Survey Open-File 

Report 83-63, 14 p. 

Lisowski, Michael, Prescott, W.H., Savage, J.C., and Johnston, M.J.S., 

1990, Geodetic estimate of coseismic slip during the 1989 Loma 

Prieta, California, earthquake: Geophysical Research Letters, v. 17, 

no. 9, p. 1437-1440. 

Maley, R.P., Acosta, A.V., Ellis, F., Etheredge, E.C., Foote, L.J., 

Johnston, D.A., Porcella, R.L., Salsman, M.J., and Switzer, J.C., 

1989, U.S. Geological Survey strong motion records from the northern California (Loma Prieta) earthquake of October 17, 1989: U.S. 

Geological Survey Open-File Report 89-568, 85 p. 

Marshall, G.A., Stein, R.S., and Thatcher, Wayne, 1991, Faulting geometry and slip from co-seismic elevation changes; the 18 October 

1989, Loma Prieta, California, earthquake: Seismological Society 

of America Bulletin, v. 8 1, no. 5, p. 1660-1693. 

McNally, K.C., Yellin, Joseph, Protti-Quesada, Marino, Simila, G.W., 

Malavassi, Eduardo, Schillinger, Walter, Terdiman, R., and Zhang, 

Zhi, 1990, The local magnitude of the 18 October 1989 Santa Cruz 

Mountains earthquake is M=6.9: Geophysical Research Letters, v. 

17, no. 10, p. 1781-1784. 

Mendoza, Carlos, and Hartzell, S.H., 1988, Aftershock patterns and 

main shock faulting: Seismological Society of America Bulletin, V. 

78, no. 4, p. 1438-1449. 

Nhbelek, J.L., 1990, Rupture process of the October 18, 1989 Loma 

Prieta earthquake from broadband teleseismic body waves labs.]: 

Seismological Research Letters, v. 61, no. 1, p. 46. 

Olson, A.H., 1987, A Chebyshev condition for accelerating convergence of iterative tomographic methods-solving large least squares 

problems: Physics of the Earth and Planetary Interiors, v. 47, p. 

333-345. 

Olson, A.H., and Apsel, R.J., 1982, Finite faults and inverse theory with 

application to the 1979 Imperial Valley earthquake: Seismological 

Society of America Bulletin, v. 72, no. 6, p. 1969-2001. 

Olson, A.H., Orcutt, J.A., and Frazer, G.A., 1984, The discrete wave 

numberlfinite element method for synthetic seismograms: Royal 

Astronomical Society Geophysical Journal, v. 77, no. 2, p. 421- 

460. 

Olson, J.A., 1990, Seismicity in the twenty years preceding the Loma 

Prieta, California earthquake: Geophysical Research Letters, v. 17, 

no. 9, p. 1429-1432. 

Oppenheimer, D.H., 1990, Aftershock slip behavior of the 1989 Loma 

Prieta, California earthquake: Geophysical Research Letters, v. 17, 

no. 8, p. 1199-1202. 

Romanowicz, B.A., and Lyon-Caen, Helene, 1990, The Loma Prieta 

earthquake of October 18, 1989; results of teleseismic mantle and 

body-wave inversion: Geophysical Research Letters, v. 17, no. 8, p. 

1191-1194. 

Ruff, L.J., and Tichelaar, B.W., 1990, Moment tensor rate functions for 

the 1989 Loma Prieta earthquake: Geophysical Research Letters, v. 

17, no. 8, p. 11 87-1 190. 

Schwartz, S.Y., Dewey, J.W., and Lay, Thorne, 1989, Influence of fault 

plane heterogeneity on seismic behavior in the southern Kurile Islands arc: Journal of Geophysical Research, v. 94, no. B5, p. 5637- 

5649. 

\ Segall, Paul and Lisowski, Michael, 1990, Surface displacement in the 

1 1906 San Francisco and 1989 Loma Prieta earthquakes: Science, v. 

1 250, no. 4985, p. 1241-1244. 

shakal<A.~., Huang, M.J., Reichle, Michael, Ventura, C.E., Cao, T.Q., 

Sherburne, R.W., Savage, Martha, Darragh, R.B., and Petersen, C., 

4989, CSMIP strong-motion records from the Santa Cruz Moun- I tains (Loma Prieta), California earthquake of 17 October 1989: 

California Division of Mines and Geology, Office of Strong Mo- ' tion Studies Report 89-06, 196 p. 

, Simila, G.W., McNally, K.C., Nava, E., Protti-Quesada, Marino, and . 

Yellin, Joseph, 1990, Evidence of very early aftershock activity 

along the northwest portion of the 18 October 1989 earthquake 

rupture zone: Geophysical Research Letters, v. 17, no. 10, p. 1785- 

1788. 

Spudich, Paul, and Frazer, L.N., 1984, Use of ray theory to calculate 

high-frequency radiation from earthquake sources having spatially 

variable rupture velocity and stress drop: Seismological Society of 

America Bulletin, v. 74, no. 6, p. 2061-2082. 

Steidl, J.H., Archuleta, R.J., and Hartzell, S.H., 1991, Rupture history 

of the 1989 Loma Prieta, California, earthquake: Seismological Society of America Bulletin, v. 81, no. 5, p. 1573-1602. 

~hkes, L.R., and Nishenko, S.P., 1984, Probabilities of occurrence of 

, large plate rupturing earthquakes for the San Andreas, San Jacinto, 

and Imperial faults, California, 1983-2003: Journal of Geophysical 

Research, v. 89, no. B7, p. 5905-5927. 

Thatcher, Wayne, and Lisowski, Michael, 1987, Long-term seismic potential of the San Andreas fault southeast of San Francisco, California: Journal of Geophysical Research, v. 92, no. B6, p. 4771-4784. 

U.S. Geological Survey staff, 1990, The Loma Prieta, California, earthquake; an anticipated event: Science, v. 247, no. 4940, p. 286- 

293. 

Wald, D.J., Helmberger, D.V., and Hartzell, S.H., 1990, Rupture process of the 1987 Superstition Hills earthquake from the inversion of 

strong-motion data: Seismological Society of America Bulletin, v. 

80, no. 5, p. 1079-1098. 

Wald, D.J., Helmberger, D.V., and Heaton, T.H., 199 1, Rupture model 

of the 1989 Loma Prieta earthquake from the inversion of strongmotion and broadband teleseismic data: Seismological Society of 

America Bulletin, v. 81, no. 5, p. 1540-1572. 

Working Group on California Earthquake Probabilities, 1988, Probabilities of large earthquakes occurring in California on the San Andreas Fault: U.S. Geological Survey Open-File Report 8 8-398, 

62 p. 

1990, Probabilities of large earthquakes in the San Francisco 

Bay region, California: U.S. Geological Survey Circular 1053, 

51 p. 

Zhang, Jiajun, and Lay, Thorne, 1990, Source parameters of the 1989 

Loma Prieta earthquake determined from long-period Rayleigh 

waves: Geophysical Research Letters, v. 17, no. 8, p. 1195-1 198. 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAWOCCURRENCE 

MAIN-SHOCK CHARACTERISTICS 

SOURCE CHARACTERISTICS OF THE EARTHQUAKE FROM 

GLOBAL DIGITAL SEISMIC DATA 

CONTENTS 

By George L. Choy and John Boatwright, 

U.S. Geological Survey 

ABSTRACT 

We analyze displacement, velocity, and acceleration 

records of P and SH body waves recorded at teleseismic 

distances to determine the static and dynamic source parameters of the 1989 Loma Prieta earthquake. Three distinct bursts of energy corresponding to three subevents 

can be recognized in most records. The displacement waveforms indicate that the first subevent contributes a negligible moment, whereas the largest releases of moment 

and energy are controlled by the second and third 

subevents, which are located north and south of the initial 

nucleation. A small fourth subevent needed to model later 

features of the P waveforms suggests that slow slip continued after the major releases of energy occurred. The 

waveforms are fitted with a fault-plane solution with a 

strike of 130Â° a dip of 65O, and a slip of 140' for all four 

subevents, The focal depths of the two major subevents 

are 16 and 12 km, and their asperity radii are 4.0 and 6.0 

km, respectively. The seismic moment, Mo, is 2.2~10~~ 

dyne-cm. From a spectral analysis of teleseismic velocity, 

the radiated energy, Es, is estimated at 1.1~10~~ dyne-cm, 

implying an apparent stress of 15 bars. From the level of 

the high-frequency end of the teleseismic acceleration spectrum and a rupture area of 440 km2, we derive a dynamic 

stress drop of 5 1 bars. 

INTRODUCTION 

The focal parameters for the 1989 Loma Prieta earthquake, as determined by the U.S. Geological Survey's 

National Earthquake Information Center (NEIC), are origin time, 0004: 15.2 G.m.t. October 18, 1989; location, lat 

37.036' N., long 121.883' W.; body-wave magnitude 

mb=6,6; and surface-wave magnitude M~7.1. This earthquake was well recorded by many digitally recording seismograph networks, The purpose of this paper is to analyze 

the source characteristics of the earthquake by using highquality broadband data selected from these stations. By 

"broadband" we mean that the data are processed so that 

they are flat to displacement, velocity, or acceleration from 

frequencies of at least 0.01 to about 5.0 Hz. The advantages of using broadband records to derive details of the 

rupture process of large earthquakes have been enumerated in recent papers (for example, Choy and Boatwright, 

1981, 1988; Choy and Dewey, 1988). Besides the usual 

parameters of depth, moment, and focal mechanism, these 

data have sufficient spectral content to provide estimates 

of radiated energy, associated stresses, and rupture complexity. 

DATA PROCESSING 

The broadband data analyzed here were obtained from 

digitally recording stations of the Global Digital Seismograph Network (GDSN), the Chinese Digital Seismograph 

Network (CDSN), and the Global Seismographic Network 

(GSN), Only stations at distances greater than 30' from 

the epicenter are used in our waveform modeling. The 

global distribution of the stations used is shown in figures 

1 and 2. Because raw data from globally recording networks are generally not directly proportional to either displacement or velocity over a wide and continuous range 

of frequencies, broadband records were obtained by using 

the method of Harvey and Choy (19821, which uses multichannel instrumeat deconvolution and, whenever necessary, recombines data recorded on separate channels with 

overlapping frequency bands. After processing, the bodywave displacements and velocities generally are well determined over the frequency range from at least 0.01 to 

5.0 Hz. 
A34 MAIN-SHOCK CHARAC'IERISTICS 

ANALYSIS OF' THE MAIN SHOCK set represents only a tiny part of the rupture process. As 

shown in the broadband displacement (fig. 3B), this onset 

From even a preliminary examination of displacement is followed by two major releases of moment. Similarly, 

and velocity records, three distinct bursts can be recog- in the velocity record (fig. 3C), this onset is followed by 

nized in most of the broadband pulse shapes. A typical two major episodes of energy release. In our modeling, 

short-period record is shown in figure 3A. The initial on- we associate each arrival of energy release with a subevent, 

AFI o lo 20 30 40 

P ~3 TIME, IN SECONDS 

Figure 1 .-P-wave displacements (solid traces) and synthetic seismograms (dashed traces) at global digital 

seismic stations (identified by letter codes) of main shock, plotted about focal sphere. Focal mechanism has 

a strike of 130Â° a dip of 65O, and a slip of 140'. Absolute amplitude of data is recoverable by measuring 

vertical amplitude, comparing it with vertical axis (scaled in microns, p), and dividing it by magnification 

factor given next to each displacement trace. Shape of average moment-release rate is plotted on time axis. 

MDJ 

s xl 

ZO] 0 -. . . . . 0 10 20 30 40 

TlUE. IN SECONDS 

Figure 2.-SH-wave displacements (solid traces) and synthetic seismograms (dashed traces) at global digital seismic stations (identified by letter codes) of main shock, plotted about focal sphere with SH-nodal 

lines of fault-plane solution. x's indicate SS takeoff angles, some of which fall near nodal lines, Absolute 

amplitude of data is recoverable by measuring vertical amplitude, comparing it with vertical axis (scaled in 

microns, p), and dividing it by magnification factor given next to each displacement trace. Shape of average 

moment-release rate is plotted on time axis. 
SOURCE CHARACTERISTICS OF THE EARTHQUAKE FROM GLOBAL DIGITAL SEISMIC DATA A35 

However, because the arrival of subevent 1 is too small to 

model, we start our modeling of the rupture process with 

subevent 2. Finally, because most stations reported only 

the initial arrival, the hypocenter computed by most reporting agencies refers to the onset of nucleation, which 

is not necessarily where the major releases of energy occurred. 

To exploit the broad-bandwidth data, we used the methods of Choy and Boatwright (1981, 1988) and Choy and 

Kind (1987) to estimate the focal mechanism, depth, and 

source duration of the subevents composing the earthquake. For a single shallow source, the far-field P-wave 

displacement, U, is given by 

where Gi and Qi are the propagation and source operators 

for body waves i=P, pP, and sP. For simple coherent 

sources, synthetic displacements are computed by using 

triangular source functions. Displacements for a complex 

rupture are synthesized by summing the waveforms from 

a sequence of coherent subevents lagged in time as a function of azimuth. For body waves recorded between distances of approximately 30Â°<A<900 the propagation 

operator accounts for geometric spreading, the crustal response at source and receiver, and the effects of propagation in the Earth. To describe attenuation, we use the 

frequency-dependent dispersive operators of Choy and 

Cormier (1986), modified, as described by Boatwright and 

Choy (19861, to account for the regionally strong attenuation along Western United States-shield ray paths (Der 

TIME, IN SECONDS 

Figure 3.-Three different representations of P wave at station TOL, 

Arrows indicate onsets of subevents 1, 2, and 3. A, Raw short-period 

data. B, Broadband displacement. Onset of subevent 1 is clearly subordinate in size to onsets of subevents 2 and 3. C, Correponding broadband velocity. 

and others, 1982). The response of the Earth is calculated 

by applying the method of Haskell (1962) to an Earth 

model that uses Jeffreys-Bullen velocities for the structure in the mantle and near the receivers, and the velocity 

model of Dietz and Ellsworth (1990) for the location of 

aftershocks in the Loma Prieta region. Displacement data 

are systematically fitted by trial and error with synthetic 

seismograms until optimal agreement is obtained between 

observed and synthetic waveforms. Any remaining discrepancies between the synthetic and observed seismograms are minor and may be due to unknown crustal 

response near the receivers. 

The P and SH displacement waveforms used in our 

analysis are plotted about the focal spheres in figures 1 

and 2, respectively. The average moment-release rate 

shows that the rupture process involving subevents 2 and 

3 was essentially over within approximately 7 s. A relatively minor fourth subevent is needed to model later features of the P waves. The best-fitting solutions for the 

subevents 2 and 3 have the same focal mechanism (strike, 

130'; dip, 65'; slip, 140'). These parameters are excepi 

tionally well constrained to within 35' because the takeoff angles of the body waves (direct P, pP, sP, SH, and 

sSH) straddle both sides of the P, SV, and SH nodal lines. 

The focal depths are 16 and 12 km, respectively, for 

subevents 2 and 3. As a small arrival, subevent 4 is poorly 

constrained; we assume that it has the mechanism and 

depth of the third and dominant subevent. Subevent 3 

releases 50 percent of the moment, while subevents 2 and 

4 release 34 percent and 16 percent, respectively. The 

total moment, Mo, is =2.0~10~~ dyne-cm. The radiated 

energy, computed by using the spectral method of Boatwright and Choy (19861, is 1.1~0.1~10~~ dyne-cm. 

From an inversion of the differential arrival times of 

the subevents, the hypocenters and delay times of 

subevents 2 and 3 can be found relative to the point of 

nucleation of subevent 1. Subevent 2 is located 4.5 km 

from subevent 1, at an azimuth of 028'. The hypocenter 

of subevent 3 is 8 km away from that of subevent 1 at an 

azimuth of 168'. The delay times of subevents 2 and 3 

relative to subevent 1 are 1.4 and 3.5 s, respectively. The 

semimajor axes of both 95-percent-confidence ellipses are 

oriented nearly north-south with lengths of 2.0 km. The 

azimuths of subevents 2 and 3 relative to subevent 1 differ from the dominant strike delineated by aftershock activity. Because of their spatial proximity and uncertainty, 

however, the locations of the subevents are not regarded 

as significantly off the main fault. Furthermore, these 10- 

cations must be considered preliminary because of the 

sparsity of data from southern azimuths. The onset of 

subevent 1 could not be reliably read above the microseism 

level on records from most island stations. 

The average source functions for subevents 2 and 3 

have rise times of 1.5 and 2.5 s, with total durations of 

7.0 and 5.0 s, respectively. Using the relation of Das and 
A36 MAIN-SHOCK CHARACTERISTICS 

Kostrov (1986) for the rise time of the source function T 

and the asperity radius a, ~=alv, where the rupture velocity v is assumed to be 75 percent of the shear velocity, we 

obtain asperity radii of 4 and 6 km for subevents 2 and 3, 

respectively. These geometries are shown as circles on a 

vertical cross section of aftershocks viewed parallel to the 

strike of the San Andreas fault (fig. 4). The subevents 

were located by using the coordinates of the main shock 

(Dietz and Ellsworth, 1990) as the location of subevent 1. 

To extract further information from the teleseismic arrivals, we used the method of Boatwright and Choy (1989) 

to examine the radiated acceleration in the frequency domain. The first step of this method is shown in figure 5A, 

where the solid curve is the logarithmically averaged acceleration spectrum, corrected for both geometric spreading and anelastic attenuation. This spectrum must still be 

corrected for the effect of the free surface, that is, the 

spectral modulations caused by interference of the depth 

and the direct phases. This free-surface interference 

(dashed curve, fig. 5A) is modeled by accounting for the 

focal mechanism, the average depth of the rupture, and 

the depth range of the rupture. Note that the shallow trough 

at 0.2 Hz in the free-surface spectrum does not fit the 

shallow trough at 0.4 Hz in the average-acceleration spectrum. This trough at 0.4 Hz is presumed to arise from the 

complexity of the moment-release rate, not the interference of the free surface. 

Dividing the average-acceleration spectrum by the freesurface spectrum yields the corrected acceleration spectrum, which is plotted in figure 5B. The m2 line that has 

been fitted to the low-frequency end of the spectrum 

(0.012-0.06 Hz) corresponds to a seismic moment Mo of 

2.2k0.5~10~~ dyne-cm, in agreement with the timedomain analysis. Overall, the spectral shape appears to be 

remarkably similar to Brune's (1970) m2 spectral model, 

notwithstanding the slight modulation from 0.07 to 0.5 

Hz. Estimating the corner frequency, fa, at 0.12 to 0.15 

Hz, using the relation 

based on Brune (1970), where a is the P-wave velocity, 

and assuming a corner frequency shift of 1.5, we obtain a 

source radius r of 13 to 16 km as an estimate of the 

overall source size. This estimate is larger than the combined asperity radii of the two major subevents derived 

from the time-domain analysis. Although time-domain 

analysis helps resolve discrete episodes of stress release, 

spectral analysis is sensitive to the overall rupture process. The corner frequency of 0.12 to 0.15 Hz is then 

representative of the overall duration of faulting, about 6 

to 8 s. The spectral estimate of source radius should be 

interpreted as a length characteristic of the overall rupture 

process. 

Our spectral estimate of the source size agrees well 

with the seismicity pattern that developed during the first 

few hours after the main shock. The distribution of aftershocks that occurred in the first 3.5 hours after the main 

shock (fig. 4) suggests that the rupture area can be approximated as an ellipse, with a semimajor axis of 20 km, a 

semiminor axis of 7 km, and a total rupture area, A, of 

440 km2. This estimate of the overall rupture area can be 

combined with the high-frequency spectral level, Rul, of 

1 .6xlo7 cm21s to estimate the rms dynamic stress drop at 

DISTANCE, IN KILOMETERS 

Figure 4.-Aftershocks within first 3.5 hours of main shock (from Eberhart-Phillips and others, 1990). 

Circular-asperity geometries of subevents 2 and 3 (circles), resolved from time-domain analysis, indicate 

heterogeneous stress release. Large ellipse outlines rupture zone used in calculating stress drop. 
SOURCE CHARACERISTICS OF THE EARTHQUAKE3 FROM GLOBAL DIGITAL SEISMIC DATA 

I , r ,111r~ I I 

FREQWNCY, IN HERTZ 

// radiated energy = O.l08E+23 dyne-em 

,#I , I I , ,,,I 

0.01 0.1 1 

FREQWNCY, IN HERTZ 

Figure 5.-Acceleration spectra. A, Logarithmically averaged acceleration spectrum from 12 stations (solid 

curve), corrected for geometric spreading and anelastic attenuation. Modulation of free-surface spectrum 

(dashed cu~e) fits modulation of averaged acceleration spectrum. Free-surface spectrum is modeled with 

focal mechanism with a strike of 130Â° a dip of 65O, and a slip of 140'; with a centroid depth of 12.0 km; 

and with a vertical range of rupture of 10.0 km. Units of square centimeters per second result from 

correction of acceleration spectrum for geometric spreading. B, Corrected acceleration spectrum, bounded 

by 85-percent-confidence limits. Low- and high-frequency parts of spectrum are fitted by a2 and flat lines, 

respectively. 
A38 MAIN-SHOCK CHARACTERISTICS 

51k12 bars, using equation 4 of Choy and Boatwright 

(1988) for a rupture direction assumed to be within 60' of 

updip. 

DISCUSSION 

From the relative locations of the major subevents and 

the distribution of aftershocks, the causative fault plane 

can be identified from the focal mechanism as the nodal 

plane striking 130'. This fault plane is both colinear with 

the dominant trend of aftershock activity (Dietz and 

Ellsworth, 1990) and consistent with the locations of 

subevents north and south of the initial hypocenter. 

The stress release of the main shock is slightly heterogeneous, as indicated by the asperity geometries resolved 

by the time-domain analysis (fig. 4). Assuming that the 

coordinates of the main shock obtained by Dietz and 

Ellsworth (1990) correspond to those of subevent 1, the 

depth of the initial nucleation is 18 km. The subsequent 

major releases of stress and energy occur both updip and 

away from this initial nucleation. 

An important characteristic of the aftershock sequence 

is that almost all the aftershock activity immediately after 

the main shock is concentrated around and beyond the 

edges of the asperities derived from seismogram modeling (fig. 4). The absence of activity within these asperities 

suggests that the areas became inactive after stress was 

relieved. After the main shock, stress would have been 

transferred to weaker patches on the fault interface adjacent to the asperities, where failure would continue to 

occur in the form of small earthquakes. 

ACKNOWLEDGMENTS 

This research was partly supported by the U.S. Nuclear 

Regulatory Commission under contract RES82001. We 

thank C. Mendoza and J.W. Dewey for their reviews, and 

A. Michael for bringing to our attention the data in figure 4. 

REFERENCES CITED 

Boatwright, John, and Choy, G.L., 1986, Teleseismic estimates of the 

energy radiated by shallow earthquakes: Journal of Geophysical 

Research, v. 91, no. B2, p. 2095-21 12. 

1989, Acceleration spectra for subduction zone earthquakes: Journal of Geophysical Research, v. 94, no. B 11, p. 15541-15553. 

Brune, J.N., 1970, Tectonic stress and the spectra of seismic shear waves 

from earthquakes: Journal of Geophysical Research, v. 75, no. 26, 

p. 4997-5009. 

Choy, G.L., and Boatwright, John, 1981, The rupture characteristics of 

two deep earthquakes inferred from broadband GDSN data: Seismological Society of America Bulletin, v. 71, no. 3, p. 691-71 1. 

1988, Teleseismic and near-field analysis of the Nahanni earthquakes in the Northwest Territories, Canada: Seismological Society 

of America Bulletin, v. 78, no. 5, p. 1627-1652. 

Choy, G.L., and Cormier, V.F., 1986, Direct measurement of the mantle 

attenuation operator from broadband P and S Waveforms: Journal 

of Geophysical Research, v. 91, no. B7, p. 7326-7342. 

Choy, G.L., and Dewey, J.W., 1989, Rupture process of an extended 

earthquake sequence; teleseismic analysis of the Chilean earthquake 

of March 3, 1985: Journal of Geophysical Research, v. 93, no. B2, 

p. 1103-1 118. 

Choy, G.L., and Kind, Rainer, 1987, Rupture complexity of a moderatesized (mb 6.0) earthquake; broadband body-wave analysis of the 

North Yemen earthquake of 13 December 1982: Seismological Society of America Bulletin, v. 77, no. l, p. 28-46. 

Das, Shamita, and Kostrov, B.V., 1986, Fracture of a single asperity on 

a finite fault; a model for slow earthquakes?, in Das, Shamita, 

Boatwright, John, and Scholz, C.H., eds., Earthquake source mechanics: American Geophysical Union Geophysical Monogragh 37 

(Maurice Ewing series, v. 6), p. 91-96. 

Der, Z.A., McElfresh, T.W., and O'Donnell, Anne, 1982, An investigation of the regional variations and frequency dependence of anelastic attenuation in the mantle under the United States in the 0.5-4 

Hz band: Royal Astronomical Society Geophysical Journal, v. 69, 

no. 1, p. 67-99. 

Dietz, L.D., and Ellsworth, W.L., 1990, The October 17, 1989 Loma 

Prieta, California, earthquake and its aftershocks; geometry of the 

sequence from high-resolution locations: Geophysical Research Letters, v. 17, no. 9, p. 1417-1420. 

Eberhart-Phillips, D.M., Michael, A.J., Reasenberg, P.A., Ellsworth, 

W.L., and Dietz, L.D., 1990, Seismological aspects of the Loma 

Prieta earthquake, in Benuska, Lee, ed., Lorna Prieta earthquake 

reconnaissance report: Earthquake Spectra, v. 6., supp. 90-01. 

Harvey, D.J. and Choy, G.L., 1982, Broad-band deconvolution of GDSN 

data: Royal Astronomical Society Geophysical Journal, v. 69, no. 

3, p. 659-668. 

Haskell, N.A., 1962, Crustal reflection of plane P and SV waves: Journal of Geophysical Research, v. 61, no. 12, p. 4751-4767. 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAKE OCCURRENCE 

MAIN-SHOCK CHARACTERISTICS 

COMPARISON OF Li AND L2 NORMS IN A TELESEISMIC-WAVEFORM 

INVERSION FOR THE RUPTURE HISTORY OF THE EARTHQUAKE 

By Stephen H. Hartzell, Gordon S. ~tewart,~ and Carlos Mendoza, 

U.S. Geological Survey 

CONTENTS 

Page 

A39 

39 

40 

40 

4 1 

42 

45 

46 

47 

ABSTRACT 

We have inverted broadband digital teleseismic body 

waves (P and SH) to obtain the slip history of the 1989 

Loma Prieta earthquake. Comparison of finite-fault waveform-inversion results, using L, and L2 norms, reveals 

some basic uncertainties in the rupture history that are not 

generally appreciated in earthquake-source studies. The 

more robust features of the source that depend less on the 

choice of minimization norm are identifiable. From a consideration of first-motion data and forward modeling of 

body waves, the strike and dip of our model fault plane 

are set at 126O and 67O, respectively. The waveform-inversion results indicate that most of the moment release 

occurs over a fault length of 35 to 40 km and a depth 

range of 2 to 18 km. The hypocenter (at 18-km depth) 

underwent a relatively small amount of slip. The rupture 

propagated upward and bilaterally, with a peak slip of 

about 3 m occurring at 10-km depth. The average velocity 

of rupture propagation is 2.5 krnls. Although the details 

of the slip distribution depend on the minimization norm, 

two main sources are identifiable, with the larger source 

above and to the southeast of the hypocenter. The rake 

vector varies considerably over the fault. The southern 

source is mostly strike slip, whereas the northern source 

is approximately equally partitioned between dip slip and 

strike slip. Also, generally more strike slip occurs at sha 

Current affiliation: Pacific Geophysics, Inc., Pasadena, Calif. 

lower depths. Most of the moment release occurs in the 

first 7.5 s, with an integrated moment of 2.6~10~~ dynecm. Including smaller, peripheral sources that are less well 

resolved raises the moment estimate to 3.0~10~~ dynecm. 

INTRODUCTION 

Numerous waveform-inversion studies over the past 10 

years have attempted to reconstruct the slip history, both 

spatially and temporally, of specific earthquakes. The problem has been linearly formulated to solve for slip amplitudes at designated places and times (Trifunac, 1974; Olson 

and Apsel, 1982; Hartzell and Heaton, 1983, 1986; Frankel 

and Wennerberg, 1989; Mendoza and Hartzell, 1989; Das 

and Kostrov, 1990), as well as linearized iterative formulations that solve for both slip amplitudes and rupture 

times (Jackson and Matsu'ura, 1985; Kikuchi and Fukao, 

1985; Fukuyama and Irikura, 1986; Yoshida, 1986; Takeo, 

1987; Beroza and Spudich, 1988; Hartzell, 1989; Hartzell 

and Iida, 1990). Different types of data have been considered, including strong-motion records and teleseismic 

waveforms. For some earthquakes, a combined data set of 

strong-motion records and teleseismic waveforms has been 

used (Hartzell and Heaton, 1983; Mendoza and Hartzell, 

1989; Hartzell and Mendoza, 1991). In these studies, wavepropagation codes are generally used to calculate synthetic Green's functions, although empirical Green's 

functions, such as aftershock records, have also been used 

(Fukuyama and Irikura, 1986; Hartzell, 1989). In addition, geodetic data have been used to invert for faultrupture histories (Langbein, 1981; Ward and Barrientos, 

1986; Segall and Harris, 1987; Vasco and others, 1988). 

All of the waveform inversions mentioned above have 

been done in the time domain; a linear frequency-domain 

inversion has also been implemented (Olson and Anderson, 1988). 

Aside from the consideration of a linear versus iterative 

formulation, the type of data to invert, the use of synthetic or empirical Green's functions, or time-domain versus frequency-domain inversion, an even more fundamental 

A39 
A40 MAIN-SHOCK CHARACTERISTICS 

question is the minimization norm to be used in the problem. This aspect of the finite-fault inversion problem is 

rarely appreciated, and its implications for the resulting 

source model are poorly understood. The norm of choice 

has generally been the L2 or least-squares norm, the popularity of which is based on an extensive literature (Lanczos, 

1961; Jackson, 1972; Wiggins, 1972; Aid and Richards, 

1980; Menke, 1984). If b is the data vector, A the matrix 

of the synthetic seismograms, and x the solution vector 

that relates A to b in the system of linear equations Ax=b, 

then the L2 norm minimizes the sum of squares of the 

differences between predictions and observations, llb-Axl12. 

The model derived from this minimization is one of many 

possible models that fit the data. Mendez and others (1990) 

described a wave-equation norm that they applied in the 

frequency domain which finds a spatially and temporally 

smooth solution. Another model is obtained by applying 

an L, norm, which minimizes the sum of absolute values 

of the differences between predictions and observations, 

Ib-Axl,. The Li norm was used by Langbein (198 1) to 

invert geodetic data and by Das and Kostrov (1990) to 

invert long-period teleseismic body waves. However, few 

inversion studies of fault-rupture history compare the results for different norms (Mendez and others, 1990), and 

no known study compares L, and L2 models derived from 

a waveform inversion. Therefore, one objective of this 

paper is to compare these two models for the 1989 Loma 

Prieta earthquake. In so doing, we also obtain a better 

idea of the resolvable features in the slip history of this 

earthquake. 

Another important aspect of this study comes from a 

comparison of our inversion results, using broadband 

teleseismic body waves, with those from studies using 

local strong-motion data. Although few such comparisons 

are known, those that have been done show encouraging 

results (Hartzell and Heaton, 1983 ; Houston and Kanamori, 

1986, 1990; Choy and Boatwright, 1988; Hartzell, 1989; 

Mendoza and Hartzell, 1989). If similar rupture histories 

can be obtained from only teleseismic data, many more 

earthquakes for which no strong-motion data are available 

can be investigated with confidence. 

L, VERSUS L, NORM 

The reasons for choosing a particular norm concern the 

distribution of errors in the data, the distribution of observation points around the source, and the characteristics of 

the source model considered to be desirable. Least-squares 

(L2) analysis assumes that errors in the data have a 

Gaussian distribution, whereas the model obtained from 

application of an L, norm assumes that the errors have an 

exponential distribution (Menke, 1984). An exponential 

distribution with the same mean and variance as a Gaussian 

distribution has a much longer tail. Thus, the probability 

of a few outlying points is much higher with an exponential distribution. Therefore, an Ln minimization can handle a 

few bad data points better by attaching less weight to them. 

An important reason for considering alternative norms 

was pointed out by Olson and Anderson (1988). An L2 

norm finds the solution that fits the data by minimizing 

llb-Axil2 and the sum of squares of the solution vector, 

11~11~. Therefore, in an inversion for fault slip, the slip 

amplitude is generally less than the true amplitude. To 

compensate, the spatial and temporal distribution of slip 

may be altered to focus energy toward the observation 

points. Thus, station-array geometry plays an important 

role in our ability to resolve the tradeoffs between slip 

amplitude and its temporal and spatial location on the 

fault, as demonstrated by Olson and Anderson. An Ll 

norm minimizes Ib-Axl, and the sum of absolute values 

of the solution vector, 1x1,. Therefore, the same tradeoffs 

exist, but with a different mathematical weighting. These 

observations motivated Mendez and others (1990) to use 

a norm that seeks a spatially and temporally smooth solution, and Hartzell and Heaton (1983), Hartzell (1989), 

and Hartzell and Iida (1990) to use spatial and temporal 

smoothing constraints with an L2 norm. Finding the 

smoothest solution that fits the data not only finds the 

simplest solution but also resists the focusing of energy 

toward observation points, although no constraint can make 

up for a poor station distribution. 

In the teleseismic problem that we solve, the tradeoff 

between slip amplitude and its spatial and temporal location is not as pronounced as it could be in the near-source 

region, using a sparse strong-motion network. With 

teleseismic data, the direct phases all leave the source 

region close to vertically downward. Significant energy, 

however, cannot be erroneously focused in this direction 

without disrupting the amplitude of the surface reflected 

phases. 

Our objective in this paper is not to find the optimum 

norm to be used in finite-fault waveform inversions; neither the L, nor Ly norm is optimal, and many others could 

be tested. The L, and L2 norms, however, are among the 

simplest and most widely used. Instead, our objective is 

to clearly show the differences that exist between Ll and 

L2 solutions for an earthquake with a good data set and to 

use that comparison to obtain a better idea of the 

earthquake's true rupture history. 

DATA 

In this study, we use teleseismic P and SH body waves 

recorded by stations in the Global Digital Seismograph 

Network, the Chinese Digital Seismograph Network, and 

the Global Seismograph Network (GSN), International De- 
COMPARISON OF L, AND L, NORMS IN A TELESEISMIC-WAVEFORM INVERSION FOR THE RUPTURE HISTORY A41 

ployment of Accelerometers (IDA), and GEOSCOPE 

(Institut de Physique du Globe, Paris) networks (table 1). 

Only stations between distances 30' and 90' are used, to 

avoid mantle triplications and shadow zones. All the seismograms are low-pass filtered with a corner frequency at 

1.0 Hz, using a Butterworth filter (Oppenheim and Schafer, 

1975), and resampled at a time step of 0.2 s. With this 

preprocessing, we lose very little of the waveform information but obtain a more manageable total number of 

data points (7,910) in the inversion. Of the stations used, 

12 have well-recorded long- and short-period P waveforms. For these stations, the inversion uses the broadband, deconvolved displacement record (Harvey and Choy, 

1982). These deconvolved records recover ground displacement from frequencies of 0.01 to 5.0 Hz. Several of these 

stations have no intermediate-period broadband channel; 

to use these stations in the inversion without a broadband 

deconvolution, we would have to use separate long- and 

short-period records. For the other waveforms, the inversion uses the broadband recording channel, with the instrument response intact. All 40 of the stations listed in 

table 1 are included in the inversions, but 6 of them (asterisks) are given near-zero weighting, owing to high levels of noise or nodal characteristics. In this study, "noise" 

is defined as any component of the waveform not described by the assumed Earth model, including anomalous propagation and receiver effects. Nodal stations are 

useful in constraining the strike and dip of the fault plane, 

which are fixed before any inversions are done. These 

stations, however, are not particularly useful in the inversions, owing to the significant changes in the waveform 

that can result from small changes in the model. The azimuthal equidistant projection in figure 1 shows all the 

stations that are given full weight in the inversion. Station 

coverage is better at azimuths of 0' to 90' and 270' to 

360' The effects of the station distribution are discussed 

in detail below. 

P- and SH-wave first-motion information for the stations used in this study is plotted in figure 2. The mechanism that we favor from these data and from forward 

modeling of P and SH waveforms has a strike, dip, and 

rake of 126', 67', and 138O, respectively. The only station 

inconsistent with this mechanism is PPT (fig. 2A), which 

has a high-frequency compressional first motion but which 

plots in a dilatational quadrant. Although the record from 

station PPT is difficult to read, the long-period energy is 

most likely dilatational. Our preferred mechanism is essentially the same as that of Romanowicz and Lyon-Caen 

(1990). 

INVERSION METHOD 

In our basic formulation of the problem, we follow 

Hartzell and Heaton (1983). A fault plane striking 126' 

and dipping 67' is divided into the equal-area subfaults 

shown in figure 3. The overall dimensions of the fault are 

chosen to encompass all the aftershocks within the 2-week 

period after the earthquake, except for a few shallow events 

to the southeast (U.S. Geological Survey staff, 1990). The 

fault is 60 km long and extends from 0.5- to 25-km depth, 

giving a downdip width of 26.6 km. A total of 200 

subfaults (20 along strike and 10 downdip) are used, each 

with dimensions of 3 by 2.66 km. The response of each 

subfault is calculated for each station in the problem by 

summing individual point-source responses. Generalized 

ray theory (Langston and Helmberger, 1975) is used to 

calculate these point-source responses. The source velocity structure (table 2) is based on the velocity structure 

used by the U.S. Geological Survey in preliminary locations of aftershocks. All rays with as many as two internal 

reflections in the layered stack and P- to SV-wave conversions at the surface and Moho are included in the calculations. Attenuation is introduced by using the frequency 

dependent t* operator of Choy and Cormier (1986) for a 

surface source, where t*=1.0, 0.6, and 0.5 for P waves at 

frequencies of 0.1, 1.0, and 5.0 Hz, respectively. The Swave operator has corresponding values approximately a 

factor of 4.5 larger. This attenuation operator was derived 

by simultaneously considering source and propagation path 

effects. Hartzell (1989) showed the effects of different 

attenuation models in a similar teleseismic body-waveform inversion. Models with lower attenuation require less 

slip to match the same observed amplitudes. A secondary 

effect of lower attenuation is a broadening of slip regions 

to fit the same pulse widths. 

The hypocenter is fixed at 18-krn depth (U.S. Geological Survey staff, 1990) at the midpoint of the model fault 

plane. The rupture velocity is assumed to be constant; 

however, we try a range of plausible values from 2.1 to 

3.1 krnls. The subfault synthetic seismograms for strikeslip (180' rake) and dip-slip (90' rake) mechanisms form 

the basis of the matrix A. The observed waveforms strung 

end to end compose the data vector b. Together, they 

form an overdetermined system of linear equations Ax=b. 

In forming these matrices, the observed record must be 

aligned in time with the subfault synthetic seismograms; 

this operation requires picking the first-arriving energy in 

the waveforms. Whenever possible, times from short-period records are used. As noted by many investigators, 

inversion for fault slip is an ill-constrained problem. We 

follow Hartzell and Heaton (1983), Hartzell (1989), and 

Hartzell and Iida (1990) by requiring the slip to be positive; this constraint translates into restricting the rake to 

between 90' and 180'. The problem is also stabilized with 

smoothing constraints on the slip that require the slip to 

vary as smoothly as possible and still fit the data. As 

discussed by Hartzell and Heaton (1983), the gridding of 

the fault plane into subfaults plays an important role in 

this smoothing process. If only a few large subfaults are 
MAIN-SHOCK CHARACTERISTICS 

Table 1 .-Seismic stations used in this study 

[Networks: GEOSCOPE, Institut de Physique du Globe, Paris; GSN, Global Digital Seismograph Network, Chinese Digital 

Seismograph Network, and Global Seismograph Network; IDAIIRIS, International Deployment of Accelerometers/Incorporated Research Institution for Seismology. Asterisks, records weighted down in inversions] 

Record type Station Distance 

(O) 

Azimuth 

(O) Network 

Broadband deconvolved AFI 

P waves. B JI 

COL 

GRFO 

GUM0 

HIA 

HON* 

KEV 

KONO 

MAJO 

SCP 

TOL 

Broadband instrumental ARU 

P waves. ESK 

HRV 

MDJ 

NNA 

OBN 

RPN 

CAY 

PPT* 

WFM 

SSB 

KIP * 

Broadband instrumental ARU 

SH waves. COL* 

ESK 

HIA 

HRV 

MDJ 

NNA 

OBN 

RPN 

SCP 

TOL 

CAY 

PPT* 

WFM 

SSB 

KIP* 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

IDAIIRIS 

GSN 

IDNIRIS 

GEOSCOPE 

GEOSCOPE 

GEOSCOPE 

GEOSCOPE 

GEOSCOPE 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

IDMRIS 

GSN 

IDMRIS 

GSN 

GSN 

GEOSCOPE 

GEOSCOPE 

GEOSCOPE 

GEOSCOPE 

GEOSCOPE 

used, there is insufficient spatial resolution of fault de- routine of Bartels and Conn (1980) is used to solve the L, 

tails. If a small subfault size is chosen and no smoothing norm problem. 

applied, however, starting and stopping phases from individual subfaults can play an erroneous role in modeling 

the data. Therefore, our approach is to divide the fault RESULTS 

into many relatively small subfaults and then apply smooth- Contours of total slip (vector sum of the strike-slip and 

ing constraints. The program NNLS of Lawson and Hanson dip-slip components) for various rupture velocities are 

(1974), a least-squares routine with constraints, is used to shown in figures 4A and 4B for the L, and L2 solutions, 

solve the L2 norm problem, and the linear-programming respectively, and the associated moment estimates and re- 
COMPARISON OF L, AND L, NORMS IN A TELESEISMIC-WAVEFORM INVERSION FOR THE RUPTURE HISTORY A43 

sidual errors for the two solutions with different rupture 

velocities are listed in table 3. As the rupture velocity 

increases, the slip distribution spreads out laterally in both 

the Ll and L2 solutions; the slip distribution is nearly 

constant with depth. These results indicate that the depth 

of faulting is well constrained by the data. The depth 

Figure 1 .-Azimuthal equidistant plot of stations from which waveform 

data were given full weight in inversion. Epicenter of earthquake (star) 

is at center of map, and map radius is 90'. 

range over which most slip occurs is from about 2 to 18 

km, regardless of the norm. Peak slip occurs at about 10- 

km depth. From the residual errors listed in table 3, a 

rupture velocity of 2.5 kds gives the best fit to the data 

in both the Ll and L2 solutions. An average rupture velocity near 2.5 kds is also preferred in several other recent 

source inversions for moderate to large earthquakes 

(Hartzell and Heaton, 1983; Hartzell and Iida, 1990; 

Hartzell and Mendoza, 199 1). 

The Ll and L2 solutions with a rupture velocity of 2.5 

kds are compared in figures 5 and 6. No strong argument can be given for one solution over the other; each 

solution fits the data fairly well, as shown in figure 7. The 

differences visible in figures 5 and 6 are due solely to the 

minimization norm. Any evaluation of an earthquake rupture-history model must be tempered with the realization 

that fundamental uncertainties can exist on the order of 

the differences visible in figures 5 and 6. 

We are now in a position to evaluate those features of 

the two solutions in figures 5 and 6 that are independent 

of the choice of an Ll or L2 norm. As stated above, both 

the Ll and L2 norms favor an average rupture velocity of 

2.5 kds and have most slip occurring between 2- and 18- 

km depth. Both the Li and L2 solutions are also characterized by two main sources, a major one to the southeast of 

the hypocenter and a secondary one to the northwest. However, the L2 solution is dominated considerably more by 

the southeastern source. Both solutions have a small 

amount of slip at the hypocenter and are characterized by 

upward and bilateral rupture. In both solutions, slip iniFigure 2.-Equal-area lower-hemisphere projections of P-wave (A) and SH-wave (B) focal mechanisms of 1989 Lorna Prieta earthquake, based on 

available teleseismic first-motion data. Strike (126') and dip (67') were used in finite-fault waveform inversions; rake (138') is free to vary spatially 

from 90' (thrusting) to 180' (strike slip). 
A44 MAIN-SHOCK CHARACTERISTICS 

tiates in the hypocentral region with a significant thrust 

component and evolves into almost-pure strike slip at shallower depths, as illustrated in figure 8C. The areas of 

peak slip amplitude have a rake of about 130Â° similar to 

the point-source values obtained by other investigators 

(Choy and Boatwright, 1990; Kanamori and Satake, 1990; 

Romanowicz and Lyon-Caen, 1990; Ruff and Tichelaar, 

1990; Zhang and Lay, 1990). The rake, however, varies 

widely with position. 

Although both the L1 and L2 solutions have most of 

their moment release occurring over a fault length of 35 

to 40 km, they also have several small sources outside 

this region. The validity of these small sources is questionable, however, because they are at the limits of our 

resolution. Comparison between the observed and synthetic seismograms shows little change in the waveforms 

when these small sources are omitted. As shown in figure 

9, the small sources all lie at rupture times greater than 

about 7.5 s from the hypocenter. In figure 8A we integrate 

the slip distribution for the L2 solution to obtain a plot of 

moment release (a comparable distribution is obtained for 

the L1 solution). Other investigators have obtained similar 

moment-release functions from teleseismic data (Choy 

and Boatwright, 1990; Kanamori and Satake, 1990; 

Romanowicz and Lyon-Caen, 1990; Ruff and Tichelaar, 

1990). The best-resolved and major component of moment release takes place in the first 7.5 s (shaded area, 

fig. 8A). The corresponding distribution of slip on the 

fault plane is plotted in figure 85. This pattern of faulting 

is nearly identical to the rupture history obtained by Choy 

and Boatwright (1990). A source duration of 7.5 s and a 

rupture length of 35 km also agree closely with the estimates of Kanamori and Satake (1990). The moment estiTable 2.-Source-velocity structure of the earthquake 

[Vp, P-wave velocity; Vc, S-wave velocity] 

VP vs Density Thickness 

(kds) (kds) (g/cm3) (km) 

mates listed in table 3 are 3.2~10~~ dyne-cm for the L1 

solution and 3.0~10~~ dyne-cm for the L2 solution. If only 

the first 7.5 s of each solution is considered, both of these 

estimates are decreased by 0.4~10~~ dyne-cm. Our results 

also agree well with the general fault parameters obtained 

from geodetic modeling by Lisowski and others (1990), 

who estimated a fault length of 37 krn, a depth range of 

faulting of 5 to 17.5 km, and a seismic moment of 3.0~10~~ 

dyne-cm. No clear surface faulting was associated with 

the earthquake, and our results are consistent with that 

observation. The main slip occurring below about 2-km 

depth is plotted in figure 85. For the L2 solution, however, a region of dip slip occurs at the northwest end of 

the fault close to the surface (fig. 55). Although slip on 

this segment of the fault is not well constrained, as discussed above, it does coincide with a region of surface 

cracking (Plafker and Galloway, 1989). 

One source parameter that we have not yet addressed is 

the rise time of the source or the duration of faulting at a 

point on the fault. The source rise time is included in our 

0 

n DISTANCE ALONG STRIKEJN KIOMETERS 

Figure 3.-Parametrization of model fault plane for 1989 Loma Prieta earthquake. Fault is divided into 200 

subfaults, each 3.0 by 2.66 km. Teleseismic waveforms are inverted by using two different minimization 

norms, L, and L2, to obtain optimal slip on each subfault. Hypocenter (star) is at 18-km depth. 
COMPARISON OF L AND L, NORMS IN A TELESEISMIC-WAVEFORM INVERSION FOR THE RUPTURE HISTORY A45 

modeling by convolving the subfault synthetic seismograms with a source-time function. All the solutions that 

we have presented so far assume a 1-s-duration, triangular source-time function that is constant over the fault 

plane. A longer-duration source-time function was tested 

by using a 3-s-duration triangle. The resulting errors, listed 

in table 3 for a rupture velocity of 2.5 kmls, are significantly worse than the previous errors. 

An important aspect of the finite-fault inversion problem that still needs to be discussed is the effect of station 

distribution. The number and location of observation 

records can significantly affect the outcome of an inversion in both teleseismic and strong-motion studies. Olson 

and Anderson (1988) showed several examples of different strong-motion-station distributions that yield divergent 

results. For the teleseismic problem, a good station distribution is particularly necessary for a bilateral rupture, such 

as in the 1989 Loma Prieta earthquake. In a bilateral rupture, the two halves of the fault radiate energy approximately simultaneously. If the fault dimensions are 

relatively small, the energy from the two halves of the 

fault will arrive at teleseismic stations with only a small 

time separation. For the northern and southern sources of 

the earthquake, the time separation is approximately 1 s 

for P waves and 2 s for S waves at stations along the 

strike of the fault. These time separations are near the 

limits of resolution of the analysis, and so the slip distribution is sensitive to the phases and stations used in the 

inversion. 

The effects of using three alternative station distributions-(1) a distribution that includes P-wave phases only, 

(2) a distribution that includes nodal phases and omits 

some nonnodal SH-wave phases, and (3) a more nearly 

uniform station distribution-are shown in figure 10. Only 

the L2 solutions are shown; the L, solutions yield the 

same results. The distributions of stations that include the 

P- and SH-wave phases used for each inversion are shown 

in figure 11. The P-wave-only solution in figure 10 uses 

the P-wave phases from the preferred station distribution 

in figure 11A. The results in figure 10 should be compared with our preferred solution in figure 5. 

The most obvious feature of figure 10 is the instability 

of the strike-slip component of motion. When only Pwave phases are used (fig. lOA), the resolution of the 

strike-slip component is worst; the inversion distributes 

the slip in a ridge approximately equally north and south 

of the hypocenter. SH-wave phases are important for the 

earthquake because of the greater separation between arrival times for sources north and south of the hypocenter, 

and because near-vertical strike-slip faulting is more efficient at producing teleseismic S waves than P waves. By 

adding nodal records to the inversion and removing some 

important nonnodal SH-wave phases (fig. lOB), the major 

strike-slip faulting shifts to the north side of the hypocenter. The net result is that the northern source is now 

larger than the southern source. Because of the less desirable station distribution, we consider this solution to be 

less likely. Finally, because our preferred distribution has 

a higher station density in Europe, we considered a more 

nearly uniform station distribution (fig. 10C). Tradeoffs 

are necessary in choosing such a distribution because the 

number of stations is limited and station quality is important. The resulting model is nearly identical to our preferred solution in figure 5, in which most strike-slip 

faulting occurs south of the hypocenter and the larger of 

the two sources is also south of the hypocenter. These 

results are consistent with the strong-motion inversion 

models of Beroza (1991) and Steidl and others (1991). 

We prefer the solution in figure 5 because it uses all the 

best-quality records and omits nodal records, which we 

do not ordinarily use for the above-mentioned reasons. 

All three solutions in figure 10 have more shallow dipslip faulting than our preferred model. This result is most 

likely erroneous and due to the exclusion of SH-wave 

phases and (or) the inclusion of nodal stations, which contain larger amounts of late-scattered energy. Shallow dipslip motion is hard to resolve (or omit) in an inversion 

using only teleseismic P waves because the downgoing Pwave phase is nearly canceled by the upgoing pP-wave 

phase. The shorter the period of the P wave, the better it 

will be at resolving shallow dip-slip motion. In addition 

to the three solutions in figure 10, we also tried several 

inversions including SV waves. A judicious selection of 

these phases added no new information or failed to change 

the solution significantly from that in figure 5. Owing to 

the uncertainties in the SV waveforms and their likely 

contamination with converted phases, these inversions are 

considered less accurate. 

The distribution of slip for the L2 solution and a rupture 

velocity of 2.5 kmls is compared with the pattern of aftershocks during the 2-week period after the earthquake (Dietz 

and Ellsworth, 1990; Simila and others, 1990) in figure 

12. Most aftershocks plot within the boundaries of the 

area of major slip. On closer inspection, aftershocks seem 

to concentrate in the areas of least slip or highest gradient 

in the main-shock slip. This conclusion is made particularly easy if all the aftershocks are plotted with the same 

symbol, regardless of magnitude. Several recent studies 

have found that foreshocks and aftershocks occur in areas 

that did not slip during the main shock or in areas of 

stress concentration due to the main-shock slip (Stein and 

Lisowski, 1983; Mendoza and Hartzell, 1988; Engdahl 

and others, 1989; Houston and Engdahl, 1989; Schwartz 

and others, 1989; Hartzell and Iida, 1990). 

CONCLUSIONS 

The effect of the minimization norm in finite-fault inversions has not been adequately considered. The solu- 
A46 MAIN-SHOCK CHARACTERISTICS 

tions obtained by using Ll and L2 norms for the 1989 

Loma Prieta earthquake differ significantly, and we are 

unable to judge which is better. Neither norm is optimal, 

and more work is needed to find norms that do not produce undesirable tradeoffs in the earthquake-source model. 

By considering L, and L2 solutions, we arrive at the 

following parameters for the earthquake that are common 

to both norms. The major faulting has a length of 35 to 40 

km and a depth extent from 2 to 18 km. The hypocentral 

region has only minimal slip. The rupture grows upward 

from the point of initiation and bilaterally at an average 

velocity of 2.5 kmls. There are two main areas of slip. 

The largest is above and southeast of the hypocenter and 

is centered at 10-km depth; this source dominates the L2 

solution and has more nearly equal weight in the Li solution. The second source is northwest of the hypocenter 

and is also centered at about 10-km depth. The rake varies with position on the fault, ranging from mostly dip 

slip in the hypocentral region to almost pure strike slip at 

shallower depths. The southern source also has a larger 

component of strike-slip motion than the northern source. 

Most of the moment release occurs in the first 7.5 s, with 

an integrated moment of 2.6~10~~ dyne-cm. This part of 

the rupture is the best resolved. Including peripheral, secondary areas of slip raises the moment to 3.0~10~~ dynecm. The peak slip amplitude is about 3 m, and the preferred 

average source-time duration is about 1 s. 

This study also raises several questions regarding future slip along this section of the San Andreas fault. First, 

because little slip occurred in the uppermost region of the 

fault (above 2-km depth), will this section of the fault 

rupture in another earthquake, or is strain being relieved 

by another mechanism? Also, both the Ll and L2 solutions show slip on the southeastern section of the fault to 

be considerably larger (fig. 5). Should we expect future 

slip on the section northwest of the hypocenter, owing to 

the slip deficit calculated for the earthquake? These questions might be answerable by taking a closer look at the 

slip history of this section of the San Andreas fault. 

ACKNOWLEDGMENTS 

The Ll norm solver was provided by Toshiro Tanimoto. 

We thank Barbara Romanowicz for supplying the 

GEOSCOPE data used in this study. The attenuation operators and the broadband, deconvolved P-wave data were 

Figure 4.-Contours of total slip (in centimeters) (vector sum of 

strike-slip and dip-slip motion), using L, (A) and L2 (B) norms and 

six different rupture velocities. Rupture velocity of 2.5 km/s gives 

lowest residual error (table 3). Star, hypocenter. 

2.1 kmls 

2.3 kmls 

01 n 

2.5 kmls 

2.7 kmls 

10 20 30 40 50 60 

DISTANCE ALONG STRIKE IN KILOMETERS 
COMPARISON OF L, AND L2 NORMS IN A TELESEISMIC-WAVEFORM INVERSION FOR THE RUPTURE HISTORY A47 

2.3 kmls 

25t1 I I I I I I ((-4 

2.7 kmls 

3.1 kmls 4 

25 ~~~11~

0 10 20 30 40 50 60 

DISTANCE ALONG STRIKE, IN KILOMETERS 

Figure 4.-Continued 

Table 3.-Results of inversion using L, and Li norms 

Time-function Rupture 

duration Norm velocity Moment Residual 

(s) (1 026 dyne-cm) error 

kindly supplied by George Choy. Aftershock locations 

were provided by Lynn Dietz. We benefited from discussions with Allen Olson on minimization norms. The manuscript was improved by thoughtful reviews by George 

Choy, Kaye Shedlock, and Terry Wallace. 

REFERENCES CITED 

Aki, Keiiti, and Richards, P.G., 1980, Quantitative seismology; theory 

and methods: San Francisco, W.H. Freeman, 2 v. 

Bartels, R.H., and Conn, A.R., 1980, Linearly constrained discrete L, 

problems: Association for Computing Machinery Transactions on 

Mathematical Software, v. 6, no. 4, p. 594-608. 

Beroza, G.C., 1991, Near-source modeling of the Loma Prieta earthquake; evidence for heterogeneous slip and implications for earthquake hazard: Seismological Society of America Bulletin, v. 81, 

no. 5, p. 1603-1621. 

Beroza, G.C., and Spudich, Paul, 1988, Linearized inversion for fault 

rupture behavior; application to the 1984 Morgan Hill, California 

earthquake: Journal of Geophysical Research, v. 93, no. B6, p. 

6275-6296. 

Choy, G.L., and Boatwright, John, 1988, Teleseisrnic and near-field 

analysis of the Nahanni earthquakes in the Northwest Territories, 

Canada: Seismological Society of America Bulletin, v. 78, no. 5, p. 

1627-1652. 

1990, Source characteristics of the Loma Prieta, California, earthquake of October 18, 1989 from global digital seismic data: Geophysical Research Letters, v. 17, no. 8, p. 1183-1186. 

Choy, G.L., and Cormier, V.F., 1986, Direct measurement of the mantle 

attenuation operator from broadband P and S waveforms: Journal 

of Geophysical Research, v. 91, no. B7, p. 7326-7342. 

Das, Shamita, and Kostrov, B.V., 1990, Inversion for seismic slip rate 

history and distribution with stabilizing constraints; application to 

the 1986 Andreanof Islands earthquake: Journal of Geophysical 

Research, v. 95, no. B5, p. 6899-6913. 

Dietz, L.D., and Ellsworth, W.L., 1990, The October 17, 1989, Loma 

Prieta, California, earthquake and its aftershocks; geometry of the 

sequence from high-resolution locations: Geophysical Research Letters, v. 17, no. 9, p. 1417-1420. 

Engdahl, E.R., Billington, Selena, and Kisslinger, Carl, 1989, Teleseismically recorded seismicity before and after the May 7, 1986, 

Andreanof Islands, Alaska, earthquake: Journal of Geophysical 
A48 MAIN-SHOCK CHARACTERISTICS 

Research, v. 94, no. Bll, p. 15481-15498. 

Frankel, Arthur, and Wennerberg, L.G., 1989, Rupture process of the 

M 6.6 Superstition Hills, California, earthquake determined from 

strong-motion records; application of tomographic source inversion: 

Seismological Society of America Bulletin, v. 79, no. 2, p. 515- 

541. 

Fukuyarna, Eiichi, and Irikura, Kojiro, 1986, Rupture process of the 

1983 Japan Sea (Akita-Oki) earthquake using a waveform inversion 

method: Seismological Society of America Bulletin, v. 76, no. 6, p. 

1623-1640. 

Hartzell, S.H., 1989, Comparison of seismic waveform inversion results 

for the rupture history of a finite fault; application to the 1986 

North Palm Springs, California, earthquake: Journal of Geophysical 

Research, v. 94, no. B6, p. 7515-7534. 

Hartzell, S.H., and Heaton, T.H., 1983, Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of 

the 1979 Imperial Valley, California, earthquake: Seismological 

Society of America Bulletin, v. 73, no. 6, p. 1553-1583. 

1986, Rupture history of the 1984 Morgan Hill, California, earthquake from the inversion of strong motion records: Seismological 

Society of America Bulletin, v. 76, no. 3, p. 649-674. 

Hartzell, S.H., and Iida, Mashiro, 1990, Source complexity of the 1987 

Whittier Narrows, California, earthquake from the inversion of strong 

motion records: Journal of Geophysical Research, v. 95, no. B8, p. 

12475-12485. 

Hartzell, S.H., and Mendoza, Carlos, 1991, Application of an iterative 

least squares waveform inversion of strong motion and teleseismic 

records to the 1978 Tabas, Iran, earthquake: Seismological Society 

of America Bulletin, v. 81, no. 2, p. 305-331. 

Harvey, Danny, and Choy, G.L., 1982, Broad-band deconvolution of 

GDSN data: Royal Astronomical Society Geophysical Journal, v. 

69, no. 2, p. 659-668. 

Houston, Heidi, and Engdahl, E.R., 1989, A comparison of the spatiotemporal distribution of moment release for the 1986 Andreanof 

Islands earthquakes with relocated seismicity: Geophysical Research 

Letters, v. 16, no. 12, p. 1421-1424. 

Houston, Heidi, and Kanamori, Hiroo, 1986, Source spectra of great 

earthquakes; teleseismic constraints on rupture process and strong 

motion: Seismological Society of America Bulletin, v. 76, no. 1, p. 

19-42. 

1990, Comparison of strong-motion spectra with teleseismic spectra for three magnitude 8 subduction-zone earthquakes: Seismological Society of America Bulletin, v. 80, no. 4, p. 913-934. 

Jackson, D.D., 1972, Interpretation of inaccurate, insufficient and inconsistent data: Royal Astronomical Society Geophysical Journal, 

v. 28, no. 1, p. 97-107. 

Jackson, D.D., and Matsu'ura, Mitsuhiro, 1985, A Bayesian approach'to 

nonlinear inversion: Journal of Geophysical Research, v. 90, no. 1, 

p. 581-591. 

Kanarnori, Hiroo, and Satake, Kenji, 1990, Broadband study of the 1989 

DISTANCE ALONG STRIKE, IN KILOMETERS 

Figure 5.-Contours of slip (in centimeters) in best-fitting L, (A) and L2 (B) solutions, showing strike slip (180Â° top plot), dip slip (90Â° middle plot) 

and vector sum of strike slip and dip slip (bottom plot), using rupture velocity of 2.5 krnls. Star, hypocenter. 
COMPARISON OF L, AND L, NORMS IN A TELESEISMIC-WAVEFORM INVERSION FOR THE RUPTURE HISTORY A49 

Loma Prieta earthquake: Geophysical Research Letters, v. 17, no. 

8, 1179-1 182. 

Kikuchi, Masayuki, and Fukao, Yoshio, 1985, Iterative deconvolution 

of complex body waves from great earthquakes-the Tokuchi-Oki 

earthquake of 1968: Physics of the Earth and Planetary Interiors, v. 

37, no. 4, p. 235-248. 

Lanczos, Cornelius, 1961, Linear differential operators: New York, D. 

Van Nostrand, 564 p. 

Langbein, J.O., 1981, An interpretation of episodic slip on the Calaveras fault near Hollister, California: Journal of Geophysical Research, v. 86, no. B6, p. 4941-4948. 

Langston, C.A., and Helmberger, D.V., 1975, A procedure for modelling shallow dislocation sources: Royal Astronomical Society Geophysical Journal, v. 42, no. 1, p. 117-130. 

Lawson, C.L., and Hanson, R.J., 1974, Solving least squares problems: 

Englewood Cliffs, N.J., Prentice-Hall, 340 p. 

Lisowski, Michael, Prescott, W.H., Savage, J.C., and Johnston, M.J.S., 

1990, Geodetic estimate of coseismic slip during the 1989 Loma 

Prieta, California, earthquake: Geophysical Research Letters, v. 17, 

no. 9, p. 1437-1440. 

Mendez, A.J., Olson, A.H., and Anderson, J.G., 1990, A norm minimization criterion for the inversion of earthquake ground motion: Geophysical Journal International, v. 102, no. 1, p. 287-298. 

Mendoza, Carlos, and Hartzell, S.H., 1988, Aftershock patterns and 

mainshock faulting: Seismological Society of America Bulletin, v. 

78, no. 4, p. 1438-1449. 

1989, Slip distribution of the 19 September 1985 Michoacan, 

Mexico, earthquake; near-source and teleseismic constraints: Seismological Society of America Bulletin, v.,79, no. 3, p. 655-669. 

Menke, William, 1984, Geophysical data analysis; discrete inverse theory: 

Orlando, Fla., Academic Press, 260 p. 

Olson, A.H., and Apsel, R.J., 1982, Finite faults and inverse theory with 

application to the 1979 Imperial Valley earthquake: Seismological 

Society of America Bulletin, v. 72, no. 6, p. 1969-2001. 

Olson, A.H., and Anderson, J.G., 1988, Implications of frequency domain inversion of earthquake ground motions for resolving the spacetime dependence of slip on an extended fault: Royal Astronomical 

Society Geophysical Journal, v. 94, no. 2, p. 443-455. 

Oppenheim, A.V., and Schafer, R.W., 1975, Digital signal processing: 

Englewood Cliffs, N.J., Prentice Hall, 585 p. 

Plafker, George, and Galloway, J.P., eds., 1989, Lessons learned from 

the Loma Prieta, California, earthquake of October 17, 1989: U.S. 

DISTANCE ALONG STRIKE IN KILOMETERS 

Figure 6.-Three-dimensional plots of total slip (vector sum of strike-slip and dip-slip motion) for bestfitting L, (A) and Ln (B) solutions. View updip from below hypocenter (star). 
A50 MAIN-SHOCK CHARACTERISTICS 

Geological Survey Circular 1045, 48 p. 

Romanowicz, B.A., and Lyon-Caen, Hdlkne, 1990, The Loma Prieta 

earthquake of October 18, 1989; results of teleseismic mantle and 

body-wave inversion: Geophysical Research Letters, v. 17, no. 8, p. 

1191-1 194. 

Ruff, L.J., and Tichelaar, B.W., 1990, Moment tensor rate functions for 

the 1989 Loma Prieta earthquake: Geophysical Research Letters, v. 

17, no. 8, p. 1187-1 190. 

Schwartz, S.Y., Dewey, J.W., and Lay, Thorne, 1989, Influence of fault 

plane heterogeneity on the seismic behavior in the southern Kurile 

Islands Arc: Journal of Geophysical Research, v. 94, no. B5, p. 

5637-5649. 

Segall, Paul, and Harris, R.A., 1987, Earthquake deformation cycle on 

the San Andreas fault near Parkfield, California: Journal of Geophysical Research, v. 92, no. B10, p. 1051 1-10525. 

Simila, G.W., McNally, K.C., Nava, E., Protti-Quesada, Marino, and 

Yellin, Joseph, 1990, Evidence of very early aftershock activity 

along the northwest portion of the 18 October 1989 earthquake 

rupture zone: Geophysical Research Letters, v. 17, no. 10, p. 1785- 

1788. 

Steidl, J.H., Archuleta, R.J., and Hartzell, S.H., 199 1, Rupture history 

of the 1989 Loma Prieta, California, earthquake: Seismological Society of America Bulletin, v. 81, no. 5, p. 1573-1602. 

Stein, R.S., and Lisowski, Michael, 1983, The 1979 Homestead Valley 

earthquake sequence, California; control of aftershocks and 

postseismic deformation: Journal of Geophysical Research, v. 88, 

no. B8, p. 6477-6490. 

Takeo, Minoru, 1987, An inversion method to analyze the rupture processes of earthquakes using near-field seismograms: Seismological 

Society of America Bulletin, v. 77, no. 2, p. 490-513. 

Trifunac, M.D., 1974, A three-dimensional dislocation model for the 

San Fernando, California, earthquake of February 9, 1971 : SeismoMAJO 

Figure 7.Ã‘Compariso of broadband deconvolved (A) and instrumental (B) P waves and broadband instrumental SH waves (0 (top trace) with 

predictions of best-fitting solutions for L2 (middle trace) and L, (bottom trace) norms in figures 5 and 6. Broadband deconvolved data records were 

obtained by performing a simultaneous deconvolution of long- and short-period records. Peak amplitudes in microns (fig. 7A) and counts (figs. 7B, 

7C). Synthetic seismograms not assigned an amplitude were downweighted in inversion 
COMPARISON OF L, AND L, NORMS IN A TELESEISMIC-WAVEFORM INVERSION FOR THE RUPTURE HISTORY A51 

logical Society of America Bulletin, v. 64, no. 1, p. 149-172. 

U.S. Geological Survey staff, 1990, The Loma Prieta, California, earthquake; an anticipated event: Science, v. 247, no. 4940, p. 286-293. 

Vasco, D.W., Johnson, L.R., and Goldstein, N.E., 1988, Using surface 

displacement and strain observations to determine deformation at 

depth, with application to Long Valley caldera, California: Journal 

of Geophysical Research, v. 93, no. B4, p. 3232-3242. 

Ward, S.N., and Barrientos, S.E., 1986, An inversion for slip distribution and fault shape from geodetic observations of the 1983 Borah 

Peak, Idaho, earthquake: Journal of Geophysical Research, v. 91, 

s 

ARU 

7422 

MDJ h 

no. B5, p. 4909-4919. 

Wiggins, R.A., 1972, The general linear inverse problem; implication of 

surface waves and free oscillations for earth structure: Reviews of 

Geophysics, v. 10, no. 1, p. 251-285. 

Yoshida, Shingo, 1986, A method of waveform inversion for earthquake rupture process: Journal of Physics of the Earth, v. 34, no. 3, 

p. 235-255. 

Zhang, Jiajun, and Lay, Thorne, 1990, Source parameters of the 1989 

Loma Prieta earthquake determined from long-period Rayleigh 

waves: Geophysical Research Letters, v. 17, no. 8, p. 1 195-1 198. 

WFM 

Figure 7.-Continued 
A52 MAIN-SHOCK CHARACTERISTICS 

c 

ARU PPT 

Figure 7.-Continued 
COMPARISON OF L, AND L, NORMS IN A TELESEISMIC-WAVEFORM INVERSION FOR THE RUPTURE HISTORY A53 

1 3 5 7 9 11 13 

TIME ,IN SECONDS 

IIT I\ \ I+\ I 

DISTANCE ALONG STRIKE, IN KILOMETERS 

Figure 8.-Best-fitting solution for Ly norm. A, Moment release. Most moment release, which also is best 

resolved, occurs within the first 7.5 s. B, Contours of total slip (in centimeters) as a function of position, 

corresponding to shaded area of moment-release function in figure 8A. C, Vector plot of rake as a function 

of position, including slip vectors on all subfaults. Size of arrows is proportional to amplitude of slip. 
MAIN-SHOCK CHARACTERISTICS 

(0 

0 

n DISTANCE 

Figure 9.-Contours of rupture front 

gave lowest residual error for both L, 

20 30 40 50 60 

ALONG STRIKE, IN KILOMETERS 

at 2.5-s intervals for a constant rupture velocity of 2.5 kmls, which 

and L2 norms. Star, hypocenter. 
Figure 10.Ã‘Contour of slip (in centimeters) in L2 solution, showing strike slip (180Â° top plot), dip slip (90Â° middle plot), and vector sum of strike slip and dip slip (bottom plot) for three alternative 

station distributions: a distribution that includes P-wave phases only (A), a distribution that includes nodal phases and omits some nonnodal SH-wave phases (B), and a more nearly uniform 

distribution (C). All inversions use a rupture velocity of 2.5 kmls and a 1-s-duration source-time function. Because rupture is bilateral, with only small time differences between phases arriving from 

sources on north and south halves of fault, solution is sensitive to phases and stations used in inversion. 
MAIN-SHOCK CHARACTERISTICS 
COMPARISON OF L, AND L, NORMS IN A TELESEISMIC-WAVEFORM INVERSION FOR THE RUPTURE HISTORY A57 

Early 3.9-4.8 1 

- I I I I 1 I I I I I 

5 

0 DISTANCE ALONG STRIKE, IN KILOMETERS 

n 

Figure 12.-Comparison of aftershock locations with distribution of slip in best-fitting L2 solution (fig. 5). 

Aftershock hypocenters are projected perpendicularly onto dipping plane of model fault. Only aftershocks 

that occurred during 2-week period after earthquake within a perpendicular distance of 2 km from fault are 

plotted. Triangles, aftershocks located by Simila and others (1990). 

4 Figure 11.-Azimuthal equidistant plots of stations from which P (left 

plot) and SH (right plot) waveform data were used in preferred model 

(fig. 5) (A), and two alternative station distributions: a distribution that 

includes nodal phases and omits some nonnodal SH-wave phases(B), 

and a more nearly uniform distribution (0. 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAmOCCURRENCE 

MAIN-SHOCK CHARACTERISTICS 

FREQUENCY-DOMAIN INVERSION FOR THE RUPTURE 

CHAMCTERISTICS DURING THE EARTHQUAKE, USING 

STRONG-MOTION DATA AND GEODETIC OBSERVATIONS 

By Stephen P. Horton, 

Columbia University, Lamont-Doherty Earth Observatory; 

John G. Anderson, 

University of Nevada, Reno; and 

Andres J. Mendez, 

GEOENVIRON 

CONTENTS 

Page 

A59 

59 

60 

6 1 

6 1 

62 

64 

69 

69 

ABSTRACT 

We have modeled strong-motion and geodetic data by 

using a frequency-domain inversion technique to infer the 

rupture characteristics of the 1989 Loma Prieta earthquake. 

The inversion determines the static offset from geodetic 

data and the slip velocity from strong-motion data for 

individual points on an assumed fault plane. Formulation 

of the inverse problem in the frequency domain allows 

inversion of both data sets and eliminates the requirement 

inherent in time-domain methods to specify the pulse 

shape, rise time, and rupture dynamics before the inversion. These properties are then derived from the inversion. The assumed fault plane is 16 by 40 km (top edge 

4.25 km below the surface), strikes 129', dips 69' SW., 

and contains the hypocenter. The total static offset is 

smoothly distributed, with a maximum slip of 1.4 m and a 

seismic moment of 2.5~10~~ dyne-cm; the largest strikeslip displacements are to the southeast, and the largest 

reverse-slip displacements are to the northwest. The geodetic data are fitted substantially better by our model, 

which agrees with aftershock locations, than by the models in previous studies, which have the slip surface outside the aftershock zone. Preliminary modeling of the 

strong-motion data suggests that rupture propagation to 

the northwest may follow propagation to the southeast, 

that the rupture velocity of 3.5 kmh (96-100 percent of 

the local shear-wave velocity) is higher than inferred by 

other studies, and that the rise time (approx 1.75 s for an 

area where the highest slip velocities occur) may be longer 

than previously reported. 

INTRODUCTION 

The 1989 Loma Prieta earthquake provides an outstanding opportunity to apply the various methods of inferring 

slip on a finite fault from records of ground motion. More 

than 25 components of strong ground motion are available from within 40 km of the epicenter, as well as recordings from standard and broadband seismic instruments 

worldwide. In addition, a dense geodetic network provides data on the permanent ground offsets caused by the 

earthquake. In this study, both strong-ground-motion 

records and geodetic data are used to derive slip models 

for the earthquake. 

We use a frequency-domain inver5ion technique (Olson 

and Anderson, 1988) with a wave-equation norm (Mendez 

and others, 1990) to calculate the slip models. Formulation of the inversion within the frequenc domain allows 

both geodetic and seismic data to be mod il ed by the same 

procedure, providing an interesting comparison of the resolving power of the two data sets. In addition, the frequency-domain inversion technique eliminates the need 

to specify source shape, rise time, and rupture dynamics 

as in most time-domain inversion methods, allowing these 

parameters in the slip model to be estimated from the 

solution after the inversion. 

We begin by briefly reviewing the results of previous 

finite-fault-modeling studies of the earthquake. Then, we 

present the method and data used in this study, along with 

the inversion results for both the geodetic and strong- 
A60 MAIN-SHOCK CHARACTERISTICS 

motion data. Finally, we compare these results with those 

of previous studies. 

PREVIOUS STUDIES 

Three studies have used geodetic data to infer fault 

geometry and slip for the 1989 Loma Prieta earthquake. 

Lisowski and others (1990) forward-modeled strain and 

displacement measurements from before and after the 

earthquake. Their best-fitting model has 1.6 m of rightlateral strike slip and 1.2 m of reverse slip uniformly distributed on a planar fault surface 37 km long-, striking 

136O, dipping 70Â° and extending from 5- to 17.5-km depth. 

The fault strike approximately parallels the surface trace 

of the San Andreas fault and overlaps the area of aftershocks with generally the same length, dip, and depth 

range. Lisowski and others determined a seismic moment 

of 3x10~~ dyne-cm for the main shock. 

Snay and others (1991) applied the same technique to 

an expanded data set and investigated nonplanar geometries. Their preferred fault is "kinked," with two segments: one dipping 90' and extending from 4.8- to 9.0-km 

depth, and the second dipping 70Â° sharing a common 

edge with the upper surface, and extending from 9.0- to 

15.1-km depth. The average slip amplitude predicted for 

each surface is similar for the strike-slip component, approximately 1.9 m. The dip-slip components, however, 

differ by a factor of 2: 1 .O m for the upper surface and 2.3 

m for the lower. Although the slip amplitudes determined 

in the "kinked" model are larger than those determined by 

Lisowski and others (1990), the estimated seismic moment (2.8~10~~ dyne-cm) is similar because the fault area 

in Snay and others' study is smaller. This result highlights the tradeoff between fault area and average slip 

amplitude for models with a constant moment. 

Marshall and others (1991) modeled vertical-displacement measurements made in the vicinity of Loma Prieta 

before and after the earthquake. They searched for the 

best planar and listric faults, finding that both types of 

faults produced results consistent with the observed data. 

Their best-fitting planar model with uniform slip is 34 km 

long, striking 12g0, dipping 60Â° and extending from 4- to 

15-km depth; the slip is 2.4 m right lateral and 1.7 m 

reverse. Interestingly, their best-fitting model faults are 

above and to the southwest of the aftershock zone. They 

obtained a better fit by dividing the fault into a northwestern segment with larger thrust component and a southeastern segment with larger strike-slip component, This 

model gives a seismic moment of 2.2~10~~ dyne-cm for 

the main shock and an average slip amplitude of 2.1 me 

Four other studies used seismic data to infer the spatial 

and temporal slip history during the earthquake. These 

studies all assumed a simple planar fault geometry related 

to the location of the hypocenter and the distribution of 

aftershocks. Like the geodetic studies, these studies also 

systematically investigated the model-parameter space to 

obtain the best solution; however, the model parameters 

of concern were rupture velocity and rise time. The studies differed mainly in the data set analyzed and the details 

of the inferred slip distribution. 

The slip model of Steidl and others (1991) was derived 

from strong-motion data covering a broad range of azimuths and distances. Their best-fitting solution is for a 

rupture velocity of 3.0 kds and a rise time of 1.0 s. They 

found that slip at the southeast end of the fault has a 

larger strike-slip component and at the northwest end a 

largir reverse-slip component. They also found larger displacements in these areas than updip from the hypocenter. 

The seismic moment after scaling by a factor of 1.5 is 

estimated at 3.5~10~~ dyne-cm. They found a complex 

rupture front that propagated faster to the south than to 

the north but that the areas of high slip at both ends radiated simultaneously. 

Beroza (1991) obtained a similar model from a smaller 

set of strong-motion stations at closer distances. He found 

that slip varies in amplitude and rake, and that little slip 

occurs updip from the hypocenter. There are two main 

areas of concentrated slip: one to the northwest with a 

larger reverse-slip component, and one to the southeast 

with a larger strike-slip component. Slip amplitudes in 

these patches exceed 4.5 m, and the total seismic moment 

after scaling by a factor of 1.8 is estimated at 2.3~10~~ 

dyne-cm. The assumed source pulse used in this study has 

an extremely short rise time, 0.3 s, and rupture was found 

to propagate bilaterally from the hypocenter at a velocity 

of 2.7 to 3.1 kds, depending on depth. 

Wald and others (1991) inverted both teleseismic and 

strong-motion data. They obtained self-consistent results 

for separate inversions of the teleseismic or strong-motion data and the combined data set. Their results are 

generally consistent with the previous seismic studies. They 

preferred bilateral rupture at a velocity of 2.7 kds and 

rise time of 0.7 s. They observed a varying slip amplitude, with slip concentrated in two patches, one to the 

northwest and another to the southeast, and with little slip 

updip from the hypocenter. They found similar rakes 

(14S0), however, at both ends of the fault and a larger 

moment release from the northeastern segment. They 

showed evidence of a foreshock occurring approximately 

2 s before the main energy release; this foreshock had the 

hypocentral location determined from regional data, 

Hartzell and others (1991) reported similar results from 

inverting teleseismic data. They found the larger moment 

release from the southeast end to be dominantly strike 

slip, whereas equal components of strike slip and reverse 

slip occurred at the north end. Of interest in their study is 

a comparison of the two norms, Ll and L2: they found 

that the details of the slip distribution are affected by the 

choice of norm (see Hartzell and others, this chapter). 
FREQUENCY-DOMAIN INVERSION FOR THE RUPTURE CHARACTERISTICS DURING THE EARTHQUAKE A6 1 

METHOD 

This study utilizes a frequency-domain inversion for 

slip velocity on a finite fault (Olson and Anderson, 1988) 

with the wave-equation norm of Mendez and others (1990). 

The method leads to a wavelike solution that is spatially 

and temporally smooth. In addition, the method is amenable to different data sets, allowing the use of both geodetic and strong-motion data. We briefly summarize the 

salient features of the method below (for details, see Olson 

and Anderson, 1988; Mendez and others, 1990; and 

Mendez and Anderson, 199 1). 

At some observation point x, the nth component of velocity can be expressed through the representation theorem as 

where dn(x,t) is the nth component of the observed velocity-time series at point x, E is the fault surface with normal v, [v(&,t)] is a velocity discontinuity across the fault 

surface at point 6, and c~~~(&,x;~) is the stress tensor at 

point & due to a point force applied in the nth direction at 

point x. We define the Fourier transform pair 

rewrite the representation theorem in the frequency domain, and discretize the fault surface to give 

where dn(x,f) is the Fourier spectral value at frequency f 

of the observed ground velocity, [vS(k,f)lk is the component of the discontinuity in the direction of strike occurring at the kth segment ([vd(k,f)]* is the dip-slip 

component), Tsn(k,x;f) is the component of traction resolved in the direction of strike at segment k on the fault 

surface due to a point force applied in the nth direction at 

point x (Tdn(k,x;f) is the dip-slip component), K is the 

total number of fault segments, and AX is the area of an 

individual fault segment. Finally, this equation can be written in matrix form as 

d = Tv, (2) 

Equation 2 is solved independently for each frequency 

over a finite bandwidth, using the Chebyshev method 

(Olson, 1987). We used an eigenvalue bandwidth (bla) of 

10.0 in determining the final solution. The time history 

for each segment on the fault can be obtained by taking 

the inverse Fourier transform of the spectral values in v 

over this frequency bandwidth. 

Equation 2 is generally underdetermined, and its solution is nonunique. A particular solution obtained by singular-value decomposition would have a minimum length 

as measured with the L2 norm. The properties of this solution were investigated by Olson and Anderson (1988) 

and found to be strongly influenced by the station distribution. Recently, Hartzell and others (1991) investigated 

the difference between time-domain inversions performed 

by using both the Ll and L2 norms and found differences 

in the characteristics of the inferred slip distributions (see 

Hartzell and others, this chapter), 

This study uses the wave-equation norm of Mendez 

and others (1990), which minimizes the importance of 

station distribution. This norm is based on the wave-equation operator 

A wavelike solution can be found by minimizing the L2 

norm of 

TD-4.1 = d 

u = Dv, 

where D represents the matrix resulting from discretization 

of the wave-equation operator for a prescribed rupture 

velocity c over the fault plane. The method produces a 

wavelike solution with the minimum slip amplitude consistent with the data. We do not perform any rescaling as 

do Mendez and others (1990) to obtain the most nearly 

constant slip amplitude. 

The model-parameter space is investigated by systematically varying the model parameters to obtain a solution 

with the minimum data-prediction error. A solution for 

the static offset is found by varying the strike and dip of 

the fault surface, and for the velocity discontinuity by 

varying the rupture velocity c used in constructing the 

wave-equation norm over the range 2.5-1,000.0 kmls. 

Varying the model parameters in this way serves to highlight certain features of the solution that are robust, returning with each new parametrization. We believe these 

robust features of the solutions are significant, and so we 

stress these characteristics in the discussion below. 

DATA 

The locations of the geodetic and strong-motion stations used in the inversion are shown in figure 1. The 

geodetic data are from the Global Positioning Satellite 

(GPS) measurements (large solid squares) of Lisowski and 

others (1990) and the leveling measurements (small open 

squares) of Marshall and others (1991). The strong-mo- 
A62 MAIN-SHOCK CHARACTERISTICS 

tion data were provided by the California Division of 

Mines and Geology (CDMG); details on the strong-motion stations are listed in table 1. 

Geodetic observations form the data set to be inverted 

for the static offset during faulting. This static offset corresponds to the value of the velocity spectrum 

and the area under the velocity-time function as 

evaluating the Fourier transform at 0.0 Hz: 

at 0.0 Hz 

shown by 

Marshall and others (199 1) reported coseismic elevation changes that are used directly in equation 1. The 

measurements of successive bench marks, however are 

highly correlated, and so treating the leveling data as independent coseismic station-elevation changes may exaggerate the importance of any measurement error made 

along the leveling line. We treat the data in this way to 

compare our results with those of Marshall and others. 

GPS measurements provide data on the horizontal and 

vertical changes in length (as vectors) between station 

LOMA and the other four GPS stations (fig. 1). These 

length changes between observations points can be accommodated by modifying equation 1 so that 

where dn(x, f) - dn(y, f) is the change in length (the vector component in the nth direction) between observation 

points x and y , and qn (k, x; f) - qn (k, y; f) is the difference 

in the strike-slip component of traction on the fault plane 

resulting from point sources applied at x and y 

T: (k, x; f) - T: (k, y; f) is the corresponding dip-slip component). Because the velocity discontinuity is linearly related to both the vertical displacement and the length 

change, both leveling and GPS data may be used simultaneously to solve for the static offset on the fault. 

Strong-motion records from SMA-1 accelerometers at 

seven CDMG stations (fig. 1) were inverted to characterize the dynamic aspects of the rupture process. The data 

were processed by the CDMG, including digitization, integration (to obtain velocity), and bandpass filtering between 0.1 to 25.0 Hz. We Fourier-transformed the data at 

intervals of 0.02 Hz for frequencies of 0.1 to 1.0 Hz. The 

lower limit is directly determined by the high-pass corner 

frequency of the filter used in processing the data. Reliable information at lower frequencies is not contained in 

the data. 

The upper limit of 1.0 Hz is related to our ability to 

adequately model the Green's functions. The Green's functions used in this study are produced by the wave-number-integration computer program PROSE (Apsel and 

Luco, 1983; Luco and Apsel, 1983). This program uses a 

one-dimensional velocity model but includes near- and 

far-field terms, The velocity model used in this study is 

based on the 10-layer model of Deitz and Ellsworth (1990) 

and is the same as that used by Steidl and others (1991). 

We believe that a layered velocity model is adequate only 

at lower frequencies, and so we set the upper frequency 

limit of the inversion at 1.0 Hz. The need to adequately 

model the Green's functions led to discarding from the 

inversion the data from stations where site response appeared to contribute significantly. 

RESULTS 

Our analysis of geodetic and strong-motion data to determine the rupture characteristics on a finite fault is accomplished in two major steps. The first step involves 

actual inversion of the data. This inversion results in spectral values (amplitude and phase) for each segment on the 

fault. 

The initial problem to be solved in the first step in the 

analysis is to define the optimum fault geometry. We prefer that the fault plane contain the hypocenter estimated 

from regional data (Dietz and Ellsworth, 1990). In addition, the fault plane is chosen to overlap the zone of aftershocks that occurred within 24 hours after the main shock 

(fig. 2A). The aftershocks appear to dip southwest, and 

the dipping trend is largely confined to depths of 4 to 18 

km, although some scattered activity occurs at shallower 

depth (fig. 2B). The fault plane dips 69'. The fault dimensions, 16 by 40 km, were largely determined from figure 

2. The fault is divided into 1- by 1-km segments, and the 

hypocenter (star, fig. 2) is near the center bottom edge of 

the fault. 

The inversion is performed independently for each frequency, and we begin by performing a single inversion at 

0.0 Hz. The result can be interpretqd directly as the static 

offset (total slip at points on the fault) and easily evaluated physically. Thus, various fault geometries can easily 

be tested to obtain a suitable geometry for the inversion at 

all frequencies. The minimum rms residual (observed minus predicted ground motion) for the inversion was obtained by setting the fault strike at 129' and the dip angle 

at 69'. The minimum rms residual is found by varying the 

strike or dip independently in separate inversions of the 

geodetic data. Fixing the dip at 7000 and varying the strike 

from 1 10' to 150' leads to a minimum rms residual at a 

strike of 129', as shown in figure 3A; fixing the strike at 

129' and varying the dip from 50' to 90' leads to a minimum rms residual at a dip of 69O, as shown in figure 3B. 

This optimum fault geometry is used to invert the geodetic and seismic data. 
FREQUENCY-DOMAIN INVERSION FOR THE RUPTURE CHARACTERISTICS DURING THE EARTHQUAKE A63 

The static offset during the earthquake, as determined 

by the inversion of the geodetic data, is plotted in figure 

4. The strike-slip component (fig. 4A) indicates that motion at the southeast end of the fault was dominantly strike 

slip. The largest strike-slip displacements, approximately 

1.2 m, are centered 7 km southeast of the hypocenter, at 

11-km depth; the dip-slip displacement in the same area 

is only 40 cm. The dip-slip component (fig. 4B) indicates 

that motion at the northwest end of the fault was dominantly dip (reverse) slip. The largest dip-slip motions, ap- 

~ proximately 1.2 m, are centered 9 km northwest of the 

hypocenter at 11-km depth. The total slip (fig. 4C) is 

more nearly uniformly distributed. The area of maximum 

total slip, about 1.4 m, is centered slightly to the northwest of the hypocenter at about 11-km depth. The seismic 

moment, based on the total slip amplitude, is 2.5~10~~ 

dyne-cm. 

The original leveling data are compared with the predicted values from the inversion of the geodetic data in 

figure 5. The largest values are positive and occur immediately over the northwestern section of the fault. The 

predicted values generally agree well in both magnitude 

and sign with the observed data, as shown in figure 5B. In 

areas where the predicted values differ in sign from the 

observed data-for example, in the east and west-both 

the actual and predicted ground displacements are small, 

Marshall and others (1991) used a misfit-to-noise (MI 

N) ratio as a measure of the goodness of fit between predictions and observations. This ratio is given by 

where AHo is the observed elevation change, AHc is the 

calculated elevation change, N is the number of bench 

marks, Nfis the number of fixed model parameters (NF~), 

Figure 1.-Loma Prieta region, Calif., showing locations of strong-motion stations (triangles) and Global 

Positioning Satellite stations (large solid squares) used in this study. Small open squares, sites of leveling 

observations; star, epicenter of earthquake; shaded rectangle, projection of assumed fault plane onto the 

Earth's surface. 
A64 MAIN-SHOCK CHARACTERISTICS 

Table 1 .-California Division of Mines and Geology strong-motion stations used in this study 

Location CDMG Latitude Longitude 

(fig- 1) code (ON.) cow.) 

CAP Capitola --------- 125 36.974 121.952 

COR Corralitos ------- 007 37.046 121.803 

Gl Gilroy ----------- 379 36.973 121.572 

G2 Gilroy ----------- 380 36.982 121.556 

G3 @Iroy ----------- 381 36.987 121.536 

SAN Santa Cruz ------ 135 37.001 122.060 

SAR Saratoga --------- 065 37.255 122.031 

and o is the observed error (see Marshall and others, 

1991). A prediction fits the observations to within the 

noise level of the data when M/NSl.O (Marshall and others, 1991). The MIN ratio for the static offset shown in 

figure 4 is 0.80. 

The inversion was also performed for each frequency 

between 0.1 and 1.0 Hz, using data from the strong-motion stations. For example, contours of the Fourier spectral amplitude determined from the inversion at 0.14 Hz 

are plotted on the fault plane in figure 6. Because this 

frequency represents one of the lowest frequencies obtained by inverting the strong-motion data, we expect some 

correlation between the areas of high slip predicted for 

the static offset and the areas of high energy release predicted for this frequency. Although both the strike-slip 

component (fig. 6A) and the dip-slip component (fig. 6B) 

are more complex than for the static offset, similarities do 

exist. In the southeastern area, displacement is dominantly 

strike slip, and in the northwestern area, dominantly dip 

slip. The increased complexity may indicate greater spatial resolution at this higher frequency but could also result from some dynamic property of the rupture. 

Contouring the Fourier spectral amplitudes on the fault 

plane (fig. 6) indicates areas of slip or energy release at a 

particular frequency but gives no information about timing, and so the second step in the analysis is to characterize the dynamic aspects of the rupture process. This step 

involves taking the inverse Fourier transforms of the spectral values determined in the inversion, resulting in a velocity history for each segment of the fault. The band 

limitation of the strong-motion data for the earthquake, 

however, introduces some ambiguity into the interpretation of these time series, as shown in figure 7. A ramp 

function with an offset of 90 cm that occurs over a period 

of 1.75 s is plotted in figure 7A. The velocity-time series 

obtained by differentiating this ramp function is plotted in 

figure 7B, and the velocity-time series after bandpass filtering with a Butterworth filter with corner frequencies at 

0.1 and 1.0 Hz is plotted in figure 7C. The filtering of low 

frequencies from the velocity-time series results in a. bandlimited signal characterized by positive and negative 

swings of approximately equal amplitude. Because the 

velocity-time series associated with the inversion are also 

band limited, figure 7C indicates that these signals are 

expected to be double sided. Finally, figure ID shows 

that integration of the filtered velocity-time series produces no permanent offset. 

Figure 8 shows that the inversion velocity-time series 

and the bandpass-filtered velocity-time series (fig. 7C) 

approximately correspond. From comparison with figure 

7, the initial motion of the bandpass-filtered velocity function evidently corresponds to the direction of slip on the 

fault, and the width of this initial pulse is approximately 

the same as the duration of slip on the fault. In our model, 

the initial strong pulses are in the negative direction for 

both the strike-slip and dip-slip components. Within the 

coordinate system that we use, this direction corresponds 

to right-lateral and reverse slip on the fault, as expected. 

Time slices of the spatial distribution of the strike-slip 

and dip-slip distribution of velocity on the fault plane at 

1-s intervals are shown in figure 9. T=O corresponds to 

the origin time for the hypocentral location reported by 

Dietz and Ellsworth (1989). Only the negative contours 

are plotted in figure 9 because we believe that the initial 

negative pulses are more directly related to the actual 

velocity pulses on the fault plane and because plotting 

both the positive and negative contours would be too confusing. The first large energy release (above the noise 

level of 10 cds) occurs after 2 s on the strike-slip component in the area of the hypocenter (star, fig. 9). The 

rupture propagates largely as strike-slip motion to the 

southeast until 5 s; the largest energy release occurs at 3 s 

approximately 7 km southeast of the hypocenter at about 

17-km depth. At 5 s, rupture begins in the area just north 

of the hypocenter on both the strike-slip and dip-slip components and propagates to the northwest until 9 s. The 

largest energy release during this period occurs on the 

dip-slip component 20 km northwest of the hypocenter. 

Contours of slip at the southeast end of the fault between 

7 and 9 s are mostly the second negative swing of the 

bandpass-filtered velocity pulse (see fig. 8). As such, these 

contours are not interpreted as velocity pulses but are 

considered noise. 

The observed and predicted seismograms at each strongmotion station used in the inversion are compared in figure 10. These predictions match the data extremely well. 

DISCUSSION 

The model for the static offset (fig. 4) during the 1989 

Loma Prieta earthquake derived in this study agrees reasonably well with those of previous studies using geodetic data, given that our model has many more fitting 

parameters. Our model suggests a smooth distribution of 

total slip and predicts a seismic moment of 2.5~10~~ dyne- 
FREQUENCY-DOMAIN INVERSION FOR THE RUPTURE CHARACTERISTICS DURING THE EARTHQUAKE A65 

cm; the seismic moment determined in other studies of 

the geodetic data ranges from 2.2~10~~ to 3.0~10~~ dynecm. Our solution is most similar to that of Marshall and 

others (1991) for a planar fault divided into two segments. 

By assigning a larger reverse-slip component to the northwestern segment and a larger strike-slip component to the 

southeastern segment, their data-prediction error was reduced. Our fault is divided into 640 subfaults, providing 

the opportunity for much spatial variation in slip on the 

fault plane. A robust feature of our solution is the dominance of dip slip to the northwest (approx 3:l) and of 

strike slip to the southeast (approx 3:1), although the total 

slip is more evenly distributed along the fault. 

Two substantial differences between our model of the 

static offset and that of Marshall and others (1991) are 

that their best-fitting model lies outside the aftershock 

-20 -15 -10 -5 0 5 10 15 20 

DISTANCE, IN KILOMETERS 

Figure 2.-Postearthquake aftershock activity. A, Loma Prieta region, Calif., showing locations of Loma 

Prieta main shock (star) and epicenters of aftershocks during 24-hour period after earthquake (asterisks). 

Shaded rectangle, projection of assumed fault plane onto the Earth's surface. Fault is 40 km long and strikes 

129'. Note that main shock is located near center of aftershock zone. B, Cross section oriented perpendicular 

to fault. Shaded rectangle, cross section of assumed fault plane. Fault dips 69' SW. and ranges in depth from 

approximately 4 to 19 km; fault plane contains hypocenter of earthquake (star) and falls within aftershock 

zone. 
A66 MAIN-SHOCK CHARACTERISTICS 

zone and their average slip amp1 itude of 2.1 m is significantly larger than the peak slip amplitude of 1.4 m that 

we obtain. Because they obtained an MIN ratio of 1.33 for 

their best (two rake) model, whereas our model has an MI 

N ratio of 0.8, our model fits the data significantly better. 

Possible explanations for the better fit include differences 

in faulting area or elastic constant between the two studies, differences related to modeling ground displacements 

with a uniform versus a layered half-space, and the ability 

in our model to concentrate slip where needed to most 

effectively account for the observations. 

The results of our dynamic solution (fig. 9) are consistent with a small foreshock occurring 2 s before the onset 

of significant energy release and little or no propagation 

of the rupture front away from the hypocenter during that 

time, as suggested by Wald and others (1991). These results also indicate a change in rake from nearly strike slip 

southeast of the hypocenter during the initial stage of faulting, through oblique slip near the hypocenter at the beginning of the second stage of faulting, to nearly reverse slip 

near the northwest edge of the fault at the end of the 

second stage. Both Beroza (1991) and Steidl and others 

(1991) observed a similar rotation in the rake vector from 

southeast to northwest. This rotation of the rake vector is 

also consistent with our model of the static offset, as well 

as that of Marshall and others (199 1). 

Several features of our model of the dynamic rupture 

(fig. 9) derived from strong-motion data are robust. The 

duration of faulting is consistently shorter than 10 s, the 

rupture velocity is consistently about 3.5 kds, and radia110 120 130 140 150 

AZIMUTH, IN DEGREES 

tion of energy typically occurs from the southeast end of 

the fault before the northwest. The propagation rate of 

rupture on the fault plane is fairly consistent for different 

assumed values of c used in constructing the wave-equation norm, leading us to regard this value as a fitting 

parameter rather than a physical quantity. This result is 

not completely unexpected because Mendez and others 

(1990) found that the right rupture velocity (for a synthetic test case) was returned by the inversion, although 

the wrong c value was used in constructing the norm. 

Thus, we considered c values as large as 1,000 km/s, which 

produced a smoothed solution with the general features 

previously mentioned. The solution in figures 9 through 

11 is for c=6 Ms. 

Although a duration of faulting shorter than 10 s was 

found in each finite-fault study using seismic data, rupture velocities in those studies range only from 2.5 to 3.1 

kds. In addition, those studies consistently found that 

energy radiates from both ends of the fault simultaneously, 

although Steidl and others (1991) determined that rupture 

propagated to the southeast faster than to the northwest. 

Because these results are somewhat inconsistent with ours, 

we investigated whether they may result from an inaccuracy in the assumed trigger time of station SAR (the trigger time was not recorded). 

Station SAR (fig. I), which lies at the northwest end of 

the fault and recorded large-amplitude arrivals, is the key 

to our solution. If this station is omitted from the inversion, the rupture does not propagate to the northwest at 

all. We estimated a trigger time for this station by assum50 60 70 80 90 

DIP, IN DEGREES 

Figure 3.-Rms residual of static offset (observed minus predicted value) determined from inversion as a function of azimuth (A) and dip (B) of fault. 

Minimum rms residual occurs at an azimuth of 129' for a constant dip of 70' (fig. 3A), and at dip of 69' for a constant azimuth of 129' (fig. 35). 
FREQUENCY-DOMAIN INVERSION FOR THE RUPTURE CHARACTERISTICS DURING THE EARTHQUAKE A67 

ing that the large pulse of about 2.5 s on the record repre- 1.8 s from the P-wave-arrival time for energy leaving the 

seats S-wave energy arriving from an area southeast of hypocenter and shortly before the predicted S-wave-arthe epicenter. This trigger time is 2.8 s later than would rival time. By varying the assumed trigger time, we deterbe expected if the P wave from the initial energy release mined that a trigger time 1 s earlier (same as that of Wald 

at the hypocenter suggested by Deitz and Ellsworth (1990) and others, 1990) scarcely affects the solution, and that a 

had triggered the instrument. Wald and others (1991) sug- trigger time about 2.8 s earlier is required to make the 

gested that the trigger time at this station was delayed by solution propagate bilaterally. Thus, although we find that 

-20 -15 -10 -5 0 5 10 15 

DISTANCE ALONG STRIKE, IN KILOMETERS 

Figure 4.-Contours of static offset (in centimeters) on assumed fault plane, as determined from inversion of 

geodetic data, showing (A) strike-slip (right lateral) component, (B) dip-slip (reverse) component, and (C) 

total slip. View downward, normal to fault plane. Top edge of fault is that approximately 4-km depth. Star, 

hypocenter of earthquake. Contour interval, 20 cm. 
MAIN-SHOCK CHARACTERISTICS 

rupture propagation to the northwest followed propaga- The rise time suggested by figures 7 and 8 (approx 1.75 

tion to the southeast, this result depends on the assumed s) is longer than those in other studies, which range from 

trigger time at station SAR. 0.3 to 1.0 s. This rise time is applicable only to the area of 

Figure 5.-Loma Prieta region, Calif., showing locations of (A) leveling observations of Marshall and others 

(1991) and (B) predicted values from inversion for static offset (see fig. 4). Circles, negative values (relative 

motion downward); plus signs, positive values (relative motion upward). Largest values are positive and 

located immediately over northwest side of fault. Star, epicenter of earthquake. 
FREQUENCY-DOMAIN INVERSION FOR THE RUPTURE CHARACTERISTICS DURING THE EARTHQUAKE A69 

high slip velocity where this segment was located. Shorter 

rise times are expected for segments of the fault that 

slipped less. In addition, the rise time measure may be 

partly related to the shape of the bandpass filter. These 

qualities of the solution have not been fully explored. 

Also, because our band-limited velocity functions produce no static offset when integrated, we have no measure 

of the actual displacement from the strong-motion data. 

ACKNOWLEDGMENTS 

This research was supported by U.S. National Science 

Foundation grant EAR-90-1 1041. Computational time on 

the Cray Y-MP computer was provided by grants from 

-20 -15 -10 -5 0 5 10 15 

DISTANCE ALONG STRIKE. IN KILOMETERS 

Figure 6.-Contours of Fourier spectral amplitude (in centimeters per 

second) on assumed fault plane, as determined by inversion at 0.14 Hz, 

showing (A) strike-slip (right lateral) component, (B) dip-slip (reverse) 

component, and (0 total velocity. View downward, normal to fault 

plane. Star, hypocenter of earthquake. Contour intervals: 10 cm/s (fig. 

6A), 20 cmls (figs. 6B, 60. 

the San Diego Supercomputer Center and the U.S. National Science Foundation. We thank M. Lisowski and G. 

Marshall for providing preprints of their papers, and P. 

Spudich and J. Savage for their thoughtful reviews of the 

manuscript. 

REFERENCES CITED 

Apsel, R.J., and Luco, J.E., 1983, On the Green's functions for a layered half-space, part 11: Seismological Society of America Bulletin, 

v. 73, no. 4, p. 931-951. 

Beroza, G.C., 1991, Near-source modeling of the Loma Prieta earthquake: evidence for heterogeneous slip and implications for the 

earthquake hazard: Seismological Society of America Bulletin, v. 

81, no. 5, p. 1603-1621. 

Dietz, L.D., and Ellsworth, W.L., 1990, The October 17, 1989, Loma 

Prieta, California, earthquake and its aftershocks; geometry of the 

sequence from high-resolution locations: Geophysical Research Letters, v. 17, no. 9, p. 1417-1420. 

Hartzell, S.H., Stewart, G.S., and Mendoza, Carlos, 1991, Comparison 

of L and L norms in a teleseismic waveform inversion for the slip 

history of the Loma Prieta, California, earthquake: Seismological 

Society of America Bulletin, v. 81, no. 5, p. 1518-1539. 

Lisowski, Michael, Prescott, W.H., Savage, J.C., and Johnson, M.J.s., 

1990, Geodetic estimate of coseismic slip during the 1989 Loma 

Prieta, California, earthquake: Geophysical Research Letters, v. 17, 

no. 9, p. 1437-1440. 

Luco, J.E. and Apsel, R.J., 1983, On the Green's functions for a layered 

half-space, part I: Seismological Society of America Bulletin, v. 

73, no. 4, p. 909-929. 

Marshall, G.A., Stein, R.S., and Thatcher, Wayne, 1991, Faulting geometry and slip from co-seismic elevation changes; the 18 October 

1989, Loma Prieta, California, earthquake: Seismological Society 

of America Bulletin, v. 81, no. 5, p. 1660-1693. 

Mendez, A.J., and Anderson, J.G., 1991, The temporal and spatial evolution of the 19 September 1985 Michoacan earthquake as inferred 

from near-source ground-motion records: Seismological Society of 

America Bulletin, v. 81, no. 3, p. 844-861. 

Mendez, A.J., Olson, A.H., and Anderson, J.G., 1990, A norm rninimization criterion for the inversion of earthquake ground motion: Geophysical Journal International, v. 102, no. 2, p. 287-298. 

Olson, A.H., 1987, A Chebyshev condition for accelerating convergence of iterative tomographic methods-solving large least squares 

problems: Physics of the Earth and Planetary Interiors, v. 47, p. 

333-345. 

Olson, A.H., and Anderson, J.G., 1988, Implications of frequency-domain inversion of earthquake ground motions for resolving the spacetime dependence of slip on an extended fault: Royal Astronomical 

Society Geophysical Journal, v. 94, no. 3, p. 443-455. 

Snay, R.A., Neugebauer, H.C., and Prescott, W.H., 1991, Horizontal 

deformation associated with the Loma Prieta earthquake: Seismological Society of America Bulletin, v. 8 1, no. 5, p. 1647-1659. 

Steidl, J.H., Archuleta, R.J., and Hartzell, S.H., 1991, Rupture history 

of the 1989 Loma Prieta, California, earthquake: Seismological Society of America Bulletin, v. 81, no. 5, p. 1573-1602. 

Wald, D.J., Helmberger, D.V., and Heaton, T.H., 199 1, Rupture model 

of the 1989 Loma Prieta earthquake from the inversion of strongmotion and broadband teleseismic data: Seismological Society of 

America Bulletin, v. 8 1, no. 5, p. 1540-1572. 
VELOCITY, IN CENTIMETERS PER SECOND 
FREQUENCY-DOMAIN INVERSION FOR THE RUPTURE CHARACTERISTICS DURING THE EARTHQUAKE 
MAIN-SHOCK CHARACTERISTICS 
FREQUENCY-DOMAIN INVERSION FOR THE RUPTURE CHARACTERISTICS DURING THE EARTHQUAKE A73 

TIME, IN SECONDS 

Figure 10.-Observed (solid curve) and predicted (dashed curve) seismograms for vertical (A), east-west (B), and north-south (C) components of 

motion at strong-motion stations used in inversion. 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAKE OCCURRENCE 

MAIN-SHOCK CHARACTERISTICS 

BROADBAND STUDY OF THE SOURCE CHARACTERISTICS 

OF THE EARTHQUAKE 

By Hiroo Kanamori, 

California Institute of Technology; 

and 

Kenji Satake, 

University of Michigan 

CONTENTS 

ABSTRACT 

We have determined the source characteristics of the 

1989 Loma Prieta earthquake, using teleseismic data. The 

solution from body waves gives a mechanism with a strike 

of 128O, a dip of 70Â° a rake of 138O, and a seismic moment of 3x10~~ dyne-cm (Mw=6.9). This solution is similar to those obtained from long-period Rayleigh and Love 

waves, PnJ waves, and first-motion data. The body-wave 

solution suggests a depth of about 15 km. The effective 

duration of the source is 6 s, suggesting lengths of 30 and 

15 km for bilateral and unilateral faulting, respectively. 

Considering the extent of the aftershock zones, we estimate a total rupture length of 35 km. The strike-slip and 

thrust components of coseismic slip are 177 and 159 cm, 

respectively. The large thrust component raises an important question regarding the recurrence pattern. If the 1989 

Loma Prieta earthquake is a characteristic earthquake with 

a recurrence interval of about 100 yr, the 159-cm displacement implies a long-term uplift rate of about 1 cml 

yr, which appears too high for this region. Three hypotheses for reconciling this apparent conflict are that (1) the 

geometry of plate motion along the Santa Cruz Mountains 

Page 

A75 

7 5 

76 

78 

78 

7 8 

79 

80 

80 

section of the San Andreas fault changes on a time scale 

of several thousand years, and so the coseismic displacement has not accumulated enough to produce high topographic relief; (2) the coseismic-slip direction varies from 

event to event; and (3) the slip plane of the 1989 Loma 

Prieta earthquake is distinct from the Pacific-North 

America plate boundary-if so, then this earthquake is a 

rather rare, noncharacteristic event. The surface slip of 

about 1 m for the 1906 San Francisco earthquake is one 

of the key data in long-term forecasting. No surface slip 

was observed in the 1989 Loma Prieta earthquake, even if 

the horizontal slip at depth was as large as 1.8 m. This 

discrepancy points to a risk of relying too heavily on surface observations for long-term seismic-risk analysis. 

Contribution No. 4846, Division of Geological and Planetary 

Sciences, California Institute of Technology, Pasadena, CA 91 125. 

INTRODUCTION ' 

The 1989 Loma Prieta earthquake occurred within a 

seismic gap that had been identified as having a higher 

than 30 percent (in 30 yr) probability of producing an 

earthquake of M=6.5-7 (Lindh, 1983; Sykes and Nishenko, 

1984; Scholz, 1985; Working Group on California Earthquake Probabilities, 1988). This forecast was based on the 

historical seismicity and low background seismicity in this 

gap, and on the amount of surface greakfapprox 1 m) in 

the 1906 San Francisco earthquake. Thatcher and iso ow ski' 

(1987) argued, however, on the basis of geodetic data, 

that the coseismic slip for the 1906 earthquake was about 

2.6 m, and so it will take more than 150 yr to accumulated 

this amount of slip (a long-term slip rate of 1.5 cmlyr is 

assumed for the San Andreas fault in this region), implying that a large earthquake is unlikely in the next few 

decades. 

Now that the 1989 Loma Prieta earthquake has occurred, 

it is important to assess how it compares with the published forecast. To this end, we have analyzed seismic 

data, primarily broadband seismograms, to determine the 

source characteristics of the earthquake. The data are summarized in table 1. 

A7 5 
A76 MAIN-SHOCK CHARACTERISTICS 

Table 1.-Stations and data sets used to determine the source characteristics of the 1989 Lorna Prieta earthquake 

Station 

ARU 

OBN 

SSB 

HRV 

WFM 

ANMO 

CAY 

RPN 

PPT 

KIP 

Phases 

MECHANISM 

Because the most complete data we could obtain are 

broadband data from International Deployment of Accelerometers/Incorporated Research Institution for Seismology (IDAIIRIS) and GEOSCOPE stations, we first describe 

the source mechanism calculated from these data. In our 

analysis, all the seismograms are deconvolved to groundmotion displacements; the data are plotted in figure 1. We 

used the method of Kikuchi and Kanamori (1989) to invert the records and determine the mechanism. The observed seismograms are matched by synthetic seismograms 

computed for a sequence of subevents distributed on a 

fault plane. The Green's functions for five independent 

moment-tensor elements are computed, and the subevents 

are represented by a linear combination of these elements. 

A 

ARU 

22.7 

OBN 

29.1 

SSB 

25.4 

HRV 

55.4 

WFM 

53.5 

B 

ARU 

37.4 

OBN 

87.5 

HRV 

76.9 

RPN 

97.8 

PPT 

104.7 

PPT 

27.3 

KIP 

93.1 

TIME, IN SECONDS 

TIME, IN SECONDS 

Figure 1.-Observed (top plot) and synthetic (bottom plot) seismograms of P-wave (A) and SH-wave (B) ground-motion displacement in 1989 Loma 

Prieta earthquake. Numbers below three-letter station codes are absolute displacement amplitude (distance from baseline to either peak or trough of 

observed displacement, whichever is larger) (in microns). Trapezoidal source and time function for three-event source are shown at bottom. Stations 

are arranged in order of increasing azimuth clockwise from north. 
BROADBAND STUDY OF THE SOURCE CHARACTERISTICS OF THE EARTHQUAKE 

By minimizing the difference between the observed and 

synthetic seismograms, we determine the moment tensor 

or mechanism of all subevents, as well as their spatial 

location and timing. 

Because many free parameters are involved in this type 

of inversion, tradeoffs between different source parameters could occur. First, we use a simplification to obtain 

the overall model. We assume a single source with a trapezoidal time function (t,, t2), as shown in figure 1; we 

vary tl and t2 to obtain the best solution. We use the 

parameters listed in table 2 for both the source and receiver structures (common to all the stations). We use an 

attenuation time constant t=1 and 4 s and weights of 3 

and 1 for P and S waves, respectively. We tried three 

discrete depths, 10, 15, and 20 km, and obtained a best fit 

at 15 km. The inversion results in t1=2.5 s, t2=5 s, a 

seismic moment (Mn) of 2.4~10~~ dyne-cm, and a focal 

mechanism with a strike of 128', a dip of 70Â° and a rake 

of 138'. Though simple, this source explains the overall 

features of the observed waveform, and the residual (observed minus synthetic) waveforms are very small. 

In the method of Kikuchi and Kanamori (1989), the 

inversion obtains successive point sources to fit the residual waveforms. In our model, the first point source 

explains most of the data, and so the other point sources 

are relatively small. 

We assume that the mechanism of all subevents is the 

same as that of the first subevent, and invert the data. 

Because later subevents are small and their significance is 

questionable, we consider the first two or three subevents 

with a total seismic moment of 2.9~10~~ or 3.1~10~~ dynecm, respectively. The synthetic waveforms in the threeevent model are compared with the observed seismograms 

in figure 1. Because of noise in the data, especially the 

significant site response at some stations (for example, 

KIP), the decision on where to terminate the sequence 

(iteration in the inversion) is arbitrary. If we include all 

Table 2.-Parameters used for source and receiver 

structures 

subevents, the total seismic moment increases considerably. Considering the total seismic moment calculated from 

long-period waves (as described below), we judge a seismic moment significantly larger than 3x10~~ dyne-cm to 

be unrealistic. In the section below entitled "Coseismic 

Slip," we use a rounded value of 3x10~~ dyne-cm for the 

seismic moment of this subevent; from body-wave data 

alone, any value between 2.5~10~~ and 3.5~10~~ dyne-cm 

is acceptable. The results are summarized in figure 2 and 

listed in table 3. 

Although the effective duration of the principal subevent 

is 5 s (fig. I), we estimate an effective duration of 6 s, 

allowing for the contributions from smaller subevents. 

We use the method of Kawakatsu (1989) and invert 

long-period surface waves to determine the centroid moment tensor (CMT) of the source. In this inversion, we 

use both the fundamental-mode and overtone Love and 

Rayleigh waves. The pass band of the filter is from 3.5 to 

7 MHz. The results are shown in figures 2A and 2B and 

listed in table 3. 

To examine the possible increase in seismic moment at 

long periods, we invert surface waves at a period of 256 s 

separately, using the method of Kanamori and Given 

(1981). In this inversion, the dip angle of one of the nodal 

planes (70') is fixed to avoid instability in the inversion; 

Figure 2.-Equal-area lower-hemisphere projections of focal mechanisms for 1989 Loma Prieta earthquake, arranged in order by decreasing period, 

obtained from different data sets: (A) long-period surface waves, (B) centroid moment tensor, (C) P-SH waves, (D) P, waves, and (E) first motions. 

Nodel-plane parameters: (b, strike; 8, dip; X, rake. Nodal planes for first-motion data (fig. 2E) are from solution obtained from 

P-SH waves. 
A78 MAIN-SHOCK CHARACTERISTICS 

Table 3.-Source characteristics of the 1989 Lorna Prieta earthquake 

Data 

P and SH waves------- 3 128 70 138 -125 5 1 26 

Surface waves --------- 2.5 128 70 137 -124 50 2 6 

Rl and GI waves------ 2.8 129 144 -127 57 24 

p waves -------------- nL 2.9 125 7 5 130 -129 42 2 3 

the mechanism is illustrated in figure 2C. The estimated 

seismic moment is 2.8~10~~ dyne-cm, essentially the same 

as in the body-wave and CMT solutions. No evidence was 

found for an increase in seismic moment with period. The 

first-motion data plotted in figure 2E are also consistent 

with the body-wave and CMT solutions. 

Woods and others (in press) used PL waves recorded 

at Pasadena, Calif., to determine the source mechanism 

by matching the waveforms with synthetic seismograms. 

Their preferred solution is plotted in figure 2D and listed 

in table 3. 

The mechanisms obtained from data sets with different 

periods are essentially the same (fig. 2; table 3), and the 

seismic moment determined from body waves (period, 

approx 10 s) is about the same as that determined from 

surface waves with a period of 256 s, suggesting a simple 

source for the earthquake. The estimated seismic moment 

is 3x10~~ dyne-cm, which gives Mw=6.9. 

SOURCE DURATION AND RUPTURE 

LENGTH 

Figure 1 shows that the effective duration of the source 

is about 6 s, a value that can be used to infer the rupture 

length. If the rupture is unilateral, then the effective duration T is given by T=(L/V)-(Lcos Wc), where L is the 

rupture length, V is the rupture velocity, 0 is the azimuth 

of the station measured from the rupture direction, and c 

is the body-wave phase velocity along the free surface. 

Because the P-wave phase velocity is much higher than 

the rupture velocity, the second term is much smaller than 

the first. Thus, the rupture length L is approximately 

L=V7=15 km if 7=6 s and V=2.5 kmls. If the rupture is 

bilateral, then the rupture length is about twice that for a 

unilateral rupture-that is, 30 krn. 

The main shock is located near the center of the aftershock zone (U.S. Geological Survey staff, 1990), suggesting bilateral faulting. If the fault rupture is bilateral, our 

estimate of the effective duration, (6 s), suggests that L=30 

km. The total length of the aftershock zone is about 40 

km (U.S. Geological Survey staff, 1990). Although 

teleseismic data cannot resolve details of the slip distribution on the fault, the rupture length almost certainly does 

not exceed the length of the aftershock zone. In the following calculations, we use L=35 km, although a shorter 

rupture length is not precluded. 

COMPLEXITY 

As shown in figure 1, the source process of the earthquake is simple. The displacement waveform of the earthquake is compared with that of the 1988 Armenia 

earthquake (Mw=6.7), as recorded at station HRV, in figure 3. Comparison at other stations exhibits essentially a 

similar difference. The seismograms in figure 3 suggest 

that the duration of the 1988 Armenia earthquake was 40 

s or even longer, in striking contrast to that of the 1989 

Loma Prieta earthquake (approx 6 s). Pacheco and others 

(1989) suggested a substantial variation in focal mechanisms during the first 10 s of the 1988 Armenia earthquake. 

This comparison clearly demonstrates the simplicity of 

the source process of the 1989 Loma Prieta earthquake, 

which involved a relatively short fault segment. This difference in source complexity may have profoundly influenced the damage potential of this earthquake. Although 

it is generally agreed that the heavy damage caused by the 

1988 Armenia earthquake was primarily due to poor building construction, the source complexity and long duration 

almost certainly contributed as well. Because source complexity is closely related to local tectonic structure, earthquakes of the same magnitude as the 1989 Loma Prieta 

earthquake in different tectonic environments can be even 

more damaging than that earthquake. 

COSEISMIC SLIP 

If we assume a fault length of 35 km, a fault width 12 

km, a rigidity of 3x10~~ dyne/cm2, we calculate a coseismic slip of 238 cm from the estimated seismic moment of 

3x lo2^ dyne-cm. The strike-slip and thrust components of 
BROADBAND STUDY OF THE SOURCE CHARACTERISTICS OF THE EARTHQUAKE A79 

displacement are 177 and 159 cm, respectively. The average stress drop is estimated at 50 bars. 

DISCUSSION AND CONCLUSION 

Two aspects of the 1989 Loma Prieta earthquake are 

noteworthy: the thrust component, as large as 159 cm, 

and the short rupture length, only 35 krn, for an M-6.9 

earthquake. The large thrust component (1.6 m) raises an 

important question regarding the recurrence interval of 

earthquakes along the Santa Cruz Mountains section of 

the San Andreas fault. 

The long-term forecast of this earthquake is based on a 

combination of the historical seismicity, the estimated slip 

rate along the Santa Cruz Mountains section of the San 

Andreas fault, and the surface slip (approx 1 m) in the 

1906 San Francisco earthquake (Lindh, 1983; Sykes and 

Nishenko, 1984; Scholz, 1985). Implicit in this forecast is 

a relatively short recurrence interval, about 80 to 100 yr. 

If the 1989 Loma Prieta earthquake is a characteristic 

event to be expected along this section of the San Andreas fault, with a recurrence interval of about 100 yr, the 

-6 

0 20 40 60 80 100 

TIME, IN SECONDS 

Figure 3.-Displacement records of 1989 Loma Prieta earthquake (A) 

and 1988 Armenia earthquake (B) from station HRV. 

thrust component of 1.6 m during the earthquake implies 

a long-term uplift rate of about 1 cmlyr, comparable to 

the highest rate observed in the world (for example, 

Yonekura, 1983). An uplift rate this large is generally 

associated with spectacular topographic relief. Although 

the long-term uplift rate in the epicentral area is unknown, 

the regional geomorphology does not seem to reflect such 

a high rate. We present three hypotheses to reconcile this 

apparent conflict. 

The first hypothesis is that the geometry of plate motion along the Santa Cruz Mountains section of the San 

Andreas fault changes on a time scale of several thousand 

years, and so not enough coseismic vertical displacement 

has accumulated to produce high topographic relief. If so, 

then the 1989 Loma Prieta earthquake can be considered 

a characteristic event along this section of the fault on 

this time scale. 

The second hypothesis is that the coseismic-slip direction varies from event to event. For example, in the 1906 

San Francisco earthquake, the motion along this section 

of the San Andreas fault was essentially strike slip, driven 

by much larger strike-slip displacements along the adjacent section. Even in the earlier events, which involved 

the Santa Cruz Mountains section only, the motion could 

have been primarily strike slip if sufficient stress had not 

accumulated there to cause vertical displacement. 

The third hypothesis is that the slip plane of the 1989 

Loma Prieta earthquake is distinct from the Pacific-North 

America plate boundary. If so, then this earthquake is a 

rather rare event and not a characteristic event along the 

San Andreas fault. Although no obvious geologic evidence 

exists, this conclusion cannot be ruled out. 

The short rupture length, about 35 km, of the 1989 

Loma Prieta earthquake is highly anomalous, in light of 

the empirical data available for shallow crustal earthquakes, 

as shown in figure 4. In fact, the estimated magnitude of 

the forecasted event is based on the empirical relation 

plotted in figure 4. For example, Scholz (1985) identified 

a 75-km-long slip-deficit segment along the Santa Cmz 

Mountains section of the San Andreas fault and forecast 

an M=6.9 earthquake. Lindh (1983) identified a 35-km 

gap and associated it with an M=6.5 earthquake. Both of 

these estimates are consistent with the empirical relation 

plotted in figure 4. The anomalous fault-lengthlmoment 

relation for the 1989 Loma Prieta earthquake is the cause 

of the discrepancy between the predicted and observed 

events. 

The surface slip of about 1 m during the 1906 San 

Francisco earthquake is one of the key data in a long-term 

forecast. Thatcher and Lisowski (1987) argued, however, 

that the slip of 2.4 m at depth determined from geodetic 

data should be used for estimating long-term probability. 

No surface slip was observed in the 1989 Loma Prieta 

earthquake, even if the horizontal slip at depth was as 

large as 1.8 m. This discrepancy points to a risk of relying 
A80 MAIN-SHOCK CHARACTERISTICS 

too heavily on surface observations for long-term seismic-risk analysis. 

The case for a long-term forecast of the 1989 Loma 

Prieta earthquake testifies to the importance of synthesizing seismologic, geologic, geodetic, and historical data to 

obtain probabilistic parameters for long-term hazard assessment and planning. The quantitative analysis of modern seismologic data has revealed many important details, 

such as source complexity, fault geometry, and rupture 

length, which, in conjunction with the probabilistic parameters, provide key information for implementing effective seismic-hazard-reduction measures. 

ACKNOWLEDGMENTS 

This research was partly supported by U.S. Geological 

Survey grants 14-08-0001-G1773 and 14-08-0001- 

G1832; the second author was supported by the Fellowship for Research Abroad of the Japanese Society for the 

Promotion of Science. We benefited from discussions with 

Don Helmberger throughout our study. We thank Holly 

Given and Barbara Romanowicz for providing us with 

key data from IDNIRIS and GEOSCOPE stations. Some 

of the first-motion data were supplied by Laura Jones. 

REFERENCES CITED 

Kanamori, Hiroo, and Allen, C.R., 1986, Earthquake repeat time and 

average stress drop, in Pas, Sharnita, Boatwright, John, and Scholz, 

C. H., eds., Earthquake source mechanics (Maurice Ewing Series, 

v. 6): Washington, D.C., American Geophysical Union, p. 227- 

235. 

Kanamori, Hiroo, and Given, J.W., 1981, Mechanism of Mt. St. Helens 

eruption determined from long-period surface waves [abs.]: Eos 

(American Geophysical Union Transactions), v. 62, no. 45, p. 966. 

Kanamori, Hiroo, and Magistrale, H.W., 1989, State of stress in seismic 

gaps along the San Jacinto fault, in Litehiser, J.J., ed., Observatory 

seismology; an anniversary symposium on the occasion of the centennial of the University of California at Berkeley seismographic 

stations: Berkeley, University of California Press, p. 179-186. 

Kawakatsu, Hitoshi, 1989, Centroid single force inversion of seismic 

waves generated by landslides: Journal of Geophysical Research, v. 

94, no. B9, p. 12363-12374. 

Kikuchi, Masayuki, and Kanamori, Hiroo, 1989, [Analysis of multiple 

events with mechanism changes] [abs.]: Seismological Society of 

Japan Program and Abstracts, no. 1, p. 3 [in Japanese]. 

Lindh, A.G., 1983, Preliminary assessment of long-term probabilities 

for large earthquakes along selected fault segments of the San Andreas fault system in California: U.S. Geological Survey Open-File 

Report 83-63, 14 p. 

Pacheco, J.F., Estabrook, C.H., Simpson, D.W., and Nabelek, J.L., 1989, 

Teleseismic body wave analysis of the 1988 Armenian earthquake: 

Geophysical Research Letters, v. 16, no. 12, p. 1425-1428. 

Scholz, C.H., 1985, The Black Mountain asperity; seismic hazard of the 

southern San Francisco Peninsula, California: Geophysical Research 

Letters, v. 12, no. 10, p. 717-719. 

Sykes, L.R., and Nishenko, S.P., 1984, Probabilities of occurrence of 

large plate rupturing earthquakes for the San Andreas, San Jacinto, 

and Imperial faults, California, 1983-2003: Journal of Geophysical 

Research, v. 89, no. B7, p. 5905-5927. 

Thatcher, Wayne, and Lisowski, Michael, 1987, Long-term seismic potential ofthe San Andreas Fault southeast of San Francisco. California: Journal of Geophysical Research, v. 92, no. B6, p. 4771- 

4784. 

U.S. Geological Survey Staff, 1990, The Loma Prieta, California, earthquake; an anticipated event: Science, v. 247, no. 4940, p. 286-293. 

Woods, B.B., Zhao, L.-S., Helmberger, D.V., Thio, H.-K., and Kanamori, 

Hiroo, in press, The Loma Prieta earthquake sequences as observed 

at Pasadena: Geophysical Research Letters. 

Working Group on California Earthquake Probabilities, 1988, Probabilities of large earthquakes occurring in California on the San Andreas Fault: U.S. Geological Survey Open-File Report 88-398, 62 

P. 

Yonekura, Nobuyuki, 1983, Late Quaternary vertical crustal movements 

in and around the Pacific as deduced from former shoreline data, in 

Hilde, T.W.C., and Uyeda, Seiya, eds., Geodynamics of the western Pacific-Indonesian region (Geodynamics Series, v. I I): Washington, D.C., American Geophysical Union, p. 41-50. 

TI 989 Lorna Prieta mil,..# 

SEISMIC MOMENT, IN DYNE-CENTIMETERS 

Figure 4.-Fault length as a function of seismic moment for shallow crustal earthquakes along active plate 

boundaries (from Kanamori and Magistrale, 1989). Solid lines indicate range of data points. Data from 

Kanamori and Allen (1986) (dots) and Scholz and others (1986) (circles). 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF' OCTOBER 17,1989: 

EARTHQUAKEOCCURRENCE 

MAIN-SHOCK CHARACTERISTICS 

GEODETIC MEASUREMENTS OF COSEISMIC HORIZONTAL 

DEFORMATION 

By Michael Lisowski, Mark H. Murray, and Jerry L. Svarc, 

U.S. Geological Survey 

CONTENTS 

Page 

A8 1 

8 1 

82 

84 

84 

8 8 

8 8 

90 

94 

95 

95 

96 

99 

101 

101 

102 

102 

ABSTRACT 

Geodolite, Global Positioning System (GPS), and very 

long baseline interferometry surveys of the Loma Prieta 

region record the rate of secular deformation during the 

decades before the earthquake and the coseismic deformation associated with the earthquake. We estimate the 

coseismic offsets along 85 Geodolite lines and at 4 GPS 

stations by projecting the average rates of line-length 

change or displacement up to tke time of the 1989 Loma 

Prieta earthquake. The rupture zones of the 1979 Coyote 

Lake, 1984 Morgan Hill, and 1987 Mount Lewis, Calif., 

earthquakes extend along the east edge of the regional 

geodetic network, and so we use the same method to calculate coseismic offsets at the times of these earthquakes 

along nearby Geodolite lines. Many measurements are from 

two stations 160 m apart on Loma Prieta, which is 11 km 

northeast of the epicenter, near the center of the rupture 

zone. Local surveys indicate that the northern station was 

coseismically displaced about 40 mm northward and 70 

mm downward relative to the southern station, assuming 

that the southern station was stable. We use a Monte Car10 

fault-parameter estimation to find a uniform-slip dislocation model of the fault rupture that best reproduces the 

observed coseismic deformation, and to assess the data 

sensitivity. Our best-fitting rupture model strikes 138OL-4O 

N,, dips 79OL-8' SW., is 34L-6 km long, extends from a 

depth of 7L-3 to 13L-5 km, and has a slip amplitude of 5&4 

m and a rake of 153O&6O. The width of the rupture zone 

and the slip amplitude correlate closely but individually 

are poorly resolved. The location of this best-fitting model 

has an uncertainty of about 3 km; the geodetic moment is 

2.7L-0.3~10~~ N-m. The geodetic data clearly preclude rupture extending to the near surface. Coseismic deformation 

between the San Andreas and Calaveras faults to the east 

and south of the rupture zone is poorly fitted by our model. 

INTRODUCTION 

The 1989 Loma Prieta earthquake ruptured a section of 

the San Andreas fault where the U.S. Geological Survey 

(USGS) has monitored crustal deformation since the early 

1970's with an extensive and frequently measured geodetic network (Lisowski and others, 1991). The subset of 

this regional geodetic network measured before and after 

the earthquake is mapped in figure 1. The geodetic data 

consist primarily of precise electronic distance measurements (EDM's) and coseismic displacements at a few Global Positioning System (GPS) stations and two very long 

baseline interferometry (VLBI) sites. The VLBI measurements were made by the U.S. National Aeronautics and 

Space Administration (NASA) and the U.S. National Geodetic Survey (NGS). Clark and others (1985) described 

precision geodesy with VLBI; general descriptions of GPS 

surveying and data reduction may be found in the reviews 

by Dixon (1991) and Hagar and others (1991). Although 

widespread secondary surface cracking accompanied the 

earthquake, no tectonic surface rupture was observed (U.S. 

Geological Survey staff, 1990). In this paper, we discuss 

these geodetic observations in detail, determine the 

coseismic offsets, and use these offsets to estimate the 

location, geometry, and slip of the buried earthquake rupture. 

We limit our discussion and analysis to the data collected and reduced by the USGS' Crustal Strain Project, 

and to the two VLBI displacements. The data set is similar 
A82 MAIN-SHOCK CHARACTERISTICS 

to that used in our initial study of the earthquake (Lisowski 

and others, 1990a). Other workers have collected and 

analyzed complementary geodetic data sets (Marshall and 

others, 199 1 ; Snay and others, 1991 ; Williams and others, 

1993). Our fault-rupture models are derived from the 

data presented in this paper, and we model the fault rupture as a single, planar dislocation with uniform slip. The 

reader interested in more complex fault-rupture models 

derived from different or more comprehensive geodetic 

data sets is referred to the reports by Marshall and others 

(1991), Snay and others (1991), ~rnadbttir and others 

(1992), Williams and others (1993), ~rnadbttir and Segall 

(1994), and Marshall and Stein (this chapter). ~rnadbttir 

and Segall (1994) used the most comprehensive data set 

and discuss uniform- and variable-slip fault-rupture models. Postseismic deformation following the 1989 Loma 

Prieta earthquake was discussed by Savage and others 

(1994) and Burgmann and others (1994). 

We measure the distance between permanent geodetic 

stations with a Geodolite, an electro-optical laser 

distancemeter. Aircraft measurements of temperature and 

humidity and ground measurements of atmospheric pressure are used to correct for variations in the refractive 

index of air. The precision CJ obtained with a Geodolite 

by using these techniques is given by 

where a=3 mm, b=0.2 ppm (dimensionless), and L is the 

distance measured (Savage and Prescott, 1973; Savage 

and others, 1986, p. 7459-7460). A precision of 5 mm is 

typical for a 20-km-long line. We occasionally use endpoint meteorology along some short-range (4 km long) 

lines, increasing the uncertainty in the scale error b to 2 

PPm. 

Geodolite surveys of the Loma Prieta region were typically conducted every 1 to 5 yr, except for a subset of 

lines (dotted, fig. 1) from station Loma USE on Loma 

Prieta to stations Eagle Rk, Allison, and Hamilton that 

have been measured monthly since 1981 (Lisowski and 

others, 1990b, 1993). Beginning in 1987, these Geodolite 

measurements were supplemented by monthly GPS observations between station LPl (approx 160 m south of 

sta. Loma USE) and stations Allison and Eagle Un (approx 

30 m south of sta. Eagle Rk). In 1988 and 1989, the 

displacement vectors between station LPl and stations 

Hamilton and Brush 2 were measured several times. The 

precision of the GPS-measured relative positions at the 

30- to 60-km separations of these stations is also about 

0.2 ppm, although it depends on the orientation of each 

line and the techniques used to process the data (Davis 

and others, 1989; Prescott and others, 1989; Larson and 

Agnew, 1991; Murray, 1991). We processed the GPS results with the computer program GAMIT (Schaffrin and 

Bock, 1988; Dong and Bock, 1989) for preearthquake 

measurements and with the Bernese software (Beutler and 

others, 1987; Davis and others, 1989) for postearthquake 

observations. We also processed the data from preearthquake surveys with the Bernese software, and obtained 

results similar to those obtained with GAMIT. As discussed by Lisowski and others (1993), we used the GAMIT 

preearthquake solutions because we were able to process 

a few more surveys; the postearthquake surveys were processed only with the Bernese software. 

METHOD USED TO ESTIMATE 

COSEISMIC OFFSET OR 

'DISPLACEMENT 

Ideally, we would like to obtain geodetic observations 

immediately before and after an earthquake: then, the 

coseismic offset would simply be the difference between 

any two observations. The Geodolite and GPS observations from Lorna Prieta come closest to that ideal, with 

surveys a few weeks before and few days after the earthquake. Measurements at other sites were less timely; several lines had not been measured for more than 5 yr before 

the earthquake. About 35 mdyr of secular deformation is 

distributed across the San Andreas fault system in the San 

Francisco Bay region (Lisowski and others, 1991). Although the rate of line-length change along an individual 

line may be only a small fraction of this secular deformation, the total change over several years can be substantial. We need a method to separate this secular change 

from the coseismic change to best estimate the coseismic 

deformation. 

Our experience indicates that secular line-length changes 

are generally a linear function of time. Therefore, we fit a 

model that includes a slope and intercept (that is, a straight 

line) and one or more coseismic offsets. In addition to an 

offset at the time of the 1989 Loma Prieta earthquake, for 

affected lines we include the offset at the time of the 1979 

Coyote Lake ML=5.9 earthquake (King and others, 1981), 

the 1984 Morgan Hill ML=6.2 earthquake (Bakun and others, 1984; Prescott and others, 19841, or the 1986 Mount 

Lewis ML=5.9 earthquake. The locations of the epicenters 

and rupture zones of these earthquakes are shown in figure 1. The slope, intercept, and coseismic offsets were 

determined by a weighted least-squares fit to the observations of each line or vector component. We assume that 

the line length, L, can be described by 

dL L = Lo+ (1- lo)- dt 

and 
GEODETIC MEASUREMENTS OF COSEISMIC HORIZONTAL DEFORMATION A83 

where Lo is the line length at time to; dLldt is the average 

rate of line-length change; and meqk is the coseismic offset at teqk, the time of the kth earthquake. Many lines are 

offset by more than one earthquake. Thus, we estimate 

the average rates of line-length change and the coseismic 

offsets along 86 Geodolite and 3 GPS lines (table 1). 

Clark and others (1990) used the same method to determine the coseismic displacements of the VLBI sites at 

Fort Ord (near sta, Brush 21, the Presidio, and Point Reyes 

We test the assumption of a constant dLldt by computing the probability that a sequence of random numbers 

(normal distribution, with o the same as the standard error in an observation for that line) would furnish a better 

fit to the straight line than do the actual observations. A 

linear rate of change with one or more coseismic offsets 

does not provide an appropriate fit to the line-length observations when the x2 probability in table 1 is greater 

than 95 percent. In most of these observations, either our 

previous error estimates are too low, or there are one or 

more measurement blunders. We delete any obvious blunders and recompute the slope and offsets. The normalized 

(fig. 1). rms residual, o0, is given by 

Figure 1.-San Francisco Bay region, showing locations of major faults (irregular lines, dashed where 

inferred; from Jennings, 19751, epicenters (stars) and rupture zones (shaded bands) of recent earthquakes, 

and stations in regional geodetic network. Triangles, Geodolite stations; squares, Global Positioning System 

stations; circles, very long baseline interferometry sites. Heavy-shaded rectangle, surface projection of bestfitting, uniform-slip dislocation model for 1989 Lorna Prieta earthquake; heavy-dashed line, intersection of 

rupture plane with surface of the Earth. Stations Loma USE and LPl are separate monuments on Lorna 

Prieta. 
MAIN-SHOCK CHARACTERISTICS 

where n is the number of data, m is the number of unknowns, Oi is the observed value, Ci is the calculated value, 

and si is the assigned standard error for the ith observation. oo=l if the normalized rms residual from our linear 

fit with offsets equals the previous error estimate. We 

scale the uncertainties in the computed values by the normalized ms residual (oo) if oo>l; that is, the standard 

deviations listed in table 1 are the larger of either the 

experimental uncertainty based on previous error estimates 

or the theoretical uncertainty derived from the weightedleast-squares fit. 

At several sites, the measurement history is complicated by the use of different, but nearby, monuments. 

When possible, we use local surveys or directly measured 

length differences to correct the line lengths observed from 

these eccentric monuments to those that would have been 

measured from the primary monuments. This technique 

gives us a longer time series that better determines the 

rate of line-length change. The precision of these eccentric corrections is generally better than that of the measured distance. Here, we assume that the standard deviation 

of a reduced line length is given by equation 1, and ignore 

any uncertainty in the eccentric correction. 

We assume a constant deformation rate before and after 

an earthquake. Postseismic slip, viscoelastic relaxation, or 

other transient deformation may occur after an earthquake 

(Thatcher, 1983). After the 1979 Coyote Lake and 1984 

Morgan Hill earthquakes, for example, .the rates of linelength change on several lines increased and then appeared 

to decay to the normal rate within about 1 yr. We exclude 

the anomalous data obtained just after these earthquakes 

from our analysis. The coseismic offsets listed in table 1 

for these earthquakes are then the offsets accumulated 

until the rate of line-length change returns to its 

preearthquake rate. We cannot do the same for the 1989 

Loma Prieta earthquake, however, because we measured 

most of the Geodolite lines only once after the earthquake. Some Geodolite lines and GPS-measured relative 

positions from Loma Prieta were measured many times 

after the earthquake, and there is a subtle, but significant 

change, in the deformation rate (Savage and Lisowski, 

1995). In our analysis of the GPS-measured coseismic 

displacements, we allow for different rates of change before and after the earthquake. We describe the north, east, 

and up vector components by 

and 

where Co is the initial value of the vector component at 

time to; dCl/dt is the average rate of line-length change 

before the earthquake; dC2/dt is the average rate of linelength change after the earthquake; and ACeq is the 

coseismic offset at teq, the time of the earthquake. 

GEODOLITE, GPS, AND VLBI 

MEASUREMENTS 

The Geodolite lines and GPS vectors measured before 

and after the 1989 Loma Prieta earthquake are parts of 

several networks (fig. 1). A network is an arbitrary regional grouping of lines with a similar measurement history. We have determined the coseismic deformation in 

the Pajaro, Hollister, Bay South, and Loma Prieta Monitor regional networks and in the Black Mountain and Chase 

small-aperture, fault-crossing networks. We discuss the 

data from each network separately, concluding with a short 

summary of Clark and others' (1990) VLBI results from 

the Fort Ord and Presidio sites. 

PA JAR0 NETWORK 

The Pajaro network extends along Monterey Bay; most 

stations are located near or west of the San Andreas fault. 

Lines from station Juan to stations Gilroy, Sargent, 

Fairview, and Hollis cross the Sargent or Calaveras fault 

and tie stations in the Pajaro network into stations in the 

Bay South and Hollister networks (fig. 1). We surveyed 

the Pajaro network nine times between 1973 and 1983, 

pnd again 3 months after the 1989 Loma Prieta earthquake (figs, 2A, 2B). Several lines in the network showed 

significant rates of line-length change. The 6- to 8-yr gap 

between the last survey and the earthquake makes the 

correction for secular change especially important in accurately estimating the coseismic offset. We directly estimate coseismic offsets at the time of the 1979 Coyote 

Lake and 1989 Loma Prieta earthquakes. Only the lines 

Brush 2 to Mulligan and Brush 2 to Fremont (fig. 1) were 

measured after the 1979 Coyote Lake earthquake and before the 1984 Morgan Hill earthquake. We use a dislocation model, with the geometry and location of the 

earthquake rupture reported by Prescott and others (1984) 

and the coseismic offsets at the time of the 1984 Morgan 

Hill earthquake listed in table 1, to estimate the coseismic 

offset in the Pajaro network at the time of the 1984 Morgan Hill earthquake; these modeled offsets are listed in 

parentheses in table 1. 

The linear rate of line-length change as a function of 

time with two coseismic offsets provides a good fit to 

most of the data from the Pajaro network (table 1). The 
GEODETIC MEASUREMENTS OF COSEISMIC HORIZONTAL DEFORMATION A85 

lines LPl to Vargo and Juan to Sargent (fig. 1) are excep- at the same time also show a larger than expected scatter; 

tions, with a x2 probability greater than 95 percent. No Savage and others (1976, 1979) speculated that.those meaindividual data points stand out as blunders in the plots, surements are contaminated by systematic error. The noralthough many of the frequent measurements of the line malized rms residual for the line LPl to Vargo is twice 

Juan to Sargent after the 1974 Hollister earthquake are the expected value. This line is steep (800-m elevation 

anomalous. Other measurements from station Sargent made change in 11 km), and trees around Vargo block or partly 

1 Chamber to Vargo 

Juan to Mulligan 600[[ -/ 

Brush 2 to Mulligan 1- Mulligan 1 Fairview to Juan 

1975 1980 1985 1990 

YEAR 

r' Canada to Fairview 

Canada 

1975 1980 1985 1990 

YEAR 

Figure 2.-Line-length change (observed line length L less a constant nominal length Lo) as a function of time for lines between stations in Pajaro and 

Hollister networks. Curves show best-fitting linear rate of line-length change from data points, with offsets at times of 1979 Coyote Lake and 1989 

Lorna Prieta earthquakes; error bars, lo. A, Lines in Pajaro network west of the Sargent fault. B, Lines in Pajaro network crossing the Sargent or 

Calaveras fault. C, Lines in Hollister network. Arrows designate data points that were excluded from analysis. 
A86 MAIN-SHOCK CHARACTERISTICS 

Table 1.-Rates of secular line-length change and coseismic offsets on networks in the Sun Francisco Bay region 

[Values in parentheses were calculated with a dislocation model; values marked with an asterisk are corrected for local motion between stations LP1 and Loma USE (fig. 

I), assuming that station LP1 is stable] 

No. Y. Coseismic offset (mm) 

Station 1 Station 2 ' Interval dLldt pi6ba- 

(km) sur- (mmlyr) bility O0 Coyote Lake Morgan Hill Mount Lewis Lorna Prieta 

veys (PCt) 1979.597 1984.313 1986.25 1989.794 

Pajaro network 

Brush 2 

Brush 2 

Chamber 

Chamber 

Chamber 

Fremont 

Fremont 

Juan 

LP 1 

Fairview 

Gilroy 

Hollis 

Juan 

Fremont 

Mulligan 

Juan 

Mulligan 

vargo 

Juan 

Mulligan 

Mulligan 

vargo 

Juan 

Juan 

Juan 

Sargent 

Hollister network 

Canada Fairview 13.3 8 75.0-90.3 1.5k1.1 39 0.83 -20.3k5.6 (4.0) --- -43.1k11.0 

Canada Sargent 14.3 9 75.0-90.3 -8.7&1,8 99 1.82 -53.3k10. 1 (-6.7) --- -91.8k18.6 

Fairview Gilroy 23.9 10 74.9-90,3 12.6k1,2 56 99 21.6k7.2 (6.9) --- -66.7k13.0 

Fremont Sargent 16.6 10 74.9-90.3 -11.9k1.2 78 1.18 2036.0 (5.1) - - - 54.2k12.9 

Gilroy Sargent 1 1.7 1 1 74.9-90.3 Okl.2 96 1.45 -6.016.1 (8.9) - - - -89.9k12.6 

Bay South network 

Canada 

Canada 

Gilroy 

Gilroy 

Gilroy 

Harnil ec Hamilton 

Llagas 

Llagas 

Allison 

Allison 

Allison 

American 

Amer RM3 

Biel 

Biel 

Butano 

Butano 

Butano 

Butano 

Cross RM1 

Dump 

Eagle Rk 

Mindego 

Gilroy 

Sheep RM2 

Llagas 

LP 1 

Sheep RM1 

Llagas 

Sheep RM2 

LP 1 

Sheep RM2 

BMT RF 

Hamilton 

Mindego 

BMT RF 

Hamilton 

Eagle Rk 

Mindego 

Dump 

Eagle Rk 

Mindego 

Porn 

Mindego 

Pom 

Mindego 

Pom 

Lorna short-range network 

Loma Geodolite monitor network 

Allison Loma USE 43.1 31 87.1-90.1 -1 1.8k2.3 3 76 --- --- --- 65.4k6.0, 

107.4Â±6.0 

Eagle Rk Loma USE 3 1.5 34 87.1-90.1 5.Okl.7 19 88 --- --- 256.4k4.5, --- 

255.4k4.5* 
GEODETIC MEASUREMENTS OF COSEISMIC HORIZONTAL DEFORMATION A87 

Table 1 .-Rates of secular line-length change and coseismic offsets on networks in the Sun Francisco Bay region-Continued 

No. x2 Coseismic offset (mm) 

Station 1 Station 2 Interval dLldt proha- 

(km) sur- (mdyr) bility Coyote Lake Morgan Hill Mount Lewis Loma Prieta 

VeYs . (pet) 1979.597 1984.3 13 1986.25 1989.794 

Loma Geodolite monitor network-Continued 

Hamilton Loma USE 31.2 32 87,l-90.1 -8.5k1.7 1 0.70 -- - --- - - - 11.9k4.6, 

52.9+46* 

Loma DWR PR 6 26.0 9 83.9-89.8 -4.7k1.5 39 .87 --- - - - - - - -273.9k10,l 

Lorna GPS monitor network 

LP 1 Allison 43.3 29 87.2-90,2 -12.1k1.6 95 1.24 --- --- --- 112.6k3.2 

LP 1 Eagle Un 31.4 21 87.7-90.2 8.3k2-9 66 1.05 --- - - - - - - 246.815.0 

LP 1 HarnilUn 31.4 12 88.1-90.2 -5.7k4.3 97 1.45 -- - - - - - - - 59.5k5.5 

-- - 

Bay South lines from station Lorna USE 

American LomaUSE 19.7 17 73.9-90.1 -3.5k0.8 99 1.74 --- 1.417.3 --- -94.417.9, 

-50.4Â±7.9 

Biel Loma USE 25.4 14 72.5-90.1 2.4k0.5 70 1-09 -- - 9.917.5 - - - 216.8k7.9. 

BMT RF Loma USE 35.4 9 78.5-90.1 .6k1.6 39 -85 --- -22.2k10.0 --- 139.9k13.8, 

158.9k13.8* 

Lorna USE Mindego 39.2 10 72.5-90.1 1.3k0.9 30 $80 --- -17.3110.8 - - - 158.0k12.8 

Chase network 

Chl 

Chl 

Chl 

Ch 1 

Ch 1 

Chl 

Chl 

Ch2 

Ch2 

Ch2 

Ch2 

Ch2 

Ch3 

Ch3 

Ch4 

Ch5 

Ch5 

Ch5 

Ch6 

Ch7 

Black Mountain network 

BMT10 

BMT 10 

BMT10 

BMT11 

BMT11 

BMT11 

BMT11 

BMT RF 

BMT RF 

BMT RF 

BMT RF 

BMT9 

PAWT 

P AWT 

BMT11 

BMT9 

PAW 

BMT RF 

BMT9 

PAWT 

Sky 1 

BMT9 

Mindego 

RF5 Reset 

Sky1 

Sky 1 

RF 1 

Sky1 
A88 

block the 

MAIN-SHOCK CHARACTERISTICS 

line-of-sight. The line-of-sight was totally 

blocked after 198 1, and we had to clear it to measure this 

line after the 1989 Loma Prieta earthquake. We have found 

larger than expected scatter in some other steep lines (Savage and others, 1992). The combination of a steep line 

and partly blocked line-of-sight could explain the low precision. Measurements of the line Vargo to Chamber were 

shifted to station Vargo RM 1 in 1979 because trees 

blocked the line-of-sight. The difference in the distances 

measured in 1979 is used to correct all subsequent measurements of the lines from Vargo RM1 to those stations 

that would have been observable from the primary station 

Vargo. 

We added the most southern station, Brush 2, to the 

Pajaro network in 1978. This station is critical to our 

analysis of the coseismic displacements because it is on 

the same hill as the VLBI site FortOrdS. Unlike the 

Geodolite and GPS measurements, the VLBI-measured 

coseismic displacements are relative to distant reference 

points (see subsection below entitled "Observations at Fort 

Ord and the Presidio"). By assigning the same coseismic 

horizontal displacement at station FortOrdS to station 

Brush 2 we fix the coseismic rigid-body translation of the 

geodetic network as a whole. 

HOLLISTER NETWORK 

Five lines from the Hollister network provide a tie between stations in the Hollister, Pajaro, and Bay South 

networks. The coseismic offsets along these lines allow 

us to compute the coseismic displacements of the stations 

Canada, Fairview, and Sargent (fig. 1). These lines were 

last surveyed in 1982. Our linear fits include coseismic 

offsets at the times of the 1979 Coyote Lake and 1989 

Loma Prieta earthquakes (fig. 2C). We use the dislocation 

model discussed in the preceding subsection to estimate 

the coseismic offset at the time of the 1984 Morgan Hill 

earthquake; the modeled values are listed in parentheses 

in table 1. The lines Fairview to Gilroy, Fremont to 

Sargent, and Canada to Sargent cross creeping sections of 

the San Andreas and Calaveras faults at low angles and 

thus have high rates of secular line-length change. All the 

lines crossing the Calaveras fault have accelerated rates of 

line-length change after the 1979 Coyote Lake earthquake 

that appear to return to normal about 1 yr after the earthquake. We exclude the anomalous 1979.9 data (arrows, 

fig. 20 from our analysis. The coseismic offsets listed in 

table 1, therefore, include this postseismic transient. 

BAY SOUTH NETWORK 

The Bay South network extends to the northwest from 

stations LP1, Gilroy, and Sheep; the subset of lines measured before and after the 1989 Loma Prieta earthquake is 

shown in figure 1. The rupture zones of the 1979 Coyote 

Lake, 1984 Morgan Hill, and 1986 Mount Lewis earthquakes are along the east edge of this network. We first 

discuss complexities in the measurement history, then the 

sites with multiple main stations, and, finally, the measurements. 

Several different survey monuments were used at stations American and Sheep (fig. 1) because tree growth 

blocked the lines-of-sight. We use local surveys to obtain 

a continuous time series for the line lengths into stations 

Sheep and American. As discussed earlier, we ignore possible error introduced by eccentric corrections. At station 

Sheep, some lines are corrected to station SheepRMl, and 

others to station SheepRM2, depending on which station 

has the most observations. We use different stations at 

Mount Hamilton and Loma Prieta, depending on the direction of the line. At Mount Hamilton, we use station 

Hamilton for most lines, and station Hamil Ec for the 

lines to stations Sheep and Llagas. At Loma Prieta, we 

use the station Loma USE for the lines to the north, and 

station LP1 for the lines to the south. The lines from 

station Loma USE are discussed in the next section. 

The nine lines between stations Canada, Gilroy, Sheep, 

Llagas, LP1, and Hamilton (fig. 1) are near the rupture 

zones of the 1979 Coyote Lake, 1984 Morgan Hill, and 

1989 Loma Prieta earthquakes, and we calculate the 

coseismic offsets for these earthquakes. The line-length 

change as a function of time for these lines is plotted in 

figure 3A. We measured the lines Llagas to SheepRM2, 

Hamilton to Sheep, and Hamil Ec to Llagas frequently 

after the 1979 Coyote Lake and 1984 Morgan Hill earthquakes and observed accelerated line-length changes for 

about 1 yr after these earthquakes. The time decay of this 

transient deformation is clearest along the line Hamil Ec 

to Llagas. We excluded the anomalous observations (data 

points marked with horizontal arrows and between vertical arrows, fig. 3A) from our analysis. 

We calculated the coseismic offsets at the times of the 

1984 Morgan Hill and 1989 Loma Prieta earthquakes along 

Figure 3.-Line-length change (observed line length L less a constant 

nominal length Lo) as a function of time between stations in Bay South 

network. Curves show best-fitting linear rate of line-length change from 

data points; error bars, lo. A, Lines east of the San Andreas fault and 

near rupture zones of 1979 Coyote Lake and 1984 Morgan Hill earthquakes. Offsets occur at times of 1979 Coyote Lake, 1984 Morgan Hill, 

and 1989 Loma Prieta earthquakes. Data points designated by horizontal 

arrows and between vertical arrows were excluded from anlaysis. B, 

Lines east of the San Andreas fault and near or north of rupture zone of 

1984 Morgan Hill earthquake. Offsets occur at times of 1984 Morgan 

Hill and 1989 Loma Prieta earthquakes; curves for lines Allison to 

Hamilton and Amer RM3 to Hamilton (dashed section of curve) include 

offset for 1986 Mount Lewis earthquake. C, Lines crossing or west of 

the San Andreas fault. Offset occurs at time of 1989 Loma Prieta earthquake. 
GEODETIC MEASUREMENTS OF COSEISMIC HORIZONTAL DEFORMATION A89 

the lines between stations Hamilton, Allison, American, RF are poorly fitted by a linear rate of line-length change 

BMT RF, and Mindego (figs. 1, 35). The lines Allison to (table 1). The lines into station American are steep, diffiHamilton, Amer RM3 to Hamilton, and American to BMT cult to measure because of poor visibility (smog) in the 

c - - - Mindego to Pom 

- 

Allison to Hamilton 

^i^S'-n-oÃ‘ Â = 

Biel to Mindego 

- - 

Llagas to SheepRM2 

- Butano to Pom - 

I- 

- 

- Butano to GTi Dump 

- 

Allison to Bmt RF 

- -: 

Butano to Mindego 

1975 1980 1985 1990 

YEAR 

Hamil Ec to Llagas 

lllllllllllllllllll 

1975 1980 1985 1990 

YEAR 

1975 1980 1985 1990 

YEAR 
A90 MAIN-SHOCK CHARACTERISTICS 

Santa Clara Valley; and Federal Aviation Administration 

regulations prohibit line-of-sight meteorologic flights. Because of these factors, our standard formula (eq. 1) probably underestimates the uncertainty in the measurements 

to station American. The line Allison to Hamilton has 

several unexplained, anomalous measurements. We included an additional coseismic offset at the time of the 

1986 Mount Lewis earthquake along the lines Allison to 

Hamilton and Amer RM3 to Hamilton. The frequent measurements of the line Allison to Hamilton just before the 

1989 Loma Prieta earthquake are from GPS surveys made 

as part of the Loma Prieta Monitor network. The GPS 

data, which allow a good determination of the coseismic 

offset at the time of the 1986 Mount Lewis earthquake, 

show no significant coseismic offset along this line from 

the 1989 Loma Prieta earthquake. The coseismic offset at 

the time of the 1986 Mount Lewis along the line Amer 

RM3 to Hamilton (dashed line, fig. 35) is insignificant 

and is omitted from table 1. 

The subset of the Bay South network west of the San 

Andreas fault is a group of relatively short lines for which 

we determined a coseismic offset only at the time of the 

1989 Loma Prieta earthquake (fig. 3C). A linear rate of 

line-length change fits all the lines except Butano to Pom. 

We offer no explanation for the misfit of this line, but as 

shown in figure 3C, the scatter in the data is relatively 

small. 

of the coseismic offsets observed on the summit and then 

discuss the coseismic offsets between the summit and distant points. 

Angle, distance, and GPS measurements on Loma Prieta 

allow us to determine the coseismic displacements between station LP1 and stations Loma USE, Loma CGS, 

Sue, and Loma DWR, and between station LP1 and stations Loma Azi and Loma No. 3 (fig. 4; table 3). We find 

that the group of stations at the north end of the peak 

moved 30 to 60 mm northeastward and 70 to 80 mm 

downward relative to station LP1. No significant change 

was noted in the interstation distance or relative elevation 

of station LP1, Loma Azi, or Loma No. 3. The coseismic 

displacements between stations on the north and south 

end of the peak are much greater than the uncertainty in 

the coseismic offset to distant stations. The important questions are whether the relative motion on Loma Prieta is 

from surficial fracturing of incompetent material and 

which, if any, of the monuments are stable. Robert 

McLaughlin (oral commun., 1989) observed no fractures 

on the peak except for a crack above a roadcut; he noted 

that the bedrock at the north end of the peak is not as 

competent as that along the ridge and at the south end of 

the peak. If the observed movements are the result of 

surficial fracturing induced by strong ground motions, then 

the sense of motion (downward relative to sta. LP1) and 

the geology suggest that the stations at the north end of 

MEASUREMENTS FROM LOMA PRIETA 

Loma Prieta, the summit of the Santa Cruz Mountains, 

is a primary point in the trilateration and GPS networks. 

The peak is covered with communication buildings and 

antennas, which limit lines-of-sight. We use two geodetic 

monuments located 160 m apart on opposite ends of the 

peak (fig. 4). Station Loma USE is a standard U.S. Army 

Corps of Engineers tablet set in a drill hole in bedrock at 

the north end of the peak, and station LP1 is a standard 

USGS National Center for Earthquake Research (NCER) 

tablet attached to galvanized pipe driven into well-consolidated sedimentary deposits at the south end of the 

peak. We use station Loma USE for most Geodolite lines 

directed to the north, station LP1 for lines directed to the 

south, and station LP1 for all GPS surveys. In 1983, vandals removed the tablet from station Loma USE; we set a 

new tablet, LomaNCER, in the drill hole and stamped it 

"Lorna NCER 1983." For all practical purposes, stations 

Loma USE and LomaNCER represent the same physical 

point, and so we refer to all measurements from either 

tablet as being from station Loma USE. Of greater concern is the stability of the geodetic monuments on Loma 

Prieta. We determine the coseismic displacements of several monuments on Loma Prieta; description of these 

monuments is given in table 2. We start with a discussion 

A LP1 (fixed) 

#3 A A Lorna Azi 

0 10 20 30 MILLIMETERS 

U,,,ud 

0 - 20 40 60 80 METERS 

Figure 4.-Schematic map of Loma Prieta area, showing locations of 

some monuments on peak and coseismic offsets relative to station LP1. 
GEODETIC MEASUREMENTS OF COSEISMIC HORIZONTAL DEFORMATION 

Table 2.-Description of monuments on Loma Prieta 

[NCER, National Center for Earthquake Research; USGS, U.S. Geological Survey] 

Station Stamping Agency Year established 

LP1 

Lorna USE 

Lorna NCER 

Lorna CGS 

Lorna DWR 

Lorna Azi 

Lorna No. 3 

Sue 

LOMA PRIETA NET 1 

LOMA PRIETA 2 1957 

LOMA 1983 

LOMA PRIETA 1851 1958 

Unstamped 

LOMA PRIETA 1954 

LOMA PRIETA #3 1960 

Sue 79 SC Cnty Survey 

USGS NCER 

U.S. Army Corps of 

Engineers. USGS NCER ---------------- 

U.S. Coast and 

Geodetic Survey. 

California Department 

of Water Resources. 

U.S. Coast and 

Geodetic Survey. 

California Department 

of Water Resources. 

Santa Clara County ---------- 

1970 

1957 (removed in 1983) 

1983 (set in drill hole 

of sta. Lorna USE) 

1958 

1960 

1954 (azimuth mark) 

1960 

1979 

the peak are more likely to have been affected. We assume that station LP1 is stable, and correct the observations from station Loma USE for the local coseismic offset. 

We return to this question in the section below entitled 

"Simple Dislocation Model of the Earthquake Rupture." 

We now discuss the coseismic offsets or displacements 

measured between Loma Prieta and distant points. 

The 6-km-long lines LP1 to LP2 and LP1 to LP4 cross 

the San Andreas and Sargent faults near the epicenter of 

the 1989 Loma Prieta earthquake (fig. 1). The orientation 

of these lines and the close proximity of these stations to 

the faults make them sensitive to shallow lateral slip across 

the faults; that is, line-length change will be a large fraction of the amount of shallow lateral slip on the faults. 

We measured the lines every few years beginning in 1970 

and last in 1981. The long gap (fig. 5) between the last 

measurement and the earthquake is not so important because of the relatively low rates of secular line-length 

change (table 1). These rates are consistent with little or 

no shallow lateral slip (creep) on the San Andreas or 

Sargent fault in the years before the 1989 Loma Prieta 

earthquake. Right-lateral shear from loading of the San 

Andreas fault would slowly shorten the north-south-trending line LP1 to LP4 and extend the east-west-trending 

line LP1 to LP2. Our linear fits show that the line LP1 to 

LP4 contracted at a significant rate (-4.Ok0.8 mm/yr) but 

that the line LP1 to LP2 also contracted (-1.5k0.8 mm/ 

yr). The scatter in these linear rates of line-length change 

are 2 to 3 times larger than the 3 mm expected for a 6- 

km-long line. The lines are steep, and at different times 

the laser was partly blocked by trees or bushes at stations 

LP2 and LP4. This combination of circumstances can result in partial illumination of the bank of retroreflectors, 

making the perceived height of the reflector incorrect and 

any misalignment of the reflectors critical. Although the 

scatter about the linear fits is larger than expected, we 

Table 3.-Coseismic displacements between monuments on Loma Prieta 

relative to station LP1 (fig. 1) 

Station North East UP Length (mm) (mm) (mm) (mm) 

Lorna USELorna NCER 42k2 12Â± -7 1k6 42k2 

Lorna CGS 47k2 35k4 -78k6 54k2 

Lorna DWR 23k3 26k3 -82k6 27k3 

Sue 21k5 27+4 -73+6 25+4 

Lorna Azi --- --- -1k6 3k2 

Lorna No. 3 --- --- -1+6 1 k2 

identified only one clear outlier, the first (Oct. 19, 1989) 

postearthquake survey of the distance from station LP1 to 

station LP4 (arrow, fig. 5). This distance is more than 20 

mm shorter than other Geodolite and GPS measurements 

made 3days to 2 months later. Both lines shortened during the earthquake, but the coseismic offsets are only a 

small fraction of the coseismic slip across the rupture 

zone and are consistent with the observation of no tectonic surface rupture. The secular and coseismic shortening of the line LP1 to LP2 suggests a component of reverse 

slip on one or both of the faults. Station LP2 is located on 

Skyland Ridge but is well beyond the south limit of a 

zone of conspicuous extensional cracks mapped by Ponti 

and Wells (1991). 

Loma Prieta is the central of four sites frequently monitored with Geodolite and GPS measurements. Monthly 

Geodolite measurements of the lines from station Loma 

USE to stations Eagle Rk, Allison, and Hamilton (fig. 1) 

began in 1981 (Lisowski and others, 1990b, 1993), and 

these lines were measured 2 weeks before and 2 days 

after the earthquake. The line from station Loma DWR to 

station PR 6 was monitored for about 1 yr, beginning in 

1983. Monthly GPS measurements of the lines between 

stations LP1, Eagle Un, and Allison began in 1987. Sta- 
A92 MAIN-SHOCK CHARACTERISTICS 

tion Eagle Un is the alternative site used for GPS measurements because the station used in Geodolite surveys, 

Eagle Rk, is located next to a large, metal-covered lookout tower. Station Hamilton was occupied once in 1988 

and regularly, beginning in 1989. GPS measurements of 

the lines between stations LP1, Eagle Un, Allison, and 

Hamilton were made 2 weeks before and a few days after 

the earthquake. Station Brush 2 was occupied once in 

1988, once in 1989, and regularly after the earthquake. A 

VLBI station, Fort Ord, located 7 km to the north was 

occupied in 1987 and simultaneously with station Brush 2 

in 1988. No direct measurements were made from station 

Brush 2 in 1987. We use the 1988 eccentric tie to reduce 

the 1987 observations at station FortOrd to those at station Brush 2. We assume no relative motion between stations Brush 2 and FortOrd, and we include the random 

error of the eccentric tie in the uncertainty of the reduced 

1987 measurements. 

We computed the secular rate of line-length change and 

the coseismic offset for the 1987-90 subset of the frequent Geodolite and GPS measurements (fig. 6). Note 

that the Geodolite measurements are from station Loma 

USE, whereas the GPS measurements are from station 

LP1. The secular rates of line-length change measured 

with Geodolite and GPS are similar, but the coseismic 

YEAR 

Figure 5.-Line-length change (observed line length L 

less a constant nominal length Lo) as a function of 

time along two 6-km-long lines measured from station 

LP1. Curves show best-fitting linear rate of line-length 

change from data points; error bars, lo. Offset occurs 

at time of 1989 Loma Prieta earthquake. Arrow designates data point that was excluded from analysis. 

offsets differ. We obtain similar coseismic offsets if we 

correct for the coseismic motion between the stations (table 

1). Savage and Lisowski (in press) discuss possible changes 

in the extension rates of these lines and vectors after the 

1984 Morgan Hill and 1989 Loma Prieta earthquakes. 

The GPS measurements provide all three components 

of the coseismic displacement between stations Allison, 

Loma USE to Eagle Rk 

1 a's to Alliso I 

O0 lLoma USE t 

0 Gl,llllllll-^llll~ LP1 to Hamilton 

YEAR 

Figure 6.-Line-length change (observed line length L 

less a constant nominal length Lo) as a function of 

time along a subset of three frequently measured lines 

between Geodolite and Global Positioning System stations. Curves show best-fitting linear rate of line-length 

change from data points; error bars, lo. Offset occurs 

at time of 1989 Loma Prieta earthquake. Note large 

difference between offsets along lines Loma USE to 

Allison and LP1 to Allison, and along lines Loma 

USE to Hamilton and LP1 to Hamilton. 
GEODETIC MEASUREMENTS OF COSEISMIC HORIZONTAL DEFORMATION A93 

Eagle Un, Hamilton, LP1, and Brush 2. The changes in and after the earthquake differ significantly (table 4). The 

the north, east, and up vector components relative to sta- rate of change in the vertical component between stations 

tion LP1 in a local coordinate system are plotted in figure LP1 and Brush 2 is not well determined, and so we also 

7. For example, the coseismic motion of station Allison compute the offset by differencing the weighted-mean 

relative to station LP1 is north, west, and up. We find that value before and after the earthquake (table 4). The only 

the rates of change in some of these components before direct measure of elevation change reported here comes 

LP1 to Allison 1 north 1 

I- east - 

YEAR 

[: LP1 to Hamilton 1 

1988 1990 1992 

YEAR 

Brush 2 

YEAR 

1988 1990 1992 

YEAR 

Figure 7.-Position change (north, east, and up vector components C less a constant nominal component Cn) as a function of time between stations 

LP1 and (A) station Allison, (5) station Eagle Un, (C) station Hamilton, and (D) station Brush 2. Curves show best-fitting linear rate of line-length 

change from data points; error bars, la Offset occurs at time of 1989 Loma Prieta earthquake. 
A94 MAIN-SHOCK CHARACTERISTICS 

Table 4.-Changes in the vector components of coseismic displacement of its stations are of the Sargent fault, and the 

and coseismic offsets along lines in the Loma Prieta Monitor network other five are northeast of the fault. We surveyed the 

[All values are Global Positioning System measurements relative to station LP1 

(fig. 1) within a local coordinate system at the second station] 

Rate before Rate after Rate change Coseismic 

earthquake earthquake (mdyr) 

offset 

Cmdyr) Cmdyr) (mm) 

LP1 to Allison 

LP 1 to Eagle Un 

North-------- 4.7k2.5 14.5k1.7 9.8k3.0 201.7k3.3 

East---------- -6.7k2.7 -9.9k2.4 -3.2k3.6 -228.2k4.8 

Up ----------- -8.1-I-9.9 4.2k7.2 12.3k12.2 186.9k13.8 

Length ------- 7.4k2.6 1 1.7k2.3 4.3k3.5 250.6k4.6 

LP1 to Hamilton 

LP1 to Brush 

~Differcncc of mean values before and after the earthquake. 

from the GPS vectors. We note that Loma Prieta subsided 

about 0.12 m relative to stations Allison and Hamilton 

and about 0.25 m relative to station Eagle Rk. 

Four Geodolite lines to stations in the Bay South network were measured from station Loma USE (fig. 8). We 

corrected these measurement after the earthquake for the 

coseismic offset of station Loma USE relative to station 

LP1. We calculated the coseismic offsets at the times of 

the 1984 Morgan Hill and 1989 Loma Prieta earthquakes 

along the lines from station Loma USE to stations 

Mindego, Biel, BMT RF, and American (fig. 1). The line 

Lorna USE to American is poorly fitted by a linear rate of 

line-length change (table 1). As mentioned above, the lines 

into station American are difficult to measure, and the 

previous error estimate is probably too small. 

CHASE NETWORK 

The 2-km-aperture Chase network (fig. 9) extends across 

the Sargent fault and has station Gilroy (Ch4) in common 

Chase network annually with a Geodolite between 1970 

and 1976, and once more in 1980. The network was surveyed again in 1990, 1 yr after the 1989 Lorna Prieta 

700 

Loma USE to Mindego 

Bmt to Loma* 

\ 1 

lo0l American to Lorna USE 

YEAR 

Figure 8.-Line-length change (observed line length L 

less a constant nominal length Lo) as a function of 

time between station Loma USE and stations in Bay 

South network. Curves show best-fitting linear rate of 

line-length change from data points; error bars, lo. 

Offsets occur at times of 1984 Morgan Hill and 1989 w 

with the South Bay and Hollister networks (fig. 1). Three Loma Prieta earthquakes. 
GEODETIC MEASUREMENTS OF COSEISMIC HORIZONTAL DEFORMATION A95 

earthquake. We used end-point meteorology in the 1990 

survey only. The relatively low rates of line-length change 

in the northeastern part of the network (fig, 10A) and the 

significant rates of extension and contraction in the lowangle fault-crossing lines (fig. 105) are consistent with 

2k.1 mdyr of shallow creep on the Sargent fault and an 

accumulation of right-lateral shear strain at the rate of 1 

ppmlyr in the network. The estimated coseismic offsets 

are substantial but poorly determined because of the long 

interval between the last survey and the earthquake. A 

few centimeters of sympathetic slip on the Sargent fault 

during the 1984 Morgan Hill and 1989 Lorna Prieta earthquakes is possible and not constrained by our observations. Such slip would shorten the north-south and extend 

the east-west fault-crossing lines by a large fraction of the 

lateral-slip amplitude. We see no such systematic pattern 

in the individual lines, possibly owing to the strain imposed by the 1989 Loma Prieta earthquake. The largest 

coseismic offsets are along in north-south-trending lines 

along the east edge of the network (lines Ch5 to Ch6, Chl 

to Ch6, Ch4 to Ch5), which show extensions of 30 to 60 

mm. 

BLACK MOUNTAIN NETWORK 

The 3-km-aperture Black Mountain network (figs. 1 1, 

12), which straddles the San Andreas fault on the southern part of the San Francisco peninsula, includes stations 

Mindego and BMT RF (also called BMT8) in common 

with the South Bay network (fig. 1). We surveyed the 

0 - 0.1 0.2 METERS 

2 KILOMETERS 

Figure 9.-Chase small-aperture network, showing observed (black vectors, with 95-percent-confidence ellipses) and calculated (gray vectors) 

coseismic displacements at Geodolite stations. Station Gilroy (CH4) is 

in common with Bay South network. 

Black Mountain network with a Geodolite nearly annually from 1970 to 1981 and less frequently thereafter; the 

last survey was just 2 months before the 1989 Loma Prieta 

earthquake. We also surveyed the network 2 months, 1 yr, 

and 2 yr after the earthquake. Aircraft-flown metrology 

was used in all but the second survey after the earthquake; therefore, the uncertainty of a typical observation 

is that given by equation 1. 

The average rate of line-length change between stations 

in the Black Mountain network is less than 1.7 mdyr 

(table I), consistent with the strain rates expected across a 

locked San Andreas fault. Fault creep (continuous shallow slip) at rate of 1.5 mmlyr could also explain the rates 

of line-length change, but no other evidence for creep 

across this section of the San Andreas fault is available. 

Coseismic offsets are as large as 17 mm. These changes 

are about that expected from the strain released by earthquake rupture. Shallow slip on the San Andreas fault does 

not appear to have occurred in the network before or after 

the 1989 Loma Prieta earthquake. Langbein (1990) reported a few millimeters of postseismic slip along the San 

Andreas fault in a network located near the northwest end 

of the Loma Prieta rupture zone. 

VLBI OBSERVATIONS AT FORT ORD AND THE 

PRESIDIO 

NASA's Crustal Dynamics Project and the NGS deployed mobile VLBI systems at Fort Ord, the Presidio, 

and Point Reyes before and after the 1989 Loma Prieta 

earthquake. The locations of these sites were determined 

with respect to a North American reference frame through 

the fixed VLBI observatories at Mojave, Hat Creek, and 

Vandenberg, Calif., and Fairbanks, Alaska. Clark and others (1990) estimated the coseismic displacement by projecting the average displacement rate from 1983 to the 

time of the earthquake. They reported that the Fort Ord 

site was displaced 49k4 mm toward N. 1 l0&4O E., and the 

Presidio site 12k5 mm toward S. 32Ok4O E. No significant 

vertical displacement was observed at any site, and no 

significant horizontal displacement was observed at Point 

Re yes. 

Two different sites were used at Fort Ord. From 1983 

to February 1988, all observations were made from the 

main VLBI site at Fort Ord. Subsequently, this survey 

monument was destroyed by construction, and VLBI observations were transferred to a site 8.9 km to the south 

called FortOrdS. At the time of Clark and others' (1990) 

report, there was some uncertainty about the tie between 

the sites, and so Clark and others determined offsets both 

at the time of the monument change and at the time of the 

1989 Loma Prieta earthquake. The VLBI station FortOrdS 

is on the same hill as the Geodolite and GPS station 

Brush 2. 
A96 MAIN-SHOCK CHARACTERISTICS 

SIMPLE DISLOCATION MODEL OF THE 

EARTHQUAKE RUPTURE 

We use the coseismic offsets and displacements to estimate the geometry, location, and slip of the Loma Prieta 

rupture zone. We represent the Earth as an elastic halfspace, and the rupture zone as a dipping rectangular cut 

(dislocation loop) buried in the half-space (Mansinha and 

Smylie, 1971). The slip across the cut (Burgers vector) is 

uniform and is allowed to have both dip-slip and strikeslip components. Our model has nine unknowns: four that 

I tllltllllt I 11 11 (1 1 

1970 1975 1980 1985 1990 

YEAR 

describe the geometry of the dislocation (strike, dip, width, 

length), three its location (latitude, longitude, depth), and 

two the slip (slip, rake). We prescribe the geometry and 

location of the dislocation, and use a least-squares inversion to determine the slip and rake that best reproduce the 

observed coseismic surface deformation, There is no 

unique solution; our best-fitting model provides the minimum normalized ms residual of the data to the model 

(eq. 5). Despite coseismic offsets that average 15 times 

larger than the instrument noise, we find that a surprisingly wide range of model faults adequately fit the data. 

Figure 10.-Line-length change (observed line length L less a constant nominal length Lo) as a function of 

time between stations in Chase network along lines that (A) do not cross or are east of and (B) cross or are 

west of the Sargent fault. Curves show best-fitting linear rate of line-length change from data points; error 

bars, lo. Offset occurs at time of 1989 Loma Prieta earthquake. 
GEODETIC MEASUREMENTS OF COSEISMIC HORIZONTAL DEFORMATION A97 

The geometry of the initial model fault is based on the 

locations of the main shock and aftershocks (Dietz and 

Ellsworth, 1990). The main shock has a focal depth of 

17.6 km. The aftershocks define a 45-km-long zone trending N. 50' W,, extending from a depth of 4 to 18 km, and 

dipping 65' SW. Aftershocks in the southeastern 10 km 

of the rupture zone are on a near-vertical plane aligned 

with the San Andreas fault and extending to a depth of 

only 10 km. 

How we treat the data from Loma Prieta is critical to 

our modeling of the fault rupture. Loma Prieta, which is 

close to the center of the rupture zone, has the largest and 

best determined coseismic offsets and displacements. The 

coseismic displacement between the monuments on Loma 

Prieta is several times larger than the uncertainty in the 

coseismic offsets to distant sites. We can use the data as 

is, correct them by assuming that one of the monuments is 

stable, downweight them, or disregard them. We assume 

that station LPl is stable and correct the data from station 

Loma USE for its coseismic offset relative to station LPl. 

Even with this assumption, which might be considered 

optimistic, some crucial rupture parameters are not well 

constrained by our geodetic data. 

The geometry, location, and slip of our best-fitting rupture model are listed in table 5. Most of the observed 

coseismic deformation can be reproduced by 5&4 m of 

slip at a rake of 153Ok6O on a 34k6-km-long buried rupture plane dipping 790&g0 SW. and extending from a depth 

of 7k3 to 13k5 km. The geodetic moment (Mo=p4b, where 

p is the rigidity [3x l0lo Pa], A is the area of the slip zone, 

and b is the slip amplitude) is 2.7k0.3~10~~ N-m. The 

\ 

RFI 

RF5Reset 

0.0 0.1 0.2 METERS I- \ 

I 2 3 KILOMETERS I , 

Figure 11 .-Black Mountain small-aperture network, showing observed 

(black vectors, with 95-percent-confidence ellipses) and calculated (gray 

vectors) coseismic displacements at Geodolite stations. Station Mindego 

and BMT RF (BMT8) are in common with Bay South network. 

normalized rms residual is 2.71; that is, the average residual is about 3 times larger than our previous error estimate. 

We used the coseismic offsets and the GPS- and VLBImeasured displacements to determine the coseismic station displacements, which are compared with those 

calculated from the best-fitting uniform-slip dislocation 

model in figures 9, 1 1, and 13. The displacements calculated from the coseismic offsets alone are uncertain by a 

rigid-body motion of the network as a whole. The VLBImeasured displacement of station FortOrdS determines 

BMT RF to 

Mindego 

BMT RF to 

RF5Reset 

PAWT to Sky1 

$$ $ * + 

BMT10 to BMT11 

$T 1 

$y BMT RF to BMT9 

+++ + b - 

'$ 6 BMT11 to PAWT 

i2 Y -r 

BMT10 to PAWT 

T 

Figure 12.-Line-length change (observed line length 

L less a constant nominal length Lo) as a function of 

time between stations in Black Mountain network. 

Curves show best-fitting linear rate of line-length 

change from data points; error bars, lo. Offset occurs 

at time of 1989 Lorna Prieta earthquake. 
A98 MAIN-SHOCK CHARACTERISTICS 

Table 5.-Parameters of best-fitting, unvorm-slip dislocation model 

[Data from station Loma USE (fig. I), corrected for coseismic offset relative to station LPl, Depth is to top of fault plane; width is downdip; 

latitude and longitude locations are surface projection of northwest corner of fault plane. Uncertainties are ranges of values with 68-percentconfidence limit of model] 

Strike (from Dip Length Width Depth 

(km) (kt-4 (km) 

Lat N. 

north) 

Slip Moment Long W. 

(m) Rake (1 019 N-m) 

the rigid-body translation of the network? and the GPS- rotation of the network. The combination of VLBI? GPSy 

measured displacement of stations Allison, Hamilton, and and EDM data thus provides a unique solution for the 

EagleUn relative to station LPl determines the rigid-body observed displacement of the stations within the geometriFigure 13.-San Francisco Bay region, showing locations of major faults (irregular lines, dashed where 

inferred; from Jenning, 1975) and observed (black vectors, with 95-percent-confidence ellipses) and calculated (grey vectors) coseismic displacements at stations in regional geodetic network (triangles). Star, epicenter of 1989 Loma Prieta earthquake; dashed rectangle, surface projection of best-fitting, uniform-slip 

dislocation model for earthquake; heavy-dashed line, intersection of rupture plane with surface of the Earth. 
GEODETIC MEASUREMENTS OF COSEISMIC HORIZONTAL DEFORMATION A99 

cally rigid part of the network. Stations Cross, LP2, LP4, 

Hollis, and PR6 are measured from only one other station, 

and so we exclude these stations from our displacement 

solution. The displacements of many stations are 

overdetermined (there are 22 degrees of freedom), and the 

normalized rms residual from the least-squares adjustment 

for the coseismic displacements is only 1.1 times larger 

than expected, indicating that the observed changes are 

self-consistent and that our previous error estimate is reasonable. 

The Black Mountain and Chase networks each include 

one station (Gilroy in the Chase network, BMT RF in the 

Black Mountain network) for which the displacement is 

uniquely determined, The displacement of station Mindego 

in the Black Mountain network also is uniquely determined, but this station is not rigidly tied to the other stations in the network. Stations Gilroy and BMT RF fix the 

rigid-body translation of these networks as a whole, but 

the displacements of the other sites in the networks are 

uncertain by a rigid-body rotation about this station. To 

test our model, we add the rigid-body rotation that best 

reproduces the predicted displacements (so-called model 

coordinate solution of Segall and Matthews, 1988). 

The station displacements most poorly fitted by the 

model are in the epicentral area (sta. Vargo, fig. I), and 

between the Calaveras and San Andreas faults (stas. Llagas, 

Gilroy, Chamber, Sargent). The measurements of lines 

between the Calaveras and San Andreas faults show 

coseismic effects and aftereffects from the 1979 Coyote 

Lake, 1984 Morgan Hill, and 1989 Loma Prieta earthquakes. We excluded anomalous data from as long as 1 yr 

after these earthquakes from our analysis. Along these 

lines, our assumption of a linear rate of line-length change 

over time, even with these anomalous data excluded, may 

be incorrect. Other known sources of deformation, such 

as triggered right-lateral slip on the Calaveras and San 

Andreas faults southeast of the rupture zone (Behr and 

others, 1990; Galehouse, 1990; McClellan and Hay, 1990) 

are small and most likely surficial phenomena. No obvious sources are known that could account for the difference between predicted and observed coseismic 

displacements in the area between the San Andreas and 

Calaveras faults. Careful modeling of the 1979 Coyote 

Lake and 1984 Morgan Hill earthquakes might eliminate 

some uncertainties about the rate of deformation during 

the decade before the 1989 Loma Prieta earthquake. 

The fit of our model to the data could also be improved 

with a more complex model of the Earth (Eberhart-Phillips 

and Stuart, 1992), the rupture geometry (Snay and others, 

1991), or the slip distribition (Marshall and others, 1991; 

~rnadbttir and Segall, 1994; Marshal and Stein, this chapter), or by including other sources of deformation, Our 

best-fitting rupture model is the simplest that can explain 

most of the coseismic deformation reported here. We show 

in the next section that the geometry, location, and slip of 

even this simple model are poorly resolved by the data. 

DISCUSSION 

How well do our geodetic data define the Loma Prieta 

rupture zone? To assess the range of model faults consistent with our data, we randomly vary the seven parameters describing the fault geometry and location, and solve 

for the slip and rake with a least-squares inversion. We 

limit our search to faults that strike 125'-145' from north, 

dip 60'-90' SW., with a length of 25 to 45 km, a downdip 

width of 1 to 19 km, a latitude and longitude position k5 

km from that in the starting model, and a depth to the top 

of the rupture plane of 2 to 10 km. We use an F-ratio test 

to approximate confidence regions. Model faults within a 

particular confidence region result in a normalized rms 

residual, oo (eq. 4), that is less than a particular value oOa. 

Given coopt for the optimal model, all models with oo<ooa 

are consistent at the 100a-percent-confidence level, where: 

Goa -~~~~~[l+~~(m,n-m,l-a)~, (7) - n-rn 

and n is the number of model parameters, m is the number 

of data, and F is the F distribution with m unknowns and 

n-m degrees of freedom (Draper and Smith, 1981). That 

is, the confidence region for each parameter is approximated from the range of values given by all the models 

consistent with the optimal model at a specified confidence level. Remember that models with a normalized 

rms residual near 1, on average, reproduce the observed 

coseismic changes within their uncertainty, ~rnadbttir and 

Segall (1994) found that the F-ratio test tends to slightly 

underestimate confidence regions relative to those predicted by bootstrapping techniques which rely on random 

resampling of the original data. 

We attempt to reproduce n=99 data, 85 line-length 

changes, and 4 GPS (three vector components each)- and 

2 VLBI (two vector components each)-measured displacements. The model fault is described by m=9 parameters. 

Our best-fitting rupture model has a normalized rms residual of 2.73, a misfit about 3 times the estimated error 

in the data. Using the F-ratio test (eq. 71, we find that 

rupture models with a normalized rms residual less than 

2.97 are within the 95-percent-confidence limit of our bestfitting model, and those models with a normalized rms 

less than 2.87 are within the 68-percent-confidence limit 

of our best-fitting model. The normalized rms residual is 

plotted as a function of the fault geometry and location in 

figures 14A through 14H. The shape and edge of the cloud 

of data points are important to our discussion. The nor- 
MAIN-SHOCK CHARACTERISTICS 

130 135 140 145 

STRIKE, IN DEGREES 

65 70 75 8'0 8'5 90 

DIP, IN DEGREES 

2 4 6 8 I0 12 

WIDTH, IN KILOMETERS 

I I I I I I I , I I 

37.16 37.17 37.18 37.19 37.2 37.21 37.22 

LATITUDE, IN DEGREES NORTH 

LONGITUDE, IN DEGREES WEST 

2.7 1 I I I I I I I I I I 

345678910 

DEPTH, IN KILOMETERS 

2345678910 

DEPTH, IN KILOMETERS 

Figure 14.-Ranges of fault geometries and locations allowed at 95-percent-confidence limit in best-fitting, uniform-slip 

dislocation model for 1989 Loma Prieta earthquake. A, Fault strike. B, Fault dip. C, Fault length. D, Fault width. E, Latitude of 

source. F, Longitude of source. G, Depth of source. H, Width versus depth of source. I, Fault slip. J, Fault rake. K, Seismic 

moment. 
GEODETIC MEASUREMENTS OF COSEISMIC HORIZONTAL DEFORMATION A101 

malized rms residual has a well-defined minimum for all 

the fault geometry and location parameters except fault 

width, which is poorly resolved and correlates closely with 

fault depth. The normalized rms residual is plotted as a 

function of the inverted parameters of slip and rake, and 

the calculated geodetic moment, in figures 147 through 

14K. The slip correlates closely with fault width, and 

because the width is poorly determined, the slip also is 

poorly determined. The rake and moment exhibit welldefined minimums. The uncertainties listed in table 5 are 

those that are within the 68-percent-confidence limit of 

our best-fitting model. We are, quite frankly, surprised at 

the range of model parameters that provide an adequate 

fit to the data, indicating that our surface geodetic data 

are rather insensitive to a buried source of deformation. 

0 2 4 6 8 10 

SLIP, IN METERS 

ABSENCE OF SURFACE RUPTURE 

The data plotted in figure 14 and listed in table 5 indicate that the geodetic observations are best fitted by a 

rupture that terminates well short of the Earth's surface. 

The lengths of the lines LP1 to LP2 and LP1 to LP4, 

which cross the San Andreas fault near the epicenter, 

changed by only a fraction of a meter (table I), even 

though the total slip was more than 2 m. These results are 

quite consistent with the absence of any surface expression of primary rupture. There has been some discussion 

in the literature on the question of how much slip occurred along this section of the fault in the 1906 San 

Francisco earthquake. Thatcher and Lisowski (1987) inferred from triangulation observations that the average 

slip amplitude from the surface to 10-km depth was 2.6k0.2 

m. Primarily on the basis of an observation of an apparent 

fault offset in the summit railway tunnel south of Wrights 

station (Lawson, 1908), Scholz (1985) argued that the slip 

amplitude along this section of the fault in 1906 was 1.5 

m, significantly less than farther north along the peninsula, and that this section of the fault must rupture more 

frequently to make up the slip deficit that was "observed" 

in 1906. The occurrence of the 1989 Loma Prieta earthquake seems to support to this argument, although no surface slip was observed in 1989. Therefore, surface slip 

does not seem to be a valid criterion for earthquake prediction along this section of the San Andreas fault. 

CONCLUSIONS 

140 145 150 155 160 165 

RAKE, IN DEGREES 

L 

2 2.5 3 3.5 

MOMENT, IN NEWTON-METERS 

Figure 14.-Continued 

We use Geodolite and GPS surveys both before and 

after the 1989 Loma Prieta earthquake to estimate the 

coseismic offsets along 85 lines and at 4 sites. The 

coseismic displacment of two VLBI sites was previously 

determined by Clark and others (1990). To correct for 

secular offsets or displacements, we project the average 

rate of change to the time of the earthquake. The offsets 

and displacements are mostly consistent with a linear rate 

of change as a function of time, with offsets at the time of 

earthquakes. Along many lines, we allowed for additional 

offsets at the times of the 1979 Coyote Lake, 1984 Morgan Hill, and 1986 Mount Lewis earthquakes. Lines near 

the ruptures zones of the 1979 Coyote Lake and 1984 

Morgan Hill earthquakes show accelerated rates of linelength change that appear to decay to the previously observed rates within about 1 yr. We excluded anomalous 

measurements after these earthquakes from the analysis. 

Local surveys on Loma Prieta, a peak 3 km from the 

San Andreas fault and 11 km from the epicenter of the 

1989 earthquake, show that monuments at the north end 

of the peak were displaced 30 to 60 mm to the northeast 

and subsided 70 to 80 mm relative to monuments about 
A102 MAIN-SHOCK CHARACTERISTICS 

160 m away on the south end of the peak. The sense of 

motion is consistent with shaking-induced instability of 

the north end of the peak, although no local ground fracturing was observed after the earthquake. In our analysis 

of the data from Loma Prieta to distant points, we assume 

that the southern stations are stable, and correct observations from the northern stations for local coseismic movements, although none of the stations on the peak may be 

stable. In any case, the occurrence of relative motion between the stations on Loma Prieta, with no obvious local 

ground fracturing, questions whether the observed changes 

to distant points truly represent tectonic deformation. 

We use a Monte Carlo fault-parameter estimation to 

find a best-fitting, uniform-slip dislocation model and to 

assess the data sensitivity. Well-defined minimums in the 

normalized rms residual exist for all parameters describing the fault geometry and location, except fault width, 

which correlates closely with fault depth. The inverted 

parameter of slip correlates closely with fault width and 

exhibits no well-defined minimum in normalized rms residual. The inverted parameter of rake and the calculated 

geodetic moment, however, are well defined. Although 

the minimums in the normalized rms residual are well 

defined for most fault-rupture parameters, the uncertainty 

is quite large (table 5). The geodetic data, however, are 

consistent with the observation of no tectonic surface 

rupture. 

The combination of Geodolite, GPS, and VLBI measurements provides a unique solution for the coseismic 

displacements. The normalized rms residual from the displacement adjustment indicates that our previous estimates 

of the average error in the coseismic offsets are only 

slightly low. The coseismic offsets of the geodetic stations located between the San Andreas and Calaveras faults 

to the east and south of the Loma Prieta rupture zone are 

poorly fitted by our dislocation model. Many of the lines 

in this area had not been measured since 1986, some since 

1982, and all were affected by the 1979 Coyote Lake and 

1984 Morgan Hill earthquakes. The deformation history 

of this region is complex, and our method may underestimate the error in the linear rates of line-length change 

and, correspondingly, in the coseismic offsets at the time 

of the 1989 Loma Prieta earthquake. There may be other 

unmodeled sources for the deformation, but the obvious 

choices of sympathetic slip on the San Andreas or Calaveras fault do not account for the observed changes. 

ACKNOWLEDGMENTS 

Immediately after the earthquake, we received valuable 

field assistance from K. Hudnut, F. Webb, and S. Larsen 

of the California Institute of Technology and M. Jackson 

of the University of Colorado. We appreciate the efforts 

of the current USGS field crew, W.K. Gross, G.D. 

Hamilton, J.M. Sutton, C. Stiffler, and K. Clark, and other 

individuals who served on past field parties. K. Wendt 

aided with the data reduction. We used a computer program provided by Paul Segall to calculate the coseismic 

displacements. 

REFERENCES CITED 

~rnadottir, Thora, and Segall, Paul, 1994, The 1989 Loma Prieta earthquake imaged from inversion of geodetic data: Journal of Geophysical Research, v. 99, no. Bll, p. 21835-21855. 

~rnadottir, Thora, Segall, Paul, and Matthews, M.V., 1992, Resolving 

the discrepancy between geodetic and seismic fault models for the 

1989 Loma Prieta, California, earthquake: Seismological Society of 

America Bulletin, v. 82, no. 5, p. 2248-2255. 

Bakun, W.H., Clark, M.M., Cockerham, R.S., Ellsworth, W.L., Lindh, 

A.G., Prescott, W.H., Shakal, A.F., and Spudich, Paul, 1984, The 

1984 Morgan Hill, California, earthquake: Science, v. '255, no. 4659, 

p. 288-29 1. 

Behr, Jeffrey, Bilham, Roger, Bodin, Paul, Burford, R.O., and Burgmann, 

Roland., 1990, Aseismic slip on the San Andreas fault south of 

Loma Prieta: Geophysical Research Letters, v. 17, no. 9, p. 1445- 

1448. 

Beutler, Gerhart, Abell, M.D., Bauersima, I., Gurtner, W., Mader, G.L., 

Rothacher, M., Schildknecht, 1987, Evaluation of the 1984 Alaska 

Global Positioning System campaign with the Bernese GPS software: Journal of Geophysical Research, v. 92, no. B2, p. 1295- 

1304. 

Burgmann, Roland, Arrowsmith, Ramon, and Dumitru, Trevor, 1994, 

Rise and fall of the southern Santa Cruz Mountains, California, 

from fission tracks, geomorphology, and geodesy: Journal of Geophysical Research, v. 99, no. B10, p. 20181-20202. 

Clark, T.A., Corey, B.E., Davis, J.L., Elgered, G., Herring, T.A., 

Hinteregger, H.F., Knight, C.A., Levine, J.I., Lundquist, G., Ma, 

Choppo, Nesman, E.F., Phillips, R.B., Rogers, A.E.E., Ronnang, 

B.O., Ryan, J.W., Schupler, B.R., Shaffer, D.B., Shapiro, I.I., 

Vandenberg, N.R., Webber, J.C., and Whitney, A.R., 1985, Precision geodesy using the Mark I11 very-long-baseline interferometer 

system: Institute of Electrical and Electronics Engineers Transactions on Geoscience and Remote Sensing, v. GE-23, no. 4, p. 438- 

449. 

Clark, T.A., Ma, Choppo, Sauber, J.M., Ryan, J.W., Gordon, David, 

Shaffer, D.B., Caprette, D.S., and Vandenberg, N.R., 1990, Geodetic measurement of deformation in the Loma Prieta, California, 

earthquake with very long baseline interferometry: Geophysical 

Research Letters, v. 17, no. 8, p. 1215-1218. 

Davis, J.L., Prescott, W.H., Svarc, J.L., and Wendt, K.J., 1989, Assessment of Global Positioning System measurements for studies of 

crustal deformation: Journal of Geophysical Research, v. 94, no. 

B 10, p. 13635-13650. 

Dietz, L.D., and Ellsworth, W.L., 1990, The October 17, 1989, Loma 

Prieta,California, earthquake and its aftershocks; geometry of the 

sequence from high-resolution locations: Geophysical Research Letters, v. 17, no. 9, p. 1417-1420. 

Dixon, T.H., 1991, An introduction to the Global Positioning System 

and some tectonic applications: Reviews of Geophysics, v. 29, p. 

249-276. 

Dong, Danan, and Bock, Yehuda, 1989, Global Positioning System network analysis with phase ambiguity resolution applied to crustal 

deformation studies in California: Journal of Geophysical Research, 

v. 94, no. B4, p. 3949-3966. 
GEODETIC MEASUREMENTS OF COSEISMIC HORIZONTAL DEFORMATION A103 

Draper, N.R., and Smith, Harry, 1981, Applied regression analysis (2d 

ed.): New York, Wiley, 709 p. 

Eberhart-Phillips, D.M., Stuart, W.D., 1992, Material heterogeneity simplifies the picture; Loma Prieta: Seismological Society of America 

Bulletin, v. 82, no. 4, p. 1964-1968. 

Galehouse, J.S., 1990, Effect of the Loma Prieta earthquake on surface 

slip along the Calaveras fault in the Hollister Calif. area: Geophysical Research Letters, v. 17, no. 8, p. 1219-1222. 

Hagar, B.H., King, R.W., and Murray, M.H., 1991, Measurement of 

crustal deformation using the Global Positioning System: Annual 

Reviews of Earth and Planetary Sciences, v. 19, p. 351-382. 

Jennings, C.W., compiler, 1975, Fault map of California, with locations 

of volcanoes, thermal springs, and thermal wells: California 

Division of Mines and Geology Geologic Data Map 1, scale 

1 :750,000. 

King, N.E., Savage, J.C., Lisowski, Michael, and Prescott, W.H., 1981, 

Preseismic and coseismic deformation associated with the Coyote 

Lake, California, earthquake: Journal of Geophysical Research, v. 

86, no. B2, p. 892-898. 

Langbein, J.O., 1990, Postseismic slip on the San Andreas Fault at the 

northwestern end of the 1989 Loma Prieta earthquake rupture zone: 

Geophysical Research Letters, v. 17, no. 8, p. 1223-1226. 

Larson, K.M., and Agnew, D.C., 1991, Application of the Global Positioning System to crustal deformation measurement 1. Precision 

and accuracy: Journal of Geophysical Research, v. 96, no. B10, p. 

16547-16565. 

Lawson, A.C., chairman, 1908, The California earthquake of April 18, 

1906; report of the State Earthquake Investigation Commission: 

Carnegie Institution of Washington Publication 87, 2 v. 

Lisowski, Michael, Prescott, W.H., Savage, J.C., and Johnston, M.J., 

1990a, Geodetic estimate of coseismic slip during the 1989 Loma 

Prieta,California, earthquake: Geophysical Research Letters, v. 17, 

no. 9, p. 1437-1440. 

Lisowski, Michael, Prescott, W.H., Savage, J.C., and Svarc, J.L., 1990b, 

A possible geodetic anomaly observed prior to the Loma Prieta, 

California, earthquake: Geophysical Research Letters, v. 17, no. 8, 

p. 121 1-1214. 

Lisowski, Michael, Savage, J.C., and Prescott, W.H., 1991, The velocity 

field along the San Andreas fault in central and southern California: Journal of Geophysical Research, v. 96, no. B5, p. 8369-8389. 

Lisowski, Michael, Savage, J.C., Prescott, W.H., Svarc, J.L., and Murray, 

M.H., 1993, No convincing precursory geodetic anomaly observed, 

The Lorna Prieta, California, Earthquake of October 17, 1989- 

preseismic observations: U.S. Geological Survey Professional Paper 15504, p. C67-C72. 

Mansinha, Lalatendu, and Smylie, D.E., 197 1, The displacement fields 

of inclined faults: Seismological Society of America Bulletin, v. 

61, no. 5, p. 1433-1440. 

Marshall, G.A., Stein, R.S., and Thatcher, Wayne, 1991, Faulting geometry and slip from co-seismic elevation changes; the 18 October 

1989, Lorna Prieta, California, earthquake: Seismological Society 

of America Bulliten, v. 81, no. 5, p. 1660-1693. 

McClellan, P.H., and Hay, E.A., 1990, Triggered slip on the Calaveras 

fault during the magnitude 7.1 Loma Prieta, California, earthquake: 

Geophysical Research Letters, v. 17, no. 8, p. 1227-1230. 

Murray, M.H., 1991, Global Positioning System measurement of crustal 

deformation in central California: Cambridge, Massachusetts Institute of Technology, Ph.D. thesis, 310 p. 

Ponti, D.J., and Wells, R.E., 1991, Off-fault ground ruptures in the 

Santa Cruz Mountains, California; ridge-top spreading versus tectonic extension during the 1989 Loma Prieta earthquake: Seismological Society of America Bulletin, v. 81, no. 5, p. 1480-1510. 

Prescott, W.H., King, N.E., and Gu Guohua, 1984, Preseismic, coseismic 

and postseismic deformation associated with the 1984 Morgan Hill, 

California, earthquake, in Bennett, J.H., and Sherburne, R.W., eds., 

The 1984 Morgan Hill California earthquake: California Division 

of Mines and Geology Special Publication 68, p. 137-148. 

Prescott, W.H., Davis, J.L., and Svarc, J.L., 1989, Global Positioning 

System measurements for crustal deformation; precision and accuracy: Science, v. 244, no. 4910, p. 1337-1340. 

Savage, J.C., and Lisowski, Michael, 1995, Changes in long-term extension rates associated with the Morgan Hill and Lorna Prieta earthquakes in California: Geophysical Research Letters, v. 22, no. 7, p 

759-762. 

Savage, J.C., Lisowski, Michael, and Prescott, W.H., 1992, Strain accumulation across the Wasatch fault near Ogden, Utah: Journal of 

Geophysical Research, v. 97, no. B2, p. 2071-2083. 

Savage, J.C., Lisowski, Michael, and Svarc, J.L., 1994, Postseismic 

deformation following the 1989 (M=7.1) Loma Prieta, California, 

earthquake: Journal of Geophysical Research, v. 99, no. B7, p. 

13757-13765. 

Savage, J.C., and Prescott, W.H., 1973, Precision of Geodolite distance 

measurements for determining fault movements: Journal of Geophysical Research, v. 78, no. 26, p. 6001-6007. 

Savage, J.C., Prescott, W.H., and Gu Guohua, 1986, Strain accumulation in southern California, 1973-1984: Journal of Geophysical Research, v. 91, no. B7, p. 7455-7473. 

Savage, J.C., Prescott, W.H., Lisowski, Michael, and King, N.E., 1979, 

Geodolite measurements of deformation near Hollister, 1971-1978: 

Journal of Geophysical Research, v. 84, no. B 13, p. 7599-7615. 

Savage, J.C., Spieth, M.A., and Prescott, W.H., 1976, Preseismic and 

coseismic deformation associated with the Hollister, California, 

earthquake of November 28,1974: Journal of Geophysical Research, 

v. 81, no. 20, p. 3567-3574. 

Schaffrin, Burkhard, and Bock, Yehuda, 1988, A unified scheme for 

processing GPS dual-band phase observations: Bulletin Geodesique, 

v. 62, no. 2, p. 142-160. 

Scholz, C.H., 1985, The Black Mountain asperity; seismic hazard of the 

southern San Francisco Peninsula, California: Geophysical Research 

Letters, v. 12, no. 10, p. 717-719. 

Segall, Paul, and Matthews, M.V., 1988, Displacement calculations form 

geodetic data and the testing of geophysical deformation models: 

Journal of Geophysical Research, v. 93, no. B12, p. 14954-14966. 

Snay, R.A., Neugebauer, H.C., and Prescott, W.H., 1991, Horizontal 

deformation associated with the Loma Prieta earthquake: Seismological Society of America Bulletin, v. 81, no. 5, p. 1647-1659. 

Thatcher, Wayne, 1983, Nonlinear strain buildup and the earthquake 

cycle on the San Andreas fault: Journal of Geophysical Research, 

v. 88, no. B7, p. 5893-5902. 

Thatcher, Wayne, and LisowSki, Michael, 1987, Long-term potential of 

the San Andreas fault southeast of San Francisco, California: Journal of Geophysical Research, v. 92, no. Bl, p. 4771-4784. 

U.S. Geological Survey staff, 1990, The Loma Prieta, California, earthquake; an anticipated event: Science, v. 247, no. 4940, p. 286-293. 

Williams, C.R, ~rnad6ttir, Thora, and Segall, Paul, 1993, Coseismic 

deformation and dislocation models of the 1989 Loma Prieta earthquake derived from Global Positioning System measurements: Journal of Geophysical Research, v. 98, no. B3, p. 4567-4578. 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAKEOCCURRENCE 

MAIN-SHOCK CHARACTERISTICS 

ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND 

THEIR USE TO INFER FAULT-SLIP GEOMETRY 

CONTENTS 

By Grant A. Marshall and Ross S. Stein, 

U.S. Geological Survey 

Page 

A105 

lo5 

lo6 

lo6 

lo6 

lo9 

110 

110 

110 

111 

111 

11 1 

116 

117 

118 

119 

120 

122 

122 

124 

125 

126 

126 

127 

129 

ABSTRACT 

Leveling surveys conducted before and after the 1989 

Loma Prieta earthquake provide observations of the 

coseismic elevation changes. We use these data to define 

the spatial pattern of elevation change and to deduce the 

faulting geometry and distribution of slip. Both planar 

and curved (listric and negatively listric) faults produce 

elevation changes consistent with observations. Using an 

elastic half-space, we treat the data as correlated observations and find that 60 percent of the observed signal can 

be modeled by a planar rupture surface that extends from 

6- to 12-km depth, is 32 km long and 7 km wide, and dips 

64' SW. With a slip amplitude of 3.6 m, this model fault 

produces a geodetic moment of 2.6xl0l9 N-m. A larger 

dip-slip component is found northwest of the epicenter 

(rake, 144') and a larger strike-slip component southeast 

of the epicenter (rake, 157'). Models with larger rake variations (>40Â° marginally reduce the fit to the data but require a seismic moment of only 1.8~10~~ N-m. The rupture 

plane lies 2 km southwest of the aftershock zone. When a 

low-modulus layer or wedge is added to the model for 

consistency with the seismic P-wave-velocity structure, 

the fault deepens and locates adjacent to the aftershock 

zone; coming within 1.5 km of the hypocenter. 

INTRODUCTION 

Precise geodetic leveling surveys conducted both before and after the 1989 Loma Prieta earthquake provide 

observations of the coseismic elevation changes. Although 

no active program of vertical-deformation monitoring using leveling has been pursued along this section of the 

San Andreas fault zone, previous leveling surveys for topographic-control and land-subsidence studies have been 

used together with postearthquake releveling to construct 

the coseismic elevation changes. Station separation for 

more than half of this extensive network of vertical-control bench marks is about 1 km. 

In this study, we focus on the broad-scale pattern of 

vertical deformation and its interpretation in terms of fault 

geometry and slip. We use simple uniform-slip elasticdislocation models to approximate the rupture surface at 

depth. In two different approaches, we treat the leveling 

observations as either independent or correlated elevation 

changes. We compare our models incorporating a heterogeneous elastic structure with the half-space models for 

consistency with the seismic-velocity models of EberhartPhillips and others (1990). We then compare the model 

rupture surface with seismologic, geologic, and other geodetic observations. 
A106 MAIN-SHOCK CHARACTEiRISTICS 

DATA 

LEVELING NETWORK 

The leveling network circumscribes the southern Santa 

Cruz Mountains and encloses most of the aftershock zone 

(fig, 1). The network spans 15 to 20 km (one hypocentral 

depth) on each side of the San Andreas fault and 67 km 

along strike. Postearthquake surveys were chosen to give 

maximum coverage of the aftershock zone and the area of 

expected vertical deformation. The leveling routes cross 

the San Andreas and Sargent faults in four places. The 

network is divided into seven routes (inset, fig. I), each 

approximately parallel or perpendicular to the* San Andreas fault. 

Preearthquake leveling surveys were performed by both 

the U.S. National Geodetic Survey (NGS) and the U.S. 

Geological Survey (USGS) between 1948 and 1989. 

Postearthquake surveys were conducted from February 

through June 1990. We treat all of the vertical deformation occurring between the preearthquake and 

postearthquake surveys as "coseismic," noting that little 

postearthquake slip was observed between October 1989 

and June 1990 (Behr and others, 1990; Langbein, 1990). 

LEVELING ERRORS 

Leveling can be contaminated by both systematic and 

random errors. Systematic errors generally produce a correlation between observed geodetic tilt and topographic 

slope, as is true for miscalibrated leveling rods (Jackson 

and others, 1981; Stein, 1981) and is sometimes true for 

atmospheric-refraction errors (Stein and others, 1986). 

Random errors have several causes: inaccurate readings 

of the leveling instrument caused by atmospheric scintillation and ground vibrations, incorrectly entered numerical values (blunders), random -variations in the degree to 

which the instrument and rods are out of plumb, and so 

on. The NGS corrects all data for level collimation, rod 

Figure 1 .-Schematic map of Loma Prieta region, Calif., showing location of leveling network of 21 1 bench 

marks. Inset shows locations of leveling routes 1 through 7; bench marks (dots) indicate zero-distance points 

in profiles shown in figure 7. Stars, epicenters of Lorna Prieta (Oct. 17, 1989; Ms=7.1), Coyote Lake (Aug. 

6, 1979; Ms=5.9), and Morgan Hill (Apr. 24, 1984; ML=6.1) earthquakes; crosses, epicenters of Lorna Prieta 

aftershocks of M>2. Quaternary faults (dashed where inferred) from Jennings (1975). AN, Point Afio Nuevo; 

AP, Aptos; BC, Boulder Creek; CA, Capitols; CO, Corralitos; CY, Coyote; DA, Davenport; F'E, Felton; FR, 

Freedom; GI, Gilroy; HP, Hecker Pass; LG, Los Gatos; LP, Loma Prieta (triangle); LS, La Selva Beach; 

MH, Morgan Hill; OL, Olympia; PG, Pajaro Gap; SA, Sargent; SC, Santa Cruz; SJ, San Jose; SO, Soquel; 

SU, Sunnyvale; SV, Scotts Valley; WA, Watsonville; ZA, Zayante. 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A107 

calibration, thermal expansion of the rod tapes, earth tides 

and associated gravitational effects, and atmospheric refraction. For the 1990 surveys, the thermal and refraction 

corrections were computed from the observed temperature gradient at the leveling instrument. 

In contrast, the third-order USGS leveling data are not 

corrected for refraction, earth tides, or thermal-expansion 

effects. Refraction, collimation, and rod-calibration errors, 

which can lead to systematic errors detectable in thirdorder work, are evaluated by searching for height-dependent correlations, Profiles of elevation change and 

topography are shown in figure 2 for leveling routes 4 

(fig. 2A) and 7 (fig. 2B), both of which cross substantial 

topography and show no correlation (positive or negative) 

between the tilt of elevation change and topographic slope. 

No such correlations are recognizable in the other 

coseismic data, although errors of 5100 mm would be 

difficult to detect in the presence of large tectonic deformation. 

Random error can be gaged from the height difference 

between adjacent bench marks when they are double-run 

(leveling in both directions), and from circuit misclosures. 

Random error accumulates with the square root of distance, expressed as a&, where ct (in millimeters per 

kilometer%) is computed from the double-run sections 

and L is the length of each section (in kilometers). The 

observed ct values listed in table 1 are derived from the 

statistics of all double-run sections and have been normalized to a distance of 1 km. The maximum allowable discrepancy between the forward and backward runs of each 

double-run section is the field tolerance, b. If this field 

tolerance is not met, the section must be rerun until the 

forward and backward runs agree to within the tolerance. 

In practice, arithmetic means of several runs are used for 

final elevation differences when the field tolerance cannot 

be met after several attempts. If random errors are normally distributed, then ct= % p. Generally, ctc % p because 

the errors are not normally distributed or because the number of double-run sections used to compute cx is small. 

We have assigned ct values to each survey on the basis 

of observed circuit misclosures. In the absence of large 

blunders or length-dependent systematic errors, observed 

circuit misclosures give an estimate of the random survey 

error. The accuracy of the 1990 surveys can be determined by examining five closed circuits. All the circuits 

are mapped in figure 3, and the observed misclosure, 

length, and allowable misclosure for each circuit are listed 

in table 2. 

The assigned ct values (table 1) are computed from the 

misclosures of circuits by the formula 

where ei is the misclosure (in millimeters), Li is the length 

(in kilometers) of the ith circuit, and n is the number of 

circuits (Bomford, 1971, p. 8 16). Generally, this calculation leads to more conservative assignments of error than - 

DISTANCE, IN KILOMETERS does the observed ct value. Where circuit-closure data are 

unavailable, the ct value is assigned by setting the ratio m 

w plct equal for all first-order surveys. All third-order sur- Id 

VJ 800 I- veys have been assigned an ct value on the basis of the 0.12 g w single preearthquake circuit 5 misclosure, which yields a I- 2 600 Z 7-mm/& mean error, whereas the expected error for 0.08 

Li third-order levels is 12 md&. Because circuit 5 was 

z 0 

- 400 closed with several rod pairs, this small misclosure is conz 0.04 5 

x 

sistent with an absence of rod-calibration error. Pure er2 

I- CJ rors represented by circuit misclosures have been used to 

4 200 

> o z scale the relative precision of each survey. w 

1 52 The error assigned to each coseismic elevation change 

0 -0.04 5 

0 10. 20 30 ~d is based on survey precision and on the uncertainty and J DISTANCE, IN KILOMETERS w magnitude of the subsidence corrections (see app. 1). Relative uncertainties, 6i, for each coseismic data point are 

Figure 2.-Profiles of topography (shaded curve) and coseismic eleva- computed as 

tion change (dots) along leveling routes 4 (A) and 7 (B) (see inset, fig. 

1). No consistent positive or negative correlation between topography 

and elevation change is observed. 
A108 MAIN-SHOCK CHARACTERISTICS 

Table 1 .-Specifications for leveling surveys 

[Agencies: NGS, U.S. National Geodetic Survey; USGS, US. Geological Survey. Assigned cc values are derived from circuit misclosures. n.a., 

not available] 

Lcvcling 

routc Survcy agcncy 

(insct, fig. 1) and designation 

Survcy 

datc 

Ordcr of Ficld Obscrvcd Assigned lcveling tolerance, a valuc a valuc 

(mn) (mm) (mm) (mm) 

1 NGS L25239.1 

NGS L25 172, L25 174 

NGS L22841 

NGS L21038, L21016.1, 

L21026.2 

2 NGS L25239.1, L25239.2 

NGS L25251.8 

NGS L25174 

NGS L24298 

NGS L2284 1, L22869 

3 NGS L25239.3 

NGS L21016.9 

NGS L18119.9 

4 NGS L25239.4 

USGS PV 80, PV 208, 

PV 220 

5 NGS L25239.6 

USGS PV 220, PV 208 

6 NGS L25239.5 

USGS PV220 

7 NGS L2525 1.7, L2525 1.8 

USGS PV218 

Jan.-Feb. 1990 

Fcb.-Mar. 1989 

July-Scpt. 1972 

Mar.-May 1967 

Fcb. 1990 

June 1990 

Mar. 1989 

1978 

July-Oct. 1972 

Fcb.-Mar. 1990 

Jan.-Mar. 1967 

Dec. 1960 

Apr. 1990 

1953 

May-June 1990 

1953154 

1 st (singlc) 

1 st (single) 

1 st (double) 

1 st (double) 

I st (single) 

1 st (single) 

1 st (single) 

1 st (doublc) 

I st (double) 

1 st (single) 

1 st (double) 

1 st (double) 

I st (single) 

3d single) 

1 st (single) 

3d (single) 

1 st (single) 

3d (single) 

1 st (single) 

3d (single) 

where apost is the a value for the postearthquake survey, 

apre is the a value for the preearthquake survey, Si is the 

subsidence correction for the ith data point, and y is a 

parameter that depends on our confidence in the estimated 

subsidence rate. For points with a subsidence correction 

based on extensometer data, y=O.l5; for all other points, 

we assign ~0.33. 

The relative uncertainty indicates the relative importance of the elevation change at a point i with respect to 

any other point j. The uncertainty between two adjacent 

points i and i+l is given by 

where L is the survey distance between the two points (in 

kilometers). The coseismic elevation changes and their 

relative uncertainties are listed in table 3. Each bench 

mark is identified by its NGS archival reference number 

(ACRN). 

The coseismic signal available for modeling is best described by a signal-to-noise (SIN) ratio. The observed 

elevation-change signal is based on section-elevation 

changes (each section consists of two adjacent bench 

marks). The signal for the ith section, AHi, is given by the 

difference between the coseismic elevation changes of the 

two bench marks at each end, AHi=dHi+l-dHi. The total 

error, oi, for each AHi is calculated from equation 3 and is 

proportional to the square root of the survey length of the 

section and to the square root of the sum of squares of the 

uncertainties of the two observations. The SIN ratio is 

given by 

where n is the total number of sections used in the calculation (table 4). The SIN ratio is 53 for 81 percent of all 

the sections in the network (leveling routes 1, 2, 5, 7). 

The area of large signal near the epicenter has a moderate 

SIN ratio of 4 to 6, because the coseismic elevation changes 

are derived from less precise preearthquake surveys that 

have poor spatial resolution and larger uncertainty (leveling routes 3, 4, 6). The SIN ratio of the entire Loma Prieta 

leveling-data set is 3.3, despite the high quality and resolution of the 1990 surveys. In effect, the leveling routes 

around the periphery of the network receive a higher 

weight by virtue of their high precision and bench-mark 

density, whereas those in the interior of the network receive a relatively lower weight. If all the data were of 

equal precision and density, the interior routes of the network would have had much larger SIN ratios. 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A109 

OBSERVED COSEISMIC ELEVATION CHANGE 

The observed coseismic elevation changes are mapped 

in figure 4A. Maximum uplift of 550 mm occurs just to 

the northwest of the epicenter, on the west side of the San 

Andreas fault (fig. 1). Maximum subsidence of 100 mm 

occurs at both the northeast and southwest ends of the 

network. Maximum coastal uplift occurs where the bench 

marks are closest to the San Andreas fault. Along the 

northwest section of the coastline, between Santa Cruz 

(SC, fig. 1) and Point Afio Nuevo (AN, fig. 1), the observations show little or no uplift. To the east of the San 

Andreas fault, a broad 50-mm downwarp extends along 

the fault zone. 

Repeated coseismic vertical deformation may give rise 

to the observed height of the coastal marine terraces. Noting the similarity between terrace-uplift profiles and the 

vertical deformation predicted by Lisowski and others' 

(1990) coseismic model of the earthquake, Anderson 

(1990), Valensise and Ward (199 I), and Valensise (1992) 

suggested that Loma Prieta-type events, if repeated every 

300 to 600 yr, could produce the observed terrace deformation. The observed coseismic elevation changes from 

the earthquake are plotted along with the observed longterm vertical deformation of the youngest (125 ka) marine 

terrace in figure 5A. At distances greater than 25 km south 

of Point Aiio Nuevo, the two profiles are similar, although 

the terrace deformation is broader, partly because the leveling route does not everywhere coincide with the terrace's 

inner edge. Within 25 km of Point Afio Nuevo, the uplift 

recorded by the terrace is not observed coseismically. 

An alternative interpretation of the long-term uplift is 

uniform coastward tilting normal to the San Andreas fault. 

If this interpretation is correct, then the terrace heights 

would be inversely proportional to their distance from the 

fault, unrelated to parameters of the earthquake. Terrace 

height as a function of distance normal to the San Andreas fault is plotted in figure SB. Uniform tilting is seen 

to be a plausible explanation for the terrace height, except 

near the San Gregorio-Hosgri fault at Point Afio Nuevo. 

Thus, although the similarity of the coseismic deformation to the 125-ka deformation suggests that permanent 

uplift associated with dip slip on the San Andreas fault is 

recorded by the terraces, uniform regional tilting may also 

account for the terrace uplift. In both cases, discrepancies 

near the San Gregorio-Hosgri fault may be due to dip-slip 

motion on the San Gregorio-Hosgri fault or to obliquity 

Figure 3.-Schematic map of Loma Prieta region, Calif,, showing locations of leveling circuits (numbered 

loops) formed by 1990 releveling survey. Circuit misclosures computed in clockwise direction as indicated 

are listed in table 1. Leveling circuit 5 is closed by both preearthquake and postearthquake leveling. Circuit 

1 is the outer perimeter loop. 
A1 10 MAIN-SHOCK CHARACTERISTICS 

Table 2.-Leveling circuits and misclosures 

[Observed misclosure is computed in clockwise direction. Allowable misclosure is 

based on normal random error, a= J^ p. NGS, U.S. National Geodetic Survey] 

Circuit Date Circuit Observed Allowable 

(fig. 3) length misclosure misclosure 

(km) mm) (mm) 

'5 km of the preseismic loop is closed with an NGS 1972 height 

difference. 

^ased on a= 12 mrn/^km. 

of the long-term San Andreas fault slip, as proposed by 

Valensise and Ward (199 1). 

MODELING ELEVATION CHANGES 

To model the observed coseismic elevation changes, 

we constructed a series of three-dimensional models, each 

of which utilizes an elastic-half-space Earth structure and 

model faults with uniform slip. We first construct planar 

rectangular model faults and search for the model that 

best fits the observations; the data are considered to be 

independent point elevation changes. Next, we allow the 

model fault to take on listric and negatively listric shapes. 

In an additional experiment, we consider the observed 

elevation changes to be correlated and model the sectionelevation changes between adjacent bench marks. In our 

final series of models, we examine faults with alongstrike 

variations in rake. 

To assess the influence of nonhomogeneous elastic Earth 

structure, we then tested several two-dimensional boundary-element models. In these tests, we compute the vertical displacement for a set of points aligned perpendicular 

to the strike of a model thrust fault embedded in a 

nonhomogeneous elastic medium. These displacements are 

then modeled with a two-dimensional elastic half-space, 

to deduce the correction that should be applied to our 

three-dimensional-half-space results to account for 

nonhomogeneous Earth structure. These nonhomogeneouselastic-media calculations are designed to test the effects 

of a realistic Earth structure on the basis of calculated 

seismic-velocity models of the Loma Prieta region. We 

consider both a layered elastic structure and a wedgeshaped low-modulus region. 

ELASTIC-HALF-SPACE MODELS 

PLANAR ONE-RAKE MODEL 

The earthquake rupture can be described as a superposition of moment-tensor point sources buried within a uniform elastic half-space (Ward and Barrientos, 1986; 

Barrientos and others, 1987). The model-fault geometry 

and source parameters are fixed; the uniform slip is defined by a least-squares inversion. When the data are considered to be independent point elevation changes, a 

constant elevation-change offset is also determined by inversion. Because the coseismic elevation changes are independent of a datum (zero-level elevation change is 

unknown), the model must include an elevation-change 

offset that, together with the slip amplitude, best fits the 

observations (in a second approach, the need for an elevation-change offset is eliminated by constructing elevationchange differences between adjacent bench marks). The 

data are weighted by the square of the observed errors, 

oQ, which are proportional to the relative uncertainties, 

CJ,, =.&ti,, where LC is a characteristic length scale for 

the network (LC-10 km). Note that we model the elevation change of each bench mark, which is treated as independent, and there are no correlations between bench 

marks. The characteristic length scale is chosen so that 

the SIN ratio calculated both by section and by bench 

mark is the same; without the characteristic length scale, 

the magnitude of the signal is unbounded, owing to the 

arbitrary datum. 

To account for correlations in the leveling observations, 

we also model the section-elevation changes. In these 

models, differencing the coseismic elevation changes of 

adjacent bench marks eliminates the elevation-change offset, and so we invert only for the slip amplitude, with the 

section-elevation changes weighted by the square of the 

uncertainties given by equation 3. Each section has a length 

scale (the leveled distance between adjacent bench marks), 

and the characteristic network length scale LC is not required. Before inverting the section-elevation changes, we 

remove bench marks that create spikes, and sections with 

excessive tilt. Spikes, defined by adjacent sections that 

have large tilts of opposite sign, indicate a disturbed bench 

mark or leveling-observation blunder. Steps in the leveling data indicate blunders in the leveling observations and 

are characterized by individual sections'that have excessively large tilt. For spikes, the causative bench mark is 

removed, and a new section is formed by differencing the 

bench marks on either side. The magnitude of tilt that is 

used to define spikes and steps is chosen to maximize the 

percentage of signal modeled, while at the same time removing as few of the data as possible (fig. 6). 

Each model fault is described by eight fixed model parameters. The location of the model fault is designated by 

the coordinates of its upper northwest corner; the latitude, 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A1 11 

longitude, and vertical depth of this corner locate the fault 

in space. The fault area is described by an alongstrike 

length and a downdip width. The strike is defined as the 

angle measured clockwise from north, and the rake is measured on the fault surface counterclockwise from the strike 

azimuth. The dip is the acute angle between horizontal 

and the fault surface. 

Our systematic forward search of parameter space begins by finding the best-fitting planar model fault. In this 

initial phase of modeling, we make no assumptions about 

fault geometry or location, as might be derived from aftershock locations, focal mechanisms, or previous studies. 

Instead, we adopt strikes and rakes that reflect the general 

strike of the San Andreas fault in the Loma Prieta region 

and a reverse-oblique style of faulting. These and all other 

model parameters, however, are assigned large ranges in 

the initial parameter-space search. During successive parameter-space searches, these ranges are narrowed, guided 

by the values that produce the best fit to the data. 

NONPLANAR ONE-RAKE MODEL 

For curved fault shapes, one additional parameter is 

required. The downdip fault shape in cross section can be 

described by the relation x=b,z+b2z2, where x is the horizontal distance perpendicular to the fault strike in the direction of dip (Ward and Barrientos, 1986), z is the depth, 

and bl and b2 describe the cross-sectional shape of the 

fault surface: bl is the cotangent of the dip at the upper 

edge of the fault, and b2 is the fault curvature. When 

b2=0, the model fault is planar (fig. 7A); when b2>0, the 

model fault is listric (fig. 75); and when b@, the model 

fault is negatively listric, a "shoulder thrust" in geologic 

parlance (fig. 7C). We examine fault curvature over a 

narrower range of initial parameters, using our acquired 

knowledge of the best-fitting planar-fault geometry. The 

ranges of parameters tested are listed in table 5. 

TWO-RAKE MODEL 

In an additional but limited modeling run, two new 

parameters are added to the model. By introducing an 

alongstrike segmentation, we create northwestern and 

southeastern fault segments with independent rakes. Slip 

is constrained to be uniform for both segments and is 

determined by inversion. Because Beroza (1991), Steidl 

and others (1991), and Wald and others (1991) modeled 

variations in rake in their analyses of strong-motion seismic data, we test whether the leveling observations also 

constrain variations in rake. This new parametrization is 

used to determine the best rakes and relative segment 

lengths for our best-fitting planar-model geometry and for 

perturbations to it. 

ELASTIC-HALF-SPACE RESULTS 

All models are ranked according to their misfit to the 

observations. Model misfits are characterized by a reduced 

x2 term here called the misfit-to-noise (MIN) ratio, computed as 

where AH is the observed elevation change, AH is the 

calculated elevation change, o is the observed error, n is 

the number of bench marks, and Nf is the number of free 

model parameters computed from the data (N~10, planar; 

NF 1 1, curved; N+2, two-rake, because we have used 

the data to find the best values of all the parameters). For 

the section-elevation-change models, the values of AHo 

and AH refer to section-elevation changes, the observed 

error is calculated by using equation 3, and n is the number of sections modeled. If a model fits the observations 

to within the noise level of the data, then MlNa.0. Our 

best-fitting one-rake model has an MIN ratio of 1.62 for 

independent data and 1.57 for correlated data, and the 

segmented two-rake model has an MIN ratio of 1.33 for 

independent data. Because all of these models have MIN 

ratios >1.0, we have not modeled all the observed signal. 

The fit is improved by 4 percent when the data are treated 

as correlated observations, as indicated by the percentage 

of signal modeled. knaddttir and others (1992) also found 

solutions for both correlated and independent data similar 

to our models, but the misfits they reported are larger. We 

calculate an MIN ratio of 1.6 1 for ~rnaddttir and others' 

best model. Our use of the characteristic length scale, 

when modeling the data as independent observations, properly scales that problem, and so we obtain MIN ratios 

comparable to those in the models with correlated data. 

Because we have removed spikes and steps from the data 

before modeling the section-elevation changes, the data 

set that we invert may differ slightly from that of knaddttir 

and others. We have also removed the adjustment (see 

app. 1) to the third-order USGS data for the section-elevation-change models. 

Parameter values and inversion results for the best-fitting planar, listric, and negatively listric model faults, the 

two-rake model fault, and the section-elevation-change 

models are listed in table 6. The uncertainties shown for 

the slip and moment are derived from the inversion and 

depend on the weighted rms residuals. Each one-rake fault 

fits the data equally well (1.575MlN51.67) and produces 

a similar moment release. With independent data, the tworake model fault significantly improves the fit and greatly 

reduces the magnitudes of slip and moment. With correlated data, the two-rake model fault does not improve the 
MAIN-SHOCK CHARACTERISTICS 

Table 3.-Coseismic elevation changes along leveling routes 

[See inset, figure 1, for locations of leveling routes. ACRN, U.S. National Geodetic Survey archival reference number. A constant can be freely added to all elevationchange observations. Note that duplicate bench marks are listed at overlapping end points of leveling routes] 

Coseismic Relative 

AcRN Latitude Longitude elevation uncertainty, 

(km) ON. OW. change 8i 

(mm) (mm) 

Coseismic Relative 

AcBN ffiz Latitude Longitude elevation uncertainty, 

(km) ON. OW. change 5i 

mm) (mm) 

Leveling route 1 Leveling route 1-Continued 

GU2172 68.187 36.9172 121.5467 5.5 4.0 

GU2171 68.274 36.9172 121.5467 -6.3 4.0 

GU2167 69.904 36.9042 121 5553 -27.7 4.0 

GU2154 71.743 36.8878 121.5567 -39.2 4.0 

GU2151 72.394 36.8825 121.5600 -42.3 4.0 

GU4097 74.431 36.8922 121.5742 -21.4 4.0 

Leveling route 2 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY 

Table 3.-Coseismic elevation changes along leveling routes-continued 

Table 4.-Signal-to-noise ratios along leveling routes 

Coseismic Relative 

Latitude Longitude elevation uncertaltlty, 

(km) ON. OW. change 8i 

(mm) (mm) 

Leveling route 3 

Leveling route 4 

Leveling route 5 

HS5281 0.000 37.068 1 121.6589 -62.2 7.0 

HS5283 2.786 37.0453 121.6519 -48.2 7.0 

HS5285 7.981 37.0108 121.6619 -35.8 7.0 

GU4175 15.066 36.9972 121.7167 -5.4 7.0 

GU4177 16.759 36.9861 121.7169 39.3 7.0 

GU4185 25.263 36.9353 121.7422 -60.3 7.0 

GU2278 48.142 36.9758 121.8975 165.0 7.0 

Leveling route 6 

Leveling route 7 

Signal-to-noise 

ratio 

fit to the observations but can provide an equally good fit 

with 13 percent less moment. Each model fault is about 

34 km long, stretching over just half the length of the 

aftershock zone of October 1989. The fault strikes 127'- 

129O, similar to the aftershock zone (Dietz and Ellsworth, 

1990), and approximately parallels the Santa Cruz Mountains section of the San Andreas fault. The depth of burial 

of the upper edge of each fault surface is 4 to 5 km; 

deeper faults are preferred when modeling with correlated 

data. The planar model fault dips 60Â° approximately the 

average dip of each of the nonplanar model faults; with 

correlated data, the faults dip slightly steeper. With independent data, the model faults lie above and to the west of 

the main-shock hypocenter and aftershocks, whereas with 

correlated data they lie at the west edge of the aftershock 

zone but still do not intersect the hypocenter. The closest 

distance between any typical good-fitting model fault and 

the main-shock hypocenter is 6 km. Contours of observed, 

predicted, and residual (observed minus predicted) elevation changes are mapped in figure 4 for the best-fitting 

planar one-rake model fault with independent data. Profiles of the elevation changes for the one- and two-rake 

model faults are plotted along with the observations in 

figures 8A and SB, respectively. In five places, notable 

misfits are visible in the one-rake model: (1) at the Sargent 

fault crossing on leveling route 1 (inset, fig. I), (2) near 

the San Andreas fault crossing on leveling route 2, (3) in 

the center of leveling route 3, (4) near the Sargent fault 

on leveling route 6, and (5) near the Sargent fault on 

leveling route 4. These misfits may occur where 

nontectonic or secondary deformation has disturbed the 

bench marks. If, for example, we remove a small fraction 

(13 percent) of the bench marks in the network at sites 

where notable misfits to our best model fault occur, then 

the MIN ratio is reduced to 1.13 for the one-rake planar 

model fault. The two-rake model fault, however, explains 

the misfits on leveling routes 2 and 6. 

To examine the variation in our best parameter values 

and the inversion results with independent data, we select 

an acceptable range of MIN ratios above the minimums 
A1 14 MAIN-SHOCK CHARACTERISTICS 

for the one-rake planar, listric, and negatively listric model 

faults. The acceptable ranges in the fixed parameters and 

the corresponding inversion results for each model fault 

at an MIN ratio of the best value plus 5 percent are listed 

in table 7. Depth of burial is well constrained between 4- 

and 6-km depth. Strike is constrained to a 5' range that at 

its upper bound includes the strike of the observed aftershock locations. For planar model faults, acceptable dips 

vary only slightly, whereas for nonplanar model faults, 

the dip of the upper edge of the rupture surface is not well 

constrained. Our results do not indicate a preference between planar and nonplanar model faults within the range 

of curvatures tested. The inversion results indicate a consistent determination of the moment release, whereas slip 

amplitude varies by a factor of as much as 2. Because the 

geodetic moment is proportional to the product of the 

fault area and the slip amplitude (Mo=pAs, where p is the 

elastic rigidity, A is the fault area, and s is the average 

slip amplitude), models with similar moment release and 

fault length exhibit a tradeoff between slip amplitude and 

fault width. The distance between the fault surface and 

the hypocenter is consistently greater than 4 km. The bestfitting faults do not pass through the main-shock hypocenter. The best-fitting model fault that passes within 1 

km of the main shock is listric and has an MIN ratio of 

2.54, whereas the best-fitting one-rake model fault has an 

MIN ratio of 1.6 1. Results of the section-elevation-change 

models, though within 5 percent of the MIN ratio for models with independent data, are omitted from table 5 and 

indicate somewhat different parameter values. We note 

that model discrimination is weaker, and the acceptable 

range of parameters values is larger, with correlated data. 

Use of a two-rake model fault significantly improves 

the fit by reducing the MIN ratio from 1.61 to 1.33 with 

independent data. Although we have added two new degrees of freedom to the model, the improvement in fit is 

significant above the 99-percent-confidence level. We follow the method of Barrientos and others (1987, 1989) to 

analyze the significance of this improvement in fit. The 

geometry of the two-rake model fault changes only slightly 

from that of the one-rake model fault: The dip is slightly 

greater at 62', the depth of burial is 4.5 km, and the 

Figure 4.-Schematic map of Loma Prieta region, Calif., showing contours of observed (A), predicted (B), 

and residual (C) (observed minus predicted) coseismic elevation change. Predicted and residual elevation 

changes for one-rake planar model fault are listed in table 4. Star, epicenter of Loma Prieta earthquake of 

October 17, 1989 (M=7.1); triangle, Loma Prieta; dots, bench marks. Map in figure 4C was constructed by 

contouring residual elevation changes, not by subtracting predicted from observed contours. Residual and 

observed contours are valid only where they are adjacent to bench marks. Contour intervals: 50 mm (figs. 

4A, 4B), 20 rnrn (fig. 4C; shaded where positive). 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A1 15 

I I \ I I I 

Figure 4.-Continued 

Figure 4.-Continued 
A1 16 MAIN-SHOCK CHARACTERISTICS 

length is 37 km. The segment lengths are equal (18.5 km 

each) and have rakes of 116' in the northwest and 163' in 

the southeast, similar to the average rake values determined from modeling of strong-motion data (115' NW., 

156' SE.; Steidl and others, 1991). The two-rake model 

fault is illustrated in figure 9. With correlated data, the 

best two-rake model fits the data no better than the onerake model. We prefer the two-rake model because it produces the same data misfit with a lower moment-it is a 

more efficient source. Furthermore, the greater width of 

the two-rake model fault is more consistent with the spatial extent of the aftershock zone. In comparison with the 

two-rake model with independent data, the variation in 

rake is subtle (13') for the section-elevation-change model. 

A still more efficient source is obtained if we use the tworake model with independent data to model the sectionelevation changes; then, the MIN ratio is 1.64, and the 

seismic moment is 1.8~10~~ N-m. 

0 10 2 0 Ow 40 

DISTANCE FROM POINT AN0 NUEVO, 

IN KILOMETERS 

DISTANCE NORMAL TO THE SAN ANDREAS FAULT, 

IN KILOMETERS 

Figure 5.-Marine-terrace deformation. A, Profiles of coseismic (circles) 

and long-term (shaded curve) coastal deformation; long-term deformation is derived from 125-ka marine terrace. Profile is projected along lat 

N. 115' E. from Point Aiio Nuevo. Note that leveling route does not 

everywhere coincide with inner edge of terrace (see fig. 1) B, Terrace 

elevation as a function of perpendicular distance from the San Andreas 

fault. Dashed line shows linear fit to data, excluding first seven data 

points. 

SENSITIVITY OF RESULTS TO DATA 

DISTRIBUTION 

Because peak-elevation changes are measured on few 

bench marks and are derived from third-order 

preearthquake levelings (route 4, inset, fig. l), we examine how these data influence the goodness of fit of onerake models with independent data. When we remove 

leveling route 4, our best-fitting planar-fault geometry 

z - 1000 

0 50 100 150 200 

SECTION 

-100 -50 0 50 100 

TILT. IN MICRORADIANS 

0 50 100 150 200 

SECTION 

-40 -20 0 20 4 0 60 

TILT, IN MICRORADIANS 

Figure 6.-Coseismic section-elevation changes, showing tilt by section 

(upper plot) and histogram of tilt populations (lower plot). A, Entire data 

set. Tilt population: standard deviation, 8 microradians; mean, -1 

microradian. B, Data set with four bench marks with spikes greater than 

40 microradians and eight sections with steps greater than 70 microradians 

omitted. Tilt population: standard deviation, 7 microradians; mean, -2 

microradians. Tilt limits: spikes, 40 microradians; steps, 70 microradians. 

Note that tilt limits are 5 and 9 times the original standard deviation, 

respectively, and that only 5 percent of data are omitted. 
ELEV'ATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A1 17 

(table 6) gives the same MIN ratio as with all the data, 

indicating that the best-model selection is insensitive to 

these data. 

If all third-order leveling and data with large subsidence corrections are removed (leveling routes 3-7, inset, 

fig. I), the precise first-order surveys (leveling routes 1, 

2) that circumscribe the aftershock zone remain. Using 

only these observations increases the acceptable range of 

fault parameters. The best-fitting planar one-rake model 

obtained using all the data (table 6), however, remains 

among the best-fitting models. Marginally better fits can 

be obtained by changing the fault geometry as follows: 

length, <34 km; width, <9 km; strike, <12g0; dip, >50Â° 

and rake, >145O; however, these faults are displaced still 

farther to the southwest of the aftershock zone. Faults 

20 I * I I 

10 0 -10 

DISTANCE. IN KILOMETERS 

Figure 7.-Profiles of model faults: (A) planar, (B) 

listric, and (Q negatively listric. In figure 7A, maximum and minimum dips are shown; in figures 75 and 

7C, maximum and minimum curvatures are shown. 

Dip of upper edge of fault is 85' in figure 7B and 45' 

in figure 7C. Downdip fault widths are arbitrary. Star, 

location of hypocenter relative to strikeline. 

with a width >10 km, a strike >130Â° a dip <50Â° a rake 

<140Â° and a depth <5 km are precluded when only leveling routes 1 and 2 are used. Thus, the less precise data 

from the interior of the network do not dictate the modeling results, although including them limits the range of 

acceptable models. 

If the model fault is restricted to lie within the aftershock zone, a substantial misfit results. Translating the 

best-fitting fault perpendicular to strike 2 km to the northeast, and increasing the dip to 65' and the downdip width 

to 13 km, so that the fault approximately coincides with 

the aftershock zone and the main-shock hypocenter, the 

minimum MIN ratio we obtain is 3.01, representing an 86- 

percent increase in the average misfit relative to our bestfitting fault. Increasing the fault dip from 60' through 

65'-70' produces large misfits adjacent to the east side of 

the San Andreas fault, resulting from excessively large 

subsidence (leveling routes 3-6, inset, fig. 1). Increasing 

the downdip width of the fault produces too much deformation in the far field at any of the three dips tested, too 

much uplift along the coast (leveling route 2), and too 

much subsidence inland (leveling route 1); in addition, 

the peak uplift along leveling route 4 cannot be modeled 

with a wider fault. 

The section-elevation-change models place nearly all 

weight on the leveling routes at the periphery of the network, owing to the high bench-mark density; the interior 

leveling routes receive less weight because the section 

lengths are longer than those of the exterior leveling routes 

(see eq. 3). For section-elevation changes, the exterior 

data have 50 times the weight of the interior data, whereas 

with independent elevation changes, the exterior data have 

17 times the weight of the interior data. The fact that 

wider variation in parameter values is acceptable for the 

section-elevation-change models stems from the absence 

of constraints furnished by the large signal of the interior 

data, consistent with results of the data-sensitivity tests. 

NONHOMOGENEOUS ELASTIC MODELS 

Next, we examine the systematic bias inherent in the 

use of an elastic half-space in place of more realistic Earth 

structure. Eberhart-Phillips and others (1990) demonstrated 

a marked velocity gradient with depth in the southern 

Santa Cruz Mountains: Seismic P-wave velocities range 

from 3.2 to 5.6 kmls in the uppermost 3 to 5 km, increasing to 6.5 to 6.8 kmls below 10- to 15-km depth. Reches 

and Zoback (1990) argued that strain is concentrated in 

the low-modulus (low velocity) layer. To test whether the 

modulus contrast caused by the velocity and associated 

rock-density gradient influences the deduced fault geometry and slip, we carry out a suite of simple boundaryelement tests. 
MAIN-SHOCK CHARACTERISTICS 

Table 5.-Ranges of parameters of one-rake model faults 

[Dip on nonplanar faults is for upper edge of fault surface. Latitude and longitude are for vertical projection onto the Earth's 

surface of northwest corner of upper edge of fault surface. Strike is measured clockwise from north. Rake is measured on 

fault surface counterclockwise from strike azimuth. Downdip fault shape is described by the relation x=b,z+b2z2, where x is 

the horizontal distance perpendicular to strike in the direction of dip and z is the depth] 

Parameter Planar fault Listric fault Negatively listric fault 

Number of models 

computed. 

Table 6.-Best-fitting uniform-elastic-half-space models 

[Length is measured along strike. Width is measured downdip. Latitude and longitude are for vertical projection onto the Earth's surface of northwest corner of upper edge 

of fault surface. Depth is to upper edge of fault surface. Strike is measured clockwise from north. Rake is measured on fault surface counterclockwise from strike azimuth. 

Downdip fault shape is described by the relation x=b1z+b2z2, where x is the horizontal distance perpendicular to strike in the direction of dip and z is the depth. Distance to 

hypocenter is closest approach between fault surface and hypocentral location of Dietz and Ellsworth (1990). Geodetic moment is based on shear modulus p=3.23x101Â Pa] 

Fixed parameters Inversion results 

Dip, Dip, Distance 

Fault Length Width upper lower Latitude Longitude Depth Strike Rake Â¥b to Slip Geodetic MIN 

style (km) (km) edge edge (ON.) (OW.) (km) (Â¡ 0 (km-') hypocenter (m) GG ratio 

(O) (Â¡ (km) 

Independent data 

Planar ---------- 34 9 60 60 37.161 122.013 4 128 145 0.000 6 2.9kO. 1 2.9kO. 1 1.62 

Listric ---------- 34 11 75 45 37.159 122.014 4 127 143 040 5 2.4k0. 1 2.9kO. 1 1.67 

Negatively 34 6 51 72 37.159 122.021 5 127 142 -.045 8 4.3k0.1 2.8k0.1 1.61 

listric. 

Two-rake '37 9 62 62 37.164 122.014 4.5 128 2116/163 ,000 6 2.1k0.1 2.2k0.1 1.33 

planar. 

Correlated data 

Planar ---------- 3 1 4 66 66 37.136 121.971 7 129 155 0.000 7 7.4k0.4 3.0k0.2 1.57 

Two-rake 32 7 64 64 37.140 121.972 6 129 2144/157 .OOO 6 3.6k0.2 2.6k0.2 1.57 

planar. 

'Two-rake fault is segmented halfway along strike; each segment is 18.5 krn long. 

^irst rake value applies to northwest segment, and second to southeast segment. 

LAYERED MODEL across the layer interface. Taking a 5-km-thick layer velocity of 4 km/s and a density of 2,700 kg/m3, with an 

We conducted three experiments to assess the effects of underlying-half-space velocity of 6.7 kmls and a density 

the modulus contrast at Loma Prieta. In the first experi- of 3,000 kg/m3, yields a contrast in Young's modulus, E, 

ment, we considered a dip-slip fault of infinite length along between the half-space and the layer of 3 (3.6~10~~ Pa 

strike embedded in a layer over a half-space, using the above and 11.2~10~~ Pa below). Poisson's ratio is 0.25 in 

boundary-element program of King and Ellis (1990). Shear both the layer and the underlying half-space. In our test, 

and normal stresses were prescribed to be continuous we used a contrast in Young's modulus of 5 to examine 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A1 19 

the maximum possible effects of the weak layer. Uniform 

slip was imposed on a 65"-dipping fault extending from 

6- to 18-lun depth. The vertical deformation calculated 

for this model was then inverted, assuming a uniform halfspace. 

WEDGE MODEL 

In the second experiment, we replaced the low-modulus layer with a wedge extending from the San Andreas 

fault 10 km to the west and extending vertically from the 

surface to a depth of 7 km, (see Eberhart-Phillips and 

Stuart, 1992). The wedge exaggerates the observed acrossfault modulus contrast, particularly near the surface, and 

thus furnishes an upper-bound case to assess how 

nonhomogeneous Earth models affect the fault parameters. 

Both the layer and wedge models are approximations to 

features observed in Eberhart-Phillips and others' (1990) 

seismic-velocity model. Young's modulus in the wedge is 

3.5x101Â Pa, and in the surrounding medium 8.8x101Â Pa, 

for a contrast of 2.5. Note that the fault contacts the wedge 

at a depth of 5 to 7 km (fig. loÂ£) Poisson's ratio within 

the wedge is 0.333, and in the surrounding medium 0.258. 

In the third experiment, we retained the wedge geometry but imposed a uniform shear-stress drop on the fault, 

rather than uniform fault slip. This condition, also used 

by Eberhart-Phillips and Stuart (1992), results in tapered 

slip. For an elastic half-space, the condition produces maximum slip at the center of the fault; in the wedge model, 

DISTANCE, IN KILOMETERS 

Figure 8.-Profiles of best one-rake (A) and two-rake (B) planar model faults and observed coseismic 

elevation changes along leveling routes 1 through 7 (see inset, fig. 1). Vertical bars indicate relative uncertainty of determinations; note that relative uncertainties are large where substantial subsidence corrections 

have been made (for example, profile 3). Arrows indicate locations where notable misfits occur; note that 

misfits are substantially reduced for two-rake model fault (fig. 8B). 
A120 MAIN-SHOCK CHARACTERISTICS 

slip is concentrated near the top of the fault because the 

wedge is more compliant than its surroundings. 

MODIFICATIONS TO HALF-SPACE MODELS 

Models with a nonhomogeneous elastic structure reduce the misfit of the geodetic fault plane to the aftershock zone and main-shock hypocenter. In the layered 

model, the location of the upper edge of the fault, its dip, 

and the slip amplitude are nearly unaffected by the lowmodulus layer. The upper edge of the fault, however, locates 1 km too shallow, and the lower depth is as much as 

2.3 km too shallow. Thus, if a contrast in Young's modulus of as much as 5 is appropriate for Loma Prieta, then 

faults would extend 2 to 3 km deeper and be slightly 

steeper than those deduced by half-space models. Inclusion of the low-modulus layer therefore moves faults several kilometers closer to the main-shock hypocenter than 

do half-space models (compare figs. 105, 10D). 

Similarly, imposing uniform slip on the fault in the 

wedge model results in the fault locating 1 km to the east 

of its former position, and the fault width increases by 

several kilometers. With the uniform-shear-stress wedge 

model, the fault again is found to locate 1 km farther east 

than for a half-space; in addition, the fault width is found 

to increase by 4 to 5 km, the slip is reduced by 25 to 30 

percent, and the dip may increase slightly (4'). The effect of these changes is shown in figure 10E. The fault 

lies closer to the aftershock zone and main-shock hypocenter, although the locations of the fault and aftershocks 

do not coincide. The improvements in fit to the aftershock 

zone gained by considering a nonhomogeneous structure 

are illustrated in figure 11, which also shows the dependence of the fit on hypocentral distance for elastic-halfspace planar model faults. 

DISTANCE, IN KILOMETERS 

Figure 8.-Continued 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A121 

Table 7.-Ranges of parameters for uniform-elastic-half-space models 

[Dip on nonplanar faults is for upper edge of fault surface. Latitude and longitude are for vertical projection onto the Earth's 

surface of northwest corner of upper edge of fault surface. Strike is measured clockwise from north. Rake is measured on 

fault surface counterclockwise from strike azimuth. Downdip fault shape is described by the relation x=b,~+b$~, where x is 

the horizontal distance perpendicular to strike in the direction of dip and z is the depth. Geodetic moment is based on shear 

modulus p=3.23x101Â Pa] 

Fixed parameter Planar fault Listric fault Negatively listric fault 

Number of models ------ 64 1 

Inversion results 

Distance to 5-7 4+7 6-43 

hypocenter (km). Slip (m) ------------------ 2.3+3.0 2.1 +4.2 2.544.6 

Geodetic moment 2.6-3.0 2.643.4 2.6j3.1 

(lo^ N-m). M/N ratio ----------------- 1.62-1.70 1.67j1.75 1.6141.69 

Although all non-half-space models move the fault uniform-slip model because the increased fault width is 

closer to the aftershock zone, none moves it far enough, compensated by the decreased slip. The top of the fault 

and so we have made the modulus contrast as large as surface undergoes increased slip in the presence of the 

permitted by the velocity data of Eberhart-Phillips and more compliant wedge under the uniform-shear-stress-drop 

others (1990). We note that the uniforrn-shear-stress-drop assumption, a plausible result for an individual earthquake. 

model produces about the same geodetic moment as the Over many earthquake cycles, however, uniform slip from 

NW DISTANCE, IN KILOMETERS SE 

0 10 20 30 40 50 60 

- 

z EXPLANATION - 

IQ: 20 X < 4.0 

Rake, 116' M7.1 Rake, 163' < 5.0 - LJ 

Figure 9.-Alongstrike cross section of two-rake model fault from southwest side. Arrowheads indicate slip 

direction of hanging-wall block. Stars, main shock and largest aftershock. Fault motion is primarily dip slip 

to northwest of hypocenter and primarily strike slip to southeast of hypocenter. 
A122 MAIN-SHOCK CHARACTERISTICS 

the Earth's surface to the base of the seismogenic layer 

must prevail, and so it is unclear which assumption best 

represents the Loma Prieta rupture. 

DISCUSSION 

COMPARISON OF GEODETIC RESULTS 

WITH STUDIES OF SEISMICITY AND GEOLOGY 

The seismic-source mechanism and waveforms of the 

1989 Loma Prieta earthquake appear to have simple characteristics, in comparison with those of other earthquakes 

of similar magnitude, such as the 1988 M=6.7 Armenia 

earthquake (Kanamori and Satake, 1990). Nevertheless, 

seismologic studies of the Loma Prieta mechanism suggest a range of source parameters, some of which are 

compatible with our geodetic results. The source mechanisms found in 10 such studies are compared with the 

results of our elastic-half-space modeling with independent data in table 8. Four of these studies provide estimates of the strike, dip, and rake that fall within our 

acceptable model range: the first-motion mechanisms of 

Plafker and Galloway (1989) and Oppenheimer (1990), 

and the body-wave inversions of Choy and Boatwright 

(1990) and Langston and others (1990). Of the 10 studies, 

5 report a fault dip and seismic moment consistent with 

our acceptable model range, and most of the studies agree 

with our values of strike and rake. The seismologic determination of the source dip, however, is least consistent 

with our results. The 10 studies report dips ranging from 

53' to 85', and several studies have solutions with dips 

>70Â¡ a value that produces significant misfits to the leveling observations. Seismic values of the fault rake, which 

range from 110' to 155', also exceed our acceptable model 

range. Seismic moments derived from surface-wave analyFigure 10.-Schematic map (A) and cross sections (B-F) of Loma Prieta region, Calif., showing locations of 

aftershocks of M23 (Dietz and Ellsworth, 1990) and vertical projection of best-fitting planar model fault 

(shaded rectangle). Dotted line, updip projection. Quaternary faults (dashed where inferred) from Jennings 

(1975). Cross sections C-C' (figs. 10B-10E) show updip projection of fault surface (dotted line) and locations of the San Andreas (SA) and Sargent (S) faults. B, Results for elastic-half-space two-rake model fault 

with independent data. C, Results for elastic-half-space two-rake model fault with correlated data: D, Corrections for low-modulus layer (shaded area) over half-space. El, E2, Young's modulus. E, Corrections for 

low-modulus wedge (shaded area) in half-space. El, E2, Young's modulus. F, Alongstrike projection of fault 

surface. Bold rectangle, elastic half-space;. dotted rectangle, layer over half-space; long-dashed rectangle, 

wedge in half-space; short-short-long-dashed rectangle, model fault with correlated data. 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A123 

ses (Romanowicz and Lyon-Caen, 1990; Zhang and Lay, 

1990) and from the body-wave solutions of Barker and 

Salzberg (1990), NfibElek (1990), and Kanamori and Satake 

(1990), however, agree with the calculated geodetic moment. Seismic moments derived from data at different frequencies and from different studies vary by a factor of as 

much as 2. 

The consistency between the seismic and geodetic results can be addressed further by examining the spatial 

DISTANCE, IN KILOMETERS 

C' SAS c' c SAS cf 

0 101 1 20 0 101 1 20 

0 1 I I *I 1 I I 1 

m 

Main shock Main shock LA 

20 [- Main shock 1 1 Main shock 1 

Figure 10.-Continued 

relation between the geodetically determined fault surface 

and the main shock and its aftershocks. Dietz and Ellsworth 

(1990) found that the aftershock distribution is approximately planar, extending upward from the main-shock 

hypocenter along a 65"-dipping zone that is 4 to 5 km 

wide perpendicular to strike. Along strike, Loma Prieta 

aftershocks tend to cluster around the periphery of a central zone that is depleted of aftershocks. The observed 

vertical-deformation field is best modeled by a rupture 

surface approximately parallel to and southwest of the 

aftershock zone, with a homogeneous elastic Earth structure and independent data. Correlated data reduce this discrepancy and place the fault closer to the aftershock zone. 

Models that lie within the aftershock zone increase the 

misfit to the correlated observations by 3 percent. Our 

models of nonhomogeneous elastic structure also suggest 

a significant reduction of the misfit of the geodetic fault 

plane to the aftershock zone and main-shock hypocenter. 

Our best-fitting planar model faults are mapped in figure 

10, with aftershocks of M23 from Dietz and Ellsworth 

(1990). In map view, the epicenter nearly bisects the fault 

plane along strike, consistent with bilateral rupture as 

modeled by Beroza (199 I), Steidl and others (199 I), and 

Wald and others (1991). The updip projection of the model 

fault surface at its northwest terminus coincides with the 

trace of the San Andreas fault; at its southeast end, the 

updip projection is equidistant between the Sargent and 

San Andreas faults. Most aftershock activity is clustered 

approximately 4 to 5 km northeast and below our elastichalf-space model fault (fig. 105). Including correlations 

in the leveling data or nonhomogeneous elastic structure 

improves the fit to the aftershocks, as shown in figures 

10C through 10F. Our acceptable range of latitudes and 

longitudes allows the elastic model fault to move less 

than 2 krn perpendicular to strike, and the results of our 

nonhomogeneous tests indicate that the half-space solutions may shift the fault plane 1 krn perpendicular to strike. 

A A ' ) 

DISTANCE, IN KILOMETERS 

0 10 20 30 40 50 6'0 

M7.1 

Main shock 

Magnitude 

X < 4.0 

x < 5.0 

Figure 10.Ã‘Continue 
A124 MAIN-SHOCK CHARACTERISTICS 

Thus, if our two-dimensional nonhomogeneous models are 

appropriate for the Loma Prieta region, then the combined 

results indicate that the discrepancy between the position 

of the geodetic fault plane and the aftershock zone is small 

(-1 km). In modeling with correlated data, this discrepancy becomes insignificant. 

Studies of teleseismic body waves place centroidal 

depths between 8 and 16 krn, shallower than the mainshock hypocenter, which is presumably the depth of rupture initiation (table 8). These teleseismic studies generally 

only weakly constrain the spatial extent of significant slip 

on the fault plane. Modeling of local strong-motion seismic data provides better resolution, and these studies suggest that moment release is concentrated in two zones 

lying between about 9- and 16-km depth (Beroza, 1991; 

Steidl and others, 1991; Wald and others, 1991). The location of the rupture surface, as constrained by vertical 

geodetic data and corrections for nonhomogeneous elastic 

structures, suggests that significant moment release occurred from 6- to 18-km depth, moderately consistent with 

these interpretations of the strong-motion data. 

Focal mechanisms of aftershocks are diverse over short 

spatial scales. Oppenheimer (1990) presented focal mechanisms for a representative sample of aftershocks; the variations in and distinctness of the aftershock mechanisms, in 

comparison with the main-shock mechanism, could mean 

that the aftershocks occurred on structures adjacent to the 

main-shock rupture surface. The misfit of our model faults 

to the aftershock zone, however, could also be due to 

unmodeled three-dimensional variations in elastic modulus or to greater variations in fault geometry or slip distribution. Inaccurate velocity models used to locate the 

aftershocks might also explain part of this misfit. 

The oblique slip inferred from geodetic observations is 

consistent with the abundance of young (Pliocene-Quaternary) fold structures and reverse faults identified throughout the Santa Cruz Mountains. The Loma Prieta rupture 

occurred within a structural domain, bounded by the San 

Gregorio-Hosgri fault in the west, the Ben Lomond, 

Zayante, and Vergeles faults in the southwest, and a discontinuous series of faults east of the San Andreas fault 

(Aydin and Page, 1984) that is characterized by southwest-dipping faults and northwest-trending folds. At the 

surface, the fault features indicate both strike-slip and reverse displacements. The surface projection of model faults 

compatible with the vertical geodetic data could match 

either the Sargent or the San Andreas fault. 

RELATION TO OTHER GEODETIC STUDIES 

A geodetic model (Lisowski and others, 1990) derived 

from precise electronic distance measurement (EDM), Global Positioning System (GPS) vectors, and very long 

baseline interferometry (VLBI) observations is not fully 

consistent with our best-fitting model fault (table 8). 

Lisowski and others modeled the offsets in the relative 

positions of geodetic stations, using an elastic dislocation, 

and determined the source mechanism: strike, 136'; dip, 

70'; rake, 144'; geodetic moment, 3.0x1019 N-m. The 

rake and moment of their solution are consistent with our 

results, whereas the strike and dip do not fall within our 

acceptable model range. Their model has a strike slightly 

different from that of the aftershock zone, producing a 

close fit to the aftershocks in the northwest but a misfit of 

about 2 krn in the southeast. Although their model agrees 

better with the locations of aftershocks, it has an MIN 

ratio of 2.4 (twice as large as that of our best fitting model) 

when used to model the coseismic elevation changes. Likewise, our model doubles the average misfit of their obserLow-modulus - 

layer Two-rake 

1 i - model 

- 

0 1 2 3 4 5 6 7 8 

DISTANCE TO HYPOCENTER, IN KILOMETERS 

Figure 11.- isf fit-td-noise ratio for one-rake (shaded area) and two-rake (black area) planar model faults 

versus distance to h pocenter. Best-fitting faults are those with smallest misfit-to-noise ratio and a correspending hypocentral distance ? of 6 km. Two-rake model substantially reduces misfit of elevation change. 

Low-modulus layer and wedge reduce misfit of model fault surface to aftershock zone, 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A125 

Table 8.-Comparison of fault parameters from seismologic studies with the results of our elastic-half-space modeling 

[Boldface values are consistent with our ranges of model parameters listed at bottom. Strike is measured clockwise from north. Rake is measured on fault surface 

counterclockwise from strike azimuth. Depth from P-wave first-motion data is depth to rupture initiation; depth from body-wave data is average depth; and depth from 

body- and surface-wave data is centroidal depth, using a 4-krn radius. Do., ditto] 

Strike Dip 

(O) (O) 

Type of data Reference 

P-wave first motions ----------- Oppenheimer (1 990). do .......................... Plafker and Galloway (1989). 

~od~ waves ..................... Barker and Salzberg (1990). 

do .------------------------- Choy and Boatwright (1990). 

do .......................... Langston and others (1 990). 

do .......................... Nabelek (1 990). 

do .......................... Romanowicz and Lyon-Caen (1990). 

do .......................... Ruff and Tichelaar (1 990). 

Body and surface waves------- Kanamori and Satake (1990). Surface waves ------------------ Romanowicz and Lyon-Caen (1990). 

do .................... --- --- Zhang and Lay (1990). 

Horizontal deformation-------- Lisowski and others (1 990). 

Vertical deformation This study. (elastic half-space). 

vations. Future studies that combine both geodetic data 

sets are needed to find the fault geometry and source 

mechanism that are most consistent with all the observations. 

CONCLUSION 

Observations of coseismic elevation changes associated 

with the 1989 Loma Prieta earthquake favor a rupture 

surface extending from 6- to 12-km depth, dipping 64'. 

With a geodetic moment of 2.6x1019 N-m, slip direction 

on this rupture surface ranges in rake from 144' northwest of the epicenter to 157' southeast of the epicenter, 

with a slip amplitude of 3.6 m. A two-rake model fault 

produces the same fit to the observations as a one-rake 

model fault, with 13 percent less moment. Thus, the tworake model fault is a more efficient source of surface 

deformation and, in our judgment, more probable. With 

independent data, two-rake models with a rake variation 

greater than 40' can be found that offer smaller model 

misfit and less moment. 

The rupture surface determined by our half-space modeling lies 1 to 2 krn southwest of most aftershocks and is 

6 km from the main-shock hypocenter. With independent 

data, preferred model faults lie still farther away from the 

aftershock zone, whereas with correlated data, faults can 

be found within the aftershock zone that produce only a 

few-percent increase in model misfit. 

The strength of the section-elevation-change modeling 

is that the correlation of the leveling observations is incorporated into the analysis. Although the section-elevation-change modeling is more sensitive to outliers (such 

as spikes and steps), we have found that these features 

can be objectively purged. The weakness of the sectionelevation-change modeling stems from the uniquely inhomogeneous distribution of the Loma Prieta data set, in 

which most of the signal is contained in a few long sections in the interior of the network. Although the influence of these sections is modest with independent data, it 

is almost nonexistent in the section-elevation-change modeling. Thus, most of the signal we seek to explain with 

the section-elevation-change modeling has no influence 

on model selection, and our ability to discriminate among 

candidate model faults is greatly diminished. 

Two-dimensional models with nonhomogeneous elastic 

structure reduce the misfit between the geodetic fault plane 

and the aftershock zone, suggesting that more complex 

(three dimensional) models of the modulus structure of 

the crust might bring the geodetic and seismic observations into even-better accord. Using a low-modulus layer 

or wedge model instead of a uniform half-space also deepens and steepens the fault. 

The connection between the Loma Prieta rupture surface at depth and the known faults mapped at the Earth's 

surface remains unclear. Because both listric and negatively listric faults are permitted by the vertical geodetic 

data, a connection can be inferred to either the San Andreas or the Sargent fault. Further study of the localized 

anomalous elevation changes seen in some of the leveling 

data, along with observations of surface displacements 

northeast of the San Andreas fault (Haugerud and Ellen, 
A 126 MAIN-SHOCK CHARACTERISTICS 

1990), may provide the necessary evidence to infer a connection to shallow surface faults. 

ACKNOWLEDGMENTS 

All of the postearthquake leveling was funded by the 

USGS, NGS, and Santa Cruz County Public Works Department. We thank the NGS leveling crew, including Richard Hattesohl, Leonard Bergman, Don Breidenbach, Jim 

Palo, Scott Hanford, Chris Jacobs, and Verland Pierson, 

for their expertise in performing a careful and timely leveling job and in releveling after the earthquake. Emery 

Balazs helped to define and organize the leveling project 

at the NGS. Gary Perasso provided field-summary books 

and helpful discussions on the USGS leveling data. Kim 

Vester provided access to and information about Santa 

Cruz County leveling data. Accurate subsidence corrections could not have been made without the depth-to-water and extensometer data provided by the Santa Clara 

Valley Water Conservation District, with the assistance of 

Adele Sheperd and Lauren Mall. Robert Johnson of the 

Monterey County Flood Control and Water Conservation 

District supplied additional depth-to-water data for 

Monterey County. We greatly appreciate the guidance and 

encouragement of Wayne Thatcher and the contributions 

of Geoffrey C.P. King and Jian Lin in creating and testing, respectively, the boundary-element program, and the 

generosity of Donna Eberhart-Phillips for sharing her finite-element results with us. Thoughtful reviews of the 

manuscript were provided by Mike Lisowski, David 

Oppenheimer, and Richard Snay . 

REFERENCES CITED 

Anderson, R.S., 1990, Evolution of the northern Santa Cruz Mountains 

by advection of crust past a San Andreas Fault bend: Science, v. 

249, no. 4967, p. 397-401. 

~rnaddttir, Thora, Segall, Paul, and Matthews, M.V., 1992, Resolving 

the discrepancy between geodetic and seismic fault models for the 

1989 Loma Prieta, California, earthquake: Seismological Society of 

America Bulletin, v. 82, no. 5, p. 2248-2255. 

Aydin, Atilla, and Page, B.M., 1984, Diverse Pliocene-Quaternary tectonics in a transform environment, San Francisco Bay region, California: Geological Society of America Bulletin, v. 95, no. 11, p. 

1303-1317. 

Bakun, W.H., Clark, M.M., Cockerham, R.S., Ellsworth, W.L., Lindh, 

A.G., Prescott, W.H., Shakal, A.F., and Spudich, Paul, 1984, The 

1984 Morgan Hill, California, earthquake: Science, v. 225, no. 4659, 

p. 288-291. 

Barker, J.S., and Salzberg, D.H., 1990, Long-period and broad-band 

teleseismic body-wave modeling of the October 18, 1989 Loma 

Prieta earthquake: Geophysical Review Letters, v. 17, no. 9, 1409- 

1412. 

Barrientos, S.E., Stein, R.S., and Ward, S.N., 1987, Comparison of the 

1959 Hebgen Lake, Montana, and the 1983 Borah Peak, Idaho, 

earthquakes from geodetic observations: Seismological Society of 

America Bulletin, v. 77, no. 3, p. 784-808. 

1989, Errata; comparison of the Hebgen Lake, Montana and the 

1983 Borah Peak, Idaho, earthquakes from geodetic observations: 

Seismological Society of America Bulletin, v. 79, no. 6, p. 2018. 

Behr, Jeffrey, Bilham, Roger, Bodin, Paul, Burford, R.O., and Burgmann, 

Roland, 1990, Aseismic slip on the San Andreas fault south of 

Loma Prieta: Geophysical Research Letters, v. 17, no. 9, p. 1445- 

1448. 

Beroza, G.C., 1991, Near-source modeling of the Loma Prieta earthquake; evidence for heterogeneous slip and implications for earthquake hazard: Seismological Society of America Bulletin, v. 81, 

no. 5, p. 1603-1621. 

Bomford, Guy, 1971, Geodesy: Oxford, U.K., Oxford University Press, 

855 p. 

Choy, G.L., and Boatwright, John, 1990, Source characteristics of the 

Loma Prieta, California, earthquake of October 18, 1989 from global digital seismic data: Geophysical Research Letters, v. 17, no. 8, 

p. 1183-1186. 

Dietz, L.D., and Ellsworth, W.L., 1990, The October 17, 1989, Loma 

Prieta, California, earthquake and its aftershocks; geometry of the 

sequence from high-resolution locations: Geophysical Research Letters, v. 17, no. 9, p. 1417-1420. 

Eberhart-Phillips, D.M., Labson, V.F., Stanley, W.D., Michael, A.J., 

and Rodriguez, B.D., 1990, Preliminary velocity and resistivity 

models of the Loma Prieta earthquake region: Geophysical Research Letters, v. 17, no. 8, p. 1235-1238. 

Eberhart-Phillips, D.M., and Stuart, W.D., 1992, Material heterogeneity 

simplifies the picture; Loma Prieta: Seismological Society of 

America Bulletin, v. 82, no. 4, p. 1964-1968. 

Haugerud, R.A., and Ellen, S.D., 1990, Coseismic ground deformation 

along the northeast margin of the Santa Cruz Mountains, stop 7 of 

Schwartz, D.P., and Ponti, D.J., eds., Field guide to neotectonics of 

the San Andreas fault system, Santa Cruz Mountains, in light of the 

1989 Loma Prieta earthquake: U.S. Geological Survey Open-File 

Report 90-274, p. 32-36. 

Jackson, D.D., Lee, W.B., and Liu, C.-C., 1981, Height dependent errors in southern California leveling, in Simpson, D.W., and Richards, 

P.G., eds., Earthquake prediction; an international review: Washington, D.C., American Geophysical Union, p. 457-472. 

Jennings, C.W., compiler, 1975, Fault map of California: Sacramento, 

California Division of Mines and Geology, scale 1 :750,000. 

Kanamori, Hiroo, and Satake, Kenji, 1990, Broadband study of the 1989 

Lorna Prieta earthquake: Geophysical Research Letters, v. 17, no. 

8, p. 1179-1182. 

King, G.C.P., and Ellis, Michael, 1990, The origin of large local uplift 

in extensional regions: Nature, v. 348, no. 6303, p. 689-693. 

King, N.E., Savage, J.C., Lisowski, Michael, and Prescott, W.H., 1981, 

Preseismic and coseismic deformation associated with the Coyote 

Lake, California, earthquake: Journal of Geophysical Research, v. 

86, no. B2, p. 892-898. 

Langbein, J.O., 1990, Post-seismic slip on the San Andreas fault at the 

northwestern end of the 1989 Loma Prieta earthquake rupture zone: 

Geophysical Research Letters, v. 17, no. 8, p: 1223-1226. 

Langston, C.A., Furlong, K.P., Vogfjord, K.S., Clouser, R.H., and 

Ammon, C.J., 1990, Analysis of teleseismic body waves radiated 

from the Lorna Prieta earthquake: Geophysical Research Letters, v. 

17, no. 9, p. 1405-1408. 

Lisowski, Michael, Prescott, W.H., Savage, J.C., and Johnston, M.J.S., 

1990, Geodetic estimate of coseismic slip during the 1989 Loma 

Prieta, California, earthquake: Geophysical Research Letters, v. 17, 

no. 9, p. 1437-1440. 

Nibglek, J.L., 1990, Rupture process of the October 18, 1989 Loma 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A127 

Prieta earthquake from broadband teleseismic body waves [abs.]: 

Seismological Research Letters, v. 61, no. 1, p. 46. 

Oppenheimer, D.H., 1990, Aftershock slip behavior of the 1989 Loma 

Prieta, California earthquake: Geophysical Research Letters, v. 17, 

no. 8, p, 1199-1202. 

Plafker, George, and Galloway, J.P., eds., 1989, Lessons learned from 

the Loma Prieta, California, earthquake of October 17, 1989: U.S. 

Geological Survey Circular 1045, 48 p. 

Poland, J.F., and Ireland, R.L., 1988, Land subsidence in the Santa 

Clara Valley, California, as of 1982: Washington, D.C., U.S. Government Printing Office, 61 p. 

Prescott, W.H., King, N.E., and Gu Guohua, 1984, Preseismic, coseismic, 

and postseismic deformation associated with the 1984 Morgan Hill, 

California, earthquake, in Bennett, J.H., and Sherburne, R.W., eds., 

The 1984 Morgan Hill, California earthquake: California Division 

of Mines and Geology Special Publication 68, p. 137-148. 

Reasenberg, P.A., and Ellsworth, W.L., 1982, Aftershocks of the Coyote Lake, California, earthquake of August 6, 1979; a detailed study, 

Journal of Geophysical Research, v. 87, no. B 13, p. 10637-10655. 

Reches, Ze'ev, and Zoback, M.D., 1990, Theoretical analysis of the 

deformation of a layered sequence above a fault-preliminary application to the Loma Prieta earthquake, chap. 10 of Nur, Amos, 

Mavko, Gary, and Zoback, Mark, eds., Stanford rock physics and 

borehole geophysics, v. 40, p.Xl-X22. 

Romanowicz, B.A., and Lyon-Caen, Helene, 1990, The Loma Prieta 

earthquake of October 18, 1989; results of teleseismic mantle and 

body wave inversion: Geophysical Research Letters, v. 77, no. 8, p. 

1191-1 194. 

Ruff, L.J., and Tichelaar, B.W., 1990, Moment tensor rate functions for 

the 1989 Loma Prieta earthquake: Geophysical Research Letters, v. 

17, no. 8, p. 1187-1190. 

Steidl, J.H., Archuleta, R.J., and Hartzell, S.H., 1991, Rupture history 

of the 1989 Loma Prieta, California, earthquake: Seismological Society of America Bulletin, v. 81, no. 5, 1573-1602. 

Stein, R.S., 1981, Discrimination of tectonic displacement from slopedependent errors in geodetic leveling from southern California, 

1953-1979, in Simpson, D.W., and Richards, P.G., eds., Earthquake prediction; an international review: Washington, D.C., American Geophysical Union, p. 441-456. 

Stein, R.S., Whalen, C.T., Holdahl, S.R., Strange, W.E., and Thatcher, 

Wayne, 1986, Saugus-Palmdale, California, field test for refraction 

error in historical leveling surveys: Journal of Geophysical Research, v. 91, no. B9, p. 9031-9044. 

Valensise, Gianluca, 1994, Geologic assessment of the relative contribution of strike-slip faulting, reverse-slip faulting, and bulk squeezing in the creation of the central Santa Cruz Mountains, California, 

in Simpson, R.W., ed., The Loma Prieta, California, earthquake of 

October 17, 1989-tectonic processes and models: U.S. Geological 

Survey Professional Paper 1550-F, p. 17-34. 

Valensise, Gianluca, and Ward, S.N., 1991, Long-term uplift of the 

Santa Cruz coastline in response to repeated earthquakes along the 

San Andreas fault: Seismological Society of America Bulletin, v. 

81, no. 5, p. 1694-1704. 

Wald, D.J., Helmberger, D.V., and Heaton, T.H., 199 1, Rupture model 

of the 1989 Loma Prieta earthquake from the inversion of strong 

motion and broadband teleseismic data: Seismological Society of 

America Bulletin, v. 81, no. 5, p. 1540-1572. 

Ward, S.N., and Barrientos, S.E., 1986, An inversion for slip distribution and fault shape from geodetic observations of the 1983 Borah 

Peak, Idaho, earthquake: Journal of Geophysical Research, v. 91, 

no. B5, p. 4909-4919. 

Zhang, Jiajun, and Lay, Thorne, 1990, Source parameters of the 1989 

Loma Prieta earthquake determined from long-period Rayleigh 

waves: Geophysical Research Letters, v. 17, no. 8, p. 1 195-1 198. 

APPENDIX 1: 

CORRECTIONS AND ADJUSTMENTS 

TO LEVELING DATA 

To isolate the elevation change associated with the earthquake ("coseismic"), each survey route must be corrected 

to eliminate other sources of elevation change, on the 

basis of knowledge of subsidence caused by ground-water 

withdrawal during the coseismic time interval, and on the 

preearthquake rate of subsidence. In some places, the 

preearthquake subsidence pattern can easily be attributed 

to tectonic or nontectonic sources (for example, water withdrawal); in other places, disturbed bench marks can lead 

to unpredictable patterns. Leveling routes 1 through 3 (inset, fig. 1) have preearthquake leveling histories; whereas 

leveling routes 4 through 7 do not. Leveling routes 4 

through 7 are primarily located in mountainous regions 

and are unlikely to be influenced by ground-water-withdrawal-induced subsidence. 

Land subsidence due to ground-water withdrawal in San 

Jose is documented by leveling surveys and compaction 

monitoring. Multiple releveling projects during 1934-67 

have documented approximately 2.5 m of land subsidence 

in San Jose. In 1960, the USGS installed several extensometers (corehole compaction-measuring devices; Poland 

and Ireland, 1988) in San Jose and Sunnyvale, five of 

which remain in operation today and are maintained by 

the Santa Clara Valley Water Conservation District. These 

extensometers provide an excellent record of the compacting aquifer system and, in comparison with leveling 

data, confirm that land subsidence is compensated by compaction at depths of 61 to 305 m. The land subsidence, 

which is correlated with ground-water withdrawal and an 

associated water-table decline, has slowed drastically since 

the introduction of substantial surface-water imports during the late 1960's (Poland and Ireland, 1988). An example extensometer record for well 7S/lE-16C11 in San 

Jose is shown in figure 12, along with depth-to-water data 

for the period 1982-90. Note that during the coseismic 

interval 1989-90 along leveling route 1, the aquifer system shows a net expansion or land-surface rebound. 

To correct leveling routes 1 through 3 (inset, fig. 1) for 

nontectonic subsidence effects, we use both preearthquake 

leveling and extensometer data. Subsidence-rate functions 

are determined from preearthquake leveling surveys, and 

subsidence corrections are computed by multiplying the 

subsidence-rate functions by the coseismic time intervals. 

In this correction, subsidence rates are implicitly assumed 

to remain constant over time. Near the extensometer sites 

where subsidence is greatest, however, the observed rates 

vary over time; for bench marks near the extensometer 

sites, the subsidence-rate functions have been modified 

by the observed rate changes. Preearthquake leveling data 
A128 MAIN-SHOCK CHARACTERISTICS 

for routes 1 through 3 are plotted in figure 13. The 

preearthquake interval for leveling route 1 (1967-89) spans 

both the August 6, 1979, ML=5.9 Coyote Lake, Calif., 

earthquake and the April 24, 1984, ML=6.1 Morgan Hill, 

Calif., earthquake (King and others, 1981; Reasenberg and 

Ellsworth, 1982; Bakun and others, 1984; Prescott and 

others, 1984). Although the vertical deformation along 

leveling route 1 from these two events is small (+8 to -10 

mm), we remove their contributions to elevation change. 

Bench marks seated in bedrock presumably are least affected by nontectonic subsidence and so are used to establish the zero-elevation-change datum for the 

preearthquake surveys. The San Jose subsidence basin is 

evident in the profiles for leveling routes 1 (1967-89) and 

3 (1960-67), and subsidence rates apparently decline after 1967. Subsidence-rate modifications are made for all 

bench marks that lie within this subsidence basin. To correct for subsidence-rate changes, the subsidence-rate functions are multiplied by a rate-correction factor, which is 

the ratio of the subsidence rate during the coseismic interval to that during the preearthquake interval. Average subsidence rates and rate-correction factors along leveling 

routes 1 and 3 are listed in table 9; these average rates are 

derived from readings of the two extensometers at the San 

Jose site. Extensometer-tape readings for the period 1982- 

90 are listed in table 10; increasing values indicate compaction during the period between readings, whereas 

decreasing values indicate expansion. Poland and Ireland 

(1988) discussed extensometers and presented compaction data for the period 1960-8 1. 

Depth-to-water records for wells along leveling routes 

1 and 2 (inset, fig. 1) were examined to assess the validity 

of our assumption of constant subsidence rates in areas 

outside the San Jose subsidence basin. The locations of 

the 16 wells whose histories we examined are shown in 

figure 13. The coupling of land subsidence to water-table 

fluctuations is not spatially uniform; except in one well, 

no large water-table fluctuations were noted that would 

require a modification of the subsidence rates represented 

by the leveling data outside the San Jose area. Well 12Sl 

2E-15E01 (fig. 13B) near Watsonville (WA, fig. 1) has a 

larger ratio of subsidence to water-table decline than that 

observed in San Jose, possibly indicating that subsidence 

is particularly sensitive to the water table there. The ratio 

of subsidence to water-table decline, and the total watertable decline during the period 1978-89, are used to predict subsidence of the junction-point bench mark between 

these two preearthquake surveys and thus to adjust the 

datum level for the preearthquake leveling survey along 

route 2. 

Corrected coseismic profiles along leveling routes 1 

through 3 were computed by subtracting the subsidencecorrection functions from the observed-elevation-change 

profiles. The correction functions may not contain all the 

bench marks of the coseismic survey, and so they are 

interpolated for missing points. Because subsidence basins and the subsidence patterns determined from 

preearthquake leveling have primarily short spatial wavelengths, elevation-change profiles generally are smoother 

after correction. Reduction of the short-wavelength com1/82 4/83 7/84 10/85 1/87 4/88 7/89 10/90 

DATE 

Figure 12.-Extensometer readings (circles) and depth-to-water records (squares) for 305-m-deep well 7Sl 

1E-16C11 in San Jose. Increasing readings indicate compaction, whereas decreasing readings indicate expansion of aquifer system in depth range 0-305 m. 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A129 

ponents serves as a test of the efficacy of the correction. 

The corrections for leveling routes 1 through 3 are all 

well behaved, except at the north end of leveling route 2 

between 55 and 84 km. We believe that this problem originates in the north half of the 1972 survey, where a heightdependent error may have occurred; thus, we neglected 

the subsidence correction for this area. The observed and 

corrected elevation changes and the correction functions 

along leveling routes 1 through 3 are plotted in figure 14. 

For the network to be self-consistent, overlapping end 

points of each survey route must have the same coseismic 

elevation change. To accomplish this agreement, we adjust the third-order USGS data. The test for the efficacy 

of these adjustments is that the circuit misclosure of the 

adjusted data must be smaller than that of the observed 

data. We use the original field data from the USGS surveys and thus remove all previous USGS adjustments. 

Bedrock sites 

l/Ã 

I- ; -0.5 F h ti ;iiM Water wells 

San Jose extensometer site < z (0.4 km from this bench mark) 

0 20 40 60 80 

DISTANCE, IN KILOMETERS 

z 

IÃ 

dCtJtIU ti h tltlh ti 

4 Water wells 

I I I I I I 

0 20 40 60 80 

DISTANCE. IN KILOMETERS 

San Jose 

extensometer site 3 

(3.3 km from 

this bench mark) 

DISTANCE, IN KILOMETERS 

Figure 13.-Preearthquake leveling data along routes 1 (A, 1989-671 

72), 2 (5, 1989-72, 1978-72), and 3 (C, 1967-60) (see inset, fig. l), 

showing locations of bedrock, water wells, and bench marks closest to 

San Jose extensometer site. 

The end point of leveling route 4 has an unadjusted 

coseismic mismatch with leveling routes 1 and 2 of 115 

mm, which, using the assigned a value (see table I), is 

about twice as great as the expected random error for the 

length of this leveling route. We apply an adjustment of 2 

mdkm to the 1953 elevations along leveling route 4, so 

that the adjusted coseismic elevation changes match at 

both ends. At the junction of leveling routes 5 and 6, the 

mismatch is 46 mm, which is about the expected random 

error at this point for both leveling routes. The misfit is 

divided equally, and so leveling route 6 is adjusted by 0.5 

mdkm and leveling route 5 by 0.6 mdkm. After these 

adjustments, the computed circuit misclosure for the 

preearthquake circuit is reduced from -70 to +15 mm. 

These adjustments reduce the 1953 circuit misclosure to 

that of the precise 1990 survey (-19 mm; see table 2). The 

adjusted and subsidence-corrected coseismic elevation 

changes used in our modeling, and their relative uncertainties, are listed in table 3; each bench mark is identified by its ACRN. The elevation changes listed in table 3 

are relative to an arbitrary datum, and so a constant can 

be added to all the bench marks. Specifications for all the 

data listed in table 3 are listed in table 1. 

APPENDIX 2: DATA TABLES 

All the postearthquake elevation-change observations 

made by the NGS are listed in tables 11 through 24, along 

with the corresponding historical leveling data, our corrections, and some additional data that were analyzed for 

use in the subsidence corrections. The title of each table 

corresponds to the survey titles as named during the 1990 

survey. 

Tables 11 through 13 contain only NGS orthometric 

heights for which all standard NGS corrections have been 

applied. These heights, however, may differ from current 

NGS data-base values because some heights were obtained 

from unadjusted ("print file") elevations. Also included in 

these tables are our earthquake and subsidence corrections to the coseismic elevation changes; these corrections are omitted from the orthometric heights listed in 

these tables. The coseismic correction was computed by 

assuming right-lateral slip on a vertical fault for both the 

1979 Coyote Lake and 1984 Morgan Hill earthquakes. 

For the 1979 Coyote Lake earthquake, we used 0.33 m of 

slip on a 20-km-long fault plane extending from 4- to 12- 

km depth. For the 1984 Morgan Hill earthquake, we used 

0.76 m of slip on a 25-km-long fault plane extending 

from 4- to 10-km depth (King and others, 1981; 

Reasenberg and Ellsworth, 1982; Bakun and others, 1984; 

Prescott and others, 1984). Tables 14 through 24 contain 

NGS, USGS, and Santa Cruz County leveling data. 

The USGS data are all from surveys dated 1953, although a few are actually from 1948. In some places, both 
MAIN-SHOCK CHARACTERISTICS 

Table 9.-Average subsidence rates along leveling routes 1 and 3 

[First, the average of the first and second readings of the cable extensometer after manual oscillation 

was computed; then, this average was combined with the reading of the pipe extensometer to compute 

the average subsidence rate] 

Average Rate-correction factor Leveling route Survey subsidence rate (Coseismic rate1 (inset, fig. 1) interval (md~r) preearthquake rate) 

1953 observed and adjusted heights are listed. The adjusted heights are the observed heights adjusted by us as 

described here; the observed heights are the original field 

observations with the original USGS adjustments removed. 

The USGS heights were measured with a three-wire leveling instrument and one 3-yd (3 m)-long, single-piece leveling rod; some rod-calibration tables are available. 

Leveling was conducted between NGS bench marks and 

adjusted to closure with previous NGS heights for those 

bench marks. 

The Santa Cruz County data are all surveys dated 

bb1970." Although the precise dates for these surveys are 

unknown, we were told by Santa Cruz County officials 

that they were conducted during the late 1960's and early 

1970's. The heights were measured with a three-wire leveling instrument and a folding leveling rod ("Philadelphia 

rod") ruled in hundredths of feet; we do not know whether 

the rods had been calibrated. Leveling was conducted between USGS bench marks and adjusted to closure with 

previous USGS heights for those bench marks. Original 

unadjusted heights may be obtained from the Santa Cruz 

County Public Works Department, Office of the Surveyor, 

where the original leveling books are kept. The designations listed for the Santa Cruz bench marks are in the 

form of a height (in feet), an equal sign, and a integer 

designation (for example, "27 1 .52=3019'); the actual 

stampings on the marks are simply the height (in feet). 

The integer following the equal sign is the index number 

given to that bench mark by Santa Cruz County. The index numbers are used to find the adjusted heights listed in 

an index-card file and to locate the bench marks on a map 

in the Office of the Surveyor. 

We did not use coseismic elevation changes constructed 

from the Santa Cruz County data for several reasons. Extensive research on the original field books is required, 

and the quality of the data is uncertain. Three leveling 

rods were used during the surveys, only one of which is 

still available for calibration, and the correspondence 

between rod serial numbers and particular surveys is 

uncertain. Tilt of elevation change and slope of topography appear to be correlated along several of the leveling routes that we examined, indicating a rod-calibration 

problem. 

The locations of all the bench marks at which coseismic 

elevation changes were measured (both those used in this 

study and those not used) are shown in figure 15. 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A131 

Table 10.-Extensometer-tape readings in two wells in Sun Jose for the 

period 1982-90 

[F.O., first reading of tape, before manual oscillation; M.O., second reading of 

tape, after counterweight was manually oscillated] 

Well 

Well 7s/1: 

-. 7SIlE-16C11 cable 

uaie nine (305 m) 

F.O. 
ELEVATION CHANGE, 

IN MILLIMETERS 

CORRECTION, 

IN MILLIMETERS 

ELEVATION CHANGE, 

IN MILLIMETERS 

I 

2 

0 

0 0 

CORRECTION, 

IN MILLIMETERS 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A133 

0 10 20 30 

DISTANCE, IN KILOMETERS 

Figure 14.-Continued 
MAIN-SHOCK CHARACTERISTICS 

Table 11 .-Leveling observations along a line from San Jose through Gilroy and Sargent to Watsonville 

Orthometric height (m) 

Latitude Longitude 2;: 1967 Subsidence Earthquake 

ACRN N. W. (3-5) 1968 I972 :-;: I990 correction correction (krn) L21038, 

L21016.l (10-112 Lzd;;Qi' C?2-911 L2517'2' dli:&.l (rnrn) mm) 

L21016.2 L25 17.4 

V 1197 U 469 Oakland 6 Oakland 8 reset K 1444 L 1444 Oakland 7 Q 148 reset 20 G San Leandro NW base N 554 M 1444 M 554 

K 738 reset 941 471 1 tidal 6 

L 554 

V 591 P 1197 Q 1197 C 1447 R 1 197 reset X 1446 

B 46 reset 

50.5 

L 177 K 177 Niles AZ MK F 148 R 874 

Q 874 

Switch 

T 591 

B 148 reset M 886 

Q 591 reset C 1371 D 1076 Jacklin RM 1 M 874 G 1447 D 176 reset Z 174 Miloitas 

K 179 reset M 1447 N 1447 X 147 B 1076 G 1448 C 1121 reset L 1447 U 174 Z 1 1 1 reset 1962 Z 876 reset 

B 112 E 1447 P 7 reset 1965 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A135 

Table 11 .-Leveling observations along a line from Sun Jose through Gilroy and Sargent to Watsonville-Continued 

Orthometric height (m) 

Designation Latitude Longitude g$t 1967 Subsidence Earthquake 

ACRN N. W . (3-5) l9 1990 correction correction (km) L21038, 1968 $% B72 (2-7) (mm) (mm) 2l0l6.l 6% ' 27-9) [J55'At L25239.1 

1,21016.2 

A 326 reset 1970 M 177 I 19=96 reset 1976 A 1122 San Jose A7. MK B 149 L 591 

2=J 19 

C 886 reset 1962 A 1076 Q 877 reset 1964 B 1121 P 453 

R 174 

g453 

JCT RM3 P 174 N 453 H 1447 L 453 

M 174 

Perrys 

Perrys RM 4 A 1448 K 453 reset 1974 B 1448 1453 

E 1080 A 812 T 19 reset 1938 

Rucker reset 1957 

E 812 reset 1973 

D 812 0 1448 

C 1193 Q 149 reset 1967 D I193 

Sargent AZ MK G 1236 F I236 
A136 MAIN-SHOCK CHARACTERISTICS 

Table 11 .-Leveling observations along a line from Sun Jose through Gilroy and Sargent to Watsonville-Continued 

Orthometric height (rn) 

Designation Latitude Longitude E$$ 1967 Subsidence Earthquake 

ACRN N. W . (3-5) 1968 (3, 1972 l9 1990 correction correction (km) ~21038, (2-7) (1-2) (mm) mrn) 

L21016.1, fkjC# L~~~~&!' L!&li pAll;2 L25239.1 L21016.2 

0112233 R 1236 36'53'5 1" 121Â°41'24 87.354 - - - - - - . . . 18.88477 18.93404 18.80269 35 -58 

GU2235 Y 149 36Â°54'03 121Â°42'20 88.805 - - - ... - - - 12.21096 12.24087 12.10724 -.82 -1.01 

GU4098 V 1448 36Â°54'05 121Â°42'42 89.397 - - - --- --- --- 14.1 1705 13.99848 -.38 - - - 

GU2237 S 1236 36Â°54'01 121Â°43'05 89.977 - - - --- --- 1.89650 11.94221 11.81938 05 00 

GU2239 T 1236 36Â°53'55 121'43'39" 90.899 - - - --- --. 10.35522 10.39775 10.28159 -. 14 00 

GU2240 U 1236 36"53'50" 12 1Â°44'04 9 1.563 - - - . - - .-- 8.63629 8.68082 8.57030 -.O2 00 

GU2242 M 20 reset 1964 36O.53'44" 121Â°44'40 92.383 - - - ..- --- 8.66899 8.68768 8.57506 -1.54 00 

Table 12.-Leveling observations along a line from Watsonville to Santa Cruz 

[See figure 1 for locations. Number(s) in parentheses below year of survey indicate month(s) when survey was conducted. L-number is U.S. 

National Geodetic Survey designation. Subsidence correction applies to 1978-90 height difference] 

Orthometric height (m) 

ACRN DesiBialion Latitude Longitude &^ Subsidence 

N. W. 1972 1978 1990 correction 

(7-9) (5) (2) () L22841 L24298 L25239.2 (mm) 

M 20 reset 1964 

V 1236 

W 1236 

H 249 reset 1979 

X 1236 

A 1455 

Z 1236 

A 1237 

E 249 

C 1237 

D 1237 

RV 6 

E 1237 

C 249 

F 1237 

G 1237 

H 1237 

J 1237 

RV 5 

RV 4 

K 1237 

L 1237 

M 1237 

N 1237 

Z 212 

P 1237 

61.94 

55.79 

51.93 

R 1237 

S 1237 

941 3745 tidal 4 

14 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A137 

Table 13.-Leveling observations along a line from Santa Cruz through Los Gatos to Sun Jose 

[See figure 1 for locations. Numbers in parentheses below year of survey indicate months when survey was conducted. L-numbers are U.S. National Geodetic Survey 

designations. Subsidence correction applies to 1967-90 height difference] 

Orthometric height (m) 

ACRN Designation Latitude 

N. 

Longitude 

w. 

Leveled 

distance 

(km) 

Subsidence 

correction 

mm) 

941 3745 tidal 4 

14 

T 1237 

11 1455 

W 212 

C 1455 

D 1455 

E 1455 

F 1455 

G 1455 

H 1455 

J 1455 

K 1455 

M 1455 

L 1455 

N 1455 

P 1455 

L 249 

RV 12 

Q 1455 

R 1455 

S 1455 

TRAILL 

T 1455 

U 1455 

V 1455 

W 1455 

X 1455 

Y 1455 

Z 1455 

A 1456 

B 1456 

R 1077 reset 1970 

C 1456 

D 1456 

E 1456 

P 878 

R 878 

F 1456 

M 878 

G 1456 

K 878 

D 177 

II 1456 

C 177 

J 1456 

K 1456 

G 386 

VASOG 875 

L 1456 

F 180 

T 1122 

M 1456 

A 887 reset 1962 

S 1122 

E 875 

U 176 reset 1940 

D 875 

T 176 reset 1962 

S 176 reset 1962 

R 176 reset 1962 

P 176 

D 877 

C 112 

B 875 

Z 11 1 reset 1962 

L 1447 

G 1448 
A138 MAIN-SHOCK CHARACTERISTICS 

Table 14.-Leveling observations along a line from Capitola through Loma Prieta to Coyote 

[See figure 1 for locations. Numbers in parentheses below year of survey indicate months when survey was conducted; month of 1953 survey is unknown. L-number is U.S. 

National Geodetic Survey designation; PV numbers are U.S. Geological Survey (USGS) field-summary-book designations. Obs., original field observations, with previous 

USGS adjustments removed; adj., observations adjusted for consistent coseisrnic network (see text)] 

ACRN Designation Latitude Leveled Longitude 

N. W. (km) 

Orthometric height (m) 

1953 

(obs .) 

N 1237 

Z 212 

N 1456 

32 WLS 

P 1456 

Q 1456 

Chiseled square A 

R 1456 

S 1456 

T 1456 

U 1456 

1940 

28 WLS 

Chiseled square B 

Z 1456 

Burdett 

27 WLS 

V 1456 

W 1456 

X 1456 

Y 1456 

A 1457 

B 1457 

C 1457 

D 1457 

E 1457 

F 1457 

G 1457 

Loma Prieta reset 1958 

LOMA 

Loma Prieta 1 

H 1457 

J 1457 

K 1457 

HJH 55 

L 1457 

M 1457 

N 1457 

P 1457 

Q 1457 

TBM angle iron 

HJH 53 

R 1457 

Chiseled square C 

S 1457 

TBM spike 

T 1457 

U 1457 

TBM manhole 

HJH 51 

V 1457 

W 1457 

X 1457 

L 174 

P 19 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A139 

Table 15.-Leveling observations along a line from 9.6 km south of Morgan Hill to Lorna Prieta 

[See figure 1 for locations. Number in parentheses below year of survey indicates month when survey was conducted; month of 1953 survey is 

unknown. L-number is U.S. National Geodetic Survey designation; PV-number is U.S. Geological Survey (USGS) field-summary-book designation. Obs., original field observations, with previous USGS adjustments removed; adj., observations adjusted for consistent coseisrnic network 

(see text)] 

Orthometric height (m) 

Leveled 

ACRN Designation Latitude Longitude distance 1953 1953 

N. W. (obs.) (adj. 1990 

(km) (4) L25239.5 

PV220 

Q 1458 

P 1458 

N 1458 

M 1458 

Chiseled square 1 

L 1458 

K 1458 

J 1458 

H 1458 

114 JD 

Y 1459 

G 1458 

X 1459 

115 JD 

W 1459 

F 1458 

P 1459 

E 1458 

Q 1459 

116 JD 

V 1459 

D 1458 

R 1459 

C 1458 

B 1458 

N 1459 

END 

A 1458 

S 1459 

Z 1457 

T 1459 

Y 1457 

M 1459 

F 1457 

E 1457 
MAIN-SHOCK CHARACTERISTICS 

Table 16.-Leveling observations along a line from Morgan Hill to Watsonville 

[See figure 1 for locations. Number in parentheses below year of survey indicates month when survey was conducted; month of 1953 survey is 

unknown. L-number is U.S. National Geodetic Survey designation; PV-numbers are U.S. Geological Survey (USGS) field-summary-book 

designations. Obs., original field observations, with previous USGS adjustments removed; adj., observations adjusted for consistent coseisrnic 

network (see text)] 

Orthometric height (m) 

ACIW Designation Latitude Longitude 1953 1953 

N. w. (o~s.) (adj.1 1990 (km) (4) 

N 1448 

P 1448 

Chiseled square 3 

R 1458 

S 1458 

Chiseled square B 

S 1458 

109 JD 

T 1458 

110 JD 

Q 1458 

U 1458 

38 WLS 

L 1459 

V 1458 

W 1458 

X 1458 

Y 1458 

Z 1458 

Chiseled triangle A 

36 WLS 

B 1459 

Chiseled square 2 

C 1459 

D 1459 

E 1459 

F 1459 

G 1459 

H 1459 

J 1459 

33 WLS reset 1965 

W 17 

W 16 

K 1459 

W9 

H 249 reset 1979 

W 1236 

V 1236 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A141 

Table 17.-Leveling observations along a line from Watsonville, through Freedom, Browns Valley Road, 

and Casserly Road, to 6.1 km northwest of Watsonville 

[See figure 1 for locations. Numbers in parentheses below year of survey indicate months when survey was conducted; 

month of 1970 survey is unknown. L-number is U.S. National Geodetic Survey designation] 

Orthometric height (m) 

ACRN Designation Latitude Longitude ~~~~~ 

N. W. 1990 

(km) 1970 L2525 (4-5) 1.1 

Gaging station 

Z 1459 

T 738 reset 1963 

K 1459 

Table 18.-Leveling observations along a line from 0.5 km west of Corralitos through Freedom Boulevard 

to Aptos 

[See figure 1 for locations. Number in parentheses below year of survey indicates month when survey was conducted; 

month of 1970 survey is unknown. L-number is U.S. National Geodetic Survey designation] 

Orthometric height (m) 

Leveled 

ACRN Designation Latitude Longitude distance N. W. 1990 

fkm) 1970 (4) 
MAIN-SHOCK CHARACTERISTICS 

Table 19.-Leveling observations along a line from 0.8 km northwest of Freedom, through Valley Road and 

Buena Vista Drive, to 0.6 km south of La Selva Beach 

[See figure 1 for locations. Numbers in parentheses below year of survey indicate months when survey was conducted; 

month of 1970 survey is unknown. L-number is U.S. National Geodetic Survey designation] 

Orthometric height (m) 

Leveled 

ACRN Designation Latitude Longitude distance N. W. 1990 

(km) 1970 (4-5) L2525 1.3 

Z 1459 

1 

158.34=96 

97 

35.89=98 

67.40=2 19 

93.74=220 

130.54=221 

277.62=223 

R 121 

227 reset 

RV 6=4 

Table 20.-Leveling observations along a line from 5.3 km north of Soquel, through 

Laurel Glen Road and Granite Creek Road, to 2.7 km north of Scotts Valley 

[See figure 1 for locations. Number in parentheses below year of survey indicates month when survey 

was conducted; month of 1970 survey is unknown. L-number is U.S. National Geodetic Survey designation] 

ACRN Designation Latitude N. 

Orthometric height (m) 

Leveled Longitude dishnce w. 1990 

(km) 1970 (5) L2525 14 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A143 

Table 21.-Leveling observations along a line from the junction of Mount Herman Road 

and Zayante Road 1 km east of Felton through Olympia to 4.3 km northeast of Zayante 

[See figure 1 for locations. Number in parentheses below year of survey indicates month when survey 

was conducted; month of 1970 survey is unknown. L-number is U.S. National Geodetic Survey designation] 

Orthometric height (m) 

Leveled ACRN Designation Latitude Longitude distance N. W. 1990 

(km) 1970 (5) 

Gaging station 37'05'09'' 122'02'45'' 

415.66=381 37'05'22'' 122'02'37'' V 1460 37'05'37'' 122'02'27'' 

Table 22.-Leveling observations along a line from Felton, through Boulder Creek and China Grade Road, 

to the Santa Cruz-San Mateo County line 

[See figure 1 for locations. Numbers in parentheses below year of survey indicate months when survey was conducted; 

months of 1953 and 1970 surveys are unknown. PV-numbers are U.S. Geological Survey (USGS) field-summary-book 

designations. Obs., original field observations, with previous USGS adjustments removed] 

Orthometric height (m) 

Leveled 

ACRN Designation Latitude Longitude distance N. W. 1953 1990 

(km) (obs.) 1970 (5-6) 

PV2 18 L25251.6 

P 1455 

W 1460 

X 1460 

296.80=74 

324.23=72 

Y 1460 

177 reset 390.58=179 

446.86=181 

457.31=182 

Z 1460 

501.74=184 

BEN 8 A 1461 

566.17=187 

640.87=188 

799.37=190 

46 WLS 

B 1461 

C 1461 

916 SF 

D 1461 

E 1461 

F 1461 

48 WLS 

G 1461 

H 1461 

J 1461 

K 1461 

49 WLS 

L 1461 

M 1461 
MAIN-SHOCK CHARACTERISTICS 

Table 23.-Leveling observations along a line from 1 km east of Felton, through Felton Empire Road and 

Bonny Boon Road, to 1.4 km southeast of Davenport 

[See figure 1 for locations. Number in parentheses below year of survey indicates month when survey was conducted; 

months of 1953 and 1970 surveys are unknown. L-number is U.S. National Geodetic Survey designation; PV-number is 

U.S. Geological Survey (USGS) field-summary-book designation. Obs., original field observations, with previous USGS 

adjustments removed] 

Orthometric height (m) 

ACRN Desicnation Latitude Longitude zz N. W. 1953 1990 

(km) (obs.) 1970 

PV218 (6) L25251.7 

HT3570 P 1455 37'03'1 9" 122'03'36'' 0.000 - - - - - - 106.74056 

HT3584 W 1460 37'03'1 1" 122'04'07" 96 1 - - - --- 85.42219 

HT3615 N 1461 37'03'04'' 122'04'40'' 1.897 - - - --- 132.66295 

HT3616 P1461 37'02'56'' 122'04'58'' 2.402 - - - --- 160.46799 

HT3617 Q 1461 37'02'59" 122'05'27" 3.192 - - - - - - 225.17783 

HT3618 R 1461 37'03'07'' 122Â°05'40 3.673 - - - - - - 270.27996 

HT3619 S 1461 37'03'14'' 122'05'44'' 4.225 --- - - - 304,49007 

HT3620 170 37'03'21'' 122'06'02'' 4.896 - - - 363.45000 363.46421 

HT3621 T 1461 37'03'28'' 122'06'20'' 5.341 --- - - - 404.93420 

HT3622 168 37'03'36" 122'06'28'' 5.838 --- 443.64000 443.64950 

HT3623 167 37'03'4 1" 122'06'45" 6.285 --- 476.87000 476.86497 

HT3624 U 1461 37'03'32'' 122'06'54'' 6.844 --- - - - 5 12.70295 

HT3625 1822.20=360 37'03'29" 122'07'21'' 7.540 - - - 555.41000 555.42330 

HT3626 V 1461 37'04'00" 122'07'17" 8.748 --- - - - 601.72882 

HT3627 163 37'04'20'' 122'07'40'' 9.672 - - - 614.27000 614.30540 

HT3628 W 1461 37'04'40" 122'07'57" 10.534 - - - - - - 663.20385 

HT3629 X 1461 37'05'26'' 122'08'18'' 10,994 - - - - - - 759.81 158 

HT3631 43 WLS 37'06'30'' 122'08'39'' 1 1.223 754.26300 754.27400 754.28303 

HT3632 Z 1461 37'04'52'' 122'08'21'' 11.453 --- - - - 638.85854 

HT3633 41 WLS 37'04'02'' 122'08'24'' 13.186 576.08000 576.09500 576.11380 

HT3634 1707.48=202 37'03'45'' 122'08'49'' 14.018 - - - 520.44100 520.45432 

HT3635 A 1462 37'03'1 1" 122'09'1 1" 15.164 - - - - - - 450.14035 

HT3636 40 WLS 37'02'40'' 122'08'56" 16.312 404.66300 404.67900 404.68017 

HT3637 REFWLS 37'02'40'' 122'08'58'' 16.33 1 404.01000 404.03000 404.02556 

HT3638 122'0.26=366 37'02'12'' 122'09'M" 17.243 - - - 371.93700 371.92109 

HT3639 B 1462 37'01'5 1" 122'09'17'' 18.108 - - - - - - 301.01995 

HT3640 C 1462 37'01'39" 122'09'27'' 18.732 --- - - - 237.56842 

HT3641 D 1462 37'01'22'' 122'09'55'' 19.645 --- - - - 173.17029 

HT3642 E 1462 37'01'02'' 122'10'02" 20.135 --- - - - 123.63265 

HT3643 86.24=199 37'00'42" 122'10'32" 21.331 --- 26.28600 26.23643 

HT1572 H 1238 37'00'04'' 122'10'45'' 22.456 --- - - - 17.38950 
ELEVATION CHANGES ASSOCIATED WITH THE EARTHQUAKE AND THEIR USE TO INFER FAULT-SLIP GEOMETRY A145 

Table 24.-Leveling observations along a line from Santa Cruz through Davenport to 1 km northwest of the Santa Cruz-San Mateo County line 

[See figure 1 for locations. Number(s) in parentheses below year of survey indicates month(s) when survey was conducted; months of 1953 and 1970 surveys are unknown. 

L-number is U.S. National Geodetic Survey designation; PV-number is U.S. Geological Survey (USGS) field-summary-book designation. Obs., original field observations, 

with previous USGS adjustments removed. Subsidence correction applies to 1978-90 height difference] 

Orthometric height (m) 

Leveled Subsidence 

ACRN Designation Latitude Longitude distance N. W. 1953 1972 1978 1990 correction 

(obs.) 

(h) PV2 18 

1970 (9- 1 0) (5) (2) (mm) 

L22869 L24298 L252.5 1.8 

GU4 167 

GU4240 

GU1954 

GU1959 

GU I 960 

GU 1964 

GU4239 

GU 1970 

GU1971 

GU4238 

GU 1972 

GUI 974 

GU1975 

GUI 976 

GU I978 

GU 1979 

HT1572 

HT3654 

HT1568 

HT1567 

HT1566 

HT1565 

HT3653 

HT1564 

HT3652 

HT1563 

HT1562 

HT365 1 

HT1559 

HT1558 

HT3650 

HT1557 

HT3649 

HT1556 

HT3648 

HT1555 

HT1554 

HT1552 

HT1549 

HT3644 

HT3647 

HT3646 

HT 1547 

HT3645 

HT1545 
MAIN-SHOCK CHARACTERISTICS 

Figure 15.-Schematic map of Loma Prieta region, Calif., showing locations of leveling network of bench 

marks used in this study (dots) and additional bench marks for which coseismic elevation changes were 

measured (triangles). Unused bench marks were surveyed by Santa Cruz County at low precision; unassessed 

elevation-dependent error evident in Santa Cruz County observations limits their utility for geodetic modeling. Quaternary faults (dashed where inferred) from Jennings (1975). LP, Loma Prieta (solid triangle). 

- 0 10 20 KILOMETERS ' \' 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAKE OCCURRENCE 

MAIN-SHOCK CHARACTERISTICS 

MAIN-SHOCK AND VERY EARLY AFTERSHOCK ACTIVITY1 

CONTENTS 

By Karen C. McNally, 

University of California, Santa Cruz; 

Gerald W. Simila, 

California State University, Northridge; 

and 

Judy G. Brown, 

University of California, Santa Cruz 

ABSTRACT 

A data set consisting of main-shock and very early aftershock records was acquired from four digital accelerometers deployed before the 1989 Loma Prieta earthquake. 

We find that 34 aftershocks of M23.8 occurred within the 

first 3 5 hours after the main shock. We outline our procedures for event location, relocation, and magnitude determination. 

INTRODUCTION 

After the August 8, 1989 (M=5.3), Lexington Reservoir, Calif. (fig. I), earthquake, four three-component digital accelerometers (Teledyne Geotech model A-700) were 

temporarily deployed by the University of California, Santa 

Cruz (UCSC), to monitor for an anticipated large earthquake in the Santa Cruz Mountains. Main-shock records 

from these four stations are shown in figure 2; the locations of the stations (triangles, fig. l) are listed in table l. 

The instruments were placed in homes and laboratories 

Contribution No. 189, Charles F. Richter Seismological Laboratory 

and Institute of Tectonics, University of California, Santa Cruz, CA 

95064. 

for electrical power, security, and ease of access, where 

they could be monitored readily by checking a light on 

the instrument to see whether it had been triggered by an 

earthquake. All the instruments were oriented to true north, 

with an estimated compass measurement error of &5O, and 

were set above ground; none was bolted down, owing to 

the temporariness of the deployment and the heavy 44-lb 

(20 kg) weight of the instrument in its cast-aluminum 

case. 

The instrument at station BRAN (fig. 1) was located at 

the residence of Richard Terdiman at 5001 Branciforte 

Drive in Santa Cruz, Calif. The site is a flat area near the 

top of a steep hill on the west side of Branciforte Creek 

(fig. 1). The instrument was placed on the concrete floor 

of a detached wood-frame garage (three sided, open in the 

front) that was located on bedrock at the cut-in side of the 

hillside. After the main shock, the house, which was on 

the outer hillslope side, was red tagged (deemed unsuitable for habitation) but still standing. The instrument was 

found with some empty cardboard boxes and an empty 

wooden chest leaning on top of it; the records obtained 

are shown in figure 2. 

The instrument at station LGPC (fig. 1) was located in 

the house of Richard Holley, caretaker of the Los Gatos 

Presentation Center, at 19600 Bear Creek Road, a mountainous area of Los Gatos within the Lorna Prieta rupture 

zone. The center used to be a private school called 

Montezuma School, as shown on the U.S. Geological Survey (USGS) map of the Castle Rock Ridge 7.5-minute 

quadrangle, and is now a convent. The instrument was 

placed on a detached concrete pad in the basementhtorage area. The wood-frame house is built on a steep hill, 

where the single-story building is essentially a two-story 

structure on the downhill side and the lower story is used 

only for storage. The house lost its chimney, and the entire foundation had to be replaced, after the main shock; a 

retaining wall behind, and the walkway leading to, the 

house were both cracked. After the main shock, the conA147 
A148 MAIN-SHOCK CHARACTERISTICS 

Crete pad beneath the instrument was found to be separated from an adjacent concrete step by a few centimeters; 

whether or not this was so before the earthquake is unknown. Fred Followell observed some evidence indicating "chatter" between the step and the pad, but no other 

evidence suggesting scraping or upending of the instrument. Also, Mr. Holley stated, "when they pulled out the 

old concrete pad, I was surprised to see that it was sitting 

on bricks." A baseline shift is visible on the vertical and 

north-south components of the records from station LGPC 

(figs. 3, 4; Yi-Ben Tsai, written commun., 1991), and so 

these records should be used with caution. However, the 

high frequencies appear valid, especially in the first part 

of the record. The baseline shifts could have been caused 

by a sudden tilt of the instrument with the pad itself. 

The instrument at station UCSC (fig. 1) was located in 

the Charles F. Richter Seismological Laboratory in the 

Applied Sciences Building at UCSC. The building is a 

three-story cast-in-place concrete structure with a basement. The instrument was placed unbolted on the first 

floor in room 195, the seismology shop. The Applied Sciences Building sustained some damage during the main 

shock, mostly due to differential settling. A free-field 

strong-motion accelerograph operated by the California 

Division of Mines and Geology (CDMG) is located near 

the parking lot adjacent to the building. The main shock 

registered peak accelerations of 0.47 g (horizontal), and 

0.40 g (vertical) on this instrument, in comparison with 

our lower values registered inside the building (fig. 5), as 

would be expected. 

Figure 1.-Schematic map of Loma Prieta region, Calif., showing locations of rupture zone (rectangle), orthogonal cross sections A-A' (see fig. 7) and 

longitudinal cross section Y-Y' (see fig. 8), main shock (large star), aftershocks that occurred during first 2 hours and 22 minutes after main shock 

(circled stars) and until November 7, 1989 (stars), and other events interpreted to lie east (large dots) and west (circles) of main aftershock zone, 

including four foreshocks (small dots) of 1988 and 1989 (see table 2). Irregular lines, major faults (dashed where inferred, queried where uncertain); 

triangles, four temporary stations installed by the University of California, Santa Cruz. 
MAIN-SHOCK AND VERY EARLY AFTERSHOCK ACTIVITY1 A149 

The instrument at station WAHO (fig. 1) was located in 

the house of Walter Schillinger at 738 Cable Court, near 

the Yacht Harbor in downtown Santa Cruz. The instrument was placed on the concrete garage floor of a twostory wood-frame house or condominium. The attached 

garage protrudes from the house, half inside and half outside the main structure. The building did not sustain any 

structural damage. The records obtained are shown in figure 6. 

These four instruments recorded the main shock and 

aftershocks, but their memories were filled within 10 hours 

of the main shock. Within 2 days of the main shock, the 

four original stations were serviced, and five additional 

stations, AHCR, BGST, CTES, LGPS, and LPVF (table 

I), also equipped with Teledyne Geotech model A-700 

digital accelerometers were installed. In addition, analog 

velocity recorders (Sprengnether model MEQ-800) were 

colocated at all nine stations. The station locations and all 

the aftershocks recorded at all nine stations are shown in 

figure 1 of Simila and others (1990) and listed in tables 1 

through 4. 

Owing to the large size of the main shock (ML=6.9k0.44, 

McNally and others, 1990; ML=6.7k0.09, Uhrhammer and 

Bolt, 1991), nearby high-gain seismographs operated by 

the USGS and the University of California, Berkeley 

(UCB), were driven offscale, and so the seismograms for 

the main shock and very early aftershocks from these 

nearby stations were nearly useless. Because the digital 

accelerometers have a wide dynamic range, however, they 

collected data for events spanning two orders of magnitude in acceleration. Three of the original four stations 

(LGPC, UCSC, WAHO, fig. 1) had trigger thresholds of 

0.0088 g and peak settings of 1.0 g, and one station 

(BRAN) had a trigger threshold of 0.0044 g and a peak 

setting of 0.5 g. Total pretrigger and posttrigger recording 

time on the instrument is 35 s, unless it is retriggered; the 

sampling rate is 200 samples per second. All the instruments triggered on the main shock and produced a 35-s 

TIME, IN SECONDS 

Figure 2.-Digital accelerograms of Loma Prieta main shock recorded at station BRAN (fig. I), showing east-west (A), north-south (B), and vertical 

(Q components. East, north, and up directions are all positive. Sampling rate, 200 samples per second; trigger threshold, 0.0044 g; full scale, 0.50 g; 

peak amplitude, 0.46 g (fig. 25; note that records in figs. 2A and 2C are probably clipped at 0.50 g). 
A150 MAIN-SHOCK CHARACTERISTICS 

record, including 17 s of pretrigger data in memory (the 

17-s setting was customized for us by the manufacturer to 

retain P-wave arrivals in special studies of large earthquakes using temporary deployments). Our aftershock 

records for the first 34 minutes after the main shock provide nearly continuous detection; subsequently, the instruments continued to retrigger and record main-shock 

and very early aftershock activity for about 41 minutes. 

This data set provides a unique opportunity to analyze the 

early fault-rupture history of the earthquake. 

DATA ANALYSIS 

To accurately locate these very early aftershocks requires a joint relocation procedure involving several steps. 

The first step is to select calibration events (Simila and 

others, 1990). We used a set of 31 well-recorded aftershocks from the period October 20 through November 7, 

1989 (see tables 2, 4). Arrival times of P and S waves 

recorded by the colocated analog and digital accelerometers, and P-wave-phase data from USGS stations within 

30 km of the main shock (see tables 1, 3), were analyzed 

with the earthquake-location computer program 

HYPOINVERSE (Klein, 1989), along with Dietz and 

Ellsworth's (1990) two-sided velocity model. From the 

combined data sets, we obtained traveltime adjustments 

for the four UCSC stations (see table 3) and an average 

local Poisson's ratio (ratio of P- to 5-wave velocities) of 

0= 1.7 1. These traveltime adjustments and a values were 

carefully calculated through an iterative procedure of locating the events, modifying the adjustments and a values, and then relocating the events until the P- and S-wave 

residuals at individual stations and the rms residuals for 

the solutions were minimized. 

The next step was to relocate the main shock, using Pand 5-wave traveltimes from the four UCSC stations with 

the new traveltime adjustments and a values and, as in 

the first step, using the P-wave traveltimes of the USGS 

stations and the model and delay times of Dietz and 

Ellsworth (1990). Both location and depth were particularly well constrained by the excellent horizontal-component 5-wave arrivals at the four original stations (BRAN, 

LGPC, UCSC, WAHO, fig. 1). Although these four sta0 10 20 30 40 

TIME, IN SECONDS 

Figure 2.-Continued 
MAIN-SHOCK AND VERY EARLY AFTERSHOCK ACTIVITY1 A151 

tions within 7 to 16 km of the main shock are all west 

(southwest to northwest) of the epicenter, the overall azimuthal coverage for the main shock is complete when the 

data from the UCSC and USGS stations are combined. 

The traveltime residuals for the USGS stations that recorded the main shock were found to be similar to the 

average rms residuals (at the same stations) for the calibration events. These average residuals were then added 

to the standard traveltime adjustments for the USGS stations. (To maintain a nearly homogeneous station-array 

configuration for all events, P-wave-phase data from the 

USGS stations that recorded sporadically were not used.) 

The calibration aftershocks were then relocated (see table 

2). 

The final step was to relocate all aftershocks of M23.8 

by using data from the UCSC stations with the new traveltime adjustments (see table 3) and 0=1.71. The first Pwave arrivals for the main-shock hypocenter were set for 

stations BRAN, WAHO, UCSC and LGPC, using the calculated traveltimes for their distances of 9.8, 12.9, 17.1, 

and 19.1 km, together with the new adjustments, as 00 h 

04 min and 18.52, 18.47, 19.10, and 19.83 s, respectively. 

Time was thus established for the remaining digital records. 

(The main-shock S-wave arrival times were 00 h 04 min 

and 21.82, 21.17, 21.90, and 22.83 s, respectively.) The 

main shock contained multiple ruptures that are evident in 

figures 2 through 6; here, we refer to the first break as the 

main-shock hypocenter. For six early aftershocks, we have 

data from only the four original UCSC stations. At these 

stations, uncertainties are larger, but the traveltime adjustments help compensate for this difficulty somewhat. 

These initial locations were obtained by using the mainshock hypocenter as the starting location. Locations were 

then recalculated with the new epicenters as the starting 

locations but with several starting depths, to estimate location stability. Also, the main shock was relocated by 

using data from the same four stations, for another measure of location uncertainty. When the starting location 

was that of the known main-shock hypocenter, the solution moved 1.9 km northwest and +0.6 km in depth. The 

statistical precision of this solution is rms=O. 16, horizontal error (ERH)=2.2 km, and vertical error (ERZ)=31.6 

km. However, when the coordinates of the closest station 

and a 12-km depth (the default) were used as the starting 

20 30 40 50 60 

TIME, IN SECONDS 

Figure 2.-Continued 
A152 MAIN-SHOCK CHARACTERISTICS 

location, the solution moved 5.2 km due west and +3.8 

km in depth. We believe that these values of -5 km may 

be a more realistic estimate of the uncertainty in location 

for early aftershocks located with only the four original 

UCSC stations than the statistical precision of rms=0.08, 

ERH=2.15 km, and ERZ=l. 15 km calculated for the test 

solution. The locations of all events of ML23.8 are summarized in table 2 and detailed in table 4. 

The event magnitudes listed in tables 2 and 4 were 

calculated from the measured Wood-Anderson amplitudes 

reported by UCB (University of California, Berkeley, 

1989), using the method of Richter (1935, 1958). These 

amplitudes were incorporated into the program 

HYPOINVERSE in conjunction with the phase data, so 

that both the location and magnitude (Mi) could be determined. UCB standard magnitude corrections were used 

for stations BRK (+0.2), MHC (+0.1), MIN (-0.1), and 

BKS (0.0). Some of our final magnitudes differ from those 

of UCB because of both roundoff and differences in earthquake locations. Also, our magnitudes should be compared with the magnitude called ML(c) by UCB in their 

1989 catalog, which indicates that the data are from 

recalibrated instruments. In addition, the local magnitude 

(ML1) was estimated from measurements of Wood-Anderson records synthesized (Uhrhammer and Collins, 1990) 

from the digital-accelerometer records, using the method 

of McNally and others (1990) with the distance corrections of Bakun and Joyner (1984) and Hutton and Boore 

(1987). A regression between Mi and ML1 yielded the 

relation ML+=(0.94&0.25)ML1-0.30. This magnitude, Mi+, 

was used for aftershocks with no UCB Wood-Anderson 

amplitudes available (7 events; pluses, table 2). 

Of the 43 events (M23.8) that we recorded within the 

first 24 hours after the main shock, 24 were of M24.0 

(table 2). Because the magnitudes and distances from the 

recording station place fundamental constraints on the 

TIME, IN SECONDS 

Figure 3.-Digital accelerograms of Loma Prieta main shock recorded at station LGPC (fig. I), showing east-west (A), north-south (B), and vertical 

(0 components. East, north, and up directions are all positive. Sampling rate, 200 samples per second; trigger threshold, 0.0088 g; full scale, 1.0 g; 

peak amplitude 0.80 g (fig. 3A; note that records in figs. 35 and 3C are probably clipped at 1.0 g). Baseline offset may reflect sudden tilting of 

instrument (see fig. 4). 
MAIN-SHOCK AND VERY EARLY AFTERSHOCK ACTIVITY' A 153 

minimum threshold for detection and location deterrnination, we analyzed several later aftershocks of M>4.0 to 

evaluate the event detectability southeastward along the 

fault zone as a function of distance, Specific aftershocks 

included in our tests are the secondary sequence at 1014 

G.m.t. October 19 near the Zayante fault at lat 36'58' N., 

long 121'50' W. (M=4.6), and the event at 0127 G.m.t. 

October 25 (M=4.6) northeast of the main shock at lat 

37'05' N., long 121Â°50 W. (Oppenheimer, 1990). These 

tests indicate that any events of M24.5 at distances 525 

krn from station BRAN along the San Andreas fault would 

have been recorded at the four original stations during the 

first 34 minutes after the main shock. 

RESULTS 

The locations of aftershocks of Mr23.8 are shown in 

figure 1. Within several minutes of the main shock, most 

aftershocks occurred near the northwestern part of the 

Loma Prieta rupture zone, in the vicinity of the San Andreas-Sargent fault intersection and northwestward. The 

first, second, and fourth aftershocks were located west of 

the San Andreas fault. Because of timing uncertainties 

and station limitations in number and azimuth, these locations may be suspect. However, the later occurrence of 

several very well recorded aftershocks (Mc3.8) in the same 

area-for example, the event at 1402 G.m.t. October 23 

(table 4)-suggests that the locations of these very early 

events may reflect a second, westerly zone of faulting 

activity. Alternatively, if errors in depth are greater than 

we estimate, these events may lie on the main-shock rupture surface, at greater depth. 

Cross sections orthogonal to the San Andreas fault (AA' through F-F', fig. 1) for all events (tables 2, 4) are 

shown in figure 7, and the distribution of hypocenters 

(M23.8) in a longitudinal cross section (Y-Y') in figure 8. 

Our early aftershock pattern for the first 2 hours and 22 

minutes after the main shock is consistent with the observation that aftershocks are generally absent in main slip 

zones of large earthquakes (Mendoza and Hartzell, 1988). 

Regarding the absence of early aftershock activity to the 

0 10 20 30 40 50 60 

TIME, IN SECONDS 

Figure 3.-Continued 
A 154 MAIN-SHOCK CHARACTERISTICS 

southeast, however, we cannot eliminate the possibility of 

magnitude detection-threshold limitations in our data set. 

CONCLUSIONS 

We find that 34 significant aftershocks of Mi23.8 occurred within 3 y& hours of the main shock. Most of these 

events are located northwest of the main-shock hypocenter, 

largely concentrated near the intersection of the San Andreas and Sargent faults. 

ACKNOWLEDGMENTS 

This research was partly supported by the William M. 

Keck Foundation, the U.S. National Science Foundation 

(grant EAR-9002704), the USGS (grant 14-08-000 1- 

G1839), and the UCSC Division of Graduate Studies and 

Research and the Division of Natural Sciences. The second author was supported by the Minority Access to Energy Related Careers (MAERC) program of the Associated Western UniversitiesN.S. Department of Energy. We 

thank the researchers, visiting researchers, staff, and graduate students of the Charles F. Richter Seismological Laboratory at UCSC, who made an extraordinary effort to 

maintain field instruments and analyze data after the earthquake, particularly Walter Schillinger, Instrument Specialist for UCSC's Department of Earth Sciences, who was 

primarily responsible for maintaining the four digital accelerometers. We also thank the following for providing 

data and information relevant to this study: David 

Oppenheimer of the USGS; Robert Uhrhammer and Rick 

McKenzie of the UCB Seismographic Observatory; and 

L. Katherine Hutton of the California Institute of Technology. We are grateful to Paul Spudich and Lynn Dietz 

for their reviews of the manuscript. Yi-Ben Tsai of the 

Pacific Gas & Electric Co. generously provided an independent assessment of the accelerograms recorded at station LGPC. 

0 10 

Figure 3.-Continued 

20 30 40 

TIME, IN SECONDS 
MAIN-SHOCK AND VERY EARLY AFTERSHOCK ACTIVITY1 A155 

REFERENCES CITED 

Bakun, W.H., and Joyner, W.B., 1984, The M, scale in central California: Seismological Society of America Bulletin, v. 74, no. 5, p. 

1827-1843. 

Dietz, L.D., and Ellsworth, W.L., 1990, The October 17, 1989 Loma 

Prieta earthquake and its aftershocks; geometry of the sequence 

from high-resolution locations: Geophysical Research Letters, v. 

17, no. 9. p. 1417-1420. 

Hutton, L.K., and Boore, D.V., 1987, The M, scale in southern California: Seismological Society of America Bulletin, v. 77, no. 6, p. 

2074-2094. 

Klein, F.W., 1989, User's guide to HYPOINVERSE, a program for 

VAX computer to solve for earthquake locations and magnitudes: 

U.S. Geological Survey Open-File Report 89-314, 58 p. 

McNally, K.C., Yellin, Joseph, Protti-Quesada, Marino, Simila, G.W., 

Malavassi, Eduardo, Schillinger, Walter, Terdiman, Richard, and 

Zhang, Zhi, 1990, The local magnitude of the 18 October 1989 

Santa Cruz Mountains earthquake is M=6.9: Geophysical Research 

Letters, v. 17, no. 10, p. 1781-1784. 

Mendoza, Carlos, and Hartzell, S.H., 1988, Aftershock patterns and 

main shock faulting: Seismological Society of America Bulletin, v. 

78, no. 4, p. 1438-1449. 

Oppenheimer, D.H., 1990, Aftershock slip behavior of the 1989 Loma 

Prieta, California earthquake: Geophysical Research Letters, v. 17, 

no. 8, p. 1199-1202. 

Richter, C.F., 1935, An instrumental earthquake-magnitude scale: Seismological Society of America Bulletin, v. 25, no. 1, p. 1-32. 

1958, Elementary seismology: San Francisco, W.H. Freeman and 

Co., 578 p. 

Simila, G.W., McNally, K.C., Nava, E.M., Protti-Quesada, Marino, and 

Yellin, Joseph, 1990, Evidence of very early aftershock activity 

along the northwest portion of the 18 October 1989 earthquake rupture zone: Geophysical Research Letters, v. 17, no. 10, p. 1785-1788. 

Uhrhammer, R.A., and Bolt, B.A., 1991, The seismic magnitude of the 

1989 Loma Prieta main- shock determined from strong-motion 

records: Seismological Society of America Bulletin, v. 81, no. 5, p. 

1511-1517. 

Uhrhammer, R.A., and Collins, E.R., 1990, Synthesis of Wood Anderson seismograms from broadband digital records: Seismological Society of America Bulletin, v. 80, no. 3, p. 702-716. 

University of California, Berkeley, 1989, Seismographic Stations Bulletin: v. 59, no. 1-2, 117 p. 

-1 .o^ I f I I I I I I I 4 5 10 

TIME, IN SECONDS 

Figure 4.-Baseline-corrected digital accelograms of Loma Prieta main shock recorded at station LGPC (fig. I), showing eastwest (A), north-south (B), and vertical (C) components. East, north, and up directions are all positive. Top plot, original record; 

middle plot, baseline correction; bottom plot, baseline-corrected record (Yi-Ben Tsai, written cornmun., 1991). 
MAIN-SHOCK CHARACTERISTICS 

TIME, IN SECONDS 

Figure 4.-Continued 
MAIN-SHOCK AND VERY EARLY AFTERSHOCK ACTIVITY' 

TIME, IN SECONDS 

Figure 4.-Continued 
MAIN-SHOCK CHARACTERISTICS 

TIME, IN SECONDS 

Figure 5. Digital accelerograms of Loma Prieta main shock recorded at station UCSC (fig. l), showing east-west (A), north-south (B), and vertical (0 

components. East, north, and up directions are all positive. Sampling rate, 200 samples per second; trigger threshold, 0.0088 g; full scale, 1.0 g; peak 

amplitudes: 0.42 g (fig. 5A), 0.31 g (fig. 5B), 0.22 g (fig. 5C). 
MAIN-SHOCK AND VERY EARLY AFTERSHOCK ACTIVITY' A159 

0 10 20 30 

TIME, IN SECONDS 

Figure 5. Continued 

MAIN-SHOCK AND VERY EARLY AFTERSHOCK ACTIVITY1 A161 

TIME, IN SECONDS 

Figure 6.-Digital accelerograrns of Loma Prieta main shock recorded at station WAHO (fig. I), showing east-west (A), north-south (B), and vertical 

(0 components. East, north, and up directions are all positive. Sampling rate, 200 samples per second; trigger threshold, 0.0088 g; full scale 1.0 g; 

peak amplitudes: 0.66 g (fig. 6A), 0.38 g (fig. 65), 0.27 g (fig. 60. 
MAIN-SHOCK CHARACTERISTICS 

0 10 20 30 40 50 60 

TIME, IN SECONDS 

Figure 6.-Continued 
MAIN-SHOCK AND VERY EARLY AFTERSHOCK ACTIVITY' 

0 10 20 30 40 50 60 

TIME, IN SECONDS 

Figure 6.-Continued 
A 164 MAIN-SHOCK CHARACTERISTICS 

Table 1 .-Temporary stations deployed by the University of California, Santa Cruz, in the Loma Prieta area 

Location 

Station Elevation 

Lat N. Long W. (m) 

Address Description and dates of operation 

BRAN 103 5001 Branciforte Drive On concrete floor in wood-frame garage detached from house. 

Santa Cruz, CA. Aug. 15-Nov. 16, 1989. 

LGPC 48 1 19600 Bear Creek Road 

Los Gatos, CA 

On detached concrete pad in basement/storage area (downhill 

side) of a wood-frame single-story house built on a moderately 

steep hillside. Aug. 15, 1989-Mar. 5, 1990. 

UCSC 243 Applied Sciences Building 

McLaughlin Drive 

University of California 

Santa Cruz, CA 

On floor of first-story seismology laboratory (room 195) in a large four-story cast-in-place reinforced-concrete office building. 

Aug. 9, 1989-Jan. 16, 1990. 

2 1 738 Cable Court 

Santa Cruz, CA 

On concrete in attached garage that protrudes from a two-story 

wood-frame condominium, Aug. 9-Nov. 17, 1989. 

WAHO 

AHCR 

BGST 

CTES 

LGPS 

LPVF 

Oct. 28, 198SJan. 11, 1990. 

Oct. 22, 1989-Mar. 5, 1990. 

Oct. 20-Nov. 7, 1989, 

Oct. 20-Nov. 7, 1989, 

Oct. 22, 1989-Mar. 7, 1990. 

Table 2.-Seismicity (ML23.8) in the Loma Prieta area 

[Magnitude (ML) of the October 18 (G.m.t.) main shock from McNally and others 

(1990); magnitudes of aftershocks with a listing of "+" were calculated from the 

local magnitude Mi, that is, Wood-Anderson records synthesized from digital 

strong-motion records at stations BRAN, LGPC, UCSC and WAHO (see figs. 1 

and 8 for locations) and calibrated to ML by the relation ML+=0.94(i0.25)ML'- 

0.30. Otherwise, ML is calculated from the University of California, Berkeley, 

Wood-Anderson amplitude relative to a specific location. Event with an "R" has a 

restricted depth; events with a listing of "0" are not in the U.S. Geological Survey 

aftershock list; events with a listing of "c" were used to calibrate joint relocation 

and redetermination of Poisson's ratio and station delay. SAF, San Andreas fault; 

events not located east (E) or west (W) of the fault occurred on the fault. ERH, 

horizontal-location error; ERZ, vertical-depth error; UCSC, University of California, Santa Cruz] 
MAIN-SHOCK AND VERY EARLY AFTERSHOCK ACTIVITY1 A165 

1988 June 27 

1989 Aug. 8 

Oct. 18 

Oct. 19 

Oct. 20 

Oct. 21 

Oct. 22 

Oct. 25 

Oct. 26 

Oct. 30 

Nov. 2 

Nov. 5 

Nov. 7 
MAIN-SHOCK CHARACTERISTICS 

Table 3.-P-wave station delays determined in this 

study and used for event relocation 

[Asterisks, delays calculated by using alternate Pacific side of 

crustal-velocity model of Dietz and Ellsworth (1990); pluses, 

UCSC stations. The 5-wave delay is equal to 1.71 (Poisson's 

ratio, determined in this study) times the P-wave delay, according to allowance of 

HYPOINVERSE (Klein, 1989)l 

the computer program 

Station Delay Station , Delay 

+BRAN 

+LGPC 

+UCSC 

+WAHO 

BSLM 

BVYM 

CADM 

CALM 

CAOM 

CCOM 

CMHM 

CMJM 

CSCM 

HAZM 

HCAM 

HCBM 

HCRM 

HDLM 

HFEM 

HFHM 

HFPM 

HGSM 

HGWM 

HJSM 

HKRM 

HMOM 

HF'RM 

HSPM 

JALM 

JBCM 

JBLM 

JBMM 

JBZM 

JCBM 

JECM 

JHLM 

JLXM 

JPLM 

JPPM 

JRGM 

JRRM 

JSCM 

JSGM 

JS MM 

JSSM 

JSTM 

JTGM 

JUCM 

+CTES 

+LPVF 

HJGM 

JBGM 

JHPM 

JPSM 
MAIN-SHOCK AND VERY EARLY AFTERSHOCK ACTIVITY' 

Table 4.-Details of seismicity in the Lorna Prieta rupture zone 

[Event with an "R has a restricted depth. DMIN, distance to nearest stations (in kilometers); GAP, largest azimuthal gap between stations; ERH, horizontal-location error; 

ERZ, vertical-depth error] 

Date Time Latitude Longitude Depth No. of 

M,PIS Rms ERH ERZ 

(yymmdd) (G.m.t.) N. W. (km) residual phases r, () (km) (km) 

Earthquakes on the San Andreas fault 
A168 MAIN-SHOCK CHARACTERISTICS 

Table 4.-Details of seismicity in the Loma Prieta rupture zone-Continued 

Date Time Latitude Longitude Depth NO. of 

MAS Rms ERH ERZ 

(yymrndd) (G.m.t.) N. W. (km) residual phases ('I () (km) (km) 

Earthquakes on the San Andreas fault-Continued 

Earthquakes east of the San Andreas fault 

Earthquakes west of the San Andreas fault 
MAIN-SHOCK AND VERY EARLY AFTERSHOCK ACTIVITY1 A 169 

-zoo c 

10 20 

DISTANCE, IN KILOMETERS DISTANCE, IN KILOMETERS 

-200 uu 

10 20 

DISTANCE. IN KILOMETERS 

-20;""""'~""'~~~"'1 10 20 

DISTANCE. IN KILOMETERS 

.zoo c 

10 20 

DISTANCE, IN KILOMETERS 

-m;""""'I""""'I""'I 10 20 

DISTANCE, IN KILOMETERS 

Figure 7.-Seismicity in the Lorna Prieta rupture zone (see fig. 1) along orthogonal cross sections A-A' (A), B-B' (B), C-C (C), D-D' (D), E-E' (E), 

and F-F (F). Same symbols as in figure 1. See tables 2 and 4 for details on events. Note that all relocated events of all magnitudes are shown in these 

cross sections. 
A 170 MAIN-SHOCK CHARACTERISTICS 

L 

-10 - *@ 0 - ^ ** &-A- 

@ ** 

-20 - @, , ,^ , , , , , , , , 1, , , , , , , , , , , , , , , , ; * 

0 10 20 3 0 40 50 

DISTANCE, IN KILOMETERS 

Figure 8.-Seismicity (M33.8) in the Lorna Prieta rupture zone (see fig. 1) along longitudinal cross section Y-I". Same symbols as in figure 1. Note 

that main part of aftershock zone is devoid of events until 3 hours and 19 minutes after main shock. 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAmOCCURRENCE 

MAIN-SHOCK CHARACTERISTICS 

DOWNDIP GEOMETRY OF THE LOMA PRIETA RUPTURE FROM 

TELESEISMIC WAVEFORM INVERSION 

CONTENTS 

By John L. NiibSlek, 

Oregon State University 

Page 

A171 

171 

171 

172 

173 

175 

175 

177 

180 

181 

181 

18 1 

ABSTRACT 

The 1989 Loma Prieta earthquake was well recorded 

by global digital seismic networks. The azimuthal coverage provided by stations is excellent, and the recorded 

body waves can be deconvolved to yield broadband displacements, with excellent consistency of waveform and 

amplitude among stations. I use broadband teleseismic P 

and SH waves from 27 stations to investigate the rupture 

process of the earthquake. An inversion using a pointsource mode1 gives the following estimates of the average 

(centroidal) parameters: strike, 127Ok2'; dip, 63'&1Â° rake, 

129Ok2'; depth, 10.5&1 km; and seismic moment, 

2.9kO. lx 1 oig N-m (Mw=6.9). The estimated source-time 

function indicates that the source duration was about 15 s 

and that about 85 percent of the moment was released 

during the first 10 s. Very little azimuthal variation in 

pulse duration is observed, indicating a bilateral rupture. 

Setting up a line grid along the indicated dip, I investigate 

the seismic-moment release and the evolution of the rupture as a function of depth. I find that the Loma Prieta 

rupture extended updip from a nucleation depth of about 

17.5 km, that 70 percent of the moment was released 

within the depth range 8-13 km, and that no significant 

moment was released at depths above 5 km. Inversions 

indicate that in the lower two-thirds of the fault surface, 

the slip had, on average, a larger strike-slip component 

than in the upper third. Two-dimensional source 

parametrizations produce unstable results, and so lateral 

variations in the moment release cannot be determined 

from this data set. 

INTRODUCTION 

In this paper, I present the results of an analysis of 

teleseismic body waves to examine the rupture process of 

the 1989 Loma Prieta earthquake. The goal of this study 

was, first, to derive basic centroidal source parameters 

and, second, to focus on the downdip geometry of the 

fault surface, to determine the seismic-moment release as 

a function of depth, and to investigate whether any 

downdip variation in fault orientation and slip direction is 

discernible. I first present the results of my analysis and 

then discuss how they compare with those of other bodywave studies using related data sets. 

DATA SET 

In this investigation, I used P waves in the epicentraldistance range 30'-95' and SH waves in the epicentraldistance range 30'-75' recorded by stations in the 

Incorporated Research Institutions for SeismologylGlobal 

Seismic Network (IRISIGSN), GEOSCOPE (Institut National des Sciences de 19Univers, France), and the Global 

Digital Seismograph Network (GDSN), and by one unaffiliated station in Japan; altogether, 41 waveforms were 

utilized. In general, the data quality is very high, with 

good coherency both in amplitude and wave shape between stations along similar wave paths. Only a few waveforms were rejected because of anomalous behavior due 

either to instrument malfunction or to unusual propagation paths; the rejected waveforms are of P waves from 

stations HON and KIP in Hawaii and of SH waves from 

station COL in Alaska. 
A172 MAIN-SHOCK CHARACTERISTICS 

I used very broad band data streams for stations with 

broadband sensors (which are proportional to ground velocity), intermediate-band streams for digital World Wide 

Seismic Station Network (WWSSN) stations, and a combination of short- and long-period streams for Seismic 

Research ObservatorylAutomatic Seismic Research Observatory (SROIASRO) stations; I used long-period streams 

(1 sample per second) for a few stations where higher 

resolution streams were unavailable. All the raw seismograms were converted to broadband ground displacement 

by removing the instrument response. The resulting data 

were resampled at a rate of 5 samples per second and 

high-pass filtered with a cutoff frequency of 0.01 Hz to 

remove long-period instabilities. 

The modeling and inversion techniques applied to the 

data are simple extensions of those described earlier 

(NiibGlek, 1984, 1985). Teleseismic body waves in the 

above-mentioned distance ranges avoid the complexities 

due to upper-mantle triplications and core interactions. 

The waveforms contain direct phases, reflections from the 

free surface, as well as converted phases due the crustal 

structure, that are accounted for in the modeling procedure. The observed seismograms were simultaneously inverted for the desired source parameters by minimizing 

the L2 norm. The waveform-inversion window always included the first 40 s after the onset of the direct P- or Swave phase, as applicable. The assumed source crustal 

structure (table 1) used to locate aftershocks is based on 

that of Dietz and Ellsworth (19901, thus allowing a direct 

comparison between my results and theirs. Most other 

investigators have used similar structural parameters. 

POINT-SOURCE MODEL 

The simplest parametric source model used here is a 

point source. Inversion using this model gives centroidal 

averages of the source parameters: The source mechanism 

(strike, dip, rake), depth, seismic moment, and sourcetime function. The estimated parameters for this inversion 

are listed in table 2, the derived source-time function is 

plotted in figure 1, and the match between the observed 

and synthetic seismograms is shown in figure 2. This 

simple model fits the general features of the observed 

seismograms remarkably well, although some consistent 

discrepancies immediately after the onset of P waveforms 

(during the first quarter-cycle of waveforms from stations 

to the east-for example, CAY-the amplitudes are 

slightly underestimated, whereas for the northwestern stations-for example, MDJ-they are slightly overestimated) 

indicating that the source mechanism may have had a 

larger-than-average strike-slip component during the early 

stages of the rupture process. Later parts of the P-wave 

seismograms from western stations also show a consistent 

phase mismatch that may indicate a change in source 

Table 1 .-Crustal model and attenuation parameters 

used in this study 

[t*=l s for P waves; t*=4 s for SH waves] 

Source 

Receiver 

mechanism toward the end of the rupture process (fig. 

2A). The source-time function (fig. 1) is rather simple: 

After an initial slow rise lasting about 4 s, 70 percent of 

the moment is released in a simple 5-s-long pulse, followed by some additional moment release over the next 

6 s. The total rupture time of the earthquake is 15 s. No 

consistent significant misfits in pulse widths occur between the model waveforms and those from stations on 

azimuths along the fault strike, indicating a bilateral rupture. The derived source orientation is similar to that found 

in many other studies. The estimate of the source mechanism is highly stable and does not depend strongly on the 

assumed crustal structure or other model parameters. The 

strongest tradeoff occurs between the estimated source 

depth and the seismic moment. To show this interplay, 

the seismic-moment estimate as a function of depth is 

plotted in figure 3, where the estimated moment decreases 

from about 3.5xl0l9 N-m at 7-km depth to about 2.5x1019 

N-m at 15-km depth. The variance of the misfit plotted in 

figure 3 shows a well-defined minimum at about 10-km 

depth, with an uncertainty of about kl km. Within this 

range, the seismic moment ranges from 2.8xl0l9 to 

3.0x10l9 N-m. 

The centroidal parameters for the Loma Prieta rupture 

obtained here generally agree with many other estimates 

from various studies, as discussed below. Here, I comment on some significant discrepancies in the seismicmoment estimates between some body-wave investigations. 

The moment of 2.9~10~~ N-m obtained here is at the higher 

end of the estimated values, some of which are as low as 

1 .9xl0l9 N-m. This discrepancy cannot be accounted for 

simply by variations in the data; figure 2 shows that the 

data are fitted in amplitude quite well. In my opinion, 

most of the lower estimates are due to a combination of 

the following factors: (1) deeper source depth for which 

the seismic moment was estimated; (2) use of a shorter 
DOWNDIP GEOMETRY OF THE LOMA PRIETA RUPTURE FROM TELESEISMIC WAVEFORM INVERSION A173 

Table 2.-Point-source parameters of the earthquake 

as determined in this study 

Strike Dip Rake MO M~v 

(N-m) 

low-pass filtered with a cutoff frequency at 0.03 Hz. The 

amplitudes of low-frequency waves are directly proportional to the seismic moment, and so this procedure provides a more direct estimate; the resulting seismic moment 

remained the same as in the broadband inversion. 

FINITE ONE-DIMENSIONAL MODEL 

source-time function, that is, assuming that the contributions after the first 10 s are insignificant; and (3) use of 

ground-velocity seismograms, which are poorer in lowfrequency components than the ground-displacement seismograms used here. 

I believe that the seismic moment estimated here is 

appropriate for the following reasons. (1) It agrees with 

estimates in several other body-wave studies that also 

found a similar source depth (for example, Hartzell and 

others, 1991; Wald and others, 1991). (2) It agrees with 

estimates based on geodetic observations, as well as those 

based on surface waves (although for such estimates the 

depth remains problematic). (3) In inversions using only 

subsets of stations over narrow ranges of distances and 

azimuths to investigate whether the moment release indicated by the last 6 s of the source-time function depends 

somewhat on a particular set of stations or waveforms, I 

have found that this later moment release is a consistent 

feature required by both P and SH waves. (4) Because the 

moment determination from broadband-displacement bodywave pulses depends on accurate integration of the estimated moment-rate-time function (source-time function), 

which may be difficult if the waveforms are rich in high 

frequencies, I have also inverted waveforms that were 

5 10 

TIME, IN SECONDS 

Figure 1 .-Moment-release-rate function of earthquake as determined in 

this study. 

We now attempt to determine how the moment release 

was distributed along the fault width (along-dip direction), considering that the rupture did not reach the surface, and so it is of interest to determine at what depth it 

stopped. Also, it has been suggested (Wallace and others, 

1991) on the basis of surface-wave observations, which 

give a substantially deeper seismic-moment centroid (-20 

km; Romanowicz and Lyon-Caen, 1990; Zhang and Lay, 

1990; Wallace and others, 1991) than body waves, that 

some significant moment release occurred below the nucleation point of the rupture, which, according to U.S. Geological Survey (USGS) estimates, was situated at about 

17-km depth. 

For this analysis, the model is parametrized as follows 

(fig. 4). Using the same source orientation as that determined in the point-source inversion, we assume that it 

remains unchanged for the whole duration of the rupture. 

We distribute nine point sources along the width at 2.8- 

km grid spacing (2.5-km depth interval): One source is 

located at the nucleation depth (17.5 km), six are located 

above it, and two are located below it. We assume a rupture-front-propagation velocity of 3 kmls between the 

gridpoints and the nucleation point. The only parameters 

that we invert for are the moment-rate functions at each 

gridpoint. The assumed rupture-front-propagation velocity is not a rupture velocity in the true sense because it 

defines only a time after which the gridpoint is allowed to 

be active. Setting the rupture velocity precisely is not critical as long as it is not too low, because once a gridpoint 

becomes active, it is allowed to be active for the entire 

source-process time. This detail distinguishes the rupture 

parametrization used here from that adopted in other studies. If the data demand that the rupture velocity be lower 

than that assumed, the moment-rate function will remain 

zero for some time after the source is allowed to turn on. 

We assign a rupture velocity to minimize the effect of 

inversion instabilities, which could result in noncausal 

moment release. To further stabilize the inversion, the 

moment-rate functions are discretized at a relatively low 

rate of 0.5 sample per second and are required to be nonnegative at all times. 

The reason why a complete two-dimensional fault model 

is not introduced at this stage is that teleseismic body 

waves, owing to their steep takeoff angles and the presence of strongly reflected phases from the free surface, 

are primarily sensitive to depth-dependent source 
A 174 MAIN-SHOCK CHARACTERISTICS 

ARU 

COL 

WMQ 

LZH 

H IA 

BJI 

MDJ 

TSK 

GUM0 

AFI 

PPT 

A 

MDJ 

MAJO 

TSK 

Kl P 

HON 

AFI 

PPT 

B 

0 10 20 30 

TIME, IN SECONDS 

0 10 20 30 

TIME, IN SECONDS 
DOWNDIP GEOMETRY OF THE LOMA PRIETA RUPTURE FROM TELESEISMIC WAVEFORM INVERSION A175 

variations; any effects related to the finite lateral extent of 

the source affect the waveforms much less and are much 

harder to resolve. 

The results of this inversion are shown in figures 5 and 

6. The moment-rate functions for each gridpoint are shown 

in figure 5. Note that the rupture, after starting at 17.5-km 

depth, propagates essentially updip. The moment release 

is rather slow* at the deepest sections of the fault but intensifies at about 12.5-km depth. At 7.5-km depth, the 

rupture is arrested for a moment and then restarts again, 

releasing some additional moment. Note that this model 

integrates the lateral rupture propagation at a given depth 

to the moment-release rate at the corresponding gridpoint; 

however, because the moment-release-rate functions at 

each depth are relatively short, the lateral extent of the 

rupture cannot be large. 

The corresponding depth distribution of the seismic 

moment is plotted in figure 6. Note that at the bottom of 

the fault plane, around the nucleation depth, only a small 

amount of moment is released, and no significant release 

occurs below 20-km depth. The moment release and, thus, 

the slip are concentrated between 12.5- and 7.5-km depth. 

Again, no significant moment release occurs above 5 km. 

The total seismic moment for this model is 2.95~10~~ Nm. Note that at 5- to 7.5-km depth, where the rupture 

appears to have been interrupted, the San Andreas fault 

apparently intersects the fault on which the earthquake 

occurred, This fault interaction appears to have affected 

the rupture, first stopping it and then allowing only a 

small additional slip in the vicinity of the intersection 

(fig. 5). 

The finite-width model generally improves the fit to 

the data over the point-source model. The improvement is 

particularly noticeable for P waves from the western stations (fig. 7), where the fit of the phase between the later 

parts of the observed and synthetic waveforms is considerably better. 

VARIABLE-MECHANISM MODEL 

In the above models, we assumed that the source orientation is constant over time. The data misfits with respect 

to the centroidal model indicate that slip in the rupturenucleation area might have had a larger-than-average 

4 Figure 2.-Match between observed (solid curve) and synthetic (dotted 

curve) seismograms for P (A) and SH (B) waves in point-source inversion. Amplitudes are normalized to 40' epicentral distance. Vertical 

dotted lines delimit inversion window. Circles in focal-mechanism solution indicate nodal planes and takeoff directions of direct waves. P and 

T, inferred axes of maximum and minimum compressional stress (pressure and tension axes), respectively. Arrow in figure 2A denotes part of 

waveforms where consistent phase mismatch occurs. 

strike-slip component and that, although the finite onedimensional model decreases the misfit in the later parts 

of the waveforms, some consistent discrepancies still remain. In the next model, we investigate whether the remaining significant inconsistencies can be removed by 

allowing the source orientation to change with depth. In 

this set of inversions, the model consists of three point 

sources distributed updip from the nucleation point (the 

previous models indicate no significant moment release 

below the nucleation depth). As before, we assume a rupture-front-propagation velocity of 3 kds and fix the strike 

to that found earlier. We invert for the dip, rake, and 

moment-release rate of each point source. The results, as 

shown in figures 8 and 9, indicate a steeper dip and a 

larger strike-slip component in the lower part of the fault 

surface, in agreement with the source mechanism derived 

from regional first-motion polarities. In its lower twothirds, the fault surface is remarkably planar,. and the 

mechanism remains constant. In the uppermost part, however, the slip appears to have a large thrust component. 

To investigate the stability of these results, I used many 

different starting models, including those with fault strike 

as one of the free parameters, but obtained essentially the 

same results. 

ATTEMPTS AT MORE DETAILED 

SOURCE MODELS 

The quality of the data is high, especially for P waves, 

for which the waveforms vary coherently from station to 

DEPTH, IN KILOMETERS 

Figure 3.-Estimated seismic moment (Mo) (dots) and variance of misfit 

(squares) as functions of assumed point-source depth. Discontinuities in 

curves are artifacts of layer boundaries in crustal model. 
A176 MAIN-SHOCK CHARACTERISTICS 

station. It is therefore tempting to see whether the fit can 

be improved further by introducing more sophisticated 

source models. The obvious next step is to introduce twodimensionality into the fault surface. Two-dimensional 

Figure 4.-Parametrization of one-dimensional finite-source model. At 

each gridpoint, only moment-release-rate function (irregular curves) was 

determined, assuming that rupture nucleated at 17.5-km depth and rupture front propagated at a velocity of 3 kmls. After passage of rupture 

front, elements of moment-release-rate function were allowed to assume 

arbitrary nonnegative values. 

0 5 10 15 20 25 30 35 

TIME, IN SECONDS 

Figure 5.-Moment-release-rate function at various depths, determined 

by using model shown in figure 4. Only nonzero elements are plotted. 

Dashed line, 3-kmls isochron. 

rupture models were, in fact, derived by several investigators, using teleseismic and strong-motion data, but they 

disagree in some important details. Although Beroza 

(1991), Hartzell and others (1991), Steidl and others 

(1991), and Wald and others (1991) broadly agreed that 

there were two primary loci of moment release, both at 

about 10- to 15-km depth and separated laterally by about 

10 km, they disagreed on the sense of slip in those regions. The models of Beroza (1991) and Steidl and others 

(1991) suggest that slip to the southeast of the hypocenter 

was essentially strike slip, whereas slip to the northwest 

of the hypocenter was almost pure dip slip; the models of 

Hartzell and others (1991) and Wald and others (1991) 

exhibit no such large lateral change in slip direction, although various scattered regions of the fault plane show 

some significant thrust components. My motivation in testing two-dimensional fault models was to see whether I 

could resolve these outstanding questions concerning partitioning of the strike-slip and dip-slip motion. 

The models that I considered were direct two-dimensional extensions of the one-dimensional models discussed 

in the preceding sections. They differed from those used 

in previous studies in having fewer restrictions on the 

time function at each gridpoint. Previous investigators assumed a uniform rupture velocity and fixed source-time 

function (rise time) at each gridpoint. Thus, each gridpoint 

was prescribed to slip at a particular time and only for a 

fixed duration; optimum rupture velocity and rise time 

were found by trial and error. In the models considered 

here, the gridpoints were not constrained to act only in a 

restricted time frame but were allowed to slip arbitrarily 

once the rupture front has passed, and the slip direction 

0 2 4 6 8 10 

SEISMIC MOMENT, IN 10 l8 NEWTON-METERS 

Figure 6.-Distribution of seismic-moment (My) release as a function of 

depth for earthquake, determined by using model shown in figure 4. 
DOWNDIP GEOMETRY OF THE LOMA PRIETA RUPTURE FROM TELESEISMIC WAVEFORM INVERSION A177 

was allowed to vary. Even simple two-dimensional models (grids of 7 or 9 points) improved the fit to the data 

considerably; however, the addition of new degrees of 

freedom to the model introduced tremendous instability 

and a tradeoff between the grid parameters, and no conclusive answers were obtainable. In comparison with other 

studies (Hartzell and others, 1991; Wald and others, 1991), 

relaxing the restrictions on the grid time functions appears to make the inversion unstable. The reason for this 

instability is the difficulty in resolving lateral source dimensions: If the rupture is tightly constrained from the 

start, seemingly stable results are obtainable; but if the 

constraint is removed, the stability disappears. The results, therefore, depend strongly on the appropriateness of 

the constraint. For the 1989 Loma Prieta earthquake, the 

resolution of lateral source dimensions is made difficult 

by the emergent features of the body waveforms, in turn 

making it difficult to pinpoint the arrivals from the nucleation point that provide the reference from which the 

rupture's lateral extent is measurable. 

One way in which the resolution of the areas of accelerated moment release could be improved is by emphasizing higher frequencies in the data. This improvement would 

be possible, however, only at the expense of decreased 

resolution of the smaller component of moment release 

and the average parameters. One straightforward way is 

to use ground-velocity waveforms instead of the grounddisplacement waveforms used here. Wald and others (199 1) 

used ground-velocity records, and Hartzell and others 

(1991) used a combination of ground-displacement and 

ground-velocity records, as data for their inversions; their 

lateral resolution of the areas of accelerated moment release should therefore in principle be better. Hartzell and 

others showed, however, that also for their data set the 

lateral distribution of moment release is quite unstable. 

Nevertheless, neither the teleseismic models of Wald and 

others (1991) and Hartzell and others (1991) nor the twodimensional models examined here indicate large lateral 

variations in slip direction. 

EFFECTS OF ASSUMED CRUSTAL 

STRUCTURE 

One additional question is whether our results could be 

significantly biased by the assumed crustal structure for 

the source region. I tested a range of structures within the 

realm of possibility, from simple half-space models to 

layered models of various complexity, and found that the 

centroidal source mechanism is highly stable with respect 

Ill1 

0 10 20 30 

TIME, IN SECONDS 

Figure 7.-Match between observed (solid curve) and synthetic (dotted curve) P-wave seismograms at representative stations in one-dimensional 

model. Amplitudes are normalized to 40' epicentral distance. Vertical dotted lines delimit inversion window. Circles in focal-mechanism solution 

indicate nodal planes and takeoff directions of direct waves. P and T, inferred axes of maximum and minimum compressional stress (pressure and 

tension axes), respectively. Phase mismatch in part of waveforms denoted by arrow is improved in comparison with point-source model (fig. 2A). 

Match for SH waves is qualitatively similar to that shown in figure 2B. 
A178 MAIN-SHOCK CHARACTERISTICS 

to all structures. The seismic moment and centroidal depth 

behave predictably: As the average velocity of the medium increases, the estimated values of both the centroidal 

surface 

Dip = 57' 

Rake = 104' 

Mo = 0.87~1 019 N-m 

Dip = 64' 

Rake = 136' 

Mo = 1 .15xlO^ N-m 

Dip = 65' 

Rake = 137' 

Mn = 1 .Ol xl 019 N-m 

Figure 8.-Results of inversion using a variable-mechanism model parametrization. 

depth and seismic moment increase slightly. Most types 

of crustal layering do not significantly affect the results 

presented here. All estimated parameters were found to be 

stable for purely homogeneous crustal models (half-space) 

and for those involving a steady increase in the medium 

velocity with depth; in particular, the assigned Moho depth 

does not play an important role. One class of structures, 

however, that could potentially influence the inference 

about the later parts of the rupture process involves a 

low-velocity zone in the lower crust. Such structures, which 

have been suggested for several areas around the San Andrea~ fault zone (Blumling and Prodehl, 1983; Bliimling 

and others, 1985), produce strong late-arriving reflections 

similar to the late-arriving energy observed in P waves in 

the west half of the focal sphere. 

P-wave synthetic seismograms for the model listed in 

table 1 are shown in figure 10A. To emphasize the effect 

of crustal reflections, only the first 10 s of the sourcetime function (fig. 1) was used. A large mismatch is evident in the later parts of the waveforms, indicating the 

need for additional moment release. The seismograms in 

figure 10B, which were calculated for a crustal model 

with a low-velocity layer at a depth of 20 krn, show large 

reflections similar to the later phases from the western 

stations. When inverting the whole data set, however, this 

model consistently produced a poorer fit to the data than 

0 10 20 30 

TIME, IN SECONDS 

Figure 9.-Match between the observed (solid curve) and synthetic (dotted curve) P-wave seismograms at representative stations in variablemechanism model. Amplitudes are normalized to 40' epicentral distance. Vertical dotted lines delimit inversion window. Circles in focal-mechanism 

solution indicate nodal planes and takeoff directions of direct waves. P and T, inferred axes of maximum and minimum compressional stress (pressure 

and tension axes), respectively. Match for SH waves is qualitatively similar to that shown in figure 2B. 
DOWNDIP GEOMETRY OF THE LOMA PRIETA RUPTURE FROM TELESEISMIC WAVEFORM INVERSION 

A 

COL 

MDJ 

GUM0 

AFI Ã‘JV ............... 

0 10 20 30 

TIME, IN SECONDS 

Figure 10.-Effect of various crustal models on P waveforms. A, Model listed in table 1, used in all 

inversions. B, Same model as in figure 10A but with a 5-km-thick low-velocity layer (v=5.37 krnts) at 20- 

km depth. C, Same model as in figure 10A but with a low-velocity layer at 15-km depth. Synthetic seismograms were computed for centroidal source parameters listed in table 2. Circles in focal-mechanism solution 

indicate nodal planes and takeoff directions of direct waves. To emphasize effect of crustal reflections, only 

first 10 s of moment-release-rate function shown in figure 1 was used. 
A180 MAIN-SHOCK CHARACTERISTICS 

the model listed in table 1. The same result was obtained 

for all crustal models with low-velocity, deep crustal layers. Structures with low-velocity zones could be admissible if the structure varied across the strike of the fault 

plane. Apparently, if low-velocity layers exist in the lower 

crust, they must be relatively deep to the west of the fault 

plane and relatively shallow or nonexistent to the east. 

DISCUSSION 

Our model results are summarized in table 2. Of these 

results, the most stable are those derived for the simplest 

source-model parametrizations. The average parameters 

represented by the point-source model agree closely with 

those derived from geodetic observations (Lisowski and 

others, 1990; Marshall and others, 1991; Snay and others, 

1991), surface waves (Zhang and Lay, 1990; Romanowicz 

and Lyon-Caen, 1990; Wallace and others, 1991; see 

Velasco and others, this chapter), and aftershock distributions (Dietz and Ellsworth, 1990; Schwartz and Nelson, 

1991), as well as with several other body-wave studies 

(for example, Hartzell and others, 1991; Wald and others, 

1991). Extensive summaries of the estimates of centroidal 

parameters from various observations are given, for example, by Marshall and others (1991), Wald and others 

(1991), and Wallace and others (1991). Other studies dealing with the source parameters of the main shock include 

those by Barker and Salzberg, (1990), Choy and Boatwright (1990), Kanamori and Satake (1990), Langston and 

others (1990), and Ruff and Tichelaar (1990). The seismic-moment estimate presented here is slightly lower than 

that obtained by NAbglek (1990), owing to the inclusion 

of GEOSCOPE data in this study. 

Most observations that bear on the depth extent of faulting appear to agree that essentially all moment release 

during the earthquake occurred within the depth range 5- 

8 km, with a large concentration near 10-km depth. A 

notable exception is the centroidal depth found from surface waves, at least 20 km, but there appear to be uncertainties in the Earth models used, which may be responsible 

for the bias in the source-depth estimate (see Velasco and 

others, this chapter). My investigation has shown that no 

significant moment release occurred below 20-km depth 

within 40 s after rupture initiation (figs. 5, 6). Because 

the seismic moment calculated here agrees well with that 

found from surface waves, it is difficult to appeal to additional slow moment release at depth, which would increase the centroidal depth derived from long-period 

surface waves. A strong argument against additional moment release on a long time scale comes from geodetic 

modeling (Lisowski and others, 1990; Marshall and others, 1991; Snay and others, 1991), whose results are consistent with the depth distribution of the moment release 

found here from body waves. 

My results indicate that the rupture propagated bilaterally updip, although I am unable to resolve the details of 

the lateral propagation. The model parametrization used 

here puts very little inherent constraint on the behavior of 

the rupture, and so the characteristics of the vertical distribution of moment release found here do not depend 

strongly on such details. All lateral variations of the moment release at a given depth, however, are integrated 

into the characteristics of the corresponding gridpoint. The 

short duration (approx 4-5 s) of the moment-rate functions at most depths does not allow a large lateral distance for the rupture to propagate. Assuming bilateral 

spreading and a rupture velocity of 3 kmls, the 5-s duration indicates a fault length (alongstrike dimension) of no 

more than 30 km. As mentioned above, in our model the 

rupture appears to stop briefly at 7.5-km depth and then 

restart for a short time, possibly in response to interaction 

with the San Andreas fault. Possibly, the rupture did not 

really stop and restart at this depth, instead, the two pulses 

in the moment rate may represent two areas of intensified 

moment release separated by a large lateral distance in 

which the later pulse represents a more distant locus delayed by the time it took for the rupture front to reach it. 

The least certain of the models presented here is the 

variable-mechanism model. Although this model appears 

to be well resolved, given the specific source parametrization, it does not have strong supporting evidence from 

other independent observations. The fault dip indicated 

by the model agrees well enough with the aftershock distribution (Dietz and Ellsworth, 1990; Schwartz and Nelson, 

1991), and the mechanism found for the deep part of the 

fault where the rupture nucleated agrees with that found 

from first-motion polarities at regional distances 

(Oppenheimer, 1990). The model indicates a planar to 

slightly concave downward geometry. In the uppermost 

part of the fault, the model indicates a large increase in 

the thrust component. Kinematically, such a change in 

mechanism is difficult to understand. If indeed present, it 

may reflect a decrease in vertical stress at shallow depth. 

It may also be due to a complex interaction with the San 

Andreas fault (slip partitioning), whereby over many earthquake cycles, the San Andreas fault takes up most of the 

strike-slip component of motion at shallow depths, while 

the Loma Prieta fault takes up the dip-slip component. 

Oppenheimer reported a predominance of thrust mechanisms for aftershocks at shallow depths, which might be 

taken as supporting evidence for the variable-mechanism 

model; however, given the wide variety of mechanisms 

observed at all depths, this evidence is weak. 

In comparison with other teleseismic body-wave studies that have investigated the change in source mechanism during the main-shock rupture, our solution is most 
DOWNDIP GEOMETRY OF THE LOMA PRIETA RUPTURE FROM TELESEISMIC WAVEFORM INVERSION A181 

similar to that of Hartzell and others (1991). They used a 

data set nearly identical to ours, except that they used 

ground-velocity records instead of displacement records 

for the broadband IRIS stations. Once the differences in 

the source parametrization are accounted for (they used a 

two-dimensional fault-surface model), the general features 

of their solution are remarkably similar to those of mine. 

They also performed an extensive analysis of the stability 

of their solutions. All of their models exhibit late-stage 

thrusting at shallow depths. Although their models show 

considerable instability in the lateral distribution of moment release, the vertical distribution appears to be stable 

and similar to that obtained here. In an earlier study, 

Romanowicz and Lyon-Caen (1990) also argued for the 

predominance of thrust faulting during the later stages of 

the rupture process. Although the teleseismic results reported by Wald and others (1991) are mostly consistent 

with mine, their model shows a remarkable uniformity in 

slip direction across the entire fault surface. In fact, their 

strong-motion model is nearly identical to mine in this 

respect. 

Two strong-motion studies (Beroza, 1991; Steidl and 

others, 1991) reported strong slip partitioning between the 

northwestern and southeastern segments of the Loma Prieta 

fault, whereby the northwestern segment is characterized 

by thrust motion and the southeastern segment by strikeslip motion. An analysis of geodetic-elevation changes 

provides some support for such a model (Marshall and 

others, 1991). None of the teleseismic body-wave studies, 

however, provides independent support for such a form of 

slip distribution. As already mentioned, the effects of the 

finite extent and variation of the source in the horizontal 

direction are difficult to resolve with our data set. Both 

strong-motion and geodetic measurements, however, are, 

in principle, sensitive to lateral effects. 

My results can be reconciled with the lateral-slip-partitioning model under the following scenario. The strongmotion modeling indicates that the rupture propagated 

nearly symmetrically during its early and main stages (possibly with somewhat more slip released in the south half). 

Two symmetrical loci of large moment release at about 

10-km depth (one to the southeast and one to the northwest of the hypocenter) ruptured nearly simultaneously. 

Under these conditions, teleseismic ground-displacement 

data would integrate the contributions from the two segments, and the resulting effective slip direction would involve nearly equal amounts of strike slip and dip slip 

(possibly slightly more strike slip during the initial stages 

if the rupture to the south was slightly faster). If the rupture in the southeastern segment stopped earlier, while in 

the northwestern segment it continued to shallower depths, 

the teleseismic data would record an effective change in 

slip direction to thrusting at shallower depth, as exhibited 

in the variable-mechanism model. 

CONCLUSIONS 

The good azimuthal distribution and high quality of 

teleseismic digital recordings of body waves from the 1989 

Loma Prieta earthquake provide an excellent data set from 

which an accurate, stable estimate of the centroidal source 

parameters can be determined. The teleseismic body-wave 

data also provide strong constraints on the depth distribution of moment release. A downdip change in slip direction is indicated but is less reliable, owing to a tradeoff 

between parameters and uncertainties in the Green's functions. The lateral extent of the source or possible lateral 

changes in slip direction, however, are unresolvable by 

the ground-displacement data used in this study. 

ACKNOWLEDGMENTS 

This research was supported by U.S. Geological Survey grant 14-08-000 1-G 1834. The manuscript was improved by comments from Anne Tr6hu and Paul Spudich. 

REFERENCES CITED 

Barker, J.S., and Salzberg, D.H., 1990, Long-period and broad-band 

teleseismic body-wave modeling of the October 18, 1989 Loma 

Prieta earthquake: Geophysical Research Letters, v. 17, no. 9, p. 

1409-1412. 

Beroza, G.C., 1991, Near-source modeling of the Loma Prieta earthquake; evidence for heterogeneous slip and implications for earthquake hazards: Seismological Society of America Bulletin, v. 8 1, 

no. 5, p. 1603-1621. 

Blumling, Peter, and Prodehl, Claus, 1983, Crustal structure beneath the 

eastern part of the Coast Ranges (Diablo Range) of central California from explosion seismic and near earthquake data: Physics of the 

Earth and Planetary Interiors, v. 31, no. 4, p. 313-326. 

Blumling, Peter, Mooney, W.D., and Lee, W.H.K., 1985, Crustal structure of the southern Calaveras fault zone, central California, from 

seismic refraction investigations: Seismological Society of America 

Bulletin, v. 75, no. 1, p. 193-209. 

Choy, G.L., and Boatwright, John, 1990, Source characteristics of the 

Loma Prieta, California, earthquake of October 18, 1989 from global digital seismic data: Geophysical Research Letters, v. 17, no. 8, 

p. 1 183-1 186. 

Dietz, L.D., and Ellsworth, W.L., 1990, The October 17, 1989, Loma 

Prieta, California, earthquake and its aftershocks; geometry of the 

sequence from high-resolution locations: Geophysical Research Letters, v. 17, no. 9, p. 1417-1420. 

Hartzell, S.H., Stewart, G.S., and Mendoza, Carlos, 1991, Comparison 

of L and L, norms in a teleseismic waveform inversion for the slip 

history of the Loma Prieta, California, earthquake: Seismological 

Society of America Bulletin, v. 8 1, no. 5, p. 1518-1539. 

Kanamori, Hiroo, and Satake, Keiiti, 1990, Broadband study of the 

1989 Loma Prieta earthquake: Geophysical Research Letters, v. 17, 

no. 8, p. 1179-1 182. 

Langston, C.A., Furlong, K.P., Vogfjord, K.S., Clouser, R.H., and 

Ammon, C.J., 1990, Analysis of teleseismic body waves radiated 

from the Loma Prieta earthquake: Geophysical Research Letters, v. 
A182 MAIN-SHOCK CHARACTERISTICS 

17, no. 9, p. 1405-1408. 

Lisowski, Michael, Prescott, W.H., Savage, J.C., and Johnston, M.J.S., 

1990, Geodetic estimate of coseismic slip during the 1989 Loma 

Prieta, California, earthquake: Geophysical Research Letters, v. 17, 

no. 9, p. 1437-1440. 

Marshall, G.A., Stein, R.S., and Thatcher, Wayne, 1991, Faulting geometry and slip from co-seismic elevation changes; the 18 October 

1989, Loma Prieta, California, earthquake: Seismological Society 

of America Bulletin, v. 81, no. 5, p. 1660-1693. 

NAbSlek, J.L., 1984, Determination of earthquake source parameters from 

inversion of body waves: Cambridge, Massachusetts Institute of 

Technology, Ph.D. thesis, 360 p. 

1985, Geometry and mechanism of faulting of the 1980 El Asnarn, 

Algeria, earthquake from inversion of teleseismic body waves and 

comparison with field observations: Journal of Geophysical Research, v. 90, no. B14, p. 12713-12728. 

1990, Rupture process of the October 18, 1989 ~oma Prieta 

earthquake from broadband teleseismic body waves [abs.]: Seismological Research Letters, v. 61, no. 1, p. 46. 

Oppenheimer, D.H., 1990, Aftershock slip behavior of the 1989 Loma 

Prieta, California earthquake: Geophysical Research Letters, v. 17, 

no. 8, p. 1199-1202. 

Romanowicz, B.A., and Lyon-Caen, Helene, 1990, The Loma Prieta 

earthquake of October 18, 1989; results of teleseismic mantle and 

body-wave inversion: Geophysical Research Letters, v. 17, no. 8, p. 

1191-1 194. 

Ruff, L.J., and Tichelaar, B.W., 1990, Moment tensor rate functions for 

the 1989 Loma Prieta earthquake: Geophysical Research Letters, v. 

17, no. 8, p. 1187-1 190. 

Schwartz, S.Y., and Nelson, G.D., 1991, Loma Prieta aftershock relocations with S-P travel times; effects of 3-D structure and true error 

estimates: Seismological Society of America Bulletin, v. 8 1, no. 5, 

p. 1705-1725. 

Snay, R.A., Neugebauer, H.C., and Prescott, W.H., 1991, Horizontal 

deformation associated with the Loma Prieta earthquake: Seismological Society of America Bulletin, v. 81, no. 5, p. 1647-1659. 

Steidl, J.H., Archuleta, R.J., and Hartzell, S.H., 1991, Rupture history 

of the 1989 Loma Prieta, California, earthquake: Seismological Society of America Bulletin, v. 81, no. 5, p. 1573-1602. 

Wald, D.J., Helmberger, D.V., and Heaton, T.H., 1991, Rupture model 

of the 1989 Loma Prieta earthquake from the inversion of strongmotion and broadband teleseismic data: Seismological Society of 

America Bulletin, v. 81, no. 5, p. 1540-1572. 

Wallace, T.C., Velasco, Aaron, Zhang, Jiajun, and Lay, Thorne, 1991, 

A broadband seismological investigation of the 1989 Loma Prieta, 

California, earthquake; evidence for deep slow slip?: Seismological 

Society of America Bulletin, v. 81, no. 5, p. 1622-1646. 

Zhang, Jiajun, and Lay, Thorne, 1990, Source parameters of the 1989 

Loma Prieta earthquake determined from long-period Rayleigh 

waves: Geophysical Research Letters, v. 17, no. 8, p. 1 195-1 198. 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAKEOCCURRENCE 

MAIN-SHOCK CHARACTERISTICS 

MECHANICAL MODELING OF A FAULT-FOLD SYSTEM, WITH 

APPLICATION TO THE EARTHQUAKE 

CONTENTS 

By Ze'ev Reches, 

Hebrew University, Jerusalem; 

and 

Mark D. Zoback, 

Stanford University 

Page 

A183 

183 

184 

184 

184 

185 

186 

186 

187 

187 

188 

188 

188 

190 

190 

191 

191 

192 

193 

ABSTRACT 

Some features of the deformation accompanying the 

1989 Loma Prieta earthquake resemble that associated with 

earthquakes along deep-seated reverse faults. These features include ground breakage, surface deformation, aftershock distribution, and a component of reverse slip 

deduced from geodetic and strong-ground-motion data. To 

explore these deformational features of the earthquake, 

we derive an analytical model for the deformation of a 

layered sequence due to slip along a deep-seated fault. 

Our model includes horizontal elastic layers, using configurations with as many as nine layers of different shear 

moduli, We applied this layered model to the Loma Prieta 

region and found that the better solutions are for fivelayer sequences in which the shear moduli of the layers 

increase downward. The model predicts the distribution 

of aftershocks in the upper 5 km better than a model with 

uniform rheology. The model also accurately predicts the 

location of the zone of horizontal extension in the Summit Road area and the zone of horizontal compression in 

the northeastern foothills of the Santa Cruz Mountains. 

INTRODUCTION 

Since the early l98O9s, deep-seated faults concealed by 

folded structures have been recognized as a significant 

source for seismic hazard (for example, Stein and King, 

1984). This recognition reflects observations of the 1980 

El-Asnam, Algiers, the 1983 Coalinga, Calif., and the 1987 

Whittier Narrows, Calif., earthquakes. In these and other 

earthquakes, the deep faults form a fault-fold system in 

which slip along a fault zone at depth appears as a fold or 

a flexure within the overlying sedimentary layers. 

Fault-fold systems have been modeled by using several 

different methods. One common approach is kinematic 

analysis, for which the balanced cross section is the best 

known representative. This technique was developed to 

analyze large-scale deformation by assuming that rock 

volume (area in two-dimensional profiles) is conserved 

during deformation (Dahlstrom, 1969). Using this approach, the initial configuration and even the deformation 

path can sometimes be reconstructed from the geometry 

of the final deformed structure. The kinematic approach, 

however, has some severe limitations: Rock rheology is 

omitted, rock layers are merely lines drawn on profiles 

without mechanical properties, and the mechanical differences between layers are ignored. Therefore, although the 

kinematic analysis maintains geometric compatibility, it 

could violate known dynamic principles. 

Another approach is the modeling of upper-crustal deformation by dislocations within a linear, elastic half-space. 

This modeling has been extensively used in the inversion 

of long-term geodetic data, as well as for seismic and 

postseismic displacements. Although half-space models 

can provide impressive fits to geodetic data (Lisowski 
A184 MAIN-SHOCK CHARACTERISTICS 

and others, 1990), they do not incorporate the layering of 

crustal rocks and are limited to small deformation. For 

example, King and others (1988) extended such models 

by considering a thick, linear elastic layer over a viscous 

half-space; they modeled the development of crustal flexures by many repeating earthquakes, incorporating seismic slip, viscous-isostatic relaxation, erosion, and 

sedimentation, One surprising result of their analysis is 

that the calculated elastic thickness of the crust is only 2 

to 4 km. 

A different approach assumes that slip along deep-seated 

faults is accommodated within the overlying rocks by flexing, faulting, and tilting, which form such fault-fold systems as monoclines or asymmetric folds (Reches, 1978). 

Reches and Johnson (1978) derived a general model for 

the development of a fault-fold system and analyzed the 

mechanics of draping, buckling, and kinking within the 

sedimentary sequence. Because crustal rocks commonly 

display mechanical layering rather then uniform rheology, 

we believe that relevant models must incorporate this property. 

The 1989 Loma Prieta earthquake resulted in several 

features that resemble the deformational features of earthquakes associated with deep-seated reverse faults: the types 

of surface deformation and ground breakage, the aftershock distribution, and the large amount of subsurface 

reverse slip deduced from inversion of geodetic (Lisowski 

and others, 1990) and strong-ground-motion data (Beroza, 

1991). To explore the deformational style in the Loma 

Prieta region, we have derived a model for a layered rock 

sequence above a deep-seated fault. The analysis is for 

horizontal, incompressible, elastic layers subjected to faultrelated displacement along the base of the sequence. Our 

model attempts to reproduce the location and style of surface deformation and aftershock distribution of the earthquake. We compare the results of this layered model with 

those from the uniform-rheology model. 

ANALYSIS OF A FAULT-FOLD SYSTEM 

APPROACH 

We derive here an analytical solution for a fault-fold 

system that includes a sequence of layers overlying a basement (fig. 1). The basement is idealized as an elastic halfspace that can deform by slip along planar faults; the 

layered sequence above the fault is idealized as horizontal 

layers with nonuniform moduli that are either bonded to 

each other or free to slip along their contacts. In theory, 

these layers can deform elastically or viscously; the analysis below is for linear, incompressible, elastic layers under plane-strain conditions. Details of the analytical 

procedure are presented below in the appendix (see Reches 

and Johnson, 1978). 

The computations provide the displacement, stress, and 

strain fields within the layered sequence. By using a Fourier series of stepped waveforms, the solutions can handle 

the combination of continuous, periodic folding processes 

in the layers and discontinuous fault displacements in the 

basement. 

DEFORMATION ABOVE A FAULTED RIGID 

BASEMENT 

We first present the solutions for a simple fault-fold 

system that is common in regions of moderate tectonic 

deformation, such as the Colorado Plateaus, the Rocky 

Mountains, and the Middle East (Prucha and others, 1965; 

Reches, 1978; Stearns, 1978; Reches and others, 1981). 

This simple fault-fold system is a zone of flexed, bent, 

and tilted layers of sedimentary rocks above basement 

faults (fig. 2). In these structures, the layers are deformed 

Layered 

Y sequence 

$/Faulted, elastic 

%Q half-space 

Figure 1.-Idealized geometry of a faulted basement overlain by a layered sequence. 

Figure 2.-Simple fault-fold system, showing a profile of the Palisades 

monocline, Grand Canyon, Ariz. Crosses, Precambrian units; dots, Paleozoic formations. Modified from Reches and Johnson (1978). 
MECHANICAL MODELING OF A FAULT-FOLD SYSTEM, WITH APPLICATION TO THE EARTHQUAKE A185 

and tilted near the fault and almost undeformed and essentially flat away from the fault. The local deformation 

of the layers reflects the response of the layered sequence 

in part to the deep-seated faulting (Stearns, 1978) and in 

part to tectonic stresses within the layers (Reches and 

Johnson, 1978). 

We restrict our analysis to fault-fold systems with small 

displacements of a few tens to a few hundreds of meters 

of fault slip. Following King and others (1988), we assume that such systems develop in cycles of seismic events 

alternating with long periods of interseismic elastic deformation. It is further assumed that in such systems, the 

interseismic elastic deformation in the basement is relaxed during seismic events, and so the basement may be 

regarded as rigid. A rigid basement implies that its top on 

both sides of the fault remains fairly planar and close to 

horizontal (fig. 2). In contrast, the overlying layers deform permanently by flexing and tilting. In systems with 

large displacements (>l km), the basement may not be 

regarded as rigid because it deflects, owing to isostatic 

relaxation, erosion, sedimentation, or a combination of 

these processes (King and others, 1988). 

REVERSE BASEMENT FAWT VERSUS NORMAL 

BASEMENT FAULT 

We now present solutions for two idealized fault-fold 

systems, one with a reverse fault in the basement and the 

other with a normal fault in the basement (fig. 3). The 

two systems include six horizontal layers that are bonded 

to each other along their contacts. Each layer is 200 m 

thick, and the shear moduli alternate between 6 and 20 

1 p=20 GPa 11 

I 

Rigid basement 

A Y 

Figure 3.-Analytical solution for deformation of a sequence of six 

layers above a rigid basement. A, Model configuration: Layers are elastic, incompressible, with bonded contacts, 0.2 km thick; shear modulus 

alternates between 6 GPa in layers 1 (top), 3, and 5 and 20 GPa in layers 

2, 4, and 6 (basal layer). B, Normal fault dipping 60Â to right. C, Reverse fault dipping 60' to left. In figures 3B and 3C, fault tip is at 0-m 

distance (center); 180 wavelengths were used in Fourier series. Continuous curved lines, displacements of contacts between layers (short lines 

connect initial and final positions); shoa heavy bars, orientations of csl axes. Gray tones (1-10 scale on right side) indicate intensity of change 

in normalized shear stress AT^ (see appendix, eq. 12). 

GPa (fig. 3A). In line with field observations (fig. 2) and 

the arguments in the preceding subsection, the top of the 

basement is maintained horizontal and planar during the 

deformation (which is linear in the two-dimensional approximation used). 

The results for a normal fault that dips 60' to the right 

(fig. 3B) and for a reverse fault that dips 60' to the left 

(fig. 30 are shown in figure 3; both systems have 1 m of 

vertical displacement of the basement. Each solution shows 

the displacement of the layers, the change in the local 

shear stress AT^ (see eq. 121, and the orientations of the 

maximum compressive stress induced by slip along the 

deep-seated fault. 

2 

DISTANCE, IN KILOMETERS 

Figure 3.4ontinued. 

VI El 

0 

I 

z 

DISTANCE, IN KILOMETERS 

Figure 3.4ontinued. 
A186 MAIN-SHOCK CHARACmRISTICS 

The most conspicuous feature in these solutions is the 

appearance of a zone of increasing shear stress AT^ above 

the fault (figs. 3B, 3C). The width of this zone varies 

significantly: It is a few hundred meters wide in the basal 

layer, about 1 km wide in the central part of the sequence, 

and a few kilometers wide close to the top (figs. 3B, 30. 

Local increases in shear stress and the width of the zone 

occur within the layers of large shear modulus, layers 2, 

4, and 6. This increase reflects the rule of thumb that the 

stiffer components in nonuniform materials-layered sequences or a medium with inclusions-concentrate the 

stresses. The stressed zone appears as a continuation of 

the basement fault: It dips generally to the right for the 

normal fault (fig. 3B), and to the left for the reverse fault 

(fig. 30. 

Another significant feature of the solutions shown in 

figure 3 are the orientations of the principal stresses within 

the stressed zone. To simplify the variations in the induced stress, we refer to three stress orientations: regions 

of layer-normal compression, in which the axes of maximum compression are inclined 60' or more to the 

subhorizontal layering; regions of layer-parallel compression, in which the axes of maximum compression are inclined 30' or less; and regions of layer-parallel shear, in 

which the axes of maximum compression are inclined 3O0- 

60'. In the normal-fault system, most regions, particularly 

those with a relative increase in shear stress, are of the 

layer-normal compression type (fig. 3B). A region of layerparallel compression appears to the right of the center, 

within the synclinal zone of the surface flexure. In the 

reverse-fault system, the situation is generally inverted, 

and most regions of shear stress increase with layer-parallel compression (fig. 3C). 

These patterns of stress orientations could profoundly 

affect the structural development. The layer-parallel compression in the reverse-fault system could invoke two 

deformational modes: propagation of the basement reverse 

fault, or buckling and flexing of the layered sequence 

(Reches and Johnson, 1978). Buckling and flexing will 

prevail if the layers are thin, if considerable differences in 

elastic moduli exists between the layers, and if the friction along the bedding surfaces is relatively low. Under 

such conditions, the basement fault will be transformed 

into a monoclinal flexure in the layered sequence, and a 

fault-fold system would develop (Reches, 1978). This process of flexure above a fault may explain the absence of 

surface rupture above some active reverse faults. 

The situation is different for the normal-fault system 

because layered sequences do not buckle under the effect 

of layer-normal compression. The stresses within the layers above a basement normal fault (fig. 3B) would enhance normal faulting and the propagation of the basement 

fault into the layered sequence. This process is further 

enhanced because rocks are significantly stronger under 

compression than under extension and the layers above 

the normal fault are more likely to yield by faulting rather 

than by folding. 

THE 1989 LOMA PRIETA EARTHQUAKE 

FEATURES OF THE EARTHQUAKE 

The 1989 Loma Prieta earthquake occurred within the 

San Andreas fault system in the Santa Cruz Mountains, 

Calif. The hypocenter of the event was about 17 km deep, 

relatively deep for the San Andreas fault system. The focal-plane solution of the main shock (Oppenheimer, 1990) 

and the distribution of aftershocks (Dietz and Ellsworth, 

1990) indicate that seismic slip occurred along a fault that 

dips about 70' SW., with mixed reverse and right-lateral 

slip. This sense was confirmed by inversion of the geodetic measurements, with a best fit of observations to 

1.6k0.3 m of right-lateral strike slip and 1.2k0.4 m of 

vertical reverse displacement (Lisowski and others, 1990). 

The slip in this earthquake was apparently heterogeneous, 

as demonstrated by inversion of the strong-ground-motion data (Beroza, 1991). This analysis indicates that the 

slip can be divided into two separate segments, a northern 

segment with almost pure reverse slip and a southern segment with almost pure right-lateral slip; for both components, the peak local slip amplitude is 2.8 m (Beroza, 

1991). Marshall and others (1991) analyzed the leveling 

data and considered solutions for two coplanar segments. 

Their best signal-to-noise ratio was obtained for a twosegment fault, dipping 62', with a rake of 116' (almost 

pure reverse slip) in the northern segment and a rake of 

163' (almost pure strike slip) in the southern segment. 

Surface fractures of apparent tectonic origin were observed in three main zones. The first zone is an area of 

extensional features along Summit Road, west of Loma 

Prieta (vertical-lined area, fig. 4; Ponti and Wells, 1991). 

This zone is about 6 km long and 1 to 1.5 km wide; it is 

subparallel to the San Andreas fault and 1 to 2 km from 

its southwest side (the Pacific block). Most of the fractures display mixed displacement: extension normal to the 

fractures with either left- or right-lateral slip. The maximum measured displacement was 92 cm, with a left-latera1 component of 42 cm (Ponti and Wells, 1991). Many 

of the observed fractures within this zone coincide in position and trend with those mapped by Sarna-Wojcicki 

and others (1975) and were also active during the 1906 

San Francisco earthquake. Several investigators attributed 

this fracture zone to gravitational sliding, in part relating 

localization of the fractures to the topographic elevation 

(Ponti and Wells, 1991). 

A second zone is situated along the northeastern foothills of the Santa Cruz Mountains, about 3 to 6 km north- 
MECHANICAL MODELING OF A FAULT-FOLD SYSTEM? WITH APPLICATION TO THE EARTHQUAKE A1 87 

east of the San Andreas fault (areas C, fig. 4). The dominant features here are fractures with reverse motion and 

small buckles mostly within manmade structures, such as 

roads or sidewalks (Plafker and Galloway, 1989). 

The third zone includes surface fractures along the main 

trace of the San Andreas fault, southeast of Loma Prieta. 

Aydin and others (1992) mapped in detail the fractures 

here and found primarily fractures with right-lateral motion (max 30 cm) and reverse slip. 

MODELING THE EARTHQUAKE AS A FAULTFOLD SYSTEM 

Some of the above-listed observations suggest that the 

1989 Loma Prieta earthquake is similar to earthquakes 

along deep-seated reverse faults. The most relevant observations are the patterns of surface rupture, the occurrence 

of extensional features in the Pacific block and compressional features in the North American block, and the mixed 

reverse and right-lateral slip at great depth, with almost 

pure reverse slip along the northern part of the slipping 

fault segment. For these reasons, we analyze the deformation associated with slip along the northern part of the 

Loma Prieta rupture zone as a deep-seated reverse fault. 

The analyzed models were restricted to a vertical profile 

trending N. 40' E. (line AB, fig. 4), perpendicular to the 

Figure 4.-Area of 1989 Loma Prieta earthquake (modified from Plafker 

and Gallowayl 1989). Star? main-shock epicenter; shaded area? aftershock zone; vertical-lined area, zone of surface rupture with predominantly extensional fractures; horizontal-lined areas, zones of surface 

rupture with predominantly compressive features; line AB, profile in N. 

40' E. direction for present model (see fig. 5); dashed rectangle, area of 

aftershocks used in present analysis (see fig. 5). 

slip surface determined by Dietz and Ellsworth (1990) 

and Oppenheimer (1 990). 

MECHANICAL LAYERING 

The Loma Prieta region reveals a complex structure 

composed of major strike-slip faults, reverse faults, and 

large folds, which are generally subparallel to the San 

Andreas fault (McLaughlin and others, 1988; Clark and 

others, 1989). The exposed rocks along the Loma Prieta 

rupture zone are marine and nonmarine clastic units of 

Tertiary age that occupy at least the upper 1 km northeast 

of the San Andreas fault and 2 km or more on the southwest side. Basement rocks are exposed either southwest 

of the Zayante fault or northeast of the Berrocal fault 

(McLaughlin and others, 1988; Clark and others, 1989). 

The sedimentary rocks are intensely deformed by tight 

and isoclinal folds and faults (mostly reverse). The block 

between the San Andreas and Sargent faults seems to be 

more intensely faulted by reverse faults than the block 

southwest of the San Andreas fault. The layering in the 

Loma Prieta region has most likely facilitated the regional 

folding and flexing during the past few million years. 

However, because the available folding analyses are restricted to inclinations gentler than lo0-15' (Johnson, 

19771, it is practically impossible to quantitatively analyze the deformation of the intensely deformed sequence 

of Loma Prieta in its present structure. 

Another layered structure is reflected in seismic profiles of the region. Seismic-velocity models of the Loma 

Prieta region reveal a low-velocity (3.3-5.8 kmls) wedge 

between the Zayante and San Andreas faults that extends 

to depths of more then 8 km (fig. 5B; Eberhart-Phillips 

and others, 1990). This wedge was interpreted as marine 

sedimentary rocks of Tertiary age (Eberhart-Phillips and 

others, 1990). A high-velocity zone (6.4-6.7 kds) that 

appears between the San Andreas and Sargent faults was 

interpreted as mafic intrusive rocks (fig. 5B). 

The upper 3 to 5 km of the crust in the study area 

displays relatively simple, subhorizontal velocity layering 

(fig. 5A), with a gradual increase in P-wave velocity 

from 3.3 kmls at the surface to about 6 kmls at 5-km 

depth (fig. 5). This simple velocity layering is apparently 

unrelated to the complex folded structure of the sedimentary layers. The seismic velocity cannot be correlated with 

clear lithologic or stratigraphic units, and so the increase 

in velocity with depth is interpreted as reflecting the compaction and cementation of Tertiary clastic sedimentary 

rocks. 

Following this interpretation of depth-controlled hardening, we consider the profile of seismic velocity (fig, 5) 

as reflecting mechanical layering in the upper 5 km of the 

crust. Accordingly, we used a ratio of 0.25 between the 
A188 MAIN-SHOCK CHARACTERISTICS 

shear modulus of the top layer to the shear modulus of the 

basal layer, in general agreement with the "0.5 ratio of 

P-wave velocities in the top layer to those in the basal 

layer (fig. 5). 

MODEL PARAMETERS 

We calculated solutions with layered sequences consisting of one to nine layers and total thicknesses of 3, 5, 

and 7 krn under plane-strain conditions. We examined 

layers that were either free to slip along their contacts or 

bonded to each other. The shear moduli of the layers were 

selected to show (1) a downward increase in modulus, 

from 4 GP~ at the top to 16 GPa at the base; (2) a downward decrease in modulus, from 16 GPa at the top to 4 

GPa at the base; or (3) a uniform modulus for the layers 

free to slip along their contacts. Depth variations of shear 

moduli were in equal steps according to the number of 

layers. As the basal displacements are specified (see appendix), the mechanical properties of the basement do not 

affect the solution. The basal displacement was calculated 

>, LL 

ra 2 DISTANCE. IN KILOMETERS 

Figure 5.-Seismic velocity structure along southwest-northeast profiles 

20 km northwest of main shock epicenter (A) and across main shock (B) 

(after Eberhart-Phillips and others, 1990). 

with the computer program DIS3D for a reverse slip of 1 

m along a 70'-dipping reverse fault (see appendix). 

A few groups of solutions were rejected in the early 

stages of the calculations for the following reasons. First, 

we correlated zones of increase in shear stress in the solution with zones of high density of aftershocks. Aftershocks 

of the earthquake were concentrated within a 2- to 3-kmwide zone that extends from 18- to about 1-km depth 

(Oppenheimer, 1990). The zones of shear-stress increase 

in an acceptable model should approximately coincide with 

the zone of high density of aftershocks, and so we rejected models that clearly do not conform to this correlation. In models with free-slip contacts, the upper layers 

are detached from the displacement at the basement, leading to shear-stress increase within a wide region of the 

basal layer, with no increase of the shear stresses in the 

upper layers. Second, models with shear moduli decreasing downward generated shear stress fields that contradicted the aftershock distribution. Furthermore, these 

models do not conform to the velocity profiles shown in 

figure 5. Similar contradictions appeared for single-layer 

solutions with a uniform shear modulus. Therefore, models with free slip between layers, with downward-decreasing moduli, and with uniform shear modulus (fig. 7) were 

all rejected in early stages of the calculations. 

RESULTS 

We found that models with five layers, downward-increasing shear moduli, and bonded contacts fit better the 

relevant field observations. The results of these models 

are displayed at different horizontal and vertical scales in 

figures 6A through 6C, which show the displacement of 

the layers, the change of the local shear stress Aig (eq. 

12), and the orientations of the maximum compressive 

stress. 

SHEAR ZONES 

One conspicuous feature of our models is the appearance of two distinct zones of intensive increase in shear 

stress. The first zone is a subvertical region above the 

basement fault and slightly to the northeast (fig. 6). This 

zone reflects the increase in shear stress within the stiffer 

lower layers, owing to the deformation localized above 

the fault. The zone is 4 to 5 km wide at the base and 

narrows to about 1 krn wide at 1- to 2-km depth. The 

orientation of q, the axis of maximum compression, varies spatially within the zone. 

The second zone of shear-stress increase is a horizontal, 10- to 12-km-wide region in the upper layer (fig. 65); 

the intense stresses here are restricted to the upper 200 to 

300 m (fig. 60. This second zone largely reflects the low 
MECHANICAL MODELING OF A FAULT-FOLD SYSTEM, WITH APPLICATION TO THE EARTHQUAKE A189 

lithostatic load at shallow depths because AtE is the change 

in shear stress normalized by the lithostatic stress (see 

appendix, eq. 12). This zone is separable into two regions: a region of horizontal (5i on the northeast side and 

a region of vertical o1 on the southwest side; the positions of maximum shear-stress increase in these two regions are 6 to 7 km apart (fig. 65). These regions correlate 

in position with the anticlinal and synclinal bends of the 

flexure of the top layer. The two regions of increased 

stresses within the subhorizontal zone (fig. 6B) correlate 

with the two regions of tectonic surface rupture mentioned 

above (fig. 4): the Summit Road zone with dominantly 

extensional fractures and the northeastern foothills of the 

Santa Cruz Mountains with compressional features. The 

projection of these two zones onto a N. 40' E. vertical 

7 Elastic basement 

A 

//-- 

?\I II 

DISTANCE, IN KILOMETERS Q 1 

B DISPLACEMENT, IN METERS 

section near California Highway 17 reveals a distance of 

6 to 7 km along the profile, in good agreement with the 

model calculations (fig. 6). We calculated that the extension normal to the fault across a 4-km-wide zone, centered 2 krn west of the San Andreas fault is about 7.5 cm. 

Ponti and Wells (1991) noted that many of the major 

cracks in the Summit Road zone correlate with the local 

slope direction and are associated with landslides and bedding-plane slippage. They found that the cumulative, faultnormal extension across the fracture zone ranges from 65 

DISTANCE, IN KILOMETERS 

c 0 u 

12 

DISPLACEMENT, IN METERS 

DISTANCE, IN KILOMETERS , 

"i^ 

DISPLACEMENT, IN METERS 

Figure 6.-Analytical solutions at different scales for deformation associated with an earthquake. A, Configuration of preferred model: a sequence of 

five elastic, incompressible layers, each 1 km thick and bonded to each other. Shear modulus (p) of top layer is 4 GPa, increasing in equal steps to 16 

GPa in basal layer. Basal displacements were calculated for 1 m of reverse slip along a 70'-dipping reverse fault within an elastic basement (see 

appendix for details). Displacement is transformed in a Fourier series with 160 wavelengths. B, Five-layer sequence. Fault is in center of base. C, 

Expanded view of figure 6B. D, Upper layer (layer 1). In figures 65 through 60, fault tip is at 0-m distance (center). Dots, 215 aftershocks for period 

October 18-31, 1989 (after Dietz and Ellsworth, 1990), with hypocenters projected horizontally to section profile (see text). Continuous curved lines, 

displacements of contacts between layers (short lines connect initial and final positions); short heavy bars, orientations of o, axes. Gray tones (1-10 

scale on right side of fig. 6B) indicate intensity of change in normalized shear stress Ate (see appendix, eq. 12). 
A190 MAIN-SHOCK CHARACTERISTICS 

to 104 cm (8 to 14 times the extension calculated in the 

present model). They proposed that the extension is due 

to ridgetop spreading rather than tectonic deformation. 

Our interpretation is that the extension in the Summit 

Road zone is due to slip during the earthquake which was 

amplified by local topographic features. Horizontal extension is a common feature associated with the anticlinal 

bend above a deep-seated normal (fig. 3A) or reverse (fig. 

30 fault. Anticlinal extensional zones were recognized 

by Sanford (1959), and Reches and Johnson (1978), who 

applied these zones to analyze the mechanisms of monocline development. The compressional zone in the synclinal bend is the complement to the extensional zone in the 

anticlinal bend (figs. 3, 6). 

We note, however, that the extension-compression pair 

reflects the local stress field associated with slip along 

the fault; the total stresses are the sum of these local 

stresses and the remote stresses (see appendix). If, for 

example, the remote stresses are compressional, they would 

enhance the compressional zone in the synclinal bend and 

diminish the extensional zone in the anticlinal bend 

(Reches and Johnson, 1978). 

AFTERSHOCK DISTRIBUTION 

Another result of our modeling is a prediction of the 

locations of shallow aftershocks. The locations of aftershocks for the period October 18-3 1, 1989, are plotted in 

figure 7. From the list of 1,173 best constrained hypocenters, we selected all 215 events with hypocenters that 

are no more than 5 km deep and with epicenters inside a 

frame 20 by 30 km on both sides of our modeling profile 

(fig. 4). These hypocenters are projected horizontally onto 

the N. 40' E.-S. 40' W. vertical surface and plotted on 

the derived solutions. 

These aftershocks are well confined to the subvertical 

zone of shear-stress increase above the fault (figs. 6A, 

6B). We examine whether this correlation between the 

aftershock pattern and the predicted zone of shear-stress 

increase depends on the layering in the model by calculating a solution for a single layer of uniform rheology (fig. 

7); other parameters are the same as in figure 6. It is 

apparent that the single-layer solution in figure 7 displays 

a poor correlation between the intensity of the shear-stress 

increase and the aftershock distribution. The difference 

between the two solutions reflects the rheologic difference between the models: The lower layers of figure 6 

have a high stiffness, and so they tend to be more highly 

stressed than the less stiff layers above them, whereas in 

the single-layer solution the shear-stress increase is concentrated at the surface, owing to the effect of the low 

normal stress (see appendix). 

CONCLUSION: LAYERED VERSUS 

UNIFORM MEDIUM 

The deformation associated with earthquakes is commonly calculated for one or more dislocations embedded 

within a uniform elastic half-space. The analytical solution presented here allows the shear modulus to vary between horizontal layers (fig. 1). By using these solutions, 

simple, but more, realistic (nonuniform), rheologic models 

can be explored. The models presented here for the Loma 

Prieta region describe a sequence of layers in which the 

shear moduli vary by a ratio of 1:4 (fig. 6), in accordance 

A -8,000 0 8,000 

DISTANCE, m 

B' DISTANCE, m 

Figure 7.-Analytical solution for deformation of a single elastic layer, 

5 km thick. Same basal displacement as in figure 6. A, Profile of entire 

layer. B, Details of upper 1.25 km. Same symbols as in figure 6. 
MECHANICAL MODELING OF A FAULT-FOLD SYSTEM, WITH APPLICATION TO THE EARTHQUAKE A191 

with the P-wave-velocity ratio (=1:2); (fig. 5). The present 

solutions seem to provide better predictions of the aftershock distribution than the uniform model (compare figs. 

6, 7). Both models provide similar explanations for the 

two zones of surface deformation (extension in the Summit Road zone and compression in the foothill zone; figs. 

4, 6B, 7). The present solution indicates that the aftershock zone should be centered between the regions of 

surface extensional deformation (Summit Road) and surface compressional deformation (foothills) (fig. 6). 

We also compared the expected vertical displacement 

at the ground surface for the layered-medium model and 

for the uniform-layer model. Figure 8 shows that the vertical displacements in these two models deviate by only 2 

to 5 percent from each other. This small difference suggests that leveling data are insensitive to rheologic variations with depth and the existence of layered media. 

The present analysis provides a method to study the 

deformation in a layered medium above a faulted basement. Even the simple geometry of the basic model presented here (fig. 1) may generate a wide variety of stresses 

and displacements (figs. 3, 6) possibly related to the wide 

variety of focal-plane mechanisms of the aftershocks. We 

consider it an important result that the layering used in 

our preferred model for the 1989 Loma Prieta earthquake 

is consistent with the mechanical layering revealed by the 

seismic-velocity structure and that the calculated stresses 

and displacements agree well with the observed surface 

deformation and aftershock locations. 

0.4 T Applied] 

Two layers, 

each 2.5 km thick 

stiff basal, soft top 

DISTANCE, IN KILOMETERS 

Figure 8.-Vertical displacements associated with a basement reverse 

fault, dipping 70' to left with 1 m of reverse slip (same conditions as in 

figs. 6, 7). Total thickness, 5 km; basal layer is 100 times stiffer than 

upper layer (dotted curve). 

ACKNOWLEDGMENTS 

This research was supported in part by U.S. Geological 

Survey grant 14080001-G-1853 to Stanford University. 

We thank Lynn Dietz of the U.S. Geological Survey for 

providing the aftershocks listing. Discussions with Paul 

Segall, Ross Stein, Bill Ellsworth, Dave Oppenheimer, 

Dan Ponti, Mike Lisowski, and Jim Dieterich are greatly 

appreciated. The reviews and comments by Ross Stein, 

Bob Simpson, Joe Andrews, and Paul Spudich contributed significantly to the manuscript. 

REFERENCES CITED 

Aydin, A., Johnson, A.M., and Fleming, R.W., 1992, Right-lateralheverse surface rupturing along the San Andreas and Sargent fault 

zones during the October 17, 1989,Loma Prieta, California, earthquake: Geology, v. 20, p. 1063-1067. 

Beroza, G.C., 1991, Near-source modeling of the Loma Prieta earthquake; evidence for heterogeneous slip and implications for earthquake hazard: Seismological Society of America Bulletin, v. 81, 

no. 5, p. 1603-1621. 

Brace; W.F., and Kohlstedt, D.L., 1980, Limits on lithospheric stress 

imposed by laboratory experiments: Journal of Geophysical Research, v. 85, no. Bll, p. 6248-6252. 

Clark, J.C., Brabb, E.E., and McLaughlin, R.J., 1989, Geologic map and 

structure sections of the Laurel 7 x' Quadrangle, Santa Clara and 

Santa Cruz counties, California: U.S. Geological Survey Open-File 

Report 89-676, 31 p., scale 1:24,000, 2 sheets. 

Dahlstrom, D.C.A., 1969, Balanced cross sections: Canadian Journal of 

Earth Sciences, v. 6, no. 4, pt. 1, p. 743-757. 

Dietz, L.D., and Ellsworth, W.L., 1990, The October 17, 1989, Loma 

Prieta, California, earthquake and its aftershocks; geometry of the 

sequence from high-resolution locations: Geophysical Research Letters, v. 17, no. 9, p. 1417-1420. 

Eberhart-Phillips, D.M., Labson, V.F., Stanley, W.D., Michael, A.J., 

and Rodriguez, B.D., 1990, Preliminary velocity and resistivity 

models of the Loma Prieta earthquake region: Geophysical Research Letters, v. 17, no. 8, p. 1235-1238. 

Erickson, L., 1987, User's manual for DIS3D. a three-dimensional dislocation program with application to faulting in the earth: Stanford, 

Calif., Stanford University, Department of Applied Earth Sciences, 

167 p. 

Johnson, A.M., 1977, Styles of folding; mechanics and mechanisms of 

folding of natural elastic materials: New York, Elsevier, 406 p. 

King, G.C.P., Stein, R.S., and Rundle, J.B., 1988, The growth of geological structures by repeated earthquakes, 1. Conceptual framework: Journal of Geophysical Research, v. 93, no. Bll, p. 13307- 

13318. 

Lisowski, Michael, Prescott, W.H., Savage, J.C., and Johnson, M.J.S., 

1990, Geodetic estimate of coseisrnic slip during the 1989 Loma 

Prieta, California, earthquake: Geophysical Research Letters, v. 17, 

no. 9, p. 1437-1440. 

Marshall, G.A., Stein, R.S., and Thatcher, Wayne, 1991, Faulting geometry and slip from co-seismic elevation changes: the 18 October 

1989 Loma Prieta, California, earthquake: Seismological Society of 

America Bulletin, v. 81, no. 5, p. 1660-1693. 

McLaughlin, R.J., Clark, J.C. and Brabb, E.E., 1988, Geologic map and 

structure sections of the Loma Prieta 7 Vy ' quadrangle, Santa Clara 

and Santa Cruz counties, California: U.S. Geological Survey Open- 
A192 MAIN-SHOCK CHARACTERISTICS 

File Report 88-752, 32 p., scale 1:24,000, 2 sheets. 

Oppenheimer, D.H., 1990, Aftershock slip behavior of the 1989 Loma 

Prieta, California earthquake: Geophysical Research Letters, v. 17, 

no. 8, p. 1199-1202. 

Oppenheimer, D.H., Reasenberg, P.A., and Simpson, R.W., 1988, Fault 

plane solutions for the 1984 Morgan Hill, California, earthquake 

sequence; evidence for the state of stress on the Calaveras Fault: 

Journal of Geophysical Research, v. 93, no. B8, p. 9007- 9026. 

Plafker, George, and Galloway, J.P., eds., 1989, Lessons learned from 

the Loma Prieta, California, earthquake of October 17, 1989: U.S. 

Geological Survey Circular 1045, 48 p. 

Ponti, D.J., and Wells, R.E., 1991, Off-fault ground ruptures in the 

Santa Cruz Mountains, California; ridge-top spreading versus tectonic extension during the 1989 Loma Prieta earthquake: Seismological Society of America Bulletin, v. 8 1, no. 5, p. 1480-1 510. 

Prucha, J.J., Graham, J.A., and Nickelsen, R.P., 1965, Basement-controlled deformation in Wyoming province of Rocky Mountains 

foreland: American Association of Petroleum Geologists Bulletin, 

v. 49, no. 7, p. 966-992. 

Reches, Ze'ev, 1978, Development of monoclines; part I. Structure of 

the Palisades Creek branch of the East Kaibab monocline, Grand 

Canyon, Arizona, in Matthews, Vincent, 111, ed., Laramide folding 

associated with basement block faulting in the western United States: 

Geological Society of America Memoir 151, p. 235-271. 

Reches, Ze'ev, and Johnson, A.M., 1978, Development of monoclines; 

part 11. Theoretical analysis of monoclines, in Matthews, Vincent, 

111, ed., Lararnide folding associated with basement block faulting 

in the western United States: Geological Society of America Memoir 151, p. 273-31 1. 

Reches, Ze'ev, Hoexter, D.F. and Hirsch, Francis, 1981, The structure 

of a monocline in the Syrian Arc system, Middle East; surface and 

subsurface analysis: Journal of Petroleum Geology, v. 3, no. 3, p. 

413-425. 

Sanford, A.R., 1959, Analytical and experimental study of simple geologic structures: Geological Society of America Bulletin, v. 70, no. 

1, p. 19-52. 

Sarna-Wojcicki, A.M., Pampeyan, E.H., and Hall, N.T., 1975, Map showing recent active breaks along the San Andreas fault between central Santa Cruz Mountains and the northern Gabilan Range, California: U.S. Geological Survey Miscellaneous Field Studies Map 

MF-650, scale 1:24,000, 2 sheets. 

Stems, D.W., 1978, Faulting and forced folding in the Rocky Mountains foreland, in Matthews, Vincent, 111, ed., Laramide folding 

associated with basement block faulting in the western United States: 

Geological Society of America Memoir 151, p. 1-37. 

Stein, R.S., and King, G.C.P., 1984, Seismic potential revealed by surface folding; 1983 Coalinga, California, earthquake: Science, v. 

224, no. 4651, p. 869-872. 

APPENDIX: ANALYTICAL PROCEDURE 

The mechanical deformation within a fault-fold system 

is derived here for the deformation of incompressible elastic or viscous layers overlying a faulted basement; the 

deformation is plane strain, restricted to the x-y plane 

(fig. 1). According to Reches and Johnson (1978, app. 1, 

eq. lo), the stress-strain relations, equilibrium equations, 

and compatibility equations are satisfied if the stress function Y satisfies the biharmonic equation 

The general solution for 'V is 

L is the longest wavelength, n is an integer indicating 

higher harmonic (n=l.. .N), and a, b, c, and d are constants to be determined from the boundary conditions. 

The formulas for the stresses, displacements and strains 

in the layers are derived from equations 2 (Reches and 

Johnson, 1978, app. 1). To generate the step geometry of 

the basement faulting we superposed as many as 180 wavelengths, as described below (also see Reches and Johnson 

(1978, app. 2). 

The normal and shear stresses written for the ith layer 

and the nth wavelength are given by 

Off = 

2@{[a, + b, (Xy - I)] exp(^) + [c, + d, (Ay + I)] exp(-Xy)} (3a) 

sin (Ax) - py 

OYY = 

-2pk{[a, + b,{\y + I)] exp(Xy) + [c, + d, (Xy - I)] exp(-Xy )} (3b) 

sin (Ax) - py 

0 = 2@[(a, + b&y) exp(Xy) - (c, + d,Xy) exp(-Xy)] (30 cos (q 

the horizontal displacement u and vertical displacement v 

by 

u = [(a, + b,Ay) exp(Xy) + (c, + d,Xy) exp(-Xy )] cos(h) (4a) 

= [('i + b, ('Y - '))I ex~(X~) - [c,+ ('Y + I)] exp(-~)} (4b) 

sin (h) 
MECHANICAL MODELING OF A FAULT-FOLD SYSTEM, WITH APPLICATION TO THE EARTHQUAKE A193 

and the normal and shear strains by 

= ^Â¥[(a + biky) exp(ky) + (c, + diky) exp(-ky)] (54 

sin (Ax) 

E, = ->.[(ai + biq exp(Ly) + (ci + di>.y) exp(-ky)] (5~) 

cos( Ax) 

where p is the shear modulus, n is an integer indicating 

the wavelength (n=l ...N), L is the longest wavelength 

considered, and a,, b,, e,, and d, are constants of the ith 

layer that depend on the geometry, properties, and boundary conditions of the problem. 

The above equations indicate that the stresses, displacements, and strains in the ith layer are completely specified by four constants a,, bi, e,, and d,. Thus, four boundary 

conditions are needed for each layer to solve for the deformation. The boundary conditions are specified at the 

contacts between layers and are based on the continuity 

of stresses and displacements. For bonded contacts, the 

conditions at the contacts are 

and for free-to-slip contacts, the conditions at the contacts 

are 

The boundary conditions at the top of the model that is a 

stress-free surface are 

The boundary conditions at the base of the layered sequence are presented in the next section (eqs. 9). 

It can be shown that these boundary conditions generate 4K linear equations where K is the number of layers. 

This system is solved simultaneously to obtain the constants a,, b,, e,, and d, for all layers. These constants are 

then substituted into the stress and displacement equations to calculate the required deformation parameter, as 

follows. 

CALCULATION AND PRESENTATION 

PROCEDURES 

A set of dedicated computer programs based on the 

above analytical solutions were written in QuickBasic for 

the IBM PC. The programs are interactive, and their results are graphically presented on the screen. The programs includes five main steps as follows. 

In the first step, the sequence of layers is selected. The 

number of layers ranges from 1 to 10, the thickness of the 

layers is unrestricted, and the contacts between them may 

be either bonded or free to slip. 

In the second step, the basal displacement, which is the 

displacement of the base of the layered sequence, is calculated. This displacement reflects the slip along the fault 

(reverse or normal and inclination) and the deformation 

of the basement. We solve here for two classes of basal 

displacements. In the first class, the basement is approximated by perfectly rigid blocks with no internal deformation, separated by a weak fault. This approximation is 

based on field observations that indicate the planar geometry of basement blocks (Reches and Johnson, 1978; see 

section above entitled "Analysis of a Fold-Fault System"). 

The vertical displacement V and the horizontal displacement U at the base of the layered sequence are determined by the following Fourier series for a step: 

where k=27in 1 L, (n=l,2 ,..... N) 
A194 MAIN-SHOCK CHARACTERISTICS 

L is the longest wavelength considered (typically, 160 km 

in the present modeling), N is the maximum number of 

Fourier components considered (N=100-200), and Vo and 

Uo are the maximum vertical and horizontal displacements, 

respectively. Uo=O indicates slip along a vertical fault, 

Uo=Vo indicates slip along a 45'-dipping reverse fault, 

and Uo=-Vo indicates slip along a 45'-dipping normal fault. 

The second class of basal displacement, for a single 

earthquake, combines fault slip and the elastic deformation of the basement. To calculate this combined deformation, we used the computer program DIS3D (Erickson, 

1987), which calculates the displacements, strains, and 

stresses in an elastic half-space due to slip along one or 

more dislocations. The selected fault slip and fault inclination were substituted into the program, and the displacements were calculated for plane-strain conditions. The 

basal displacements along a horizontal surface that is at 

the depth of the base of the layered sequence (generally, 

5-km depth) are then transformed into a Fourier series in 

which the vertical component is the sine series and the 

horizontal component is the cosine series. We used 100 to 

200 waves to obtain a good approximation of the displacement. The results of this transformation are substituted into the analytical solution of the layered sequence 

as the basal-displacement boundary condition. In so doing, we assume that the displacements at the top of the 

basement (that is, the base of the layers) due to slip along 

a fault embedded within it are only slightly affected by 

the layering above the basement. 

The third step is the main computation stage. The stress 

and displacement equations (eqs. 3, 4) are substituted into 

the boundary conditions between the layers (eq. 6 or 7), at 

the top (eq. 8), and at the base (eq. 9). The 4K linear 

equations for each wavelength are solved simultaneously 

to determine the set of unknown constants ai, b,, ci, and 

di. These process is repeated for all N wavelengths. Now, 

the stresses and displacement (eqs. 3, 4) can be calculated 

for every point within the layered sequence by summation 

of the N waves' contributions. The results are presented 

in cross sections that include the displacements and the 

orientation of the maximum-compressive-stress axes and 

the intensity of the shear stress (figs. 3, 6, 7). 

The distribution and mode of aftershocks could serve 

as indicators for the slip during the earthquake and 

preearthquake stresses (Oppenheimer and others, 1988). 

The aftershocks of the Loma Prieta earthquake display a 

rather-confusing distribution of focal-plane solutions, with 

focal solutions of reverse faulting side by side with normal faulting or strike-slip events (Michael, 1991). Because this disorganized pattern persists also in the upper 5 

km, we disregard here the focal solutions of the aftershocks and use their spatial distribution . This distribution 

is correlated with the intensity of the calculated shear 

stresses (see subsection above entitled "Aftershock Distribution"). 

The intensity of the shear stress is evaluated by the 

procedure of Brace and Kohlstedt (1980), who assumed 

that upper-crustal rocks yield by frictional slip according 

to Coulomb criteria, with the coefficients of Byerlee's 

law. Their equation 3 indicates that at a depth of a few 

kilometers, yielding occurs when 

where ol and 03 are the magnitudes of the maximum and 

minimum compressive stresses (assuming that p=0.85). 

Because the lithostatic load strongly affects frictional sliding T is divided by the lithostatic pressure to obtained the 

normalized shear stress, 

where p is the mean rock density, g is the acceleration 

due to gravity, and Y is the local depth. tE can be related 

to field conditions if the principal stresses are assumed to 

be horizontal and (or) vertical, in which case it can be 

shown that 

= oH > oh > o = o3 for thrusting, 

o1 = ou > o > oh = 9 for strike-slip conditions, 

and ol = o > oH > oh = 03 for normal faulting, 

where oH and oh are the maximum and minimum horizontal stresses and oV=pgY is the vertical stress. Substituting equation 10 and the conditions of the last three 

equations into equation 11 reveals that ~~22 for thrusting, 

TE>l for strike-slip conditions, and ~~20.4 for normal faulting. 

The above equations are for the total stresses, which 

include the unknown preearthquake stress; this stress is 

modified because of the slip during the earthquake. 

Oppenheimer and others (1988) selected various 

preearthquake stresses to calculate their failure parameter 

F (which is equivalent to the present parameter T~). Because the preearthquake stresses for the Loma Prieta region are unknown, we consider here only changes in the 

shear stresses. We anticipates that an increase in the shear 

stress would increase the tendency for local aftershocks. 

From equation 11, the change in the shear stress during 

the earthquake is defined as 

which is equivalent to the parameter AF of Oppenheimer 

and others (1988). 

In the calculations presented here, we consider shearstress changes to be significant if AT~>O.O~T~ (see 

Oppenheimer and others, 1988, p. 9020-9021). Rock density is assumed to be uniformly equal to 2,650 kg/m3. 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAKEOCCURRENCE 

-- 

MAIN-SHOCK CHARACTERISTICS 

ARE RUPTURE MODELS CONSISTENT WITH GEODETIC 

MEASUREMENTS?l 

By Jamison H. Steidl and Ralph J. Archuleta, 

Un 

CONTENTS 

versity of California, Santa Barbara 

ABSTRACT 

We have inverted strong-motion waveform data from 

the 1989 Loma Prieta earthquake to determine the spatial 

and temporal distribution of slip during the rupture process. The best-fitting solution determined by matching 

numerically computed waveforms with the observed data 

is bimodal, with large slip amplitudes north and south of 

the hypocenter. South of the hypocenter, the slip is predominantly strike slip; north of the hypocenter, the slip is 

predominantly dip slip. This slip occurs between 7- and 

19-km depth. These two regions both have at least 1.0 m 

of slip, and some interior localized areas have 3.0 to 4.0 

m of slip. This heterogeneous distribution of slip produces a static-strain field that can be compared with the 

coseismic geodetic observations. The strain field determined from the strong-motion inversion (independent of 

the geodetic data) predicts many, but not all, of the geodetic measurements. We present forward calculations of 

the static-strain field and examine the source of misfit to 

the observations by comparing observed with calculated 

line-length changes. We compare the use of homogeneous 

velocity models with that of vertically heterogeneous velocity models in calculating the strain field. The geodetic 

monument on Loma Prieta peak is located in a nodal pol Contribution No. 0095-13EQ, Institute for Crustal Studies, University 

of California, Santa Barbara, CA 93106. 

sition with respect to the inferred fault surface. This location makes the observations at Loma Prieta difficult to 

match by using a fault surface located along the aftershock distribution, When the Loma Prieta monument is 

removed from the data set, faulting models offset from 

the aftershock distribution fit the rest of the data no significantly better than do faulting models located along the 

aftershock distribution. 

INTRODUCTION 

The 1989 Loma Prieta earthquake provided one of the 

most complete sets of near-source strong-motion data ever 

recorded. In addition, it occurred within a region where 

surface displacements have been monitored frequently, using electronic distance measurement (EDM), the Global 

Positioning System (GPS), and very long baseline interferometry (VLBI). This paper compares the static-strain 

field calculated by using the slip model determined from 

the acceleration records (Steidl and others, 1991) with 

these geodetic measurements. 

Complex spatial distributions of slip have been demonstrated for many earthquakes (for example, Aki, 1968; 

Trifunac, 1974; Heaton and Helmberger, 1979; Archuleta 

and Day, 1980; Bouchon, 1982; Olson and Apsel, 1982; 

Hartzell and Heaton, 1983, 1986; Archuleta, 1984; 

Fukuyama and Irikura, 1986; Beroza and Spudich, 1988; 

Hartzell, 1989; Mendoza and Hartzell, 1989; Hartzell and 

Iida, 1990; Beroza, 1991; Hartzell and Mendoza, 1991; 

Hartzell and others, 1991; Steidl and others, 199 1; Wald 

and others, 1991). Determination of the static-slip distribution is important because this distribution sets the stage 

for future events. Under the seismic-gap hypothesis, regions of high slip would have a lower probability of producing another event in the near future. The Loma Prieta 

rupture failed to reach the surface, leaving no direct measurements of the slip. The determination of slip is therefore left to be examined by an analysis of seismologic and 

geodetic data sets. 

Our understanding of the rupture process and energy 

release during dynamic rupture cannot be examined by 

using- geodetic measurements. Most geodetic modeling 

A195 

ARE RUPTURE MODELS CONSISTENT WITH GEODETIC MEASUREMENTS? 

Table 1 .-Strong-motion stations 

[APEEL, Andreas Peninsula Earthquake Engineering Laboratory; SAGO, San Andreas Geophysical Observatory; SLAC, 

Stanford Linear Accelerator Center; UC, University of California; VA, Veterans' Administration. Station owners: C, California Division of Mines and Geology; U, U.S. Geological Survey] , 

Station Owner 

Latitude Longitude Epicentral 

ON. OW. distance Components 

Code Name (km) No. 

COR 

WAT 

CAP 

ucs 

GOF 

GGC 

GI 1 

GI2 

GI3 

GI4 

GI6 

GI7 

S AR 

HOL 

ASH 

FRS 

ADL 

ADD 

SUN 

HOA 

PAH 

SLA 

HCH 

SPG 

MPH 

FRE 

RED 

LEX 

CLD 

CL A 

HVL 

SAG 

SAL 

MCH 

WFS 

css 

CSP 

FMS 

Corralitos 12 ----------------------------....-....-..--. 

Watsonville2 -------------------.---------------------- 

Capitola' ................................................ 

UC Santa Cmzl ..................................... 

Gilroy, Historical Building2------------- 

Gilroy, Gavilan Colle el ---------------- Gilroy array station 1f2 ------------------ Gilroy array station 22 .................... 

Gilroy array station 32 .................... 

Gilroy array station 42 .................... Gilroy array station 61'2 ------------------ 

Gilroy array station 71 .................... 

Saratogal ................................... 

Hollister (South and Pine st~.)~ -------- 

Agnews State Hospital2------------------ 

Foster City, Redwood Shores2 --------- 

Anderson Dam, abutment'--------------- 

Anderson Dam, downstream1v2------------- 

sunnyvale2 ................................ 

Hollister Airport2 ......................... 

Palo Alto VA Hospital .................... 

Stanford, SLAC2 ......................... 

Hollister City Hall2 ....................... Stanford parking garage ------------------ 

Men10 Park VA Hospital----------------- 

Fremont, Emerson Court1 --------------- 

Redwood City, APEEL station 2 ------- 

Lexington Dam, abutment2 ------------- Coyote Lake Dam, d~wnstream~,~ ----- Coyote Lake Dam, abutment2 ----------- Halls Valley, Grant Parkl.2-------------- 

SAGO South, Hollisterl.2 ..................... 

salinas 12 ----.....-..-..----------------------------.... 

Monterey City Hal11,2 .................... Woodside Fire Station' ------------------ 

Crystal Springs Reservoir, Skyline]------ 

Crystal Springs Reservoir, Pulga~~?~ -- Fremont, Mission San Jose1v2 ---------- 

'Station used in model 14 of Steidl and others (1991). 

Station with absolute time. 

this study are low uniform slip and a constant rupture 

velocity of 3.0 krnls. The slip-rate function used is an 

isosceles triangle with a pulse width of 1.0 s (model 14 of 

Steidl and others, 1991, table 3). Subfault synthetic seismograms for strike-slip (180' rake) and dip-slip (90' rake) 

mechanisms are generated from each of the 152 subfaults, 

for all components, at every station. These subfault synthetic seismograms are summed to produce a total station 

synthetic seismogram. Slip-amplitude and rupture-velocity perturbations are determined simultaneously for each 

subfault at each iteration by solving an overdetermined 

system of linear equations that relates the synthetic to the 

observed time histories. The model is updated, and new 

synthetic seismograms are calculated, using the new perturbed model. This procedure is done iteratively until further iterations fail to provide a significant reduction in the 

rms residual error (Euclidean norm between observed and 

synthetic seismograms). The strike-slip component is constrained to be right lateral, and the dip-slip component is 

separately constrained to be reverse slip or thrusting. Both 

components have minimization and smoothing constraints, 

as used by Hartzell and Iida (1990). 

GEODETIC MODELING 

The method described above calculates the ground velocity at a particular location due to traction on the fault. 

This response includes zero frequency. Thus, we can use 

this technique to do a forward calculation of the static 

displacement at a particular location due to a specified 

rupture model. This method allows us to model the static 

displacements at geodetic stations, using a layered elastic 

half-space. We first use a three-dimensional-dislocation 

computer program, DIS3D (Erickson, 1986), to calculate 

the displacements for all models that use a homogeneous 

half-space. The elastic field equations in the program 

DIS3D are similar in form to those of Mansinha and oth- 
MAIN-SHOCK CHARACTERISTICS 

SAN ANDREAS FAULT 

Figure 1 .-Loma Prieta region, Calif., showing locations of strong-motion stations used in this study (triangles) and surface projection of inferred rupture zone (shaded area). Star, epicenter of 1989 earthquake. See 

table 1 for station names and codes. 

0 4 8 12 16 19 22 26 30 34 38 

DISTANCE ALONG STRIKE, IN KILOMETERS 

Figure 2.-Cross section of model fault used in this study, comprising a total of 152 subfaults with equal 

dimensions (2 by 2.125 km). Enlarged subfault shows inversion parameters. 
ARE RUPTURE MODELS CONSISTENT WITH GEODETIC MEASUREMENTS? A199 

Table 2.-One-dimensional velocity structure 

ers (1971). We then apply our method to the case of the 

layered elastic half-space listed in table 2 (Dietz and 

Ellsworth, 1990). 

The parameters we vary in the geodetic forward calculation are the strike, the slip distribution, the fault locationlgeometry, and the medium properties. We examined 

strikes of 126' and 136'. We looked at the difference 

between using a single fault with uniform slip and using a 

nonuniform slip distribution with the fault parametrization shown in figure 2. We used two locations for the 

fault: (1) along the aftershock distribution, as mentioned 

in the fault parametrization of the strong-motion inversion; and (2) in the same place as Lisowski and others 

(1990), offset from the aftershock distribution. The various 

fault geometries used in this study are listed in table 3. 

We use either a homogeneous, isotropic elastic half-space 

or a vertically layered elastic half-space for the medium 

properties. 

Our objective is to see how consistent the rupture models determined from the strong-motion data (independent 

from the geodetic data) are with the observed ground displacements. We are also interested in the difference between modeling the geodetic measurements with a uniform 

half-space (as most geodetic modeling has been done in 

the past) with a layered half-space. We did not, however, 

try to search the parameter space for a best fit to the 

geodetic data, but only examined end-member models. 

We determine the error for all our models from the 

equation 

where the rms residuals, Rl, are the absolute value of the 

observed minus calculated line-length changes. Each rms 

residual is weighted by the standard deviation of the measured line-length change (or); the total error, Wm, for 

each model is the square root of the sum of the squares of 

these weighted rrns residuals divided by the number of 

station pairs (Np). The results of our geodetic forward 

modeling are summarized in table 4. 

RESULTS 

STRONG-MOTION MODELING 

The slip distribution presented here is the best-fitting 

solution using horizontal and vertical records for 20 stations (fig. 1; table I), as described by Steidl and others 

(1 99 1). Other nonuniform-slip models have been proposed 

by Beroza and others (1991), Hartzell and others (1991), 

and Wald and others (1991). Contours of the slip distribution, projected onto the fault plane, are shown in figure 3. 

The bimodal distribution of slip, characteristic of all nonuniform-slip models for this event, is clearly visible in 

figure 3. Strike slip is dominant south of the hypocenter 

(fig. 3A; table 5), whereas dip slip is dominant north of 

the hypocenter (fig. 3B; table 6). The rake vector for the 

south and north halves of the fault clearly shows rotation 

in all the models presented by Steidl and others (1991). In 

figure 3, the average rake on the south half of the fault is 

156O, whereas the average rake of the north half of the 

fault is 115'. We use the convention of Aki and Richards 

(1980) here in defining the rake angle. The average rake 

over the whole fault is 137O, comparable to the 135'&10Â 

found in teleseismic and longer period studies (Choy and 

Boatwright, 1990; Kanamori and Satake, 1990; 

Romanowicz and Lyon-Caen, 1990; Zhang and Lay, 1990; 

Wallace and others, 1991). Far-field studies seem to show 

an average rake for the bimodal slip distribution in figure 

3. 

The slip in this model occurs between 7- and 19-km 

depth. Both the northern and southern fault patches have 

at least 1.0 m of slip, and some interior localized areas 

have 3.0 to 4.0 m of slip. The rupture front propagates 

outward from the hypocenter bilaterally at an average velocity of 3.0 krnls, and the main moment release, 3.35~10~~ 

dyne-cm, is complete within 7.0 s. The unusually small 

amount of slip at the hypocenter agrees with the idea that 

the main shock began as a smaller event which then triggered the larger rupture. Ellsworth (1991, 1992) and Wald 

and others (1991) discussed evidence for this foreshock. 

GEODETIC MODELING 

The results of forward modeling of the geodetic data 

are summarized in table 4, where the column labeled "E1" 

contains the Wrms error using all line-length changes. 
A200 MAIN-SHOCK CHARACTERISTICS 

Table 3.-Fault geometry 

Location of Depth 

Depth upper northwest corner to upper 

Geometry interval (km) 

northwest Strike Dip 

(km) corner Lat N. Long W. (km) 

Table 4.-Geodetic forward-modeling results 

Model Dislocation type Slip Geometry Percentage of El 

from station LP 

1 1 dislocation surface---- Lisowski and others (1990) A 3.01 29 2.76 

2 1 dislocation surface---- do. B 4.16 5 3 3.10 

3 1 dislocation surface---- NL 14 (average) C 3.87 3 0 3.49 

'4 152 dislocations--------- NL 14 C 5.56 75 3.08 

'5 152 dislocations--------- NL 14 D 5.04 75 2.76 

'One-dimensional layered half-space (see table 2). 

Model 1, which has the lowest W error (El) and could 

be considered the best-fitting model for the complete data 

set, is the model of Lisowski and others (1990), with 1.19 

m of dip slip and 1.66 m of strike slip. The fault geometry 

and location used in model 1 (fig. 4; geometry A, table 3) 

are identical to those of Lisowski and others. Model 1 is 

the control model for this study. We compare the error 

from models 2 through 5 with that from model 1 (table 4) 

for comparison with the preferred geodetic model of 

Lisowski and others. This difference does not become statistically significant (F test, 95-percent-confidence level) 

until the ratio of the W error (model Nlmodel 1, where 

N=2-5) exceeds 1.47. Therefore, the difference between 

models 1, 2, and 3 is not statistically significant (table 4). 

Models 4 and 5, however, which use a nonuniform slip 

distribution (fig. 3) and the one-dimensional layered halfspace (table 2), fit the data significantly worse (table 4). 

Station LP is located in a nodal position with respect to 

a fault surface defined by the distribution of aftershocks. 

This location makes the observed large displacements at 

station LP anomalous. Approximately 20 percent of the 

line-length measurements are tied to station LP. We now 

investigate the anomalously large displacements observed 

at station LP as a possible source for the misfit in the 

models. The contribution to the Wrms error from only the 

line-length changes tied to station LP ("percentage of El 

from station LP") and the error from all line-length measurements except station LP ("E2") are listed in table 4. 

We compare the fit to the line-length changes of models 1 and 2 to examine why the geodetic measurements 

prefer the fault-plane offset from the aftershock distribution. Model 2 uses a fault with the same dimensions, orientation, and slip as model 1 but with a location moved 

onto the aftershock distribution (fig. 5; geometry B, table 

3). Model 2 has 53 percent of the error due to station LP, 

whereas model 1 has 29 percent of the error due to station 

LP. The geodetic modeling of Lisowski and others (1990) 

prefers a fault plane offset from the aftershock distribution to better fit the line-length changes at station LP and 

reduce the overall error. The overall error (El) and the 

error excluding the data tied to station LP (E2) are slightly 

larger, but not significantly different, for model 2 than for 

model 1 (table 4). 

Next, we examine how well the average slip determined 

in the strong-motion model of Steidl and others (1991) 

can predict the geodetic measurements. Model 3 uses geometry C (table 3) and the average slip amplitudes from 

the nonuniform slip distribution shown in figures 3A and 

3B (1.02 m of dip slip and 1.13 m of strike slip), adjusted 

for use in a homogeneous half-space. The fault geometry 

and location in model 3 are identical to that used in the 

strong-motion model. We find that the error due to station 

LP in model 3 is 30 percent, close to that in model 1. The 

overall error (El) and the error excluding the data tied to 

station LP (E2) are slightly larger, but not significantly 

different, for model 3 than for model 1 (table 4). 

Models 4 and 5 test the use of a vertically heterogeneous medium (table 2) and a nonuniform slip distribution (fig. 3) when calculating the displacements. Using a 

more complex (realistic) velocity structure and slip distri- 
ARE RUPTURE MODELS CONSISTENT WITH GEODETIC MEASUREMENTS? A20 1 

bution, intuition suggests that we should be better able to 

predict the geodetic measurements. Contrary to intuition, 

however, table 4 shows that the overall error (El) is significantly larger after making these changes to more realistic models. Initial interpretation of these results suggests 

that the geodetic measurements are inconsistent with the 

rupture model determined from the strong-motion data. 

Closer examination of the source of error in these models 

allows for reinterpretation of these results. 

The geometry of models 4 and 5 is listed in table 3 

(geometries C and D, respectively). The only difference 

between models 4 and 5 is the strike of the fault. The 

overall error is less for a fault that strikes 136O, suggesting that the geodetic measurements prefer this strike, although the error does not differ significantly from that for 

a fault which strikes 126'. Models 4 and 5 have 75 percent of their error from station LP. When we remove station LP from the data set ("E2", table 4), the errors decrease 

NW SE 

DISTANCE ALONG STRIKE, IN KILOMETERS 

0 8 16 24 32 40 

NW SE 

DISTANCE ALONG STRIKE, IN KILOMETERS 

0 8 16 24 32 40 

NW SE 

DISTANCE ALONG STRIKE, IN KILOMETERS 

0 8 16 24 32 40 

SLIP 

AMPLITUDE, IN 

CENTIMETERS 

SLIP 

AMPLITUDE, IN 

CENTIMETERS 

SLIP 

AMPLITUDE, IN 

CENTIMETERS 

Figure 3.-Fault slip determined by inverting 40 horizontal and 20 vertical time histories (20.0 s) of ground 

velocity (model 14 of Steidl and others, 1991). Cross section of fault surface with depth is oriented perpendicular to fault from southwest; that is, variables are plotted on footwall. A, Strike-slip motion. B, Dip-slip 

motion. C, Total slip. 
MAIN-SHOCK CHARACTERISTICS 

Table 5.-Strike-slip displacements in strong-motion inversion for model 14 of Steidl and others (1991) 

[All values in centimeters at center of each subfault; positive values correspond to a rake of 180'. Distance along strike is 

from northwest end to center of each subfault] 

Depth to center of subfault (krn) 

Distance along 

strike (km) I 6 8 10 12 14 16 18 

Table 6. -Dip-slip displacements in strong-motion inversion for model 14 of Steidl and others (1991) 

[All values in centimeters at the center of each subfault; positive values correspond to a rake of 90'. Distance along strike 

is from northwest end to center of each subfault] 

Distance along 

strike (km) 

Depth to center of subfault (km) 
ARE RUPTURE MODELS CONSISTENT WITH GEODETIC MEASUREMENTS? A203 

to a level that is statistically indistinguishable from that in 

the other models, suggesting that the geodetic measurements are consistent with the strong-motion model except 

at one station, LP. 

The calculated displacements (dashed vectors with tail 

located at station) for models 3 and 5 are plotted on top of 

the observed displacements (solid vectors) in figures 4 

and 5, respectively. The observed displacements were calculated by using the "model coordinate" solution of Segall 

and Matthews (1988). The vertical surface projections of 

the four fault geometries used in this study are also shown 

in figures 4 and 5. 

DISCUSSION 

The results presented in the preceding section show 

that in modeling the geodetic measurements, the results 

can be strongly influenced by a single station. Station LP 

is used for many of the geodetic measurements; its location, almost directly updip from the buried fault surface, 

is nearly nodal in our theoretical fault geometry. With so 

many of the geodetic measurements tied to only one station, LP, modeling the horizontal deformation is strongly 

controlled by the fit to this station. The GPS and 

trilateration measurements at station LP show relatively 

large displacements, a result inconsistent with its nodal 

location. This seems to be the reason why geodetic modeling of the horizontal deformation has to force the location of the nodal plane to the southwest, either by moving 

the entire fault surface southwestward (Lisowski and others, 1990) or by placing a kink in the fault and projecting 

the upper half of the fault vertically upward to the surface 

(Snay and others, 199 1). Unless evidence exists as to why 

the aftershocks and main-shock hypocenter would occur 

of Figure 5B \ \ 

FAULT 

Figure 4.-Loma Prieta region, Calif., showing observed geodetic-station displacements (solid vectors) and 

displacements calculated by using slip distribution of model 3 (dashed vectors) (see table 4). Large clear 

rectangle, surface projection of fault geometry used in this model, with epicenter (star) located at bottom 

edge, midway along strike (geometry C, table 3); shaded rectangle, surface projection of fault geometry used 

in model 1 (geometry A, table 3). Small clear rectangles show areas of smaller networks in figures 5B and 5C. 
A204 MAIN-SHOCK CHARACTERISTICS 

systematically offset from the fault surface, we argue that 

better fits to the geodetic measurements must come from 

more realistic models of the local velocity structure and 

of the slip distribution, not from repositioning the fault. 

Three-dimensional velocity models of the Loma Prieta 

region show large variations in the velocity structure from 

the simple one-dimensional model used in this study 

(Eberhart-Phillips and others, 1990a, b; Lees, 1990; 

Michael and Eberhart-Phillips, 199 1 ; Eberhart-Phillips and 

Stuart, 1992; Lees and Shalev, in press). These variations 

affect the calculated surface deformations. The large velocity gradient from the hanging wall to the footwall (low 

to high velocity) in the vicinity of station LP has the 

effect of shifting the nodal plane of the surface displacements and increasing their amplitudes (Eberhart-Phillips 

and Stuart, 1992). This effect would account for the 

underprediction of the displacement at station LP when 

using simple homogeneous or vertically heterogeneous 

velocity models and a fault surface located along the aftershock distribution (figs. 4, 5). 

The average seismic moment calculated from the strongmotion inversions, 3.5~ 1 026 dyne-crn (Steidl and others, 

1991), is comparable to the seismic moment determined 

from the geodetic data, 3.0~10~~ dyne-cm (Lisowski and 

others, 1990). Increasing the slip amplitude to match the 

underprediction of the displacement at station LP would 

produce a seismic moment inconsistent with the accepted 

range of values for the earthquake, as well as destroy the 

fit to the amplitude of particle velocities in the strongmotion data. Owing to the band limitation of the strongmotion data, a long-duration, low-amplitude tail in the 

slip-rate function is unresolvable. We could add this tail 

to our slip-rate function without destroying the fit to the 

strong-motion data, and simultaneously increase the static 

Figure 5.-Loma Prieta region, Calif. (A), showing observed geodetic-station displacements (solid vectors) 

and displacements calculated by using slip distribution of model 5 (dashed vectors) (table 4). Large open 

rectangle, surface projection of fault geometry used in this model, with epicenter (star) located at bottom 

edge, midway along strike (geometry D, table 3); shaded rectangle, surface projection of fault geometry used 

in model 2 (geometry B, table 3). B, Black Mountain network. C, Southern network. 
ARE RUPTURE MODELS CONSISTENT WITH GEODETIC MEASUREMENTS? A205 

displacements measured at the geodetic monuments, but 

not without increasing the seismic moment to values inconsistent with geodetic and far-field studies. 

The fact that the strong-motion modeling produces the 

same seismic moment as do the longer period studies suggests that the slip is completely recovered by the strongmotion inversion. If local movements on faults in the 

vicinity of station LP had occurred aseismically immediately after the coseismic faulting, these movements could 

explain the anomalous displacement at this station. We 

choose to account for the underprediction of the displacement at station LP by invoking some local site condition 

(for example, lateral heterogeneities or aseismic movement on faults in the vicinity), not an absence of seismic 

moment in our model. 

Apparently, we have run into the same limitations when 

modeling the geodetic measurements as when fitting the 

strong-motion data. We fail to take into account the 

inhomogeneities from the source to each specific receiver 

and therefore are unable to reproduce the response at each 

site exactly. In modeling the geodetic measurements from 

the earthquake, we chose not to relocate the fault surface 

offset from the aftershock distribution but to accept the 

misfit to the data as inherent to the simplification in our 

Figure 5.-Continued 
A206 MAIN-SHOCK CHARACTERISTICS 

model. This study clearly shows that we need to focus our 

research efforts in the direction of gaining a better understanding of path and site effects. Two- and three-dimensional finite element modeling of wave propagation 

through a heterogeneous medium should further this aim. 

CONCLUSIONS 

With our better understanding of how the observations 

at a single geodetic monument, station LP, can affect the 

results, we conclude that the rupture models are indeed 

consistent with geodetic measurements. The overall error 

for models that have a fault surface located along the 

aftershock distribution is strongly controlled by this one 

station. The nodal position of station LP relative to the 

faulting geometry defined by the aftershocks makes the 

large displacement observed at station LP anomalous. We 

suggest that the underprediction of the displacement at 

station LP is due either to inaccurate representation of the 

local elastic properties of the Earth or to local aseismic 

movements in the vicinity of this station. When station 

LP is removed from the data set, faulting models offset 

from the aftershock distribution fit the rest of the data no 

significantly better than do faulting models located along 

the aftershock distribution. Although moving the fault 

plane to account for more complex elastic properties of 

the Earth can improve the fit to the complete data set, we 

chose not to take this approach. Once agreement is 

achieved as to the location of the fault surface, improvement in fit to the complete data set must come from either 

a more complex velocity structure or a more complex 

model fault (for example, nonplanar). 

ACKNOWLEDGMENTS 

This research was supported in part by U.S. Geological 

Survey grant 14-08-0001-G1842. We thank Bob Simpson 

for providing the computer program DIS3D and for many 

helpful discussions. Mike Lisowski provided the "model 

coordinate" solution for the displacement vectors, as well 

as many helpful discussions. We thank Jim Savage and 

Paul Spudich for their careful reviews of the manuscript. 

REFERENCES CITED 

Aki, Keiiti, 1968, Seismic displacements near a fault: Journal of Geophysical Research, v. 73, no. 16, p. 5359-5376. 

Aki, Keiiti, and Richards, P.G., 1980, Quantitative seismology; theory 

and methods: San Francisco, W.H. Freeman, 2 v. 

Archuleta, R.J., 1984, A faulting model for the 1979 Imperial Valley 

earthquake: Journal of Geophysical Research, v. 89, no. B6, p. 

4559-4585. 

Archuleta, R.J., and Day, S.M., 1980, Dynamic rupture in a layered 

medium, the 1966 Parkfield earthquake: Seismological Society of 

America Bulletin, v. 70, no. 3, p. 671-689. 

Beroza, G.C., 1991, Near-source modeling of the Loma Prieta earthquake; evidence for heterogeneous slip and implications for earthquake hazard: Seismological Society of America Bulletin, v. 81, 

no. 5, p. 1603-1621. 

Beroza, G.C., and Spudich, Paul, 1988, Linearized inversion for fault 

rupture behavior; application to the 1984 Morgan Hill, California, 

earthquake: Journal of Geophysical Research, v. 93, no. B6, p. 

6275-6296. 

Bouchon, Michel, 1982, The rupture mechanism of the Coyote Lake 

earthquake of 6 August 1979 inferred from near-field data: Seismological Society of America Bulletin, v. 72, no. 3, p. 745-759. 

Choy, G.L., and Boatwright, John, 1990, Source characteristics of the 

Loma Prieta, California, earthquake of October 17, 1989 from global digital seismic data: Geophysical Research Letters, v. 17, no. 8, 

p. 1183-1186. 

Dietz, L.D., and Ellsworth, W.L., 1990, The October 17, 1989, Loma 

Prieta, California, earthquake and its aftershocks; geometry of the 

sequence from high-resolution locations: Geophysical Research Letters, v. 17, no. 9, p. 1417-1420. 

Eberhart-Phillips, D.M., Labson, V.F., Stanley, W.D., Michael, A.J., 

and Rodriguez, B.D., 1990a, Preliminary velocity and resistivity 

models of the Loma Prieta earthquake region: Geophysical Research Letters, v. 17, no. 8, p. 1235-1238. 

Eberhart-Phillips, D.M., Michael, A.J., Fuis, G.S., and Luzitano, R.D., 

1990b, Three-dimensional crustal velocity structure in the region of 

the Loma Prieta, California, earthquake sequence from inversion of 

local earthquake and shot arrival times [abs.]: Seismological Research Letters, v. 61, no. 1, p. 48. 

Eberhart-Phillips, D.M., and Stuart, W.D., 1992, Material heterogeneity 

simplifies the picture; Loma Prieta: Seismological Society of 

America Bulletin, v. 82, no. 4, p. 1964-1968. 

Ellsworth, W.L., 1991, Nucleation and growth of the Loma Prieta earthquake [abs.]: Eos (American Geophysical Union Transactions), v. 

72, no. 72, p. 293. 

1992, Imaging fault rupture without inversion [abs.]: Seismological Research Letters, v. 63, no. 1, p. 73. 

Erickson, L.L., 1986, A three dimensional dislocation program with 

applications to faulting in the earth: Stanford, Calif., Stanford University, M.S. thesis. 

Fukuyama, Eiichi, and Irikura, Kojiro, 1986, Rupture process of the 

1983 Japan Sea (Akita-Oki) earthquake using a waveform inversion 

method: Seismological Society of America Bulletin, v. 76, no. 6, p. 

1623-1640. 

Hartzell, S.H., 1989, Comparison of seismic waveform inversion results 

for the rupture history of a finite fault; application to the 1986 

North Palm Springs, California, earthquake: Journal of Geophysical 

Research, v. 94, no. B6, p. 7515-7534. 

Hartzell, S.H., and Heaton, T.H., 1983, Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of 

the 1979 Imperial Valley, California, earthquake: Seismological Society of America Bulletin, v. 73, no. 6, p. 1553-1583. 

1986, Rupture history of the 1984 Morgan Hill, California, earthquake from the inversion of strong motion records: Seismological 

Society of America Bulletin, v. 76, no. 3, p. 649-674. 

Hartzell, S.H., and Iida, Mashiro, 1990, Source complexity of the 1987 

Whittier Narrows, California, earthquake from the inversion of strong 

motion records: Journal of Geophysical Research, v. 95, no. B6, p. 

12475-12486. 

Hartzell, S.H., and Mendoza, Carlos, 1991, Application of an iterative 

least-squares waveform inversion of strong motion and teleseismic 

records to the 1978 Tabas, Iran, earthquake: Seismological Society 

of America Bulletin, v. 81, no. 2, p. 305-331. 
ARE RUPTURE MODELS CONSISTENT WITH GEODETIC MEASUREMENTS? A207 

Hartzell, S.H., Stewart, G.S., and Mendoza, Carlos, 1991, Comparison 

of L and L, norms in a teleseismic waveform inversion for the slip 

history of the Loma Prieta, California, earthquake: Seismological 

Society of America Bulletin, v. 8 1, no. 5, p. 15 18-1539. 

Heaton, T.H., and Helmberger, D.V., 1979, Generalized ray models of 

the San Fernando earthquake: Seismological Society of America 

Bulletin, v. 69, no. 5., p. 1311-1341. 

Kanamori, Hiroo, and Satake, Kenji, 1990, Broadband study of the 1989 

Loma Prieta earthquake: Geophysical Research Letters, v. 17, no. 

8, p. 1179-1 182. 

Langston, C.A., Furlong, K.P., Vogfjord, K.S., Clouser, R.H., and 

Ammon, C.J., 1990, Analysis of teleseismic body waves radiated 

from the Loma Prieta earthquake: Geophysical Research Letters, v. 

17, no. 9, p. 1405-1408. 

Lees, J.M., 1990, Tomographic P-wave velocity images of the Loma 

Prieta earthquake asperity: Geophysical Research Letters,-v. 17, no. 

9, p. 1433-1436. 

Lees, J.M., and Shalev, Eylon, 1992, On the stability of P-wave 

tomography at Loma Prieta; a comparison of parameterizations, 

linear and non-linear inversions: Seismological Society of America 

Bulletin, v. 82, no. 4, p. 1821-1839. 

Lisowski, Michael, Prescott, W.H., Savage, J.C., and Johnston, M.J.S., 

1990, Geodetic estimate of coseismic slip during the 1989 Loma 

Prieta, California, earthquake: Geophysical Research Letters, v. 17, 

no. 9, p. 1437-1440. 

Mansinha, Lalatendu, Smylie, D.E., and Orphal, D.L., 1971, The displacement fields of inclined faults: Seismological Society of America 

Bulletin, v. 61, no. 5, p. 1433-1440. 

Marshall, G.A., Stein, R.S., and Thatcher, Wayne, 1991, Faulting geometry and slip from co-seismic elevation changes; the 18 October 

1989, Loma Prieta, California, earthquake: Seismological Society 

of America Bulletin, v. 81, no. 5, p. 1660-1693. 

Mendoza, Carlos, and Hartzell, S.H., 1988, Aftershock patterns and 

main shock faulting: Seismological Society of America Bulletin, v. 

78, no. 4, p. 1438-1449. 

1989, Slip distribution of the 19 September 1985 Michoacan, 

Mexico, earthquake; near-source and teleseismic constraints: Seismological Society of America Bulletin, v. 79, no. 4, p. 655-699. 

Michael, A. J., and Eberhart-Phillips, D.M., 199 1, Relations among fault 

behavior, subsurface geology, and three-dimensional velocity models: Science, v. 253, no. 5020, p. 651-654. 

Olson, A.H., and Apsel, R.J., 1982, Finite faults and inverse theory with 

applications to the 1979 Imperial Valley earthquake: Seismological 

Society of America Bulletin, v. 72, no. 6, pt. A, p. 1969-2001. 

Olson, A.H., Orcutt, J.A., and Frazier, G.A., 1984, The discrete wave 

numberlfinite element method for synthetic seismograms: Royal 

Astronomical Society Geophysical Journal, v. 77, no. 2, p. 421-460. 

Romanowicz, Barbara, and Lyon-Caen, H61&ne, 1990, The Loma Prieta 

earthquake of October 18, 1989; results of teleseismic mantle and 

body wave inversion: Geophysical Research Letters, v. 17, no. 8, p. 

1191-1194. 

Segall, Paul, and Matthews, M.V., 1988, Displacement calculations from 

geodetic data and the testing of geophysical deformation models: 

Journal of Geophysical Research, v. 93, no. B12, p. 14954-14966. 

Snay, R.A., Neugebauer, H.C., and Prescott, W.H., 1991, Horizontal 

deformation associated with the Loma Prieta earthquake: Seismological Society of America Bulletin, v. 81, no. 5, p. 1647-1659. 

Steidl, J.H., Archuleta, R.J., and Hartzell, S.H., 1991, Rupture history 

of the 1989 Loma Prieta, California, earthquake: Seismological Society of America Bulletin, v. 81, no. 5, p. 1573-1602. 

Trifunac, M.D., 1974, A three-dimensional dislocation model for the 

San Fernando, California, earthquake of February 9, 197 1: Seismological Society of America Bulletin, v. 64, no. 1, p. 149-172. 

U.S. Geological Survey staff, 1990, The Loma Prieta, California, earthquake; an anticipated event: Science, v. 247, no. 4940, p. 286-293. 

Wald, D.J., Helmberger, D.V., and Heaton, T.H., 199 1, Rupture model 

of the 1989 Loma Prieta earthquake from the inversion of strong 

motion and broadband teleseismic data: Seismological Society of 

America Bulletin, v. 81, no. 5, p. 1540-1572. 

Wallace, T.C., Velasco, A.A., Zhang, Jiajun, and Lay, Thorne, 1991, A 

broadband seismological investigation of the 1989 Loma Prieta, 

California, earthquake; evidence for deep slow slip?: Seismological 

Society of America Bulletin, v. 81, no. 5, p. 1622-1646. 

Zhang, Jiajun, and Lay, Thorne, 1990, Source parameters of the 1989 

Loma Prieta earthquake determined from long-period Rayleigh 

waves: Geophysical Research Letters, v. 17, no. 8, p. 1195-1 198. 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAmOCCURRENCE 

MAIN-SHOCK CHARACTERISTICS 

LONG-PERIOD SURFACE-WAVE OBSERVATIONS OF THE 

 EARTHQUAKE^ 

By Aaron A. ~elasco,~ Thorne Lay, and Jiajun Zhang, 

University of California, Santa Cruz 

CONTENTS INTRODUCTION 

ABSTRACT 

The 1989 Loma Prieta earthquake produced a high-quality data set of global digital, long-period seismic recordings. Given the social and scientific importance of this 

earthquake, we display here many of the three-component 

long-period recordings from stations in the Global Seismic Network (GSN), International Deployment of Accelerometers (IDA), and GEOSCOPE (Institut National des 

Sciences de 19Univers, France), In combination, these stations provide azimuthally dense coverage that has enabled 

unprecedented high-resolution analysis of the long-period 

source process in several studies. Although the data presented here have been the most widely distributed and 

extensively analyzed, our compilation is not comprehensive, and additional high-quality records are available from 

international stations and arrays, Many direct Rayleighand Love-wave arrivals propagating along the short arc 

from the source to the station were recorded onscale and 

are particularly useful for studying the source process. 

The standardization of data-exchange format, with the 

major networks all adopting the Standard for the Exchange 

of Earthquake Data (SEED) format, has greatly simplified 

data retrieval and analysis procedures. 

Contribution No, 161, Charles F. Richter Seismological Laboratory 

and Institute of Tectonics, University of California, Santa Cruz, CA 

95064. 

Current affiliation: Science Applications International Corporation, 

San Diego, CA 92121. 

Determination of the complexity involved in an earthquake rupture requires extensive ground-motion recordings. The 1989 Loma Prieta earthquake produced 

high-quality ground-motion data, ranging from *ear-field 

accelerations to teleseismic body waves, surface waves, 

and free oscillations. Both the location and timing of the 

earthquake were propitious in this regard because the Santa 

Cruz Mountains is a densely instrumented area, with many 

accelerometers, regional seismic array stations, and geodetic bench marks, and because 1989 was preceded by 15 

years of development and deployment of global digital 

seismologic instrumentation and development of advanced 

data-analysis procedures. The completeness of the various 

data sets has allowed many detailed analyses of the earthquake rupture process, as described by other papers in 

this chapter. The long-period and broadband seismograms 

from global seismic networks in particular provide an excellent demonstration of the progress made during the 

1980's in broadband, large-dynamic-range instrumentation, digital-recording capacity, and calibration technology. In this paper, we display many of the high-quality 

long-period observations for the 1989 earthquake. 

GLOBAL LONG-PERIOD SEISMIC DATA 

Although many seismic networks were operational at 

the time of the earthquake, we focus here on a subset of 

long-period global data that was readily available after 

the event. The data considered here are from long-period 

(LH) channels of three-component recordings from the 

Global Seismic Network (GSN; Incorporated Research 

Institution for Seismology, 19891, the very long period 

LaCoste-Romberg accelerometer recordings from the International Deployment of Accelerometers (IDA; Agnew 

and others, 1976) network, and very long period (VLP) 

channels of the three-component recordings from the 

broadband GEOSCOPE network (Institut National des 

Sciences de 19Univers, France; Romanowicz and others, 
A210 MAIN-SHOCK CHARACTERISTICS 

1984, 1991). The collective long-period data for the earth- the event were in the former Soviet Union (IDAIIRIS), 

quake from these three networks have extensive surface Japan, Germany, Canada, Great Britain, and China. These 

coverage (fig, 1A). Additional digital stations that recorded data, which are also of high quality, in the future will be 

Figure 1.-The world. A, Distribution of long-period stations (triangles) in Global Seismic Network (GSN), GEOSCOPE 

(Institut National des Sciences de l'univers, France), and International Deployment of Accelerometers/Incorporated Research 

Institution for Seismology (IDNIRIS) seismic networks. B, Great-circle paths of minor- and major-arc surface-wave arrivals 

at these stations. Note excellent azimuthal coverage attainable for 1989 Loma Prieta earthquake. 
LONG-PERIOD SURFACE-WAVE OBSERVATIONS OF THE EARTHQUAKE1 A21 1 

Table 1 .-Long-period suvace-wave data quality for the earthquake for Seismology, 1989). The GEOSCOPE network was rela- 

[Channels: LH, long period; VLP, very long period. Data quality of arrivals: C, tively uniform in 1989. The data centers that distribute 

clipped; g, glitches; m, missing; 0, clear; x, noisy; - -, no horizontal components1 these data-the IRIS Data Management Center (IRIS/ 

DMC; Ahern, 1989), IDA (Agnew and others, 19761, 

Station channel Azimuth Distance R2 G2 Project GEOSCOPE (Romanowicz and others, 1991), and 

(fig. 1) (O) (O) the ORPHEUS data-management center-all provide comGlobal Seismic Network (GSN) plete digital recordings and instrument-re~ponse information for the recorded signals. In this paper, we utilize the 

AFI LH 232.77 069.14 o o 0 x long-period or very long period channels from each staANMO LH 094.91 012.66 o x o o ANTO LH 019.46 099.83 m m m m tion. 

BCAO LH 050.3 I 124.60 o o o o BJI LH 319.37 086.47 o o c o The azimuthal coverage of minor- and major-arc surCMB LH 049.68 001.55 

COL LH 339.34 031.81 face waves recorded by the combined GSN, GEOSCOPE, 

CTAO 

GUM0 

HI A 

HON 

HRV 

mv 

KMI 

KONO 

LON 

LZH 

MAJO 

MDJ 

NWAO 

PAS 

SCP 

SLR 

TAU 

TOL 

WMQ 

xooo 

0000 

0000 

cxcx 

0000 

oxox 

0000 

OX00 

cxcx 

0000 

OX00 

0000 

0000 

0000 

cocx 

xxxx 

xxoo 

ooox 

0000 

and IDA networks is excellent (fig. 1B) and superior to 

the coverage by any one network alone. Owing to variations in the dynamic range of the recording systems, not 

all stations recorded useful long-period Rayleigh- and 

Love-wave arrivals. Those stations with long-period or 

very long period channels from the three seismic networks 

that we collected, and the quality of the primary Rayleighwave (Rl, R2) and Love-wave (GI, G2) great-circle arrivals, are listed in table 1. All the GEOSCOPE recordings 

provided onscale Rl and Gl arrivals. Upgraded GSN and 

IDA stations recorded onscale minor-arc arrivals; some of 

GEOSCOPE (Institut National des Sciences de l'univers, Fmnce) the older GSN and IDA stations with lower-dynamic-range 

recorders clipped on the vertical and (or) horizontal comBNG VLP 050.30 124.60 o o - - - - ponents of the minor-arc arrivals (Rl, GI), or had low 

CAN VLP 240.45 109.68 o o o x CAY VLP 098.41 070.76 signal-to-noise ratios for various reasons, as indicated in HYB VLP 336.85 122.38 o o -- - - ---- KIP VLP -- 253.72 034.90 table 1. Despite these data dropouts, the overall data qual- PPT VLP RER VLP 210.74 00793060*39 164.01 z z ity is quite high, and many useful long-period recordings SSB VLP 034.69 084.73 o o o o can be retrieved. 

TAM VLP 048.52 102.45 o o o o 

WFM VLP 065.60 038.59 o x o x To provide a visual appraisal of the long-period signal 

International Deployment of Accelerometers (IDA) 

BDF 

B JT 

CMO 

GUA 

HAL 

KMY 

NNA 

PFO 

SJG 

SUR 

TWO 

quality, we constructed seismogram profiles of edited subsets of the higher quality observations. The profiles of 

three-component seismograms, bandpass filtered between 

125 and 500 s, are shown in figure 2. Multiple Rayleighwave (Rl, R2, R3) arrivals can be identified on the vertical-component seismograms (fig. 2A). The signal-to-noise 

ratio varies between traces, owing to both site conditions 

and the azimuthal radiation pattern of the Rayleigh waves. 

These seismograms show high signal-to-noise ratios for 

Rl and R2 arrivals, but R3 arrivals tend to be noisier. The 

low signal-to-noise ratio for R3 arrivals is due to the relareadily available from various data centers. We do not tively small seismic moment of the earthquake, which 

discuss here these additional recordings or the historical places a great value on the high-dynamic-range systems 

development and instrumentation of any of the various that record Rl arrivals onscale, because the Rl arrivals 

international seismic arrays; for comprehensive informa- are more reliable for source analysis. 

tion on instrumentation, the reader should contact the data The horizontal ground motions transverse to the greatcenters for each network directly. Our purpose here is to circle paths connecting the source and receivers are shown 

demonstrate only the general characteristics of the long- in figure 2B. The strong Love-wave (GI, G2, G3) arrivals 

period waves excited by the earthquake. have high signal-to-noise ratios except at stations near 

The GSN and IDA networks were in a transitional state radiation nodes (for example, sta. SLR, fig. IA). These 

at the time of the earthquake; various instrumentation as- traces show a few isolated glitches that produce spurious 

sociated with earlier networks was being upgraded to very pulses in the filtered records wliich must be eliminated 

broad band three-component recording, and new stations manually before any full waveform or spectral analysis. 

were being deployed (Incorporated Research Institution These glitches tend to be a larger problem on the less 
A212 MAIN-SHOCK CHARACTERISTICS 

stable horizontal components than on the vertical components. 

The horizontal longitudinal components of motion along 

great-circle paths are shown in figure 2C. The fundamental-mode Rayleigh-wave (Rl, R2, R3) arrivals have lower 

signal-to-noise ratios than on the vertical components, as 

expected, but the Rayleigh-wave overtones (Xl, X2, X3, 

X4) have higher amplitudes than on the verticals, particularly for shorter period passbands from 50 to 100 s. Note 

that several signals appear to have substantial Love-wave 

contamination on the longitudinal components (for example, 

stas. NWAO, TAU, ANMO, fig. 1). Although these signals tend to be from stations that recorded large-amplitude 

Love waves and small-amplitude Rayleigh wave;, most of 

this contamination appears to stem from path deflections 

from a great circle, rather than from errors in relative gains 

of the horizontal-component recordings. Ultraprecise analysis of surface-wave polarization and phase, however, probably requires critical examination of the instrument responses of the horizontal components, rather than simple 

utilization of the nominal instrument-response curves given 

for each trace. 

The 1989 Loma Prieta earthquake was sufficiently large 

that stable long-period signals were recorded globally, and 

so this data set has received much attention from many 

investigators in analyzing the long-period characteristics 

of the source process (see Velasco and others, this chapter). Accessing these data was more straightforward than 

ever for several reasons. First, there was the ongoing development of seismologic data centers that distribute the 

data in response to user requests, including the IRISDMC 

and the ORPHEUS data center, which distributes data collected in Europe. These centers assist in resolving instrument-response issues as well, and numerous questions 

RER 

SLR 

w NWAO 

IQ 0 BCAO 

HYB 2 2 TWO 

8 CAN 

KMY 

n TAM 

HAL 

HRV 

KIP 

COL 

ANMO 

U' - ! 1 1 

0 50 100 150 200 250 300 

TIME IN MINUTES 

Figure 2.-Seismic profiles of bandpass-filtered (125-500 s) seismograms for long-period channels from three global seismic 

networks (Global Seismic Network, GEOSCOPE, International Deployment of Accelerometers). A, Vertical-component seismograms showing minor-arc (Rl, R3) and major-arc (R2) great-circle Rayleigh waves. Data have fairly high signal-to-noise 

ratios except for some R3 arrivals. Amplitude of each trace is normalized, and so some varying noise levels reflect radiationpattern variations of Rayleigh waves. Most traces with onscale R 1 phases are from stations operating with high-dynamic-range 

systems, whereas nonlinear signals at other stations have been cut out. B, Transversely polarized horizontal-component 

seismograms for stations with clear great-circle Love-wave arrivals (GI, G2, G3). Rotation is with respect to great-circle 

paths. A few stations have minor glitches that produce spurious pulses. C, Longitudinally polarized horizontal-component 

seismograms showing great-circle Rayleigh-wave arrivals (Rl, R2, R3), as well as multiple Rayleigh-wave overtone arrivals 

(Xl, X2, X3, X4). Rl and R2 arrivals have high signal-to-noise ratios, whereas R3 arrivals are noisy. Multiple-overtone 

arrivals also are noisy over this period range. 
LONG-PERIOD SURFACE-WAVE OBSERVATIONS OF THE EARTHQUAKE1 A213 

arose about the new broadband responses of some systems soon after the earthquake. Second, a major development in the analysis of long-period data is the adoption by 

the major seismic networks of the Standard for the Exchange of Earthquake Data (SEED) format (Federation of 

Digital Seismographic Networks, 19901, which greatly facilitates computation of instrument responses and dataretrieval processes. With future efforts by the seismologic 

networks to fully conform to the SEED format for station 

information and data format, analysis of the data should 

become even easier. 

CONCLUSION 

The 1989 Loma Prieta earthquake occurred during a 

time when the global digital seismic network was extensive. The long-period data have excellent onscale Rayleighand Love-wave arrivals, with high signal-to-noise ratios, 

extensive azimuthal coverage, and reliable instrument calibration. Enough stations were available to record largeamplitude minor-arc arrivals, which are critical to a 

detailed analysis of the long~period source process. 

ACKNOWLEDGMENTS 

This research was partly supported by U.S. Geological 

Survey grant 14-08-000 1-G 1843 and U.S. National Science Foundation grant EAR-9017767, with facilities support from the W.M. Keck Foundation. We thank the many 

individuals involved in the various international efforts to 

collect global broadband digital seismic data for the earthquake, in particular, the Project IDA, GEOSCOPE, and 

GSNIIRIS personnel who assisted us in accessing these 

data and resolving instrumentation issues. 

REFERENCES CITED 

Agnew, D.J., Berger, Jon, Buland, R.P., Farrell, W.E., and Gilbert, J.F., 

1976, International deployment of accelerometers; a network for 

very long-period seismology: Eos (American Geophysical Union 

Transactions), v. 57, no. 4, p. 180-187. 

Ahern, T.K., 1989, Activities at the IRIS Data Management Center: 

Incorporated Research Institution for Seismology Newsletter, no. 8, 

p. 3-11. 

Federation of Digital Seismographic Networks, 1990, Standard for the 

Exchange of Earthquake Data; reference manual: 149 p. 

SLR 

I 

NWAO 

BCAO 

0 50 100 1 SO 200 250 300 

TIME IN MINUTES 

Figure 2.-Continued 
A214 MAIN-SHOCK CHARACTERISTICS 

Incorporated Research Institution for Seismology, 1989, IRIS Global Romanowicz, Barbara, Karczewski, J.F., Cara, Michel, Bernard, Pascal, 

Seismographic Network: Newsletter, no. 8, p. 19-24. Borsenberger, Jean, Cantin, J.-M., Dole, Bernard, Fouassier, 

Romanowicz, Barbara, Cara, Michel, Pels, J.F., and Rouland, Daniel, Danielle, Koenig, J.-C., Morand, Michel, Pillet, Robert, Pyrolley, 

1984, GEOSCOPE; a French initiative in long-period three-compo- Annick, and Rouland, Daniel, 1991, The GEOSCOPE program; 

nent global seismic networks: Eos (American Geophysical Union present status and perspectives: Seismological Society of America 

Transactions), v. 65, no. 42, p. 753-754. Bulletin, v. 81, no. 1, p. 243-264. 

1 I 1 I / 

1 SLR 

/ 

I 

ANMO 

LON 

Figure 2.-Continued 

150 200 

TIME IN MINUTES 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAmOCCURRENCE 

MAIN-SHOCK CHARACTERISTICS 

SOURCE PARAMETERS OF' THE EARTHQUAKE, 

DETERMINED BY USING LONG-PERIOD SEISMIC WAVE@ 

By Aaron A. ve1asco2, Thorne Lay, and Jiajun Zhang, 

University of California, Santa Cruz 

CONTENTS 

Page 

A215 

2 15 

217 

218 

220 

223 

223 

227 

228 

230 

232 

232 

232 

ABSTRACT 

We have performed simultaneous seismic-moment tensor inversions of long-period (157-288 s) fundamentalmode Rayleigh and Love waves from the 1989 Loma Prieta 

earthquake to determine the long-period source process of 

the earthquake. Utilizing a two-step spectral-inversion technique, we explore the model dependence and centroidlocation sensitivity of the surface-wave analysis to assess 

the confidence bounds of the inversion results, We find 

that estimates of the source duration and depth depend 

heavily on the choice of propagation, attenuation, and 

source-velocity-structure models. Including centroid-location parameters in the inversion stabilizes the momenttensor estimates but yields a biased location away from 

the epicenter, owing to model inaccuracies. Our sourceduration estimate is 1 lk5 s, using a recent velocity model, 

with the centroid time of 6 s significantly less than in 

earlier surface-wave studies (10-22 s) and thus more comContribution No. 156, Charles F. Richter Seismological Laboratory 

and Institute of Tectonics, University of California, Santa Cruz, CA 

95064. 

Current affiliation: Science Applications International Corp., San 

Diego, CA 92121. 

patible with estimates of both body-wave and strong-motion durations. An unconstrained moment-tensor inversion 

at the optimum centroid location yields a stable majordouble-couple solution (strike, 124Ok6O; dip, 67Oh6O; rake, 

l26Ok7O) and a seismic-moment estimate ((3 .0k0.2)~ 1 0l9 

N-m; Mw=6.9) similar to those of earlier long-period studies and to body-wave and geodetic results. The surfacewave centroid-depth estimate is 22kll km, which overlaps 

the body-wave estimates (13h5 km). Thus, surface-wave 

source parameters for the earthquake, allowing for plausible model dependence, are fully compatible with bodywave determinations, and there is no evidence for any 

anomalous coseismic long-period source process. 

The 1989 Loma Prieta earthquake may be the best instrumentally recorded earthquake to date, with high-quality ground-motion data ranging from short-period strong 

ground motions (10-Hz signals) to static offsets (ground 

deformation). his unusually complete data set allows a 

detailed analysis of the earthquake rupture process by using the various signals, each of which has a different sensitivity to the source process. These data, in turn, provide 

an excellent opportunity to explore the compatibility and 

resolution of the different data sets and the associated 

seismic-inversion techniques. Ideally, earthquake source 

models should be independent of data type, frequency, or 

inversion technique; thus, strong-ground-motion results 

should be consistent with geodetic models. For many large 

earthquakes, however, results obtained by using short-period waves differ from those obtained by using long-period waves or geodetic measurements, and similar 

discrepancies have been reported for the 1989 Loma Prieta 

earthquake (Wallace and others, 199 1). 

The focal mechanisms from first motions and teleseismic 

body- and surface-wave studies, as summarized in figure 

1, are virtually identical, suggesting negligible frequency 

dependence or faulting complexity. Furthermore, estimates 

of seismic moment, centroid depth, and rupture duration 
A216 MAIN-SHOCK CHARACTElRISTICS 

obtained from local, regional, and teleseismic body-wave 

studies are generally consistent with each other (Wallace 

and others, 199 1). Long-period-surface-wave results, however, generally give larger seismic moments, deeper centroid depths, and longer rupture durations than do 

body-wave studies. These systematic discrepancies suggest a complex source phenomenon, such as deep, slow 

rupture propagating into the mantle (Wallace and others, 

1991). Before accepting the possibility of such a complex 

source process, the reliability of the long-period results 

must be tested, and this study will demonstrate that no 

anomalous long-period source process occurred during the 

earthquake. 

The various investigations of long-period seismic waves 

for the earthquake have yielded consistent focal mechanisms and seismic-moment estimates, as listed in table 1. 

Owing to the limited resolution of long-period waves, however, several studies have necessarily constrained some 

parameters of the inversions or used only limited surfaceFigure 1.-Loma Prieta region, Calif., showing epicentral location (dot) 

from National Earthquake Information Center, locations of major faults 

(irregular thin lines), and approximate location of rupture area (for example, Wald and others, 1991) of 1989 earthquake. Major double-couple 

focal mechanisms from P-wave first motions (Oppenheimer, 1990), average teleseismic body-wave solutions (Barker and Salzberg, 1990; Choy 

and Boatwright, 1990; Kanamori and Satake, 1990; Langston and others, 1990; NfibGlek, 1990; Romanowicz and Lyon-Caen, 1990; Ruff and 

Tichelaar, 1990; Wallace and Lay, 1990; Wallace and others, 1991), 

average surface-wave solutions (Dziewonski and others, 1990; Kanamori 

and Satake, 1990; Romanowicz and Lyon-Caen, 1990; Zhang and Lay, 

1990b; Wallace and others, 1991), and centroid-moment-tensor (CMT) 

solution show nearly identical strike, dip, and rake. "P" on focal mechanisms denotes compressional axis. CMT solution has a centroid location 

east of epicenter (asterisk). 

wave data sets. Romanowicz and Lyon-Caen (1990) and 

Zhang and Lay (1990b) used only Rayleigh-wave (Rl, R2) 

arrivals from 15 and 25 stations, respectively, in spectral 

inversions for the source parameters (duration, depth, moment tensor). The only significant difference in the results 

of these two studies is the source-duration estimate, modeled in terms of a boxcar or trapezoidal time function 

(table I), for which Romanowicz and Lyon-Caen calculated a total duration of 36 to 44 s, whereas Zhang and 

Lay (1990b) estimated a duration of 20 to 22 s. The difference is mainly due to the choice of phase-velocity model 

used to correct for propagation-phase delay; Romanowicz 

and Lyon-Caen (1990) preferred the PREM model (Dziewonski and Anderson, 198 I), whereas Zhang and Lay 

(1990b) preferred the aspheric M84C model (Woodhouse 

and Dziewonski, 1984). This difference indicates the model 

dependence of the long-period-source-parameter determinations and raises questions about the true uncertainties 

of the estimates. 

Kanamori and Satake (1990) applied both centroid-moment-tensor (CMT) and spectral-inversion methods to a 

small set of Rayleigh-wave (Rl) and Love-wave (GI) arrivals from 10 stations. They constrained the source depth 

and rupture duration in their inversions, as well as the 

fault dip in the spectral inversion, which used only data at 

a period of 256 s. Their results (table 1) are similar to 

those from other long-period investigations, although they 

calculated the largest (most strike slip) rake (137'-144') 

and among the smallest seismic-moment estimates ((2.5- 

2.8)xl0l9 N-m) of the published values. Dziewonski and 

others (1990) performed a CMT inversion of long-period 

body waves and surface waves with a more extensive data 

set, including the effects of the aspheric M84C model, 

and calculated a lower rake (128') than Kanamori and 

Satake but a comparable moment (2.7x10lg N-m) (table 1). 

Wallace and others (1991) inverted a very large data 

set of fundamental-mode Rayleigh-wave (Rl, R2) and 

Love-wave (GI, G2) arrivals for the moment tensor, using 

a spectral technique for periods from 150 to 300 s. Their 

surface-wave data were from 31 globally distributed stations in the Global Seismic Network (GSN, long period 

three component) and networks of the International Deployment of Accelerometers (IDA, very long period vertical component) and GEOSCOPE (Institut de Physique du 

Globe de Paris, France, very long period three component). In the moment-tensor inversion, h.owever, Wallace 

and others did not use the Love-wave estimate of the Myz 

term of the moment tensor, owing to instability of the 

inversion relative to the Rayleigh-wave Myz determination. They also did not use Love waves in solving for 

centroid depth, because the excitation functions calculated 

for various source structures varied little with depth and 

the uncertainties in the source-velocity structure cause 

problems in simultaneous modeling of Rayleigh- and Lovewave excitation. 
SOURCE PARAMETERS OF THE EARTHQUAKE, DETERMINED BY USING LONG-PERIOD SEISMIC WAVES A217 

Table 1 .-Major double-couple source parameters for the earthquake from suflace waves and free oscillations 

[References: D, Dziewonski and others (1990); J, Jordan (1991); K, Kanamori and Satake (1990); R, Romanowicz and Lyon-Caen (1990); T, this 

study; W, Wallace and others (1991); Z, Zhang and Lay (1990b). Comments: CMT, centroid moment tensor; FO, free oscillations; G, Love 

waves; R, Rayleigh waves] 

Strike Dip Rake Depth Mo 

(O) (O) (O) (h) (1 019 N-m) 

Reference Commcnt 6) 

R, G 

R, G 

CMT 

CMT 

R, G 

R 

R 

FO 

Iconstrained in inversion. 

Jordan (1991) analyzed free oscillations with periods 

from 67 to 400 s from nine vertical-component IDA 

accelerograms to determine a centroid time of 12.6k2.8 s, 

and a characteristic duration T~ of 2&11 s. For a boxcar 

source-time function, this T~ value corresponds to a source 

duration of about 35 s, whereas the centroid time would 

suggest 25 s. Jordan did not report results for the source 

depth or focal mechanism but estimated a seismic moment of (3.2k0.4)~10~~ N-m. In his analysis, Jordan found 

no evidence for any statistically significant precursory 

long-period radiation from the source. 

The small differences in the results of long-period analyses of the earthquake are largely attributable to different 

model assumptions. Wallace and others (1991) explicitly 

explored the model dependence of surface-wave spectral 

inversions to assess the resolution of the source parameters and to determine whether they could resolve any 

anomalous long-period source process. They found that 

the choice of propagation model, global-attenuation model, 

and source-velocity structure directly affects the determinations of depth, moment, and duration. By comparing 

their body- and surface-wave results, Wallace and others 

suggested that deep, slow slip may have occurred during 

the earthquake. The long-period-surface-wave inversions, 

however, were shown to have sufficient model dependence that this hypothesis could not be confirmed, and 

Wallace and others speculated that improved model corrections may eliminate any evidence for anomalous radiation. 

In this paper, we further explore the model dependence 

of the long-period inversions by using various attenuation, phase-velocity, and source-velocity models. The introduction of new surface-wave-propagation models that 

have better resolution of Earth structure is a continuing 

process, and we apply one of the latest models that was 

not considered by Wallace and others (1991). We also 

investigate the sensitivity of long-period spectral inversions to the source-centroid location, which has not been 

done previously for very long period analyses. This investigation is motivated by the work of Zhang and Lay 

(1990a), who demonstrated the effects of incorrect source 

location on such inversions, and by the parametrization of 

the CMT inversion, which allows for a pseudosource 10- 

cation in the form of an optimal centroid location. Finally, we compare the result of our long-period source 

models to those of previous investigations, to assess the 

existence of any anomalous long-period radiation from 

the earthquake. 

DATA 

The long-period data for the 1989 Lorna Prieta earthquake are of high quality, allowing a complete investigation of long-period source-parameter determinations. Some 

of these data, with well-defined Rayleigh-wave (Rl, R 

2' R3) arrivals observed at stations in three global seismic 

networks (GSN, IDA, GEOSCOPE), are plotted in figure 

2, The Rl and R2 arrivals haye a high signal-to-noise ratio. With the ongoing global deployment of very broad 

band stations during the late l98O9s, numerous onscale Rl 

arrivals were recorded that were unavailable for many 

previous events in such quantity. These onscale Rl arrivals are desirable because the effect of inaccuracies in propagation models increases with the distance traveled by the 

waves. The 1989 Loma Prieta earthquake was a bit too 

small to generate high-quality recordings of long-period 

waves traveling more than one orbit on the surface; thus, 

the signal-to-noise ratio decreases significantly for R3 arrivals. Zhang and Lay (1990b) found that existing propagation models have too much uncertainty to reliably 

estimate the short source duration of the earthquake from 
A218 MAIN-SHOCK CHARACTERISTICS 

R3 arrivals, and so R3 and G3 arrivals are not used in our 

analysis. 

Our data set, which is moderately increased over that 

used by Wallace and others (1991), comprises a total of 

38 stations with 88 separate arrivals; the phases used are 

listed in table 2. Given the high signal-to-noise ratio and 

the good azimuthal coverage, these signals compose an 

excellent long-period data set for constraining the source 

parameters. 

METHOD 

We analyze long-period (157-288 s) Rayleigh and Love 

waves, utilizing the moment-tensor spectral-inversion 

method of Kanamori and Given (1981), modified to a 

two-step procedure that separates source-finiteness effects 

from determination of the centroid depth and moment tensor (Romanowicz and Guillemant, 1984). The simultaneous Rayleigh- and Love-wave inversion procedure was 

further described by Zhang and Kanamori (1988a). The 

complex source spectrum of surface waves excited by a 

point source is a linear function of the frequency-independent moment tensor (Mn, Myy, Mzz, Mq, Myz, Mxz). Our 

linear-inversion method uses the complex spectra of multiple surface-wave arrivals at several discrete periods. We 

use a group-velocity window for each fundamental-mode 

Rayleigh-wave (Rl, R2) and Love-wave (GI, G2) arrival, 

and calculate the amplitude and phase spectra, from which 

we choose seven different periods (157, 175, 200, 225, 

256, 275, 288 s) for our analysis. The observed surfacewave spectra must be corrected for instrument response, 

propagation effects, and source-finiteness effects, and these 

corrections affect the estimates of duration, depth, and 

moment tensor. 

STATION 

RER 

SLR 

R3 

NWAO 

BCAO 

HYB 

Two 

CAN 

KMY 

TAM 

WMQ 

BDF 

TOL 

HIA fg 

RPN 

PPT 

v HAL 

HRV 

KIP 

COL 

4- ANMO 

0 50 100 150 200 250 300 

TIME, IN MINUTES 

Figure 2.-Filtered (125-500 s) vertical-component velocity seismograms for long-period channels at stations in three seismic networks (GSN, IDA, 

GEOSCOPE). Amplitudes for all traces are scaled equally. Multiple great-circle Rayleigh waves (Rl, R2) show high signal-to-noise ratios. Many 

broadband instruments recorded onscale Rl phases from earthquake; however, owing to moderate magnitude of main shock, R3 arrivals are noisy and 

so were not used in our analysis. 
SOURCE PARAMETERS OF THE EARTHQUAKE, DETERMINED BY USING LONG-PERIOD SEISMIC WAVES A219 

Table 2.-Stations and phases used in this study 

[Networks: GEO, GEOSCOPE (Institut de Physique du Globe de Paris, France); 

GSN, Global Seismic Network (U.S. Geological Surveyflncorporated Research 

Institution for Seismology); IDA, International Deployment of Accelerometers (IDA/ 

Incorporated Research Institution for Seismology)] 

Phase 

AFI 

BCAO 

BJI 

COL 

CTAO 

GUM0 

HIA 

HRV 

KEV 

KMI 

KONO 

LZH 

MAJO 

M D J 

NWAO 

SCP 

TAU 

TOL 

2EQ 

CAN 

CAY 

HYB 

KIP 

PPT 

RER 

SSB 

TAM 

WFM 

BDF 

CMO 

HAL 

KMY 

NNA 

RPN 

S JG 

TWO 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GSN 

GEO 

GEO 

GEO 

GEO 

GEO 

GEO 

GEO 

GEO 

GEO 

GEO 

IDA 

IDA 

IDA 

IDA 

IDA 

IDA 

IDA 

IDA 

Before the source-duration determination, we must correct the phase for propagation delay, assuming a phasevelocity model. We assume great-circle paths in calculating 

the phase-propagation corrections and neglect focusing and 

defocusing because these factors have been shown to have 

only second-order effects on waves for our period range 

for existing smooth-Earth models (Schwartz and Lay, 

1988). 

In the first-step inversion, we calculate the source-finiteness correction (eq. 9 of Zhang and Kanamori, 1988b) 

for a range of trapezoidal source durations. The source is 

assumed to be a point source because none of the previous analyses has resolved any source directivity affecting 

the long-period signals. A trapezoidal source model is 

used for convenience because the long-wavelength signals studied cannot resolve any fine structure in the short 

source-time function. Because the rise time appears to be 

approximately 10 percent of the observed rupture time for 

many earthquakes (Kanamori and Anderson, 1975), we 

assume a trapezoidal rise time equal to 10 percent of the 

source duration. We measure the misfit between the observed and theoretical source phase by using a weighted 

rms error, o (Zhang and Lay, 1989); the duration that 

yields a minimum o value is our estimate. The weighted 

rms error is a function of the source-process time and the 

propagation corrections, making the duration dependent 

on the propagation model used for correcting the phase 

back to the source. 

In the second-step inversion, we determine the pointsource depth and moment tensor, where the moment-tensor solution depends on the surface-wave-excitation 

functions used in the inversion. To proceed, we must account for attenuation of the surface-wave arrivals when 

correcting the observed spectral amplitudes back to the 

source. Thus, we must assume a global attenuation, or Q, 

model. The excitation functions, as given by Kanamori 

and Stewart (19761, depend on the elastic properties of 

the source region and the source depth, making the moment-tensor solution dependent on the assumed source 

structure. The global Q and source-velocity structure thus 

affect the moment-tensor and depth estimates. For a range 

of trial depths, using the optimal source-finiteness corrections obtained from the first step, we measure the misfit 

between the observed and synthetic spectra by using a 

weighted rms error, p, for this second step (Zhang and 

Lay, 1989). The depth at which we obtain a minimum p 

value gives the best depth and moment-tensor estimates. 

The decision to use the spectral method is largely based 

on the ease with which various models can be used in 

correcting for propagation effects, in contrast to normalmode-based spectral or time-domain procedures, such as 

the CMT inversion. However, we lose the advantage of 

including information from overtones or long-period body 

waves, which become a source of noise in this fundamental-mode analysis. Another advantage of the spectral-inversion technique is that it allows a separation of 

source-time-function determination from depth and moment-tensor estimation, making it an ideal method for 

studying the effects of various models on the inversions, 

In performing a simultaneous inversion of Rayleigh and 

Love waves, we can either jointly estimate the momenttensor terms from both data types, typically with some 

variance-based weighting functions, or separately estimate 

the combined moment-tensor terms for each data type and 

then merge the estimates. One advantage of determining 

the Rayleigh- and Love-wave moment-tensor elements 

separately is that inconsistencies can be easily identified. 

For example, an inconsistency between the M estimates J? for Rayleigh and Love waves for the Loma Prieta earthquake prompted Wallace and others (1991) to not use the 

Myz estimate from Love waves (this procedure was more 

stable than any simple averaging strategy implicit in the 

joint-estimation approach). Wallace and others attributed 

the instability of the Love-wave M estimate to the shalJ'z. low depth of the earthquake, in combination with the noise 
A220 MAIN-SHOCK CHARACTERISTICS 

in the data, which generally is somewhat greater for Love 

waves than for Rayleigh waves. In general, the uncertainties in the Myz and M moment-tensor terms for both 

Rayleigh and Love waves are greatest for fundamentalmode surface waves from shallow events, making it necessary to identify such inconsistencies to assess the 

reliability of the solutions. Furthermore, the characteristic 

signal quality between Rayleigh and Love waves differs 

from event to event. Thus, we prefer to estimate momenttensor terms separately for each data type and then combine the estimates. 

The assumed source location also affects the mornenttensor inversion of long-period surface waves, as demonstrated by Zhang and Lay (1990a); this effect may be an 

alternative explanation for the My inconsistency reported 

by Wallace and others (1991). Wallace and others assumed the source location given by the National Earthquake Information Center (NEIC) determination, forcing 

any residual phase anomalies into the moment-tensor inversion. Inaccuracies in the propagation models, particularly when anomalous relative results between Rayleigh 

and Love waves exist, may be reduced by determining an 

optimal centroid location, following the strategy of the 

CMT inversion. Zhang and Lay (1990a) found that an 

optimal centroid location determined by using Rayleigh 

waves alone may not give a good source model because 

of direct tradeoffs between location and source mechanism. Because Rayleigh and Love waves have different 

radiation patterns, a search for centroid location is more 

stable when simultaneously inverting both Rayleigh and 

Love waves, and most effective when including bodywave trains and overtones, as in the CMT inversion. We 

explore whether centroid-location optimization affects the 

source depth, duration, and moment-tensor solutions for 

the earthquake in the following analysis. 

SOURCE-DURATION ESTIMATION 

For the 1989 Loma Prieta earthquake, Wallace and others (1991) used a spectral-inversion method similar to ours 

and explored the model dependence of the duration estimate associated with phase velocities for two models, 

PREM (Dziewonski and Anderson, 1981) and M84C 

(Woodhouse and Dziewonski, 1984). We include a new 

model, MPA (Wong, 1989), which was derived by using 

far more data than were used in the development of the 

M84C model. The spatial patterns of phase velocities for 

Rayleigh and Love waves for the M84C and MPA models 

for periods near 220 s are compared in figure 3. The MPA 

model gives a somewhat more detailed picture of the Earth 

than does the M84C model, reflecting the truncation of 

the spherical-harmonic expansions of the heterogeneity at 

degrees 12 and 8, respectively. The MPA model appears 

to better match the expectations of global tectonics, with 

better definition of slow regions near active oceanic ridges, 

as well as in the tectonically active source region of the 

Western United States, and with fast regions beneath continents more closely related to shields. Although these 

models are still of limited resolution, the MPA model 

represents progress since 1984 toward developing more 

accurate models for very long period surface waves, and 

we now assess whether that progress affects our source 

models for the earthquake. 

For a point source with the NEIC epicentral location 

and origin time, duration estimates for the PREM, M84C, 

and MPA propagation models demonstrate a substantial 

model dependence (fig. 4). To estimate duration, we plot 

the normalized, spectral-amplitude-weighted rms error, CT 

(Zhang and Lay, 1989), as a function of assumed trapezoidal source duration for Rayleigh and Love waves of a 

given period (157, 175, 200, 225, 256, 275, 288 s). The 

minimum of each curve is the best duration estimate from 

the corresponding period. The trapezoidal duration estimate (7) is parametrized to be period independent. Thus, 

some of the scatter between periods could reflect more 

complex phenomena, such as slow slip, for which longer 

periods should give longer durations. Although a frequency-dependent trend is weakly indicated for the MPA 

model (~,~~=l2 s; ~~~~=7 s; ~9 s; -9 s; ~~~~=17 s; 

~~~~=19 s; T288=.18 s), the scatter suggests uncertainties in 

the phase-velocity model rather than a source phenomenon. The period range is rather small for confidently 

establishing any complex source model, but the greater 

range considered by Jordan (1 99 1) in a free-oscillation 

analysis also reveals no strong frequency dependence of 

the centroid time in the phase spectra. 

For each propagation model, we estimate the source 

duration (7) at the minimum G value calculated for the 

seven different periods. The PREM model has the highest 

G value and gives ~=30 s (fig. 4). The M84C model significantly reduces the overall variances for all periods and 

gives a shorter average duration (T=20 s). This uniform 

improvement of the fit strongly indicates the need for 

aspheric-propagation corrections for the earthquake, as 

noted by Romanowicz and Lyon-Caen (1990) and Zhang 

and Lay (1990b). The MPA model further reduces the T 

estimate to approximately 11 s, but the overall variance 

reduction is comparable to that for the M84C model. With 

both models, the G value is similar to that obtained using 

Rayleigh waves alone (Zhang and Lay, 1990b; Wallace 

and others, 1991), indicating that the Rayleigh and Love 

waves are generally compatible in terms of a systematic 

source-phase shift and that both wave types have comparable residual phase scatter after propagation correction. 

This result is not general, at least with the current generation of aspheric models. In detail, we find that the shorter 

durations found for the MPA model relative to the M84C 

model reflect small shifts of the average phase velocities 
SOURCE PARAMETERS OF THE EARTHQUAKE, DETERMINED BY USING LONG-PERIOD SEISMIC WAVES A22 1 

at each period in the models, rather than systematic im- and is most likely due to the inadequacies of the models. 

provement in path-specific corrections. The scatter be- Although both the M84C and MPA models reduce the 

tween duration estimates at different periods is not reduced normalized error relative to the PREM model and thus 

LONGITUDE, IN DEGREES 

Figure 3.-Aspheric phase-velocity models used for phase-propagation corrections. A, M84C Rayleigh-wave model (degree 8) at 225 s (Woodhouse 

and Dziewonski, 1984). B, MPA Rayleigh-wave model (degree 12) at 220 s (Wong, 1989). C, M84C Love-wave model at 225 s. D, MPA Love-wave 

model at 220 s. Path anomalies calculated by integrating along great circle from source to receivers. 

DURATION, IN SECONDS 

PERIOD, 

IN SECONDS 

Figure 4.-Normalized error versus assumed trapezoidal source duration obtained in the first-step inversion, using PREM (A), M84C (B), and MPA 

(C) Earth models to make propagation corrections in combined inversion of Rayleigh and Love waves. Minimum of each curve is duration estimate 

from inversion of waves of that particular period. Estimates at each period are combined to determine optimal mean duration over period range. Mean 

duration estimates are 30, 20, and 11 s for PREM, M84C, and MPA models, respectively. 
A222 MAIN-SHOCK CHARACTERISTICS 

appear to give better estimates of the source duration, 

choosing between the two is difficult. The MPA model 

gives a source duration that is virtually identical to durations estimated from shorter period studies, and additional 

evidence favoring this solution is described below. 

To test the propagation models further, we explored the 

effects of assuming different source locations in the firststep inversion. If systematic errors in the models can be 

mapped into a source relocation, this procedure can reduce those errors and potentially may reduce any bias in 

the duration estimate. This process can be visualized as 

locating the effective source position with a "best" pointsource trapezoidal source-time function. Surface waves 

alone are not generally used for source-location deterrninations, owing to the limited resolution of the long-wavelength signals, which lack sensitivity to small location 

perturbations. Because our data set is of unusually high 

quality, we proceed to search for the source location that 

minimizes the first-step error, using a 112- by 112-km 

grid centered at the NEIC location. The gridpoints have 

8-km spacing, and the spectra were corrected to each location by assuming that the NEIC origin time is unperturbed. We then invert for duration, using the first-step 

inversion at each gridpoint. By contouring the normalized 

rms error, a, given by the average residual error for a 

given source duration for the seven different periods, we 

identify the optimal source location consistent with the 

corresponding propagation model and a trapezoidal representation of the source-time function. 

The contours of a over the grid obtained by using the 

PREM, M84C, and MPA models are shown in figures 5A, 

5B and 5C, respectively. The contoured surfaces have welldefined minimums with a value ai, which are reasonably concentrated spatially. For the PREM model (fig. 

SA), omi=0.483, larger than for the other models, and the 

minimum is located approximately 35 km northeast of the 

epicenter. This result should not be confused with a centroid location because we are not finding a best moment 

tensor in this search. Instead, we are determining how 

compatible the propagation models are with the observed 

traveltimes from the actual source location to the set of 

stations. The overall error reduction is only 15 percent 

over the grid for the PREM model. For the M84C model 

(fig. 5B), omin-0.325, the smallest value of the three 

models, and the apparent source location is just north of 

the epicenter. The area with a values within 4 percent of 

ai encompasses the epicentral region. The variance reduction for the M84C model as a function of position 

over the grid is 30 percent, twice as large as for the PREM 

model. The results for the MPA model (fig. 5C) give 

amin=0.340, and the spatial-variance reduction in the grid 

is also 30 percent. The MPA model, however, locates the 

optimal source position directly on the actual epicenter, a 

remarkable demonstration of the consistency of the propagation corrections with the independently known source 

location. This result leads us to place additional confidence in the duration estimate using the MPA model, 

complementing the consistency with the body-wave analyses. For all three models, the actual duration estimate varies by only a few seconds over the grid (from 10 to 13 s 
SOURCE PARAMETERS OF THE EARTHQUAKE, DETERMINED BY USING LONG-PERIOD SEISMIC WAVES A223 

for the MPA model), and the variations are less than 1 s 

within the region of the lowest contour that includes the 

minimum. This result is important for the second-step inversion, in which we specify the source duration and then 

invert for the depth and moment tensor. It is thus reasonable to use a single value for the duration associated with 

a given propagation model when searching over the same 

grid for an optimal centroid location that yields the best 

moment-tensor fit to the data. 

MOMENT TENSOR, CENTROID 

LOCATION, AND DEPTH ESTIMATION 

The second-step inversion depends on the choice of Q 

model and source-velocity structure. Zhang and Lay 

(1990b) and Wallace and others (1991) explored the effect of a global Q model on source-depth determination, 

using the three models shown in figure 6, which are those 

of Masters and Gilbert (1983), Dziewonski and Steim 

(1982), Dziewonski and Anderson (1981) (subsequently 

referred to as the MG, DS, and PREM models, respectively). Depth determinations varied by 10 km for the 

1989 Loma Prieta earthquake, depending on which model 

was assumed. We use the same global Q models in the 

present analysis because they represent a reasonable range 

of one-dimensional models. Although a new generation 

of aspheric Q models is presently emerging, correct utilization of these models requires simultaneously accounting for complex focusing and defocusing effects, owing 

to the velocity inhomogeneity. Such analysis is being undertaken but is not discussed further here. 

The source-velocity structure used for calculating the 

excitation functions may be the least constrained set of 

model parameters required for the second-step inversion, 

given the complex tectonic history of the source region. 

Wallace and others (1991) used the four source-velocity 

models shown in figure 7, including the average- and 

young-ocean models of Regan and Anderson (1984), the 

average PREM model structure, and a case-specific model 

called LOMA, composed of the crustal P-wave-velocity 

model of Walter and Mooney (1982), the mantle P-waveFigure 5.-Loma Prieta region, Calif., showing contours of residual rms 

error in first-step inversion using PREM (A), M84C (B), and MPA (C) 

propagation models for different assumed source locations. 112- by 112- 

km grid of assumed epicentral locations, consisting of 225 points (triangles), was constructed around epicenter. Spectra were corrected back 

to each source location, with origin time held fixed at National Earthquake Information Center origin time. Minimum error gives optimal 

epicentral location for a point source. For PREM model, minimum error 

is located northeast of actual epicenter; for M84C model, minimum 

error is located slightly north of epicenter; and for MPA model, minimum error is located directly on epicenter. Duration estimates vary by 

only a few seconds over grid for each model. 

velocity model for the Western United States (GCA) of 

Walck (1985), and the mantle 5-wave-velocity model for 

tectonic North America (TNA) of Grand and Helmberger 

(1985) (subsequently referred to as the RA, RA-yo, PREM, 

and LOMA models, respectively). Although these models 

span a reasonable range of upper-mantle structures expected for the tectonically active source region, a localized lithospheric model specific to the area is unavailable. 

Thus, an intrinsic uncertainty exists in all the source inversions. Because we have no new information regarding 

the appropriate structure, we utilize the same four models. 

Wallace and others found that the centroid depth varied 

by about 10 km, depending on the choice of source-excitation structure, but that other parameters are only weakly 

affected. 

MOMENT TENSOR AND CENTROID LOCATION 

The source location affects the moment tensor through 

both its effects on the phase and minor amplitude effects 

due to propagation and attenuation, as demonstrated by 

Zhang and Lay (1990a). We proceed to use both Rayleighand Love-wave spectra to find the centroid location, depth, 

and moment tensor by searching over the same 112- by 

112-km grid as used in the duration determination. Setting the source duration at the optimum for each propagation model, we performed numerous inversions to 

determine the moment tensor and depth at each gridpoint 

for the suite of global Q models (MG, DS, PREM), sourcevelocity models (RA, RA-yo, PREM, LOMA), and propagation models (PREM, M84C, MPA). The p values for 

each gridpoint were then contoured over the grid; the minimum p value gave an optimal centroid location because p 

is a measure of how well the data are fitted by the associated moment tensor for that source position. We found 

0 200 250 300 

PERIOD, IN SECONDS 

Figure 6.-Rayleigh-wave global Q models MG (short-dashed curve; 

Masters and Gilbert, 1983), PREM (long-dashed curve; Dziewonski and 

Anderson, 1981), and DS (solid curve, Dziewonski and Steim, 1982). 

Frequency-dependent variations trade off with excitation functions for a 

given source-velocity model, resulting in uncertainty in source depth. 
A224 MAIN-SHOCK CHARACTERISTICS 

that for each gridpoint the depth-resolution curves are relatively flat; however, the p values vary substantially over 

the grid, providing a fair estimate of the centroid location. 

We first explore the effect of the propagation models 

on the second-step inversion by specifying the excitation 

DENSITY, I N G R A M S PER 

CUBIC CENTIMETER 

LOMA 

- - RA-YO 

RA ------- PREM 

P-WAVE VELOCITY, IN 

KILOMETERS PER SECOND 

structure to be the RA-yo model and the global Q model 

to be the MG model, and then inverting for depth and 

moment tensor at every gridpoint for the PREM, M84C, 

and MPA models. The resulting contours of p are shown 

in figure 8, where the duration is fixed at 30 s for the 

5-WAVE VELOCITY, IN 

KILOMETERS PER SECOND 

LOMA 

- - RA-YO 

RA ------- PREM 

DENSITY, 5-WAVE VELOCITY, 

AND P-WAVE VELOCITY 

Figure 7.-Source-region velocity structures used in computation of excitation functions for surface-wave analysis. A, Density. 

B, P-wave velocity. C, 5-wave velocity, D, Combined density, P-wave velocity, and 5-wave velocity. LOMA model has Pwave-velocity crustal structure of Walter and Mooney (1982), with mantle-velocity structures from Walck (1985) and Grand 

and Helmberger (1985). RA and RA-yo models of Regan and Anderson (1984) are for average and young oceans, respectively. PREM model is from Dziewonski and Anderson (1981). Although significant uncertainty exists in correct structure to 

use for depths of 100 to 200 km, this suite of models spans plausible range of upper-mantle models for tectonically active 

source region of earthquake. 
SOURCE PARAMETERS OF THE EARTHQUAKE, DETERMINED BY USING LONG-PERIOD SEISMIC WAVES A225 

PREM model, 20 s for the M84C model, and 11 s for the 

MPA model. In the moment-tensor inversion, the spectra 

at each period are inversely weighted by the corresponding residual rrns errors for the first-step inversion to accommodate the scatter in phase indicated in figure 4. 

Because significant differences in pi exist between the 

phase-velocity models, the contour plots have been separately normalized to their pmin value, with the scale showing a range in p values from 1.0 to 1.5. For the PREM 

model (fig. 8A), the error reduction over the grid is only 

about 30 percent, and the minimum encompasses a broad 

region centered just north of the epicenter. The smallest p 

value (pmin=O.lOO) is about 30 percent higher than that 

for the M84C (pmin-0.0773, fig. 85) and the MPA 

(pmin=0.0724, fig. 8C) models. For the M84C model (fig. 

SB), the variation in p over the grid is approximately 50 

percent, and the contours show a steep-sided well with a 

flat bottom encompassing the epicenter. The results for 

the MPA model (fig. 8C) are comparable to those for the 

M84C model, although pmin is slightly lower for the MPA 

model. 

For the different propagation models, the location of 

pi varies little. For the PREM, M84C, and MPA models, the centroid location is shifted just offshore about 24 

km west of the epicenter. However, using the PREM propagation and excitation models shifts pi 24 km northeast 

of the epicenter (fig. 8A). These shifts are comparable to 

those found for the CMT solution (fig. I), which is heavily 

influenced by long-period body-wave trains in the records 

rather than fundamental-mode arrivals. Thus, the choice 

of propagation model affects not only the residual variance in the second-step inversion but also the centroid 

location. 

The next model sensitivity that we test is the influence 

of the excitation structure, using the RA-yo, PREM, and 

LOMA models, where we specify the propagation model 

(MPA) and the global Q model (MG). The resulting contours of p as a function of point-source location in the 

source grid are shown in figure 9. The contours are scaled 

over a 40-percent variation in p to accentuate any possible differences. The LOMA model has a broad minimum (fig. 9A), with pmin=0.0985, whereas the PREM 

model (fig. 95) has a lower pmin=0.0872. The result for 

the RA-yo model shown in figure 9C involves the same 

combination of models as in figure 8C but is plotted on a 

slightly different scale for comparison. This model has 

pmin=0.0724, the smallest value for the three excitation 

structures considered. Although a baseline shift occurs in 

the pi estimates, depending on the excitation structure 

used, the pmin value on each surface does not vary and is 

located 24 km west of the epicenter. This result is obtained for various propagation models in combination with 

the different excitation structures. Thus, the centroid location is not affected significantly by the choice of sourcevelocity structure. 

Our final sensitivity test is with respect to the global Q 

model used in the inversion. We specify the propagation 

model (MPA) and the excitation model (RA-yo), and then 

invert for the centroid depth and moment tensor, using the 

three global Q models (PREM, DS, MG). The centroid 

location results for the PREM, DS, and MG Q models are 

shown in figures 10A, 105, and 10C, respectively. The 

choice of global Q model does not affect our centroid 

location or the shape of the minimum, and the pi values 

are all virtually identical. Thus, the choice of global Q 

model strongly influences the centroid-depth and momentFigure 8.-Loma Prieta region, Calif., showing contours of residual rms error in second-step inversion for full moment tensor as a function of pointsource location (triangles) for PREM (A), M84C (B), and MPA (C) propagation models. Second-step inversion is affected by choice of propagation 

models for a given excitation model (in this case, RA-yo young-ocean model of Regan and Anderson, 1984) and of global Q model (in this case, MG 

model of Masters and Gilbert, 1983). For PREM, M84C, and MPA models, centroid location (square) is shifted just offshore about 24 km west of 

epicenter (triangle). Minimum second-step error (pmin), which gives optimal centroid location for a particular combination of models, is 0.100, 

0.0773, and 0.0724 for PREM, M84C, and MPA models, respectively. Using PREM propagation and excitation models results in a 20-km shift of 

centroid northeast of epicenter (fig. 8A). In each figure, minimums are broad and flat, and epicenter is encompassed by lowest contour level. 
A226 MAIN-SHOCK CHARACTERISTICS 

tensor estimates but not the centroid location. This result 

may change, however, with the advent of new aspheric 

global Q models that are currently under development. 

The estimated optimal centroid locations are shifted from 

the epicenter, as in the CMT solution, but this location 

brings the Rayleigh- and Love-wave estimates of the Myz 

moment-tensor element into better agreement for the MPA 

and M84C propagation models, yielding unconstrained moment-tensor inversions that are consistent with body-wave 

studies. The location bias is most likely due to errors in 

the models because the source does not have a significant 

spatial finiteness. Although the p value at the epicenter is 

within a few percent of that at the optimal centroid location for any of the model combinations, we found that the 

results generally are significantly more stable if we use 

the centroid location. Even a difference of a few percent 

in variance reduction can destabilize the inversion for such 

poorly constrained terms as M and My. Inversions at 

the epicenter generally give strikes and rakes that are 10' 

lower than the centroid results, which are less consistent 

with the body waves. Thus, centroid optimization gives 

improved results over those of Wallace and others (1991), 

who considered only sources at the epicenter. 

The stability of the moment-tensor inversions around 

the centroid location is illustrated in figure 11 for the 

particular combination of the MPA, RA-yo, and MG models, where the best double-couple solutions for each moment-tensor inversion are shown at nine source positions 

around the optimum centroid, as well as at the epicenter. 

Because the nine source locations are within the region 

where p is minimized (for example, fig. 100, the mechanisms vary only slightly (4 in strike, 4 in dip, 6 in 

rake). At the epicenter, which is slightly farther from the 

minimum, the rake and strike vary by as much as lo0, and 

Figure 9.-Loma Prieta region, Calif., showing contours of residual rms error in second-step inversion for full moment tensor as a function of pointsource location (triangles) for LOMA (A), PREM (B), and RA-yo (0 excitation models. Propagation model is MPA, and global Q model is MG. 

Centroid location (square) does not depend on the choice of excitation model, although RA-yo model has lowest absolute error and most spatially 

concentrated minimum. 

Figure 10.-Loma Prieta region, Calif., showing contours of residual rms error in second-step inversion for full moment tensor as a function of pointsource location (open triangles) for PREM (A), DS (B), and MG (C) global Q models. Propagation model is MPA, and excitation model is RA-yo. 

Centroid location (square) does not depend on choice of global Q model. 
SOURCE PARAMETERS OF THE EARTHQUAKE, DETERMINED BY USING LONG-PERIOD SEISMIC WAVES A227 

the variations increase with distance from the optimum 

centroid. The results shown here are comparable to those 

obtained by using the RA-yo and MG models in combination with the M84C model, whereas using the PREM 

model with these models gives greater stability, with a 

difference of only a few degrees in mechanisms at the 

centroid and the epicenter. Using the PREM model alone, 

however, for propagation and excitation does not yield 

good results. 

It is by no means obvious that using an effective source 

location which gives the best variance reduction for the 

moment tensor will necessarily give the best momenttensor estimate. This consideration also holds for the CMT 

procedure. We find the encouraging result that no matter 

what the choice of phase velocity and attenuation model 

and for most reasonable source-excitation structures, the 

solutions for the simultaneous Rayleigh- and Love-wave 

inversion are essentially identical when performed at the 

optimal centroid location for the particular model combination. This stability suggests that the primary differences 

in the spectra corrected for the different models are small, 

slowly varying phase and amplitude patterns, as is apparent in the significant differences between moment-tensor 

inversions for different model combinations when the epicenter location (or any other common source location) is 

Figure 11.-Loma Prieta region, Calif., showing sensitivity to pointsource location (triangles) for simultaneous Rayleigh- and Love-wave 

focal mechanism determinations for MPA phase-velocity, MG global Q, 

and RA-yo excitation models. Major double-couple solutions are plotted for centroid locations at trial source locations (asterisks). Dot, solution at actual epicenter; square, solution at optimum centroid location as 

defined by minimum error (p) of second-step inversion. Strike, dip, and 

rake vary little around minimum and are approximately 123O&4O, 71Â°&40 

and 124O&6O, respectively. 

assumed. The centroid-location procedure projects most 

of these small, low-degree azimuthal patterns into the 

source relocation, finding in each case a comparable moment-tensor fit to the Rayleigh- and Love-wave spectra. 

This fit is stable only because of the significant differences in radiation pattern for these spectra, and the centroid optimization may not converge to the correct solution 

if only Rayleigh waves are used, as noted by Zhang and 

Lay (1990a). The CMT inversion is similarly stabilized 

by the differences in radiation pattern of the body- and 

surfaces-wave arrivals in the wave trains that are inverted. 

Because the centroid optimization somewhat reduces the 

dependence on the model parameters, we can establish 

realistic confidence bounds on our source-parameter estimates by comparing the suite of results for different model 

combinations. 

DEPTH 

Associated with the moment-tensor inversions is a search 

over point-source depth at each source location. Depthresolution curves generally have fairly well defined minimums for inversions that use only Rayleigh waves, whereas 

simultaneous only Rayleigh- and Love-wave inversions 

give flattened depth curves (fig. 12), as noted by Wallace 

and others (1991), owing largely to the absence of depth 

dependence of the Love-wave-excitation functions but also 

reflecting some source-model incompatibility with the joint 

Rayleigh- and Love-wave data. For example, results using different excitation structures, the MPA phase-velocity model, and the MG global Q model are plotted in 

figures 12A and 12C for the Rayleigh-wave and the simultaneous Rayleigh- and Love-wave inversions, respectively. In both figures, the RA-yo model significantly 

reduces the overall variance and gives shallower depth 

estimates relative to the other source structures. The simultaneous inversions show greater sensitivity to the excitation models, and the case-specific LOMA model 

apparently does not fit the Love-wave data particularly 

well relative to the other models, accounting for some of 

the unstable solutions found using this model. 

The choice of global Q model also affects the depth 

estimate, as shown in figures 125 and 12D; shallower 

depths are obtained when using the MG model, which 

gives a slightly lower residual variance for the Rayleighwave inversion (fig. 125) but no significant difference for 

the simultaneous inversions (fig. 12D). Clearly, a substantial uncertainty exists in the depth estimates, given 

both the flatness of these curves and our ignorance of 

which source-velocity structure is most appropriate. (The 

LOMA model is probably inadequate.) Thus, we assign 

large uncertainties to our depth estimate. Taking into account the variation in depth determinations for the different global Q models and source-velocity structures, our 
A228 MAIN-SHOCK CHARACTERISTICS 

final depth estimate is 225-1 1 km. For the models with 

water layers (PREM, RA-yo) the depth into the solid crust 

is 5 km less, giving a centroid depth in the crust of about 

175-11 lun; however, changing the crustal structure from 

oceanic to continental has little effect on the depth estimate (Zhang and Lay, 1990b). 

global Q model to demonstrate the fit to the data. In figure 13, the azimuthal patterns of observed amplitude (dots) 

and phase (squares) spectra are compared with the theoretical moment tensor (solid curves) found in the simultaneous inversion of Rayleigh and Love waves for six of 

the seven periods used in the inversion. (The 288-s data 

are not shown, but they closely resemble the 275s data.) 

Each point is an observed spectral measurement of amplitude or phase for Rayleigh-wave (R,, R2) or Love-wave 

(GI, G2) arrivals. The high signal-to-noise ratio apparent 

in the time domain in figure 2 results in high-quality spectral measurements with very little scatter. Amplitude scatPREFERRED SOLUTION 

In our final inversion, we use the MPA phase-velocity 

model, the RA-yo source-structure model, and the MG 

Rayleigh Waves Rayleigh and Love Waves 

EXPLANATION I 

G 

s 

REV 

. . 

DEPTH, IN KILOMETERS 

Figure 12.-Residual rms error versus depth for various combinations of excitation and global Q models at 

optimal centroid location, using MPA model for propagation corrections. A, Rayleigh-wave results using 

MG global Q model for RA-yo, PREM, and LOMA excitation models. B, Rayleigh-wave results using RAyo excitation model for MG, DS, and PREM global Q models. C, Simultaneous-inversion Rayleigh- and 

Love-wave results using MG global Q model for RA-yo, PREM, and LOMA excitation models. D, Simultaneous-inversion Rayleigh- and Love-wave results using RA-yo excitation model for MG, DS, and PREM 

global Q models. Inclusion of Love waves in inversion flattens normalized error curve for second-step 

inversion, giving poor depth resolution. Overall depth estimate is 22Â±1 km for our preferred choices of 

source model (RA-yo) and global Q model (DS or MG). 
SOURCE PARAMETERS OF THE EARTHQUAKE, DETERMINED BY USING LONG-PERIOD SEISMIC WAVES A229 

ter increases for shorter periods, but the data generally are are listed in table 3, along with those for the CMT soluvery well behaved and clearly exhibit coherent radiation tion of Dziewonski and others (1990); these results are 

patterns. The moment-tensor terms for this final solution generally quite compatible. 

rA 

Raylcigh Waves Rayleigh Waves 

4 "* 4' 0: /* & 

l.oL- . 1' 

Rayleigh Waves 1 .o Rayleigh Waves 

AZIMUTH. IN DEGREES 

Figure 13.-Moment-tensor-inversion results from simultaneous inversions of Rayleigh and Love waves at periods of (A) 157, 

(B) 175, (0 200, (D) 225, (E) 256, and (F) 275 s. Curves are theoretical fits determined from solution using RA-yo excitation, 

MG global Q, and MPA phase-velocity models. Dots, amplitude data; squares, phase data. Note excellent fit to observed 

spectra over period range investigated. 
MAIN-SHOCK CHARACTERISTICS 

Table 3.-Moment-tensor solutions for the earthquake 

[All values in 1019 N-m. CMT, centroid moment tensor] 

This study Resulting terms CMT 

It is encouraging to note that the new phase-velocity 

model, MPA, yields a stable solution consistent with those 

of previous studies, without employing any constraints on 

the inversions. The duration estimate of 11 s and the consistency of the phase with the epicentral location for the 

MPA model provides evidence that this model gives the 

most reliable results. We find, however, that for the simultaneous inversion of Rayleigh and Love waves, it is 

still important to determine an optimal centroid location 

to ensure a stable solution. On the basis of our preference 

for the MPA model, along with our consideration of the 

uncertainty in the source structure and global Q model, 

our final duration is ~=l lk5s, and our depth estimate is 

22k11 km. 

Taking into account the slight changes in mechanism 

due to uncertainties in choosing a preferred Earth-model 

combination, our preferred major double-couple representation for the earthquake has a mechanism with a strike of 

124Ok6', a dip of 67'&6', and a rake of 126'k7', where 

the stated uncertainties include our assessment of the model 

dependence. Seismic-moment estimates vary little in the 

vicinity of the centroid, and for all model combinations 

that give reasonable solutions (some of the inversions with 

the LOMA model excitation functions do not), we obtain 

a moment Mo of (3.0k0.2)~10~~ N-m. The non-doublecouple component varies by 5 to 30 percent, depending 

on the source location, global Q model, and source-velocity model; solutions near the centroid have about 10 percent minor double couples, which we deem to be noise 

effects. Comparison of these final parameters with the 

other long-period results listed in table 1 indicates a good 

consistency, particularly with the CMT solution of Dziewonski and others (1990). 

DISCUSSION 

We now compare our results with those of other investigations of the Loma Prieta source, with an emphasis on 

assessing any systematic frequency-dependent differences. 

Understanding any discrepancies between short- and longperiod source models is essential for understanding the 

rupture processes of large earthquakes. One physical explanation for the frequency dependence of source properties may be a variation in energy release along a fault 

surface, with "patches" of large displacement that fail with 

rapid rupture, producing high-frequency body-wave radiation, while the surrounding regions slip slowly, with a 

predominantly long period signature. Both teleseismic and 

strong-motion investigations of the earthquake suggest 

some nonuniform slip on the fault, which would be 

unresolvable by our surface-wave analysis but could give 

rise to some frequency dependence of the source parameters. Another possible cause of a discrepancy could be 

slow coseismic slip in the lower crust or uppermost mantle 

at the base of the aftershock zone. High strain rates during the main-shock rupture may induce coseismic failure 

on the downdip extension of the fault, where grain size 

and thermal conditions may cause differences in rupture 

or particle velocities affecting the spectrum of seismic 

radiation (for example, Das, 1982). 

All the available source-parameter determinations for 

the 1989 Loma Prieta earthquake are summarized in figure 14. Wallace and others (1991), in discussing the differences between their body- and surface-wave results, 

observed that the surface-wave rupture-duration and depth 

estimates were both larger than the body-wave estimates, 

Figure 14.-Summary of (A) moment, (B) depth, and (Q duration estimates from this study and previous body-wave studies by (1) Wallace 

and others (1991), (2, 3) Kanarnori and Satake (1990), (4) Choy and 

Boatwright (1990), (5) Ruff and Tichelaar (1990), (6) Romanowicz and 

Lyon-Caen (1990), (7, 8) Langston and others (1990), (9) Barker and 

Salzberg (1990), (10) Wallace and Lay (1990), (11) NAbelek (1990), 

(12) Ammon (1991), and (13) Wald and others (1991); long-period surface-wave studies of (14) this study, (15) Wallace and others (1991), 

(16) Dziewonski and others (1990), (17, 18) Kanamori and Satake (1990), 

(19) Romanowicz and Lyon-Caen (1990), (20) Zhang and Lay (1990b); 

and free-oscillation study of (21) Jordan (1991). Our moment and depth 

estimates overlap with those of other investigations. Duration results for 

our preferred propagation model (MPA) are consistent with those of 

body-wave studies. 
SOURCE PARAMETERS OF THE EARTHQUAKE, DETERMINED BY USING LONG-PERIOD SEISMIC WAVES A23 1 

whereas the seismic moment at long periods was marginally larger than at least some body-wave results, suggesting that deep, slow slip may have occurred during the 

earthquake. With our further surface-wave analysis, our 

seismic-moment estimate is slightly reduced to 

(3.0Â±0.2)~10~ N-m; other surface-wave and free-oscillation results give estimates of 2.5x1019 to 3.4~10~~ N-m. 

. ~dee oscillations i i ig! *19 1 i 

^lilfjj 15 I A surface Waves t: A. 1 

1 1.5 2 2.5 3 3.5 4 

SEISMIC MOMENT, IN 1019 NEWTON-METERS 

DEPTH, IN KILOMETERS 

- - 

DURATION, IN SECONDS 

The body-wave results (fig. 14) for seismic moment range 

from 1.7x1019 to 3.0~10~~ N-m, and the most complete 

body-wave studies (for example, Wald and others, 1991) 

yield the larger values. If these body-wave results are not 

biased by the renormalization procedure used in scaling 

up poorly matched strong-motion waveforms to fit peak 

amplitudes, then we can conclude that there is no discrepancy in the moment estimates, suggesting a fairly high 

corner frequency for the source. Comparing depth estimates (fig. 14), we note that our depth estimate has a 

larger uncertainty than other long-period estimates. This 

larger uncertainty in part reflects our inversion of both 

Rayleigh and Love waves, which increases the sensitivity 

of our estimate to poorly known source structure but includes our awareness of the strong model dependence. 

Thus, our error bars overlap with the results of previous 

body-wave studies, as well as of surface-wave and freeoscillation studies (fig. 14). Therefore, at present, no resolvable discrepancy appears to exist between long- and 

short-period depth estimates. 

Finally, our results for source duration range from 11 s 

for the MPA model to 30 s for the PREM model. We 

prefer the results from the MPA model, for the reasons 

stated above. Thus, the centroid time of the moment release is 6.1 s after the onset of rupture. The surface waves 

we use are more sensitive to the centroid time than to the 

shape of the source function. To compare this result with 

the body-wave results, we must ensure a common origin 

time for reference. Wald and others (1991) discovered a 

1.6-s precursor to the main rupture, which cannot be seen 

teleseismically but appears to correspond to the origin 

time of the local-array trigger, as reported by Dietz and 

Ellsworth (1990). Because we use this origin time 

(0004:15.21 G.m.t. Oct. 18, 1989) in our analysis, our 

time function must be shifted slightly from those obtained 

from teleseismic body-wave results (fig. 15). The sourcetime function from our study and that from teleseismic 

broadband body-wave deconvolutions (Wallace and others, 1991) have highly consistent centroid times. Given 

our preference for the results from the MPA model, we 

find no duration discrepancy. Thus, we see no evidence 

supporting the hypothesis of a significant frequency dependence of the source parameters, and thus no evidence 

for deep, slow slip or other anomalous long-period radiation. 

Although our procedure provides an optimal centroid 

location for each model combination, we attach no significance to this location because it is probably a manifestation of model inadequacies. Comparing our centroid 

location from the second-step inversions to the CMT solution (fig. l), we find that our centroid location is shifted 

to the west, whereas the CMT inversion shifts the centroid to the east, of the epicenter. This difference probably results from the different types of data used. If we 

use the CMT centroid location in the surface-wave inver- 
A232 MAIN-SHOCK CHARACTERISTICS 

sion, we obtain unacceptable results, suggesting that the 

CMT inversion and centroid location primarily fit the bodywave part of the seismograms. We have demonstrated that 

global Q and source-velocity models have little effect on 

the centroid location. Furthermore, we note that the phasevelocity-propagation models affect the centroid location 

in the second-step inversion, despite our use of optimal 

source durations for the different models. This effect indicates that residual phase anomalies from the first-stage 

inversion can be suppressed in the second-stage inversion, which uses a complex-number representation of the 

spectra. We find that by minimizing the second-stage erI I surface-wave source-time function 

Body-wave source-time function 

I Local broadband (SAO Z) 

TIME. IN SECONDS 

Figure 15.-Comparisons of our surface-wave source-time function, a 

deconvolved body-wave source-time function (Wallace and others, 1991), 

with local and teleseisrnic data (after Wald and others, 1991) for 1989 

Loma Prieta earthquake. BSR Z, TOL Z, SAR Z, and SAO Z are vertical-component displacement seismograms recorded at local or teleseismic 

distances. Labels 1, 2, and 3 on TOL Z seismogram denote identified 

pulses of energy corresponding to subevents. A 1.6-s time shift of strong 

motions and teleseismic signals relative to local-array-triggering arrival, 

caused by a small precursory radiation, was identified by Wald and 

others (1991). Note consistency in centroid time of moment release 

between surface- and body-wave source-time functions. 

ror, p, we can stabilize the estimation of source parameters, regardless of which propagation model is utilized, 

as long as the excitation and Q structures are compatible 

with the data. 

CONCLUSIONS 

In this study, we have extended the analysis of longperiod fundamental-mode Rayleigh and Love waves for 

periods ranging from 157 to 288 s for the 1989 Loma 

Prieta earthquake, and further explored the stability of the 

estimates of focal mechanism, seismic moment, centroid 

depth, source duration, and centroid location. Source duration and centroid location are both influenced by the 

choice of propagation model. By including a recent spherical-harmonic degree 12 phase-velocity model, MPA, the 

long-period analysis gives a source duration and source 

location consistent with those from other studies. Attenuation and source-velocity-structure models mainly affect 

centroid-depth and moment-tensor estimates. We introduce a procedure for searching for an optimal centroid 

location that appears to significantly stabilize focal-mechanism determinations for simultaneous inversions of 

Rayleigh and Love waves. Although significant model 

uncertainty increases the confidence bounds on our sourceparameter estimates, we find no significant discrepancies 

in the long-period parameters relative to the results for 

shorter period waves. Thus, we conclude that no evidence 

exists for anomalous long-period radiation from the main 

shock. Better resolution of frequency-dependent source 

phenomena will require improved propagation and attenuation models, many of which are currently being developed. Future application of these new models to the 

excellent Loma Prieta data is well justified, given the large 

confidence bounds in the present work and the value of 

this event for calibrating methodologies. 

ACKNOWLEDGMENTS 

This research was partly supported by U.S. Geological 

Survey grant 14-08-0001-G1843 and U.S. National Science Foundation grant EAR-90 17767, with facilities support from the W.M. Keck Foundation. We thank the many 

individuals at IRIS and IDA, and Jean-Paul Montagner of 

GEOSCOPE, who supplied us with the long-period data. 

We also thank Barbara Romanowicz and Paul Spudich for 

their constructive reviews of the manuscript. 

REFERENCES CITED 

Ammon, C.J., 1991, A contribution to the inversion of seismic body 

waves for earth structure and seismic source parameters: University 

Park, Pennsylvania State University, Ph.D. thesis, 194 p. 
SOURCE PARAMETERS OF THE EARTHQUAKE, DETERMINED BY USING LONG-PERIOD SEISMIC WAVES A233 

Barker, J.S., and Salzberg, D.H., 1990, Long-period and broad-band 

teleseismic body waves modeling of the Loma Prieta earthquake: 

Geophysical Research Letters, v. 17, no. 9, p. 1409-1412. 

Choy, G.L., and Boatwright, John, 1990, Source characteristics of the 

Loma Prieta, California, earthquake of October 18, 1989 from global digital seismic data: Geophysical Research Letters, v. 17, no. 8, 

p. 1183-1186. 

Das, Shamita, 1982, Appropriate boundary conditions for modeling very 

long earthquakes and physical consequences: Seismological Society of America Bulletin, v. 72, no. 6, pt. A, p. 1911-1926. 

Dietz, L.D., and Ellsworth, W.L., 1990, The October 17, 1989, Loma 

Prieta, California, earthquake and its aftershocks; geometry of the 

sequence from high-resolution locations: Geophysical Research Letters, v. 17, no. 9, p. 1417-1420. 

Dziewonski, A.M., and Anderson, D.L., 1981, Preliminary reference 

Earth model: Physics of the Earth and Planetary Interiors, v. 25, no. 

4, p. 297-356. 

Dziewonski, A.M., Ekstrom, Goran, Woodhouse, J. H., and Zwart, 

Gretchen, 1990, Centroid-moment tensor solutions for October-December 1989: Physics of the Earth and Planetary Interiors, v. 62, 

no. 3-4, p. 194-207. 

Dziewonski, A.M., and Steim, J.M., 1982, Dispersion and attenuation of 

mantle wave through waveform inversion: Royal Astronomical Society Geophysical Journal, v. 70, no. 2, p. 503-527. 

Grand, S.P., and Helmberger, D.V., 1985, Upper mantle shear structure 

of North America: Royal Astronomical Society Geophysical Journal, v. 76, no. 2, p. 399-438. 

Jordan, T.H., 1991, Far-field detection of slow precursors to fast seismic 

ruptures: Geophysical Research Letters, v. 18, no. 11, p. 2019-2022. 

Kanamori, Hiroo, and Anderson, D.H., 1975, Theoretical basis of some 

empirical relations in seismology: Seismological Society of America 

Bulletin, v. 65, no. 5, p. 1073-1095. 

Kanamori, Hiroo, and Given, J.W., 1981, Use of long-period surface 

waves for rapid determination of earthquake-source parameters: 

Physics of the Earth and Planetary Interiors, v. 27, no. 1, p. 8- 

31. 

Kanamori, Hiroo, and Satake, Kenji, 1990, Broadband study of the 1989 

Loma Prieta earthquake: Geophysical Research Letters, v. 17, no. 

8, p. 1179-1 182. 

Kanamori, Hiroo, and Stewart, G.S., 1976, Mode of strain release along 

the Gibbs fracture zone, mid-Atlantic Ridge: Physics of the Earth 

and Planetary Interiors, v. 11, p. 312-332. 

Langston, C.A., Furlong, K.P., Vogfjord, K.S., Clouser, R.H., and 

Ammon, C.J., 1990, Analysis of teleseismic body waves radiated 

from the Loma Prieta earthquake: Geophysical Research Letters, v. 

17, no. 8, p. 1405-1408. 

Masters, Guy, and Gilbert, Freeman, 1983, Attenuation in the earth at 

low frequency: Royal Society of London Philosophical Transactions, ser. A, v. 308, no. 1504, p. 479-522. 

Nhbglek, J.L., 1990, Rupture process of the October 18, 1989 Loma 

Prieta earthquake from broadband teleseismic body waves [abs.]: 

Seismological Research Letters, v. 61, no. 1, p. 46. 

Oppenheimer, D.H., 1990, Aftershock slip behavior of the 1989 Loma 

Prieta, California, earthquake: Geophysical Research Letters, v. 17, 

no. 8, p. 1199-1202. 

Regan, Janice, and Anderson, D.L., 1984, Anisotropic models of the 

upper mantle: Physics of the Earth and Planetary Interiors, v. 35, 

no. 4, p. 227-263. 

Romanowicz, Barbara, and Guillemant, Philippe, 1984, An experiment 

in the retrieval of depth and source mechanism of large earthquakes 

using very long-period Rayleigh wave data: Seismological Society 

of America Bulletin, v. 74, no. 2, p. 417-437, 

Romanowicz, Barbara, and Lyon-Caen, H61&ne, 1990, The Loma Prieta 

earthquake of October 18, 1989: results of teleseismic mantle and 

body wave inversion: Geophysical Research Letters, v. 17, no. 8, p. 

1191-1 194. 

Ruff, L.J., and Tichelaar, B. W., 1990, Moment 'tensor rate functions for 

the 1989 Loma Prieta earthquake: Geophysical Research Letters, v. 

17, no. 8, p. 1187-1 190. 

Schwartz, S.Y., and Lay, Thorne, 1988, Effects of off great-circle propagation on the phase of long-period surface waves: Royal Astronomical Society Geophysical Journal, v. 91, no. 1, p. 143-154. 

Walck, M.C., 1985, The upper mantle beneath the north-east Pacific 

rim; a comparison with the Gulf of California: Royal Astronomical 

Society Geophysical Journal, v. 81, no. 1, p. 243-276. 

Wald, D.J., Helmberger, D.V., and Heaton, T.H., 199 1, Rupture model 

of the 1989 Loma Prieta earthquake from the inversion of strong 

motion and broadband teleseismic data: Seismological Society of 

America Bulletin, v. 8 1, no. 5, p. 1540-1572. 

Wallace, T.C., and Lay, Thorne, 1990, Source model for the Loma 

Prieta earthquake from regional and teleseismic body waves [abs.]: 

Seismological Research Letters, v. 61, no. 1, p. 46. 

Wallace, T.C., Velasco, A., Zhang, Jiajun, and Lay, Thorne, 1991, A 

broadband seismological investigation of the 1989 Loma Prieta, 

California, earthquake; evidence for deep, slow slip?: Seismological Society of America Bulletin, v. 8 1, no. 5, p. 1622-1646. 

Walter, A.W., and Mooney, W.D., 1982, Crustal structure of the Diablo 

and Gabilan ranges, central California; a reinterpretation of existing 

data: Seismological Society of America Bulletin, v. 72, no. 5, p. 

1567-1590. 

Wong, Y.K., 1989, Upper mantle heterogeneity from phase and amplitude data of mantle waves: Cambridge, Mass., Harvard University, 

Ph.D. thesis, 209 p. 

Woodhouse, J.H., and Dziewonski, A.M., 1984, Mapping the upper 

mantle; three-dimensional modeling of Earth structure by inversion 

of seismic waveforms: Journal of Geophysical Research, v. 89, no. 

B7, p. 5953-5986. 

Zhang, Jiajun, and Kanamori, Hiroo, 1988a, Depths of large earthquakes 

determined from long-period Rayleigh waves: Journal of Geophysical Research, v. 93, no. B5, p. 4850-4868. 

1988b, Source finiteness of large earthquakes measured from 

long-period Rayleigh waves: Physics of the Earth and Planetary 

Interiors, v. 52, no. 1-2, p. 56-84. 

Zhang, Jiajun, and Lay, Thorne, 1989, Duration and depth of faulting of 

the 22 June 1977 Tonga earthquake: Seismological Society of 

America Bulletin, 79, no. 1, p. 51-66. 

1990a. Effects of centroid location on determination of earthquake mechanisms using long-period surface waves: Seismological 

Society of America Bulletin, v. 80, no. 5, p. 1205-1231. 

1990b, Source parameters of the 1989 Loma Prieta earthquake 

determined from long-period Rayleigh waves: Geophysical Research 

Letters, v. 17, no. 8, p. 1195-1 198. 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAKE OCCURRENCE 

MAIN-SHOCK CHARACTERISTICS 

STRONG-MOTION AND BROADBAND TELESEISMIC ANALYSIS OF THE 

EARTHQUAKE FOR RUPTURE PROCESS AND HAZARDS ASSESSMENT* 

CONTENTS 

By David J. Wald and Thomas H. Heaton, 

U.S. Geological Survey 

and 

Donald V. Helmberger, 

California Institute of Technology 

Page 

A235 

235 

236 

236 

236 

237 

239 

240 

242 

242 

243 

243 

243 

244 

244 

244 

244 

246 

247 

248 

248 

250 

253 

255 

256 

259 

26 1 

26 1 

ABSTRACT 

We have used broadband records from 18 teleseismic 

stations and three-component records from 16 local strongmotion stations in a formal inversion to determine the 

temporal and spatial distribution of slip during the earthquake. Separate inversions of the teleseismic (periods, 3- 

Contribution No. 4935, Division of Geological and Planetary 

Sciences, California Institute of Technology, Pasadena, CA 91 125. 

30 s) and strong-motion (periods, 1-5 s) data sets result in 

similar source models. The data require bilateral rupture, 

with relatively little slip in the region directly updip from 

the hypocenter. Slip is concentrated in two patches: one 

centered 6 km northwest of the hypocenter at 12-km depth 

with an average slip amplitude of 250 cm, and the other 

centered about 5 km southeast of the hypocenter at 16-km 

depth with an average slip amplitude of 180 cm. This 

bilateral rupture results in large-amplitude ground motions at sites both to the northwest and southeast along 

the fault strike. The northwestern patch, however, has a 

larger seismic moment and overall stress drop and thus is 

the source of the highest ground-motion velocities, a result consistent with observations. The bilateral rupture also 

results in relatively moderate ground motion directly updip 

from the hypocenter, in agreement with the ground motions observed at Corralitos, Calif. Furthermore, there is 

clear evidence of a foreshock (M-4.5-5.0) or slow rupture nucleation about 2 s before the main rupture; the 

origin time implied by strong-motion trigger times is systematically nearly 2 s later than that predicted from the 

high-gain regional-network data. The seismic moment obtained from either or both data sets is about 3.0~10~~ 

dyne-cm, and the seismic potency is 0.95 km3. Our analysis indicates that the rupture model determined from the 

teleseismic data set alone, independent of the strong-motion data set, is adequate to predict many characteristics 

of the local-strong-motion recordings. 

INTRODUCTION 

In this study, we use a least-squares linear inversion of 

strong-motion and teleseismic data to solve for the spatial 

and temporal distribution of slip during the 1989 Loma 

Prieta earthquake (Me7.1). Although the geometry of the 

fault plane is fixed in the inversion, we chose it to be 

compatible with the teleseismic waveforms and the aftershock distribution. Our estimates of the spatial and temA235 
A236 MAIN-SHOCK CHARACTERISTICS 

poral distribution of slip should enhance studies of fault 

segmentation and earthquake recurrence (Working Group 

on California Earthquake Probabilities, 1988; King and 

others, 1990), which depend on reliable estimates of the 

rupture dimensions and slip amplitude. Furthermore, the 

variation in rake angle as a function of position along 

strike and downdip on the fault plane is critical to analyses of the complex fault interactions within the SargentSan Andreas fault system (Dietz and Ellsworth, 1990; 

Olson, 1990; Schwartz and others, 1990; Seeber and 

Armbruster, 1990). 

We use the method of Hartzell and Heaton (1983), which 

has been shown to provide valuable insight into the rupture history of other California earthquakes (Hartzell and 

Heaton, 1986; Mendoza and Hartzell, 1988; Wald and 

others, 1990), as have other finite-fault approaches (Olson 

and Apsel, 1982; Archuleta, 1984; Beroza and Spudich, 

1988). In addition to providing an estimate of the rupture 

history for individual earthquakes, these studies also give 

new insight into the general characteristics of the rupture 

process that are common to many events. After studying 

slip models for several earthquakes, Mendoza and Hartzell 

(1988) suggested that large gaps in aftershock patterns 

commonly coincide with regions of relatively high slip. 

From the distribution of slip, we can also constrain the 

location and depth extent of significant energy release 

and characterize the distribution of stress changes on the 

fault. These results provide a starting point for calculating 

ground motions in future events comparable in size to the 

1989 Loma Prieta earthquake. Such ground-motion calculations are important for augmenting the sparse data base 

of near-source strong-motion recordings of Af>7 crustal 

earthquakes. 

The 1989 Loma Prieta earthquake was well recorded at 

both local-strong-motion and teleseismic broadband stations. The strong-motion velocity recordings used here 

are dominated by energy in the range 1-5 s, whereas the 

broadband teleseismic recordings show energy in the range 

3-30 s. This wealth of data provides an opportunity to 

compare rupture models that are derived independently 

from either strong-motion or teleseismic data sets with 

those derived from combined data sets and over a wide 

range of frequencies. Our results give insight into the limitations of previous studies that used less extensive data 

sets. 

DATA 

Ground motions from the 1989 Loma Prieta earthquake 

were recorded over a wide range of frequencies and distances, from high-frequency waveforms observed on local 

accelerometers and regional seismic networks to very low 

frequency waveforms observed in teleseismic surface 

waves and geodetic line-length changes. Deterministic 

waveform inversion of high-frequency (>3 Hz) motion, 

however, requires an accurate and detailed knowledge of 

the wave propagation in the geologically complex structure of the Loma Prieta region. Furthermore, inversion of 

high-frequency waveforms requires a proliferation of free 

variables that significantly increases computation time and 

decreases the stability of the inversion process. Therefore, 

we chose to concentrate our study on the lower-frequency 

part of the rupture history. Near-source, low-pass-filtered 

strong-motion and teleseismic body waves seem to be the 

most suitable data sets to study the general characteristics 

of the slip history. Although geodetic data can also provide important constraints on an earthquake slip-distribution model, they can be overly sensitive to the geometry 

of the inferred fault plane and so are not always suitable 

for determining detailed variations in slip. 

TELESEISMIC WAVEFORMS 

The teleseismic stations chosen for this study are listed 

in table 1. The data are digital recordings obtained from 

Chinese Digital Seismograph Network (CDSN), Institut 

National des Sciences de l'univers, France (GEOSCOPE), 

and Incorporated Research Institution for Seismology 

(IRIS) broadband components and Global Digital Seismograph Network (GDSN) intermediate-period components. 

These stations provide a uniform azimuthal coverage of 

the focal sphere and contain several near-nodal observations for both P- and SH-wave source radiation (fig. 1). In 

this analysis, instrument responses were deconvolved from 

the original recordings to obtain true ground velocities. 

STRONG MOTION 

The distribution of near-source ground velocities used 

in this study is mapped in figure 2; station abbreviations, 

station geometries with respect to the epicenter, and trigger times (where available) are listed in table 2. The velocity waveforms were obtained by integrating corrected 

acceleration recordings provided by the California Division of Mines and Geology (CDMG) (Shakal and others, 

1989) and the U.S. Geological Survey (USGS) (Maley 

and others, 1989), and uncorrected recordings from the 

University of California, Santa Cruz (UCSC). The velocity waveforms were bandpass filtered between 0.1 and 1.0 

Hz, using a zero-phase, third-order Butterworth filter. The 

horizontal components are rotated with respect to the epicenter to obtain "radial" and "tangential" components. 

Although this rotation is correct for energy originating 

near the epicenter, it is only approximate for source regions farther northwest and southeast along the fault. 
STRONG-MOTION AND BROADBAND TELESEISMIC ANALYSIS OF THE EARTHQUAKE FOR RUPTURE PROCESS A237 

Table 1 .-Teleseismic stations used in this study 

Station Distance Azimuth Backazimuth Phases 

(fig. 1) (O) (O) used 

A FI 

ARU 

CAY 

COL 

HIA 

HON 

HRV 

MDJ 

NNA 

OBN 

PPT 

RPN 

SCP 

SSB 

TOL 

WFM 

Two criteria were used to select stations for inclusion 

in the inversion: The observations should be both close to 

the aftershock zone and well distributed in azimuth. Within 

the epicentral region, peak ground motions are relatively 

independent of surface geology (Benuska, 1990). Care was 

also taken to avoid stations that seemed to have unusual 

site responses. For this reason, the CDMG station Agnew 

was not used, although it is at a similar distance and azimuth to station LEX (fig. 2). UCSC stations BRN, LGP, 

UCS, and WAH were included to provide important station coverage to the west and southwest of the epicenter. 

These stations, however, did not record absolute time and 

required additional processing to remove a few random 

spikes in the raw acceleration data. Although the despiking 

process that we used may be inadequate at high frequencies, it provides useful velocity recordings at the frequencies of interest in this analysis (0.1-1 Hz). The station 

LGP acceleration recording exhibited a permanent step on 

the vertical component that does not carry through in our 

bandpassed data; the horizontal components were apparently unaffected. Station BRN was set for 0.5 g maximum 

amplitude, and because amplitude reached close to that 

value, the accuracy of the response is unknown. We address the issue of estimating absolute time for these stations in the section below entitled "Inversion Method." 

FAULT-RUPTURE MODEL 

The fault parametrization and modeling procedure that 

we employ was described by Hartzell and Heaton (1983) 

in their study of the 1979 Imperial Valley, Calif., earthquake. Faulting is represented as slip on a planar surface 

that is discretized into numerous subfaults. The ground 

motion at a given station can be represented as a linear 

sum of subfault contributions, each appropriately delayed 

in time to simulate fault rupture. Formal inversion procedures are then used to deduce the slip distribution on these 

subfaults that minimizes the difference between the observed and synthetic waveforms. 

EXPLANATION 

+ COMPRESSIONAL 

Â DILATIONAL Â DOWN 

s 0 NODAL s 0 NODAL 

Figure 1.-Focal spheres with plot of takeoff angles of P (A) and SH (B) waves from 1989 Loma Prieta earthquake, showing global distribution of 

broadband teleseisrnic stations used in this study. Radiation patterns are for a source mechanism with a strike of 128O, a dip of 70Â° and a rake of 138O. 

For SH waves, "up" refers to clockwise motion. 
A23 8 MAIN-SHOCK CHARACTERISTICS 

In this study, we represent the Loma Prieta rupture as a 

40-km-long plane striking N. 128' E. and dipping 70' 

SW. As a point of reference, the northernmost corner of 

our assumed fault plane in at lat 37.193' N., long 122.020' 

W. The fault extends from 1.5- to 20.3-km depth and has 

a downdip width of 20 km (fig. 3). 

We chose the overall dimensions of the fault to enclose 

the region of major aftershock activity (Dietz and 

Ellsworth, 1990); possible vertical strike-slip faulting on 

a second plane extending past the south end of our inferred rupture area is discussed below. The strike and dip 

of our fault plane (128' and 70Â° respectively) were chosen from the broadband-inversion results of Kanamori and 

Satake (1990). This fault plane is also consistent with the 

aftershock lineation (Dietz and Ellsworth, 1990), the focal mechanism determined from first-motion data 

(Oppenheimer, 1990) and the P- and SH-wave teleseismic 

waveforms plotted in figure 4. Slight discrepancies in strike 

and dip would have little effect on our model results and 

conclusions. 

The fault-plane geometry chosen for this study differs 

somewhat from that used by Lisowski and others (1990) 

to model the geodetic data. Although they also used a dip 

of 70Â° they found that a strike of N. 136' E. (8' more 

northerly than ours) was needed to explain their data. Furthermore, their fault plane was shifted about 2 km to the 

west of our assumed plane, which was chosen to coincide 

with the aftershock distribution. In general, the geodetic 

data are more sensitive to fault geometry than are the 

waveform data, but they are not as powerful in resolving 

details of the slip distribution. Differences in the fault 

geometry inferred from static offsets, in comparison with 

waveform studies, may reflect complexities in the rupture 

process, such as a nonplanar fault surface or multiplefault rupture. These complexities are not considered further in this study. 

Our fault plane is discretized into 12 subfaults along 

strike and 8 subfaults downdip, each 2.5 km long and 

3.33 km wide vertically (fig. 3). This subfault area is a 

compromise chosen to give sufficient freedom so as to 

allow the rupture variations needed to successfully model 

the ground motions and yet minimize computation time. 

The computation time for the inversion is proportional to 

the cube of the number of unknown parameters, in this 

- 

0 

u 

Sec 30 

Figure 2.-Loma Prieta region, Calif., showing locations of strong-motion stations (triangles), epicenter of 1989 earthquake (star), and surface 

projection of model fault plane used in this study (shaded rectangle). Curves represent seismograms of radial (A) and tangential (B) components of 

velocity recorded at each station; number to right of each curve is peak velocity (in centimeters per second). Irregular thin lines, faults (dashed where 

inferred), digitized from major Quaternary faults mapped by Jennings (1975). Crosses (fig. 2B), aftershocks. Dashed outline (fig. 20, modified 

Mercalli intensity (MMI) contour separating regions of MMI VII and VIII (from Stover and others, 1990). 

A240 MAIN-SHOCK CHARACTERISTICS 

Table 2.-Strong-motion stations in the Loma Prieta region 

[Data sources: CDMG, California Division of Mines and Geology; UCSC, University of California, Santa Cruz; USGS, U.S. Geological Survey. Distance and azimuth 

measured from epicenter at lat 37'02.37' N., long 121'52.81' W. Station display adjusted to absolute time (see text). Trigger times measured from 0004:00.00 G.m.t. 

October 18, 1989; origin time measured from main shock at 0004:15.21 G.m.t. October 18, 19891 

Station 

(fig. 2) 

Station name Data Station Distance Azimuth Delay Trigger Origin 

source No. (km) (O) (s) time (s) time (s) 

AND 

BRN 

CAP 

CLD 

COR 

GGC 

GHB 

GL6 

HOL 

LEX 

LGP 

SAR 

SNJ 

ucs 

WAH 

WAT 

Anderson Dam, downstream 

Branciforte Drive 

Capitola Fire Station 

Coyote Lake Dam 

Corralitos 

Gavilan College 

Gilroy Historical Building 

Gilroy array station 6 

Hollister, Pine Street 

Lexington Dam 

Los Gatos Presentation Center 

Saratoga, Aloha Avenue 

San Jose, Santa Theresa 

University of California, Santa Cruz 

Walter's house 

Watsonville 

USGS 

ucsc 

CDMG 

CDMG 

CDMG 

CDMG 

CDMG 

CDMG 

CDMG 

CDMG 

ucsc 

CDMG 

CDMG 

ucsc 

ucsc 

CDMG 

'Accurately estimated from time at Gilroy array station 1. 

Digital instrument with memory before trigger time (P wave at 1.7 s). 

VELOCITY MODEL added a thin, lower-velocity layer to this model to better 

approximate elastic properties just beneath the strong-moThe velocity model used to compute the DWFE Green's tion stations. 5-wave velocities were calculated by assumfunctions is listed in table 3. P-wave velocities were cal- ing that the structure is a Poisson solid. 

culated by averaging the two velocity-depth profiles con- The velocity model used to compute the teleseismic 

structed by Dietz and Ellsworth (1990) for regions Green's functions (table 4) is a four-layer approximation 

northeast and southwest of the San Andreas fault. We to the local-velocity structure used in the strong-motion 

Point source 

DISTANCE ALONG STRIKE, IN KILOMETERS 

Figure 3.-Northwest-southeast cross section of fault-rupture model along fault plane, showing layout of subfaults (numbers 1-96) used in analysis. 

Enlargement shows distribution of point sources within each subfault. Largest circle radiating outward from hypocenter (star) represents position of 

rupture front after 5 s; smaller concentric circles delimit (slightly overlapping) fault regions slipping in time windows 1 (twl, shaded), 2 (tw2), and 3 

(tw3) (see fig. 18). 
STRONG-MOTION AND BROADBAND TELESEISMIC ANALYSIS OF THE EARTHQUAKE FOR RUPTURE PROCESS A241 

inversion (table 3). Heaton and Heaton (1989) discussed ample, the seismic velocities are nearly constant for both 

difficulties that arise when the seismic moments derived the teleseismic and strong-motion velocity models in the 

from different velocity models are compared. In this ex- depth range 7-18 km (the region of highest slip). This 

CAY 

1.40 

HON 4.13 

3.28 

NN A 

OBN 

PPT 

RPN 

NNA 

OBN 

PPT 

Figure 4.-Comparison of observed (upper curve) and synthetic (lower curve) seismograms recorded at broadband teleseismic stations (see fig. 1 for 

locations). First 16 stations are P waves, and last 8 stations are SH waves. Arrows denote arrivals detailed in figure 8. 
A242 MAIN-SHOCK CHARACTERISTICS 

Table 3.-Loma Prieta velocity structure for strong-motion data modeling 4-km depth. The position of the rupture front 5 s after the 

[V , P-wave velocity; V, 5-wave velocity] 

V, Density Thickness Depth (k$s) (kds) (g/cm3) (km) (km) 

Table 4.-Loma Prieta velocity structure for teleseismic data modeling 

[V , P-wave velocity; V,, 5-wave velocity] 

nucleation time is mapped in figure 3. 

Some flexibility in the rupture-velocity and slip-time 

history is achieved by introducing time windows (Hartzell 

and Heaton, 1983). In all inversions, each subfault is allowed to slip in any of three identical 0.7-s time windows 

after passage of the rupture front, thereby allowing for a 

possibly longer slip duration or a locally lower rupture 

velocity. Hartzell and Mendoza (1991) obtained nearly 

identical dislocation models for the 1978 Tabas, Iran, earthquake (Mc=7.4) using both a linear inversion parametrizing slip with three time windows (as is done here) and a 

nonlinear iterative inversion that allows a single rupture 

at each point on the fault but a varying rupture velocity. 

In this study, each time window is separated by 0.6 s, 

allowing a small overlap in the 0.7-s-duration subfault 

source-time function. Thus, as mapped in figure 3, the 

region of the fault that is allowed to slip 5 s (for example) 

after rupture nucleation is within concentric bands occupied by the three time windows. We did not test for the 

possibility of a faster rupture velocity because initial indications from our modeling showed that regions toward 

the northwest required slightly lower rupture velocities 

than 2.7 kds, which can be approximated given the flexibility allowed for by the three time windows. 

INVERSION METHOD 

favorable coincidence means that a simple comparison of 

the seismic moments derived from teleseismic and strongmotion inversions is approximately valid. 

SOURCE-TIME FUNCTION AND RUPTURE 

VELOCITY 

The subfault synthetic seismograms are convolved with 

a dislocation-time history that we represent by the integral of an isosceles triangle with a duration of 0.7 s. This 

slip function was chosen on the basis of comparison of 

the synthetic velocity-pulse width for a single subfault 

with the shortest velocity-pulse width observed, as well 

as from previous experience with this inversion method 

(Heaton, 1990). As Hartzell and Mendoza (199 1) pointed 

out, resolution of the slip function is difficult, although 

we are required by the strong-motion recordings to use a 

relatively short (~0.8 s) duration. 

The rupture velocity is assumed to be a constant 2.7 

kds, or 75 percent of the shear-wave velocity in the main 

source region (table 3). Many observations, including the 

absence of tectonic surface slip (U.S. Geological Survey 

staff, 1990), indicate that little dislocation occurred above 

A constrained, damped, linear least-squares inversion 

was used to determine the subfault dislocations that give 

the best fit to the strong-motion velocity waveforms. The 

inversion is stabilized by requiring that the slip be everywhere positive and that the difference in dislocation between adjacent subfaults (during each time window), as 

well as the total seismic moment, be minimized, as discussed by Hartzell and Heaton (1983). 

Smoothing, or minimizing the difference is slip between 

adjacent subfaults, is required to avoid instabilities, as 

well as downplay the role in the inversion played by starting and stopping phases associated with each subfault, If 

large variations in slip are allowed, such phases dominate, 

although they represent artifacts of the subfault 

discretization. Because numerous subfaults are required 

to resolve the spatial variations in slip, smoothing constraints are needed. We expect the smoothing required for 

the teleseismic and strong-motion data to differ, in that 

the number of subfaults and their size remain fixed for 

each data set, although the dominant period of the energy 

varies. 

The teleseismic data can generally be fitted with somewhat-isolated spikes of large slip, which would predict 

enormous (unphysical) localized slips and excessive highfrequency radiation. Thus, in practice, we increase the 

spatial-slip smoothing until the waveform fits begin to 
STRONG-MOTION AND BROADBAND TELESEISMIC ANALYSIS OF THE EARTHQUAKE FOR RUPTURE PROCESS A243 

degrade. Because the strong-motion inversion is more sensitive to higher-frequency radiation, the inversion automatically limits extreme variations in rupture, which 

produce excessive short-period radiation. Therefore, the 

strong-motion inversion needs minor additional smoothing. And in fact, substantial smoothing would degrade the 

strong-motion waveform fits. 

In essence then, the teleseismic rupture model may represent a lower bound on the actual fault roughness and 

thus represents a lower limit to high-frequency radiation. 

Similarly, we might expect the strong-motion model, derived from velocity waveforms, to underestimate muchhigher-frequency accelerations, but it may be adequate 

for frequencies slightly higher than used in the inversion, 

possibly as high as 5 Hz. 

Both the strong-motion observations and subfault synthetic seismograms were bandpass filtered from 0.1 to 1.0 

Hz with a zero-phase Butterworth filter and resampled at 

a uniform rate of 10 samples per second. The teleseismic 

data were similarly filtered from 0.02 to 1.0 Hz with a 

time step of 10 samples per second. The upper-frequency 

limit is imposed by the characteristics of the strong-motion recordings. In general, more coherence is noticeable 

in the waveforms at periods above 1 s than at higher 

frequencies. Originally, the strong-motion data were lowpass filtered at 3 Hz, but we noticed significant complexity, apparently caused by local site responses. We modeled 

the first 25 s of the record for teleseismic data and between 14 to 22 s of the strong-motion records (depending 

on the individual record). 

TIMING 

The initial alignment over time of the observed and 

synthetic seismograms is a critical issue in modeling waveform data to determine the temporal and spatial distribution of slip on the fault plane. In this type of study, two 

approaches are possible. One approach (commonly used 

for teleseismic-waveform inversions) is to time-shift the 

synthetic waveform from a point-source hypocenter until 

the first significant motion aligns with that of the observed recording. Later source contributions (from the developing rupture process) can then be determined by 

modeling the remaining features of the record. This method 

is adequate when (1) the observed first arrival time is 

unambiguous and (2) the initial arrival is actually from 

the locally determined hypocenter (including the origin 

time). However, the first arrivals (observed on local seismic networks) for waves from the hypocenter may be too 

small to be seen teleseismically or on strong-motion recordings. These first arrivals are used to determine the 

hypocenter and origin time of the earthquake. Serious problems arise if the first arrival on a teleseismic-waveform or 

strong-motion record is erroneously assumed to be from 

the hypocenter determined from local-seismic-network 

data. Hartzell and Heaton (1983) showed how serious this 

problem is when interpreting the 1979 Imperial Valley, 

Calif., earthquake. 

In the second approach, all correlations are done in 

absolute time, with appropriate time delays to accommodate errors introduced by inadequacies of the assumed 

velocity model. At teleseismic distances, these delays can 

be substantial, and so master-event techniques must be 

used (for example, Hartzell and Heaton, 1983). For localstrong-motion data, the use of absolute time is preferable 

if it is known for most of the recordings. We use this 

second approach in our strong-motion-modeling study. 

When the trigger time on local strong-motion records is 

available (see table 2), both the observed and synthetic 

waveforms are aligned in absolute time. Slight adjustments are also made to allow for variations in traveltime 

not predicted by the assumed one-dimensional velocity 

structure (station delays, table 2). Although this procedure provides an approximate, static station delay, it does 

not eliminate timing errors introduced by lateral variations due to subfault-to-station travelpaths that vary significantly along the fault. This issue can be addressed 

later with the analysis of aftershock recordings at strongmotion sites when these data are available. 

For strong-motion stations without absolute time, both 

the observed and synthetic waveforms will be aligned is 

we assume that the initial P wave triggers the instrument. 

The stations with timing are weighted heavily in the inversion, and those without timing are downweighted, effectively removing them from the inversion. Using the 

preliminary inversion results, synthetic waveforms were 

calculated for those stations without timing, and new time 

estimates were obtained by comparing the observed with 

the synthetic waveforms. At some stations (UCS, WAH, 

fig. 2), the forward modeling was insufficient to estimate 

the timing, and so these stations were not given significant weighting in subsequent inversions. We did, however, continue to compute waveforms for these stations 

for comparison with the observed waveforms and for later 

analysis. 

TELESEISMIC MODELING 

PRELIMINARY ANALYSIS 

Several broadband teleseismic studies of the 1989 Loma 

Prieta earthquake have been completed; their overall conclusions were summarized by Wallace and others (1991). 

As pointed out by Choy and Boatwright (1990), three 

distinct arrivals are recognizable on most of the broadband teleseismic velocity recordings (arrows, fig. 4). The 

first arrival is quite small but is visible on the P-wave 

records, about 1 s into the trace, at stations ARU, OBN, 
A244 MAIN-SHOCK CHARACTERISTICS 

and TOL (fig. 1). The first subevent is at the threshold of 

resolution for waveform modeling of teleseismic data. 

In general, previous teleseismic models describe the 

earthquake as a simple two-point-source combination representing two later, dominant subevents. The seismic moments determined in these broadband studies range from 

2.0~10~~ to 3.0~10~~ dyne-cm and show a wide variation 

in the ratio of the seismic moments for the third subevent 

relative to the second subevent, depending on the assumptions of the individual researcher. In addition, the estimate of the best point-source depths vary widely for the 

second and third subevents, or for a single estimate of the 

centroid location. This variation suggests that the rupture, 

though over a finite area, was not extensive enough to be 

easily resolved teleseismically (that is, S35 km), a result 

consistent with the limited extent of the rupture inferred 

from the aftershock distribution alone (Dietz and Ellsworth, 

1990). 

When teleseismic velocity waveforms are integrated into 

the displacements, arrivals become difficult to distinguish 

from individual subevents. In particular, the arrival from 

the second subevent appears as a subtle inflection in the 

large pulse from the third subevent. Although nearly identical results were obtained by modeling the teleseismic 

displacement waveforms, we find it easier to compare observed and synthetic velocity waveforms. 

INVERSION RESULTS 

The spatial distribution of slip obtained from inversion 

of only the teleseismic-waveform data is plotted in figure 

5. We use a large contour interval (50 cm) to emphasize 

the robust features of our model; the dislocations shown 

represent the combined slip for the three time windows 

previously mentioned. 

Our teleseismic model has a seismic moment of 2.8~10~~ 

dyne-cm. The observed teleseismic records (upper curves) 

are compared with the synthetic seismograms (lower 

curves) predicted by the teleseismic dislocation model in 

figure 4. The main features of this model are (1) a twolobed bilateral rupture with a slightly higher slip to the 

northwest, (2) concentration of the highest slip at a depth 

of 11 krn for the northwestern patch and slightly deeper 

for the southeastern patch, and (3) low slip in the region 

updip from the hypocenter. 

Directivity controls the waveform and amplitude only 

when the rupture front propagates at a velocity comparable to that of the phase of interest. Thus, the teleseismic 

body waves, all with steep takeoff angles, are limited in 

their ability to resolve rupture directivity along strike but 

are quite sensitive to updip or downdip rupture propagation. The absence of vertical directivity is apparent in our 

solution. Because the teleseismic-waveform data do not 

allow significant slip updip or downdip from the hypocenter, most slip must occur along strike from the hypocenter. Bilateral rupture is indicated by the timing of the 

second and third arrivals and by the absence of significant 

azimuthal arrival-time differences between the two dominant arrivals. As discussed in the next section, this model 

explains many of the features observed in the local-strongmotion data. 

STRONG-MOTION MODELING 

PRELIMINARY ANALYSIS 

PEAK MOTIONS 

Inspection of the pattern of near-source peak ground 

velocities (fig. 2) reveals that the largest motions occurred 

at stations located near the northwest (LEX, LGP, SAR) 

20 40 

DISTANCE ALONG STRIKE, IN KILOMETERS 

Figure 5.-Northwest-southeast cross section of model fault (fig. 3), 

showing contours of dislocation for strike slip (A), dip slip (B), and 

oblique slip (0 predicted from teleseismic inversion. Contour interval, 

50 cm. Star, hypocenter of 1989 Loma Prieta earthquake. 
STRONG-MOTION AND BROADBAND TELESEISMIC ANALYSIS OF THE EARTHQUAKE FOR RUPTURE PROCESS A245 

and southeast (HOL, WAT, GHB) ends of the aftershock 

zone. A tendency for large motions at both ends of the 

aftershock zone, particularly to the northwest, is evident 

in the modified Mercalli intensity (MMI) VII isoseismal 

map (fig. 2C), in contrast to the relatively small amplitudes recorded at station COR, directly updip from the 

hypocenter, where we expected to see a strong directivity 

from a rupture propagating updip. 

Additional evidence for bilateral rupture is the timing 

and similarity of the velocity recordings at stations GGC 

and SAR (fig. 6); these stations are symmetrically located 

about the fault plane and at nearly the same epicentral 

distance (fig. 2). Polarities for the radial and vertical components at station SAR are reversed to correct for the 

change in sign of the P- and SV-wave-radiation patterns 

and to enhance the comparison. Although absolute time 

unavailable for station SAR, the timing at this station was 

estimated by noting the similarity of the S waveform to 

that at station LEX (fig. 2) and then correcting for the 

additional shear-wave-propagation time from station LEX 

to station SAR. The timing and waveforms of the main 

arrivals at stations GGC and SAR are similar, although 

they are slightly earlier at station GGC than at station 

SAR; however, the peak amplitudes are considerably larger 

at station SAR (fig. 2). These observations demand a nearly 

symmetrical, bilateral rupture, with considerably more 1- 

Hz energy radiated northwestward. A single asperity centered at or above the hypocenter could also explain the 

symmetry in timing and waveform at these stations, although it is inconsistent with the small amplitudes observed at stations located near the center of the aftershock 

region (BRN, CAP, COR, UCS, WAH, fig. 2) that should 

otherwise be enhanced by a slip concentration in the center of the fault. Furthermore, a central asperity cannot 

easily account for the larger amplitudes observed to the 

northwest and the lower amplitudes observed to the south0 - 10 SECONDS 

Figure 6.-Comparison of radial (left), tangential (middle), and vertical (right) components of velocity 

recorded at strong-motion stations GGC (A) and SAR (B) (see fig. 2 for locations), aligned vertically in 

absolute time, normalized to peak velocity, and shown at same scale. Polarities of components are reversed 

in figure 65 to enhance comparison. Obs., observed seismograms; syn., synthetic seismograms, with contributions from northwest (NW.) and southeast (SE.) halves of model fault. 
A246 MAIN-SHOCK CHARACTERISTICS 

east. These observations agree with the main features found 

from inversion of the teleseismic-waveform data. 

TRIGGER TIMES AND RUPTURE INITIATION 

We use the hypocentral parameters of Dietz and 

Ellsworth (1990), as listed in table 2. In figure 7, we 

compare the theoretical P-wave traveltimes at each station with the corresponding trigger times. Because strongmotion accelerometers are triggered only by vertical 

motions, they probably were triggered by P-wave arrivals. The accelerometers, however, were actually triggered 

nearly 2 s later than the P-wave arrival time predicted 

from the hypocentral parameters of Dietz and Ellsworth 

(1990). At station COR, nearly directly above the hypocenter (fig. 2), the observed trigger time is about 1.8 s 

after the P-wave-arrival time predicted by using the velocity model listed in table 3. Other stations show similar 

delays. We examine this delay in figure 8 by plotting the 

waveforms and timing of data from various instrument 

types: the low- and high-gain vertical components at USGS 

station BSR, teleseismic station TOL, strong-motion station SAR, and station SAO (San Andreas Geophysical 

Observatory), a University of California, Berkeley, broadband Streckeisen instrument. The waveforms for stations 

BSR and SAO are aligned on their first motions, and stations TOL and SAR are aligned according to our interpretation of the rupture initiation. That is, the simplest 

@/ EXPLANTATION 

- Theoretical P times - - - - Theoretical S times 

Trigger time I 

o~ft"'i~'i~'$~"~i'~~~i'~~"~*5"~~'~~ 

EPICENTRAL DISTANCE, IN KILOMETERS 

Figure 7.-Strong-motion trigger time versus epicentral distance for velocity model listed in table 3, based on origin time of main shock at 

0004:15.21 G.m.t. October 18, 1989. Dot at 7 km distance is COR, 

Corralitos strong-motion station (fig. 2). 

explanation for this 2-s delay is that a foreshock, too small 

(MS) to trigger the strong-motion instruments, occurred 

about 2 s before the main rupture; this foreshock was 

used to locate the hypocenter from the high-gain regionalnetwork data. We suggest, however, that the initial 2 s 

represents the initial stage of rupture, possibly a smooth, 

slow growth episode (Wald and others, 1991). As plotted 

in figure 8, the initial stage of rupture clipped the nearby 

high-gain station BSR but shows a long-period characteristic in the low-gain component. This low-gain component clipped after about 1.6 s, after which (1) the first 

teleseismic energy becomes visible, (2) the strong-motion 

stations begin to trigger, and (3) the local broadband stations change from a long-period one-sided waveform and 

dramatically clip. These observations can be interpreted 

as a slow rupture nucleation that generated insufficient 

long-period energy to be seen teleseismically and insufficient high-frequency radiation to trigger the strong-motion instruments. 

The observation that led to the discovery of this timing 

problem was the initial inversion of the strong-motion 

waveforms, using absolute time. The resulting slip-distribution model required a two-lobed pattern similar to that 

in the teleseismic-waveform data, but the centers of these 

lobes were forced toward the sides of the fault. This slip 

distribution was inconsistent with that derived from the 

teleseismic-waveform data and with the source region suggested by the aftershock pattern (Dietz and Ellsworth, 

1990). Furthermore, it generated inferior fits to the strongmotion data. 

Thus, the failure to account for this delay can seriously 

affect source models based on waveform inversion, using 

absolute timing. In particular, the modeled rupture front 

would already have progressed 5 km away from the hypocenter during this 2-s interval, when, in fact, probably 

very little rupture propagation occurred during this period. Owing to the initial weak 1.8 s of rupture, the strongmotion records appear to be delayed by 1.8 s with respect 

to Dietz and Ellsworth's (1990) origin time. We thus 

choose to ignore the foreshock or rupture initiation, and 

we begin modeling at the time of the first significant 

strong-ground motion. We assume that the main rupture 

began at or near Dietz and Ellsworth's (1990) hypocentral 

location 1.8 s after their origin time, and then allow the 

rupture to propagate outward from that location. This approach is consistent with our analysis of the teleseismicwaveform data, which also begins with the first significant 

rupture, because the initial rupture or foreshock was too 

small to be recorded teleseismically. 

It is not uncommon for the hypocenter determined from 

high-gain regional-network data to represent a foreshock 

or an earlier stage of rupture not observed on other data 

sets. Wald and others (1990) discussed the rupture process of the 1987 Superstition Hills, Calif., earthquake and 

suggested that the network hypocenter represents an ear- 
STRONG-MOTION AND BROADBAND TELESEISMIC ANALYSIS OF THE EARTHQUAKE FOR RUPTURE PROCESS A247 

lier foreshock and not the main rupture initiation. Therefore, on the basis of the strong-motion and teleseismic 

data, that event began rupturing in a different location 

from the hypocentral coordinates determined from the regional-network data. 

INVERSION RESULTS 

The distribution of slip calculated from the inversion of 

only the strong-motion velocities is plotted in figure 9, 

and the observed (upper curve) and synthetic (lower curve) 

strong-motion velocities are compared in figure 10. The 

strong-motion rupture model is similar to that derived from 

the teleseismic inversion (fig. 5). Again, slip is concentrated in two patches, one centered about 8 km northwest 

of the hypocenter at 12-km depth with a peak slip amplitude of 350 cm, and the other centered about 6 km southeast of the hypocenter at 16-km depth with a peak slip 

amplitude of 460 cm. These parameters are summarized 

in table 5. As for the teleseismic inversion, the largest 

localized slip concentrations are northwest of the hypocenter. 

The overall pattern of the strong-motion slip duration 

and waveform complexity is explainable by the relative 

positions of individual stations with respect to the two 

lobes of concentrated slip. The observed (first curve) and 

synthetic (second curve) velocities at selected strong-motion stations are compared in figure 11, along with the 

surface projection of the fault plane and strong-motion 

slip distribution. To better understand our synthetic waveforms, the synthetic seismograms that result from rupture 

on only the northwest (third curve) and southeast (bottom 

curve) halves of the fault are also compared in figure 11. 

A similar breakdown of the synthetic ground motions for 

all components at stations GGC and SAR (fig. 2)is shown 

Local Array (BSR V) 

I I Local Arrav Low Gain fBSR Z) 

I I 

I I 

1 I 

I I 

I I Local Broadband (SAO Z) 

I ll 

1 1 TIME, IN SECONDS I I 

Figure 8.-Comparison of waveforms at broadband teleseismic stations (see fig. 1 for locations) indicating 

delay to main part of rupture, aligned in absolute time except for record at station TOL. Vertical dashed lines 

indicate times of 0.0 and 1.8 s. Z, vertical component of velocity. Numbers 1 through 3 on station TOL 

record refer to arrivals denoted by arrows in figure 4. 
A248 MAIN-SHOCK CHARACTERISTICS 

in figure 6. 

strike (LEX, 

the nearby sl 

Velocities at stations located nearly along 

SAR, GGC, GHB, fig. 2) are controlled by 

ip concentration and show little contribution 

from the farther lobe. This result is attributable to both 

the additional distance from the farther lobe of concentrated slip and the favorable source directivity at stations 

in the direction of rupture. Thus, the waveforms at 

alongstrike stations are simple, large in amplitude, and 

short in duration. Stations in the central section of the 

fault (CAP, COR, fig. 2) show smaller amplitudes and 

more waveform complexity, resulting from the absence of 

rupture directivity and the interference of contributions 

from the northwest and southeast regions of high slip. We 

expect these waveforms to be the most difficult to model, 

because the synthetic seismograms are controlled by interference of the wavefields from two propagating rupture 

fronts that are diverging from one another. 

0 

10 

ran 

'"0 20 40 " 

DISTANCE ALONG STRIKE. IN KILOMETERS 

Figure 9.-Northwest-southeast cross section of model fault (fig. 3), 

showing contours of dislocation for strike slip (A), dip slip (B), and 

oblique slip (C) predicted from strong-motion inversion. Contour interval, 50 cm. Star, hypocenter of 1989 Loma Prieta earthquake; dots, 

aftershocks of m4.0 projected onto model fault plane. 

SENSITIVITY TO STATION COVERAGE 

Of concern when inverting waveform data for source 

rupture processes is the consideration of possible contamination from site effects and flawed data. John Vidale 

(oral commun., 199 1) suggested that the strong-motion 

instrument at station LGP (fig. 2) moved during the main 

shock, resulting in data of questionable reliability. Although we believe that the data from this station are well 

behaved on the basis of its waveform data, frequency content, and amplitude similarities to the data from neighboring stations LEX and SAR (see figs. 2B, 20, we performed 

a test inversion excluding the data from station LGP to be 

certain of the role of that station in the final solution. The 

result indicated that removal of the data from station LGP 

has almost no effect on the source model. This result 

might have been anticipated because any single station 

has only a limited role in the total solution and, in particular, the data from station LGP are nearly redundant, 

considering that the waveforms at adjacent stations SAR 

and LEX require a similar source contribution. In fact, 

forward modeling for station LGP with the solution determined without considering those data fits that record well, 

confirming our observation that the waveform is properly 

behaved and dominated by useful source information. 

JOINT TELESEISMIC AND 

STRONG-MOTION INVERSION 

Although the teleseismic and strong-motion models have 

several features in common, variations in the results are 

apparent. The teleseismic model shows considerably more 

strike slip in the shallow southeastern section of the fault. 

In addition, the overall depth of the slip concentration in 

the southeast half of the fault is deeper in the strongmotion model. 

To test the compatibility of the teleseismic-waveform 

and strong-motion data, and to establish a model consistent with both, we performed a combined inversion of 

both data sets. In the combined inversion, we used the 

average of the smoothing weights used in the separate 

inversions. Also, because of the relatively small source 

dimensions, the near-source strong-motion data have more 

resolving power than the teleseismic-waveform data, which 

are dominated by a single velocity pulse that is not as 

sensitive to subtle changes in the details of the rupture 

process as are the higher-frequency strong-motion data. 

Accordingly, we chose to weight the strong-motion data 

by a factor of 2 over the teleseismic-waveform data in the 

combined inversion. 

The slip distribution resulting from the combined inversion of the strong-motion and teleseismic-waveform 

data (fig. 12) is nearly identical to that resulting from the 
STRONG-MOTION AND BROADBAND TELESEISMIC ANALYSIS OF THE EARTHQUAKE FOR RUPTURE PROCESS A249 

inversion of either data set. This result could have been The combined model, which we prefer, represents a comanticipated because our previous models, which were de- promise between our two previous source models. To best 

rived from these independent data sets, are so similar. satisfy both data sets, however, slip is more concentrated 

AND R 

AND T 

AND Z 

BRN R 

BRN T 

BRNZ --vv^I^" + 11.5 

CAP R 

CAP T 

CAP 7. 6.6 

9.9 

CLD R 14.2 

10.1 

CLD T 13.7 

13.8 

* CLDZ 6.7 

7.1 

COR R 

COR T 

COR Z 

GGC R 

GGcT tr 

GGC Z 

0 14 Seconds 

Figure 10.-Comparison of observed (upper curve) and synthetic (lower curve) seismograms of velocity at local-strong-motion stations (see fig. 2 for 

locations). Number to right of each curve is peak velocity (in centimeters per second). Stars, forward modeling only. 
A250 MAIN-SHOCK CHARACTERISTICS 

in the central part of the northwest lobe of dislocation, in FORWARD MODELING OF 

comparison with the more diffuse slip in the previous GROUND MOTION 

models. The matchup of teleseismic waveforms is only 

slightly degraded, and the strong-motion synthetic seis- In this section, we use our finite-fault-source inversion 

mograms are only slightly affected by the increased results to characterize ground motions more generally. 

smoothing constraints. 

GHBR 

GHB T 

GHBZ 

First, we seek to determine whether the teleseismic-waveHOL R 

HOL T 

HOL Z 

LEX R 

LEX T 

LEX Z 

SAR R 

SAR T 

SAR z 

0 14 Seconds 

IJ 

Figure 10.-Continued. 
STRONG-MOTION AND BROADBAND TELESEISMIC ANALYSIS OF THE EARTHQUAKE FOR RUPTURE PROCESS A25 1 

form data alone are sufficient to adequately resolve the 

source characteristics necessary to predict local strong 

ground motions. In forward modeling, this hypothesis was 

tested by predicting the strong motions, using the teleseismically derived source model. We then compared the 

SNJ R 

SNJ T 

* SNJZ 

UCS R 

UCS T 

* ucsz 

0 14 Seconds 

strong motions predicted by the teleseismic source model 

with those predicted by the strong-motion source model. 

Second, we show that the inversion of strong-motion 

data is useful for estimating the ground motions over the 

entire source region. The overall distribution of strongWAHR 

WAH T 

WAH Z 

WAT R 

WATT 

WAT Z 

Figure 10.-Continued. 
MAIN-SHOCK CHARACTERISTICS 

Table 5.-Inversion model 

["Northwest" and "southeast" refer to halves of the fault. Radius is of asperity used in stress-drop calculations (figs. 12-14). 

Stress drop is of asperities in northwest and southeast halves of the fault (shading, fig. 12)] 

Seismic moment Peak slip Radius Average Stress drop Model (1 026 dyne-cm) amplitude (cm) (km) slip (cm) (bars) 

Strong motion: 

Northwest ------- 1.9 

southeast -------- 1.2 

Tclcscismic: 

Northwest ------- 2.0 

Southeast -------- .8 

Strong motion and 

tclcscismic: 

Northwest ------- 2.2 

Southeast -------- .8 

0 20 KILOMETERS 

SECONDS 

OBS. 

SYN. 

NW 

SE 

Figure 11.-Loma Prieta region, Calif., showing locations of strong-motion stations (triangles), epicenter of 1989 earthquake (star), and surface 

projection of model fault plane used in this study (shaded rectangle). Curves represent observed (uppermost) and synthetic (second) seismograms of 

ground motion, with synthetic contributions from northwest (third) and southeast (lowermost) halves of model fault. Number to left of uppermost 

curve is common peak velocity to which all curves for each station are scaled. 
STRONG-MOTION AND BROADBAND TELESEISMIC ANALYSIS OF THE EARTHQUAKE FOR RUPTURE PROCESS A253 

motion velocities was characterized by predicting ground 

motions at various sites not represented by strong-motion 

recordings. In addition, we modified the source-rupture 

model and analyzed the overall effect of fault geometry 

and rake on the resulting ground motions. Specifically, 

we preserved the slip distribution of the strong-motion 

model, constrained the slip to be strike slip on the adjacent vertical, shallow segment of the San Andreas fault, 

and then compared the resulting ground motions to those 

from the dipping, oblique-slip Loma Prieta rupture. This 

scenario of vertical strike-slip rupture is plausible for a 

future earthquake on this section of the San Andreas fault, 

and might be considered 

motions sustained during 

quake. 

GROUND-MOTION PREDICTION FROM 

TELESEISMIC MODEL 

Given the rupture model determined from inversion of 

the teleseismic-waveform data exclusively (fig. 5), it is 

straightforward to compute the local ground motions at 

the 16 stations that recorded the strong motions (table 2): 

We simply replace the strong-motion slip model with the 

teleseismic slip model and forward-model the resulting 

ground velocities. Recall that the fault-model parametrization is identical for both the strong-motion and 

teleseismic-waveform data; only the spatial smoothing and 

a lower bound on the ground final slip distribution, including the relative weights within 

the 1906 San Francisco earth- each of the three time windows, vary. 

We might expect that, given the similarities of the 

teleseismic model to the strong-motion model (figs. 5, 9), 

comparable strong motions would be predicted. The observed ground-motion velocities at selected stations are 

compared with the synthetic waveforms predicted by the 

strong-motion and teleseismic source models in figure 13. 

The various stations were chosen as representative of regions above the northwestern, central, and southern sections of the fault. This waveform comparison indicates 8 300 that the teleseismic synthetic ground motions (lower curve) 

g 200 fit the overall amplitudes and durations of the observed 

3 100 ground motions (upper curve) quite well. We expected 

$0 the amplitudes and phases of individual arrivals to differ 

from the strong-motion data, considering that this phase 

information was omitted from the teleseismic inversion. 

We note, however, a slightly longer period quality in the 

teleseismic synthetic ground motions (lower curve) than 

in the strong-motion synthetic (middle curve) and observed 

(upper curve) seismograms. This shift to longer periods is 

noticeable at station LEX (fig. 13). 

For a more systematic comparison, we can quantify the 

misfit to observations for both the strong-motion and 

teleseismic source models by examining the difference in 

the response spectra of the observed and synthetic seismograms. We use the methodology of Abrahamson and 

others (1990) to evaluate the uncertainty in numeric strongmotion predictions as appropriate for engineering applications. We calculate the natural logarithm of the spectral 

acceleration at 5-percent damping on each horizontal component and then average the spectra for the two horizontal 

components. As shown by Abrahamson and others (1990), 

the estimated model bias is given by the mean error, e, as 

a function of spectral frequency, f, by the relation: 

I 2 0 

DISTANCE ALONG STRIKE. IN KILOMETERS &(~)=--~(I~SA~-I~SA;), lN 

Figure 12.-Northwest-southeast cross section of model fault (fig. 3), 

showing contours of dislocation for strike slip (A), dip slip (B), and 

oblique slip (Q predicted from combined inversion of teleseismic-wave- where SAY is the observed and SAis is the synthetic specform and strong-motion data. Contour interval, 50 cm. star, hypocenter tral acceleration for the ith recording, and N is the total 

of 1989 Loma Prieta earthquake. number of recordings. We compute the mean error only 
A254 MAIN-SHOCK CHARACTERISTICS 

for spectral frequencies within the bandpass of the inversion (0.2-1.0 Hz). 

The mean error averaged over both horizontal components of all stations, and the 90-percent-confidence interval of the bias for the strong-motion and teleseismic source 

models, are compared in figure 14. The model is considered unbiased if its bias does not differ significantly from 

zero at the 90-percent-confidence level (Abrahamson and 

others, 1990). Over this frequency range, the strong-motion synthetic seismograms show very little bias in comparison with the observed seismograms. This result is not 

surprising, considering that the solution was determined 

by using a least-squares fit between the synthetic and observed strong-motion seismograms. 

In the teleseismic model, within the 90-percent-confidence interval, the bias differs only marginally from zero. 

The synthetic seismograms slightly overpredict the velocity at frequencies below 0.4 Hz and underpredict it at 

higher frequencies. This result indicates, however, that 

the teleseismic source models, determined independently 

from the strong-motion data, can be used to predict the 

near-fault ground motions for comparable earthquakes that 

might lack strong-motion recordings. 

We note that the forward prediction of strong motions 

from the teleseismic-waveform data is sensitive to the spatial smoothing chosen for the teleseismic model. For this 

reason, the 1989 Loma Prieta earthquake, with abundant 

teleseismic-waveform as well as local data, presents a 

COR R 

COR T 

COR Z 

GLH R 

GLHT -^A/ 

LEX R 28 

GLH 7 LEXZ 21 

SECONDS 

Figure 13.-Comparison of observed seismograms (top curve), synthetic seismograms produced with strong-motion dislocation model (middle curve), 

and synthetic seismograms produced with teleseismic dislocation model (bottom curve) for radial (R), tangential (T), and vertical (Z) components of 

velocity at local-strong-motion stations COR, GLH, and LEX (fig. 2). Number to right of curve is peak velocity (in centimeters per second). 
STRONG-MOTION AND BROADBAND TELESEISMIC ANALYSIS OF Tm EARTHQUAKE FOR RUPTURE PROCESS A255 

unique chance to examine the relation between these parameters. Because inversions of teleseismic-waveform data 

alone generally tend to prefer solutions with numerous 

isolated, high-slip subfaults, significant smoothing was 

required to minimize the variation of slip between adjacent subfaults. Thus, as presented here, the teleseismicwaveform model represents a lower estimate of the fault 

slip heterogeneity. The net effect is a noticeable 

underprediction of the higher-frequency (>0.7 Hz) energy, 

as shown in figure 14, and a slight overprediction of 

longer-period (~0.4 Hz) energy. 

Our estimation of the smoothing required for the 

teleseismic model appears to be reasonable, considering 

the sufficient fit to the strong-motion predictions (figs. 

13, 14). In our future work, we will more fully examine 

the relation between the theoretical spatial smoothing used 

for teleseismic modeling and the effects on estimations of 

higher-frequency radiation. 

ESTIMATED PEAK-GROUND-VELOCITY 

DISTRIBUTION 

The dislocation model derived from inversion of the 

teleseismic and strong-motion data can also be used to 

characterize the ground motions at a site anywhere within 

the source region (fig. 1). For example, Hartzell and Iida 

(1990) used their rupture model of the 1987 Whittier Narrows,, Calif., earthquake, derived from inversion of local 

strong-motion data, to forward-model the ground motions 

over the entire epicentral region. In using this approach, 

we are limited only by the farthest distance to which adI I 1 I Ill1 , 

- A 

2 - Mean - 

0.1 1 

SPECTRAL FREQUENCY, IN HERTZ 

equate Green's functions are available. For the Loma Prieta 

source area, we computed synthetic ground-motion velocities over a grid of stations (crosses, fig. 151, with eastwest separations of 9 km and north-south separations of 5 

km, at a total of 64 locations in addition to the 16 original 

station locations (table 2). The peak ground velocity was 

determined at each gridpoint station, and then these values were contoured over the source area. 

Two lobes of high peak velocities are apparent in figure 15, one in the southeastern section of the fault and the 

other in the northwestern section. The largest-amplitude 

simulations, more than 70 cds, are concentrated above 

the northwestern section of the fault. These two lobes 

represent the combined effects of the two asperity depths 

and locations (fig. 9), together with the source radiation 

pattern. The oblique mechanism, with an average rake of 

142O, favors radiation toward the northwest, even for a 

uniform slip distribution. 

The overall pattern of peak velocities (fig. 15) agrees 

well with many of the observed indicators of strong ground 

shaking during the earthquake, confirming that areas above 

the northwestern section of the fault underwent the strongest shaking, The largest ground velocities were measured 

at stations (LEX, LGP, SAR, fig. 2) within the northwest 

lobe of large computed ground motions. Furthermore, the 

MMI map of Stover and others (1990) (fig. 2C) shows a 

localized concentration of MMI VIII observations within 

the northwest lobe of large computed ground motions. 

This area of the southern Santa Cruz Mountains was also 

where most ground ruptures and fissures formed during 

the earthquake, particularly along Summit Road and 

Skyline Ridge. Ponti and Wells (1991) attributed these 

SPECTRAL FREQUENCY, IN HERTZ 

Figure 14.-Bias and 90-percent-confidence interval of bias versus spectral frequency for strong-motion inversion (A) and teleseismic inversion (B). 
A256 MAIN-SHOCK CHARACTERISTICS 

displacements to shaking-induced gravitational spreading 

of ridges and downslope movement, and noted that the 

greatest damage to competent structures and the highest 

concentration of topped trees, displaced boulders, and 

seismically activated landslides were in this area. 

Finally, to further characterize the ground-motion hazards in this area, we modified the strong-motion rupture 

model to simulate a vertical strike-slip rupture along the 

San Andreas fault with a comparable slip distribution to 

the Loma Prieta strong-motion model. By rotating the 

model fault to a vertical plane and constraining the dislocation to be pure right-lateral strike slip, we approximate 

rupture along the San Andreas fault. For consistency with 

the average depth of significant slip from other strongmotion waveform inversions of California vertical strikeslip earthquakes (Hartzell and Heaton, 1983; Beroza and 

Spudich, 1988; Wald and others, 1990), we needed to 

decrease the asperity depth relative to the Loma Prieta 

model fault by bringing the top of the fault to within 0.5 

km of the surface and translating the slip (see fig. 9) 5 km 

closer to the top of the fault (fig. 16). The strike was kept 

identical to that in the Loma Prieta model, causing a minor discrepancy in the strike of the model fault (straight 

line, fig. 17) relative to the strike of the San Andreas 

fault. The absolute amplitude of slip was preserved, resulting in a slightly smaller total seismic moment (owing 

to the reduced rigidity at the depths of the shallower slip). 

The slight difference in the contours (compare figs. 9 and 

16) results from compressing the fault width over which 

slip occurs. 

The overall pattern of the resulting peak ground velocities computed with the vertical strike-slip-fault model (fig. 

16) is shown in figure 17. Note that the overall velocities 

are higher than in the Loma Prieta model. These higher 

velocities are attributable to the relatively shallow slip 

relative to the Loma Prieta model. Note that the asperity 

toward the northwestern section of the fault is shallower 

than that toward the southeastern section (fig. 16), suggesting that near-source ground motions during the earthquake were moderated by the relatively large average depth 

of significant slip. 

DISCUSSION 

We have presented our slip models by using contour 

maps that are spatially smoothed to deemphasize the abrupt 

subfault boundaries used in our inversion scheme. To comFigure 15.-Lorna Prieta region, Calif., showing epicenter of 1989 earthquake (star), surface projection of model fault plane used in this study (shaded 

rectangle), and contours of peak ground velocity predicted from strong-motion source model. Contour interval, 10 Ws. Crosses, grid of stations used 

in forward modeling. 
STRONG-MOTION AND BROADBAND TELESEISMIC ANALYSIS OF THE EARTHQUA= FOR RUPTURE PROCESS A257 

pare our inversion models in more detail, the slip vectors 

for individual subfaults are shown in figure 18, and the 

maximum absolute slip amplitudes are listed in table 5. 

The average rake angles, based on the relative components of strike slip and dip slip for the strong-motion, 

teleseismic, and combined inversions are 142', 144', and 

14S0, respectively, in agreement with the range of values 

DISTANCE hONG STRIKE, IN KILOMETERS 

Figure 16.-Northwest-southeast cross section of model fault (fig. 3), 

showing contours of dislocation for vertical strike slip predicted from 

strong-motion model, Contour interval, 50 cm. Star, hypocenter of 1989 

Loma Prieta earthquake. 

reported in teleseismic point-source studies by other researchers and with the geodetic modeling results (Lisowski 

and others, 1990). 

Although inversion of only the teleseismic-waveform 

data does not result in systematic spatial variations of the 

rake angle (fig. 18B), inversion of the strong-motion data 

(figs. 18A, 18C) shows a clear tendency for more nearly 

vertical rake angles of slip to the northwest of the hypocenter and more nearly horizontal rake angles of slip to 

the southeast. Although our model assumes that all slip 

occurs on a single, 70'-dipping plane, this systematic 

change in rake angle coincides with an apparent change in 

dip of the aftershock zone from about 70' for the segment 

northwest of the hypocenter to nearly vertical near the 

southeast edge of the fault plane (Dietz and Ellsworth, 

1990). 

One shortcoming of our model is its failure to predict 

the large transverse motions observed at station HOL (fig. 

lo), although site-response studies indicate significant site 

amplifications at this station (Keiiti Aki, written commun., 

1991). Station HOL, which is located along the southeastward projection of the fault, has an unusually large motion perpendicular to the fault strike (fig. 2B). This 

Figure 17.-Lorna Prieta region, Calif., showing predicted contours of peak ground velocity from a vertical strike-slip rupture along the San Andreas 

fault, based on 1989 Lorna Prieta slip distributions. Contour interval, 10 cds. Irregular thin lines, faults (dashed where inferred), digitized from major 

Quaternary faults mapped by Jennings (1975); straight line, model fault length; star, epicenter of 1989 Loma Prieta earthquake. 
A258 MAIN-SHOCK CHARACTERISTICS 

waveform suggests strike-slip faulting on a separate, vertically dipping, southeast-trending fault plane at the southeast end of the aftershock area (possibly the San Andreas 

fault). The radiation pattern from a vertical strike-slip 

mechanism would greatly enhance the tangential component and yet not contribute to the near-nodal radial and 

vertical components. Such a model is consistent with the 

near-vertical aftershock distribution and strike-slip mechanisms near the southeast edge of the inferred rupture zone 

DISTANCE ALONG STRIE, IN KILOMETERS 

Figure 18.-Northwest-southeast cross section of model fault (fig. 31, 

showing rake angle (vector) for each subfault as determined from inversion of strong-motion (A) and teleseismic (B) data sets, and from combined inversion of both data sets (0. Length of each vector is normalized 

to peak slip on model fault plane. Shaded circles, patches where most 

slip is concentrated; star, hypocenter of 1989 Loma Prieta earthquake. 

(Dietz and Ellsworth, 1990). Although a minor amount of 

pure strike-slip motion occurs on the shallow southeastern section of our model fault inferred f'rom the teleseismicwaveform data (2.5-7.5 km downdip, 23-36 km along 

strike; fig. 18), such motion is not seen in models inferred 

from the strong-motion data. 

To estimate the stress drop for the regions of concentrated slip, we approximate their area with a circle and 

calculate the average slip amplitude within that circle 

(shaded circles, fig. 18). Using the stress-drop relation of 

Eshelby (1957) for a circular fault, Ao=7npii/16a9 where 

p is the rigidity (3.4 x1o1 dyne/cm2), ii is the average 

dislocation, and a is the radius, we obtain the stress drops 

listed in table 5. For the entire fault rupture, the relation 

of Parsons and others (1988) is more appropriate for a 

long, buried strike-slip fault: Ao=Cp.ii/w, where w is the 

downdip fault width and C is a constant dependent on the 

fault-plane dimensions. Using -our fault dimensions, their 

results require that Czl .75. Setting w=17 km, we obtain 

the stress drops for all three inversions listed in table 5. 

In general, the rupture dimensions of significant slip 

agree well with the overall slip dimensions based on the 

active perimeter of the aftershock zone (Dietz and 

Ellsworth, 1990). This result is consistent with the observation of Mendoza and Hartzell (1988) that aftershocks 

commonly cluster along the margin of fault regions that 

underwent large coseismic slips. The regions of major 

slip in our model coincide with a region of relatively few 

aftershocks in the central part of the aftershock zone, although our model suggests less updip rupture than that 

inferred by Dietz and Ellsworth (1990) from the aftershock distribution alone. Thus, whereas the general features of the rupture can generally be inferred from 

aftershock activity, significant features of the rupture may 

be obscured in the aftershock patterns. The exact details 

of the aftershock pattern from the earthquake vary significantly, depending on the time period chosen for the analysis (for example, Dietz and Ellsworth, 1990, figs. 3a-3c). 

Therefore, we consider only larger (M>4.0) aftershocks, 

including those within the first 34 minutes after the main 

shock (Simila and others, 1990), and find that they tend to 

cluster around the major slip concentrations in our model 

(fig. 9C), particularly in the northwestern section of the 

fault. 

The use of three time windows (each of 0.7 s) allows 

several general observations about the rupture-velocity and 

slip-time history. We expect regions requiring a locally 

lower rupture velocity to make use of the later time windows so as to compensate for the lower, fixed rupture 

velocity. Likewise, regions with a higher rupture velocity 

would take advantage of only the first rupture window. 

Overall, in both the strong-motion and teleseismic inversions, slip in time window 1 dominates, and only minor 

slip occurs in time windows 2 and 3 (fig. 19) over much 

of the fault. This result implies that the rupture timing in 
STRONG-MOTION AND BROADBAND TELESEISMIC ANALYSIS OF THE EARTHQUAKE FOR RUPTURE PROCESS A259 

our model satisfies the data and that large variations in 

rupture velocity are unnecessary. In addition, a locally 

lower rupture velocity or somewhat longer slip duration 

may be evident along the outer northwestern margin of 

the northwestern asperity, in the same region where most 

M>4.0 aftershocks occurred. 

The concentration of most slip in time window 1 indicates that short slip durations (<I s) are preferred in our 

model at a given point on the fault, implying that only a 

small part of the entire rupture surface is slipping at any 

given time. For example, the section of the fault rupturing 

5 s after the nucleation time in figure 3 is shown as the 

shaded area within time window 1. Short slip durations, 

which have also been inferred for other earthquakes, have 

CONCLUSIONS 

From our analysis of the three inversions, we find a 

bilateral dislocation pattern, with two main regions of oblique slip: the first centered about 6 to 8 km northwest of 

the hypocenter at 11- to 13-km depth and the other centered at 7 to 9 km southeast of the hypocenter at 15- to 

16-km depth. The northwestern patch, which has a larger 

seismic moment, a larger average slip amplitude, and thus 

a higher overall stress drop (table 5), is the source of the 

largest observed strong-motion velocities, recorded about 

20 km northwest of the epicenter (see figs. 2, 11). Dominant radiation toward the northwest is also confirmed by 

the overall damage patterns and landslides concentrated 

an important implications for rupture mechanics (Heaton, in areas northwest of the epicenter (Benuska, 1990). Like1990). wise, an azimuthal dependence in the peak ground motions was observed by Boore and others (1989) (see fig. 

6), who noted a tendency for high residuals relative to 

predicted peak velocities at rock sites toward the northwest relative to all other azimuths. 

A We now compare our slip model with the other finitefault dislocation models for this earthquake (Beroza, 199 1 ; 

Hartzell and others, 1991; Steidl and others, 1991). Although significant differences in the amplitude and direction of slip vectors exist between our model and the others, 

they all agree remarkably well on the overall characteristics of this rupture. All researchers conclude that a bilateral rupture with relatively low slip updip from the 

hypocenter best explains the waveforms, and researchers 

DISTANCE ALONG STRIKE, IN KILOMETERS 

Figure 19.-Northwest-southeast cross section of model fault (fig. 31, 

showing contours of oblique slip predicted from strong-motion inversion for time windows 1 (A), 2 (B), and 3 (Q. Contour interval, SO cm. 

Star, hypocenter of 1989 Lorna Prieta earthquake. 

find that most slip occurred on two relatively small patches 

nearly equidistant from the hypocenter, one to the northwest and the other to the southeast. All studies indicate 

that a fairly uniform rupture velocity of approximately 80 

percent of the local shear-wave velocity, together with a 

relatively short slip duration at arry point (s1.5 s) best 

explains the observed waveforms. 

Although our model is similar in most respects to the 

others presented in this chapter, it differs substantially in 

two aspects. First, the local rake vectors vary significantly 

among the models discussed below. On average, the rake 

vectors of about 145' in the area southeast of the hypocenter agree between our model and that of Hartzell and 

others (1991). Both of these models have similar oblique 

rake components in the northwestern asperity. In contrast, 

the southeastern asperity in the models of Beroza (1991) 

and Steidl and others (1991) shows rake angles indicating 

nearly pure strike slip (rake, -160'-170Â° yet they have 

almost pure thrusting rake vectors (80'-90') within the 

northwestern asperity, These two models require an approximately 80' change in rake vector from the south half 

to the north half of the fault and no corresponding change 

in dip. We emphasize that, although the slip distributions 

of Beroza (199 1) and Hartzell and others (1 99 1) look similar, the rake vector in the region of dominant slip for 

these models (the southeastern asperity) differs by about 
A260 MAIN-SHOCK CHARACTERISTICS 

40' and would likely produce substantially different nearfield ground motions. 

Second, in addition to variation in the local rake directions, the partitioning of total slip along strike in asperities northwest and southeast of the epicenter in our model 

requires more slip in the northwestern asperity (figs. 5, 9, 

18; table 5); the other models require most of the slip in 

the southeastern asperity. Considering that rise times, rupture velocities, and source geometries are similar among 

the various models, disparities in the resulting slip distribution most likely reflect variations in the data sets employed. Other parameters being comparable, station 

coverage and weighting may be the most critical elements 

controlling the slip partitioning. A source of dominant 

radiation northwest of the epicenter is required by the 

strong-motion data used in our study (see fig. 2). In particular, the large coherent arrivals at stations SAR, LEX, 

and LGP require significant slip and directivity. A comparison of the waveform fits at station SAR by the various models is particularly revealing and reflects the 

differences in modeling strategy. 

The strategy adopted by Steidl and others (1991) was 

to obtain the largest possible azimuthal coverage by including stations out to 60 km. Thus, they modeled several 

distant stations to the north quite well, while doing a 

relatively poor job in fitting both waveform and amplitude at station SAR (fig. 2). They did not use stations 

LEX and LGP, which recorded the largest ground velocities, and so the wavefield at these ray parameters is 

downweighted relative to distant samples. If their Green's 

functions are adequate for these distant stations and ours 

prove iess than desirable at stations LEX, SAR, and LGP, 

then they have a more reasonable interpretation. A detailed study of aftershock recordings at the various 

stations is one way to resolve this particular issue, because local receiver structures can be recognized and the 

adequacy of the theoretical Green's functions may be 

examined. 

It is not so clear why the slip distribution of Beroza 

(1991) differs from ours. Although he did not use the 

vertical components of ground motion, his station selection in the northwestern section of the fault is similar to 

that in our study. Waveforms fits at his northwestern stations, however, show significant differences from those 

of our model. The differences in slip distribution may 

partly be due to differences in the applied Green's functions, as he suggested; we used the complete layeredspace solutions, whereas he used only geometric-ray 

approximations. Again, a comparison of near- and farfield Green's functions with simple aftershocks at stations 

SAR and other stations should help resolve this issue. 

Slip in the southeastern asperity is evidently constrained 

by the southeastern stations, as described in figure 11. We 

used station WAT (fig. 2) and a few of the Gilroy array 

stations. We observed that the other Gilroy array stations 

have complex receiver functions, and so we omitted these 

stations from our analysis. The data sets used in the other 

studies excluded station WAT and included additional stations from the Gilroy array. The use of a dense-set of 

stations over limited distance and azimuthal'iTanges provides redundant coverage and may favor slip in the southern section of the fault. 

Clearly, the teleseismic-waveform data have less resolving power along strike than the strong-motion data, as 

shown by comparison of the P and SH waveforms from 

this study and those of Hartzell and others (1991). Although the slip models differ considerably and are nearly 

northwest-southeast reversed, they produce nearly identical teleseismic waveforms, suggesting an absence of resolution from this data set. The teleseismic-waveform data, 

however, resolve updip directivity and require a bilateral 

rupture with little updip slip. Again, the differences in the 

teleseismic source models probably result from variations 

in station coverage. Hartzell and others (1991) used similar teleseismic stations to ours but added several additional stations, particularly in the northwestern and 

northeastern azimuths. These additional stations, however, 

do not substantially augment azimuthal coverage and may 

actually bias the results. Removal of these stations 

from their inversion results in a model similar to ours, 

favoring northwestern slip (S.H. Hartzell, oral commun., 

1990). 

We note that even though the slip distribution and rake 

vectors vary, the net result of any of these models will be 

nearly the same at long periods. This similarity can be 

explained by the fact that the bilateral rupture radiates 

from both asperities simultaneously. Thus, as long as the 

net rake vector and total seismic moment are preserved, 

the resulting models should produce similar and adequate 

teleseismic-waveform matches, though not necessarily for 

the near-field data. That the waveform comparisons for 

all the strong-motion models are less than remarkable may 

reflect the need for a more complex rupture surface than 

the idealized flat-planar models used here. 

In general, the rupture process of the 1989 Loma Prieta 

earthquake was fairly simple for an Mz7.1 earthquake, 

rupturing only a relatively short (~35 km long) fault segment (Kanamori and Satake, 1990). The relatively short 

duration of strong motion is partly attributable to the bilateral rupture. Furthermore, the relatively great depth of 

slip concentrations moderated the amplitude of ground 

velocities in the near-source region. 

Most of our current knowledge of fault-asperity characteristics has been derived from ground-motion frequencies lower (el Hz) than the frequency range of most 

interest in earthquake engineering. Wald and others (1987, 

1988) found that large-scale asperity models derived from 

longer-period velocity data also explained many characteristics of the higher-frequency accelerograms. Our results here indicate that the asperities which control 
STRONG-MOTION AND BROADBAND TELESEISMIC ANALYSIS OF THE EARTHQUAKE FOR RUPTURE PROCESS A261 

broadband teleseismic waveforms (3-30 s) also dominate 

higher-frequency strong motions (1-5 s). 

In an effort to understand the radiation of the higherfrequency motions during the 1989 Loma Prieta earthquake, we performed an inversion with the observed and 

synthetic seismograms bandpass filtered from 0.1 to 3 Hz. 

We used a finer discretization of the fault plane into 200 

subfaults, each with dimensions of 2.0 km along strike 

and 2.0 km downdip. We also reduced the duration of the 

source-time function to 0.5 s. Our results indicate that the 

same regions of large slip which control the longer-period 

teleseismic waveforms and the strong-motion velocities 

as high as 1 Hz are also responsible for higher-frequency 

(>l .O Hz) radiation. We also note that the inversion using 

higher-frequency data appears to favor slightly more concentrated asperities. Understanding the relation between 

long-period source models of large earthquakes and the 

radiation of high frequencies is critical for a prediction of 

ground motions in the frequency range of engineering interest. Our future work will address the characteristics of 

the high-frequency radiation further. Such study will require more sophisticated timing corrections based on the 

aftershock data recorded at many of the strong-motion 

stations used here, as well as a more detailed treatment of 

the variations in propagation paths and site effects at individual stations. 

ACKNOWLEDGMENTS 

This work was supported by the U.S. Geological Survey under contracts 14-08-0001-2 19 12 and 14-08-0001- 

G 1 832. Reviews by Hiroo Kanamori, Paul Somerville, 

Paul Spudich, and Lisa Wald improved the manuscript. 

We thank Steve Hartzell for useful discussions and advice 

on the use of his inversion software, and Norm 

Abrahamson and Nancy Smith for providing programs to 

compute the response-spectral bias. 

REFERENCES CITED 

Abrahamson, N.A., Somerville, P.G., and Cornell, C.A., 1990, Uncertainty in numerical strong motion predictions: U.S. National Conference on Earthquake Engineering, 4th, Palm Springs, Calif., 1990, 

Proceedings, v. 1, p. 407-416. 

Archuleta, R.J., 1984, A faulting model for the 1979 Imperial Valley, 

California, earthquake: Journal of Geophysical Research, v. 89, no. 

B6, p. 4559-4585. 

Benuska, Lee, ed,, 1990, Loma Prieta earthquake reconnaissance report: 

Earthquake Spectra, v. 6, supp. 90-01, 448 p. 

Beroza, G.C., 1991, Near-source modeling of the Loma Prieta earthquake; evidence for heterogeneous slip and implications for earthquake hazards: Seismological Society of America Bulletin, v. 81, 

no. 5, 81, p. 1603-1621. 

Beroza, G.C., and Spudich, Paul, 1988, Linearized inversion for fault 

rupture behavior; application to the 1984 Morgan Hill, California, 

earthquake: Seismological Society of America Bulletin, v. 93, no. 

B6, p. 6275-6296. 

Boore, D.M., Seekins, L.C., and Joyner, W.B., 1989, Peak accelerations 

from the 17 October 1989 Loma Prieta earthquake: Seismological 

Research Letters, v, 60, no. 4, p. 15 1-166. 

Choy, G.L., and Boatwright, John, 1990, Source characteristics of the 

Loma Prieta, California, earthquake of October 18, 1989 from global digital seismic data: Geophysical Research Letters, v. 17, no. 8, 

p. 1183-1186. 

Dietz, L.D., and Ellsworth, W.L., 1990, The October, 17, 1989, Lorna 

Prieta, California, earthquake and its aftershocks; geometry of the 

sequence from high-resolution locations: Geophysical Research Letters, v. 17, no. 9, p. 1417-1420. 

Eshelby, J.D., 1957, The determination of the elastic field of an ellipsoidal inclusion, and related problems: Royal Society of London Proceedings, ser. A, v. 241, no. 1226, p. 376-396. 

Futterman, W.I., 1962, Dispersive body waves: Journal of Geophysical 

Research, v. 67, no. 13, p. 5279-5291. 

Hartzell, S.H., and Heaton, T.H., 1983, Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of 

the 1979 Imperial Valley, California, earthquake: Seismological 

Society of America Bulletin, v. 73, no. 6, pt. A, p. 1553-1583. 

1986, Rupture history of the 1984 Morgan Hill, California, earthquake from the inversion of strong motion records: Seismological 

Society of America Bulletin, v. 76, no. 3, p. 649-674. 

Hartzell, S.H., and Iida, Mashiro, 1990, Source complexity of the 1987 

Whittier Narrows, California, earthquake from inversion of strong 

motion records: Journal of Geophysical Research, v. 95, no. B8, p. 

12475-12485. 

Hartzell, S.H. and Mendoza, Carlos, 1991, Application of an iterative 

least-squares waveform inversion of strong motion and teleseismic 

records to the 1978 Tabas, Iran, earthquake: Seismological Society 

of America Bulletin, v. 8 1, no. 2, p. 305-331. 

Hartzell, S.H., Stewart, G.S., and Mendoza, Carlos, 1991, Comparison 

of L, and L2 norms in a teleseismic inversion for the slip history of 

the Loma Prieta, California, earthquake: Seismological Society of 

America Bulletin, v. 81, no 5, p. 1518-1539. 

Heaton, T.H., 1982, The 1971 San Fernando earthquake; a double event?: 

Seismological Society of America Bulletin, v. 72, no. 6, p. 2037- 

2062. 

1990, Evidence for and implications of self-healing pulses of 

slip in earthquake rupture: Physics of the Earth and Planetary Interiors, v. 64, no. l, p. 1-20. 

Heaton, T.H., and Heaton, R.E., 1989, Static deformations from point 

forces and force couples located in welded elastic Poissonian halfspaces; implications for seismic moment tensors: Seismological Society of America Bulletin, 79, no. 3, p. 813-841. 

Jennings, C.W., compiler, 1975, Fault map of California, with locations 

of volcanoes, thermal springs, and thermal wells: California Division of Mines and Geology Geologic Data Map 1, scale 1 :750,000. 

Kanamori, Hiroo, and Satake, Kenji, 1990, Broadband study of the 1989 

Loma Prieta earthquake: Geophysical Research Letters, v. 17, no. 

8, p. 1179-1 182. 

King, G.C.P., Lindh, A.G., and Oppenheimer, D.H., 1990, Seismic slip, 

segmentation, and the Loma Prieta earthquake: Geophysical Research Letters v. 17, no. 9, p. 1449-1452. 

Langston, C.A., and Helmberger, D.V., 1975, A procedure for modelling shallow dislocation sources: Royal Astronomical Society Geophysical Journal, v. 42, no. 1, p. 117-130. 

Lisowski, Michael, Prescott, W.H., Savage, J.C., and Johnston, M.J.S., 

1990, Geodetic estimate of coseismic slip during the 1989 Loma 

Prieta, California, earthquake: Geophysical Research Letters, v. 17, 

no. 9, p. 1437-1440. 

Maley, R.P., Acosta, A.V., Ellis, F., Etheredge, E.C., Foote, L.J., 

Johnston, D.A., Porcella, R.L., Salsman, M.J., and Switzer, J.C., 

1989, U.S. Geological Survey strong-motion records from the north- 
A262 MAIN-SHOCK CHARAC'IERISTICS 

ern California (Loma Prieta) earthquake of October 17, 1989: U.S. 

Geological Survey Open-File Report 89-568, 85 p. 

Mendoza, Carlos, and Hartzell, S.H., 1988, Aftershock patterns and 

main shock faulting: Seismological Society of America Bulletin, v. 

78, no. 4, p. 1438-1449. 

Olson, A.H. and Apsel, R.J., 1982, Finite faults and inverse theory with 

application to the 1979 Imperial Valley earthquake: Seismological 

Society of America Bulletin, v. 72, no. 6, p. 1969-2001. 

Olson, A.H., Orcutt, J.A., and Frazier, G.A., 1984, The discrete wave 

numberlfinite element method for synthetic seismograms: Royal 

Astronomical Society Geophysical Journal, v. 77, no. 2, p. 421- 

460. 

Olson, J.A., 1990, Seismicity in the twenty years preceding the Loma 

Prieta, California earthquake: Geophysical Research Letters, v. 17, 

no. 9, p. 1429-1432. 

Oppenheimer, D.H., 1990, Aftershock slip behavior of the. 1989 Loma 

Prieta, California earthquake: Geophysical Research Letters, v. 17, 

no. 8, p. 1199-1202. 

Parsons, I.D., Hall, J.F., and Lyzenga, G.A., 1988, Relationships between the average offset and the stress drop for two- and threedimensional faults: Seismological Society of America Bulletin, v. 

78, no. 2, p. 931-945. 

Ponti, D.J., and Wells, R.E., 1991, Off-fault ground ruptures in the 

Santa Cruz Mountains, California; ridge-top spreading versus tectonic extension during the 1989 Loma Prieta earthquake: Seismological Society of America Bulletin, v. 81, no. 5, p. 1480-1510. 

Schwartz, S.Y., Orange, D.L., and Anderson, R.S., 1990, Complex fault 

interactions in a restraining bend on the San Andreas Fault, southern Santa Cruz Mountains, California: Geophysical Research Letters, v. 17, no. 9, p. 1207-1210. 

Seeber, Leonardo, and Armbruster, J.G., 1990, Fault kinematics in the 

1989 Loma Prieta rupture area during 20 years before that event: 

Geophysical Research Letters, v, 17, no. 9, p, 1425-1428. 

Shakal, A.F., Huang, M.J., Reichle, Michael, Ventura, C.E., Cao, T.Q., 

Sherburne, R.W., Savage, M., Darragh, R.B., and Petersen, C., 1989, 

CSMIP strong-motion records from the Santa Cruz Mountains (Loma 

Prieta), California earthquake of 17 October 1989: California Division of Mines and Geology, Office of Strong Motion Studies Report OSMS 89-06, 196 p. 

Simila, G.W., McNally, K.C., Nava, E., Protti-Quesada, M., and Yellin, 

Joseph, 1990, Evidence of very early aftershock activity along the 

northwest portion of the 18 October 1989 earthquake rupture zone: 

Geophysical Research Letters, v. 17, no. 10, p. 1785-1788. 

Steidl, J.H., Archuleta, R.J., and Hartzell, S.H., 1991, Rupture history 

of the 1989 Loma Prieta, California, earthquake: Seismological Society of America Bulletin, v. 81, no, 5, p. 1573-1602. 

Stover, C.W., Reagor, B.G., Baldwin, F.W., and Brewer, L.R., 1990, 

Preliminary isoseismals map for the Santa Cruz (Loma Prieta), California, earthquake of October 18, 1989 UTC: U.S. Geological Survey Open-File Report 90-18, 24 p. 

U.S. Geological Survey staff, 1990, The Loma Prieta, California, earthquake; an anticipated event: Science, v. 247, no. 4940, p. 286-293. 

Wald, D.J., Burdick, L.J., and Somerville, P.G., 1988, Simulation of 

acceleration time histories close to large earthquakes, in Von Thun, 

J.L., ed., Proceedings; Earthquake Engineering and Soil Dynamics 

11; recent advances in ground-motion evaluation: American Society 

of Civil Engineers Geotechnical Special Publication 20, p. 430- 

444. 

Wald, D.J., Helmberger, D.V., and Hartzell, S.H., 1990, Rupture process of the 1987 Superstitions Hills earthquake from the inversion 

of strong-motion data: Seismological Society of America Bulletin, 

v. 80, no. 5, p. 1079-1098. 

Wald, D.J., Helmberger, D.V., and Heaton, T.H., 1991, The rupture 

initiation process of a large earthquake; Loma Prieta [abs.]: Seismological Research Letters, v. 62, no. 1, p. 29. 

Wald, D.J., Somerville, P.G., and Helmberger, D.V., 1987, Compatibility of accelerograms of the 1979 Imperial Valley earthquake with 

slip-distribution asperity models Labs.]: Seismological Research Letters,~. 58,no. 1,p. 10. 

Wallace, T.C., Velasco, A.A., Zhang, Jiajun, and Lay, Thorne, 1991, A 

broadband seismological investigation of the Lorna Prieta, California, earthquake; evidence for deep slow slip?: Seismological Society of America Bulletin, v. 81, no. 5, p. 1622-1646. 

Working Group on California Earthquake Probabilities, 1988, Probabilities of large earthquakes occurring in California on the San Andre~ Fault: U.S. Geological Survey Open-File Report 88-398, 62 p. 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUA= OCCURRENCE 

MAIN-SHOCK CHARACTERISTICS 

COSEISMIC DISPLACEMENTS MEASURED WITH THE GLOBAL 

POSITIONING SYSTEM 

CONTENTS 

By Chesley R. Williams and Paul Segall, 

Stanford University 

Abstract .................................................................... 

Introduction ............................................................... 

Data collection ........................................................... 

Data analysis ............................................................. 

GpS measurement errors ............................................... 

Preemhqu&e survey ............................................. 

Postemhqu&e survey ............................................ 

Coseismic displacements ............................................... 

Conclusions ............................................................... 

Acknowledgments ....................................................... 

References cited ......................................................... 

Page 

A263 

263 

264 

265 

269 

269 

27 1 

27 1 

274 

274 

274 

ABSTRACT 

Coseismic displacements during the 1989 Loma Prieta 

earthquake were measured with the Global Positioning 

System (GPS). During February and March 1989, the California Department of Transportation (Caltrans) conducted 

a GPS survey in the Santa Cruz, Calif., area and southward to Watsonville, using single-frequency Trimble 

4000SL GPS receivers. In March 1990, we reoccupied 

eight of the Caltrans stations with dual-frequency Trimble 

4OOOSDT GPS receivers. Relative displacements were determined by differencing the two sets of station coordinates obtained from the preearthquake and postearthquake 

GPS surveys. During both surveys, U.S. Geological Survey GPS receivers were collecting data on Loma Prieta at 

station LPl. Incorporation of these data allowed us to tie 

the relative displacements in the local network to the 

coseismic displacement of station LPl determined by GPS 

measurements from the very long baseline interferometry 

site at Fort Ord, Calif, The peak horizontal displacement 

is 41.3k1.9 cm, and the peak vertical displacement is 

34.1k2.7 cm. The uncertainty in the observed displacements is dominated by the Caltrans survey because the 

data are single frequency and the observation sessions 

were short in duration (15-90 minutes). Examination of 

repeated baseline measurements indicates that the precision of the preearthquake data is 1 cm in the horizontal 

components and 3.5 cm in the vertical components. Because our data were collected with dual-frequency receivers during 6-hour sessions, errors in the postearthquake 

survey are significantly smaller (0.5 cm in the horizontal 

components and 2-3 cm in the vertical components). 

INTRODUCTION 

The 1989 Loma Prieta earthquake was the largest to 

occur in northern California since the great 1906 San Francisco earthquake, which geologic and geodetic data indicated was a vertical right-lateral strike-slip event (Lawson, 

1908). It was assumed that crustal deformation in the Santa 

Cruz Mountains resulted solely from strike-slip motion 

along a vertical San Andreas fault, but this assumption is 

clearly invalid. The 1989 earthquake exhibited large components of both right-lateral strike slip and reverse slip. 

The focal mechanism and aftershock distribution for this 

earthquake indicate that the rupture occurred on a 70' 

SW dipping plane (Dietz and Ellsworth, 19901, suggesting that the earthquake occurred on a different fault from 

that in 1906 and that crustal deformation in the Santa 

Cruz Mountains involves complex fault interactions 

(Olson, 1990; Segall and Lisowski, 1990). 

To effectively assess the seismic hazards in the Santa 

Cruz Mountains, a more complete understanding of crustal 

deformation in the region is needed. The first step is to 

examine the deformation associated with the 1989 Loma 

Prieta earthquake by determining the surface displacements, which will provide important constraints on fault 

geometry and slip distribution. The earthquake occurred 

within a region where the U.S. Geological Survey (USGS) 

maintains a geodetic network that was reoccupied shortly 

after the earthquake; coseismic displacements were reported by Lisowski and others (1990). The USGS has 

occupied stations throughout the San Francisco Bay region for 25 years using electronic distance measurement 

(EDM) and during the past 10 years using the Global Positioning System (GPS). For 15 years, the U.S. National 

Aeronautics and Space Administration (NASA) and the 

U.S. National Geodetic Survey (NGS) have also occupied 

stations in the region, using very long baseline interfer- 
A264 MAIN-SHOCK CHARACTERISTICS 

ometry (VLBI) (Clark and others, 1990). These VLBI measurements provide changes in station coordinates (displacements) relative to sites on "stable" North America, far 

removed from effects of the earthquake. EDM provides 

information about the distance between stations, whereas 

GPS allows high-precision determinations of the threedimensional vectors between stations. In addition, leveling bench marks were reoccupied after the earthquake. 

These data provide information about relative vertical 

coseismic displacements throughout the Santa Cruz Mountains, including the epicentral region (Marshall and others, 1991). Both VLBI and GPS data provide displacements 

relative to sites outside the deformation zone of the earthquake. We refer to the displacements determined relative 

to such sites as "absolute," and to the displacements determined relative to local sites as "relative." 

This study was undertaken to determine coseismic displacements in the epicentral region west of the San Andreas fault, where the USGS network was sparse. Shortly 

after the earthquake, we learned that the California Department of Transportation (Caltrans) had performed a GPS 

survey in the epicentral region during February and March 

1989. We reoccupied eight of their stations with GPS receivers in March 1990 (fig. 1). Relative displacements are 

determined by differencing the preearthquake and 

postearthquake station coordinates. We can obtain absolute displacements by incorporating data collected at Loma 

Prieta (sta. LPl, fig. 1) during both the preearthquake and 

postearthquake surveys. The displacement of station LPl 

is determined relative to the VLBI site at Fort Ord, Calif. 

We have calculated the precision of our relative displacements through a statistical examination of repeated measurements and found it to be within l to 2 cm for the 

horizontal components and within 3 to 4 cm for the vertical components. 

DATA COLLECTION 

During February and March 1989, 7 months before the 

earthquake, Caltrans conducted an extensive GPS survey 

in the Santa Cruz-Watsonville area (fig. 1). The Caltrans 

survey consisted of 36 stations, which were occupied with 

single-frequency Trimble 4000SL GPS receivers during 

multiple sessions of 15 to 90 minutes. The Caltrans data 

used in this project are listed in table 1. Because this 

survey was made in the epicentral region on the hangingwall block, the coseismic displacements were expected to 

be much larger than the noise level in this short-session, 

single-frequency data set. In March 1990, we reoccupied 

eight of these Caltrans stations to determine the 

postearthquake relative coordinates. The stations were chosen to provide the widest distribution across the region, 

with five stations in a line parallel and four stations in a 

line perpendicular to the fault (fig. 1). The Stanford GPS 

data were collected on dual-frequency Trimble 4OOOSDT 

receivers during the 6-hour sessions (table 2). Relative 

coseismic displacements were calculated by comparing 

the relative coordinates of the stations before and after the 

earthquake. 

During both the preearthquake and postearthquake surveys, the USGS collected data on Loma Prieta at station 

LPl (fig. 1) with a dual-frequency TI4100 receiver (table 

3). Station LPl is part of an extensive USGS geodetic 

network that allows us to tie the Santa Cruz network to 

stations which were not disturbed by the earthquake. GPS 

measurements from stations LPl to Brush2 (Fort Ord) 

before and after the earthquake enabled us to determine 

the motion of station LPl relative to the absolute, VLBIderived coseismic displacement of Fort Ord (Clark and 

others, 1990). Absolute displacements within the Santa 

Cruz network are determined by using this displacement 

for station LPl. 

An important part of the data collection is centering the 

GPS antenna on the tripod directly over the bench mark 

and measuring the vertical distance between the antenna 

and the bench mark. We used a rotating optical plumb to 

center the tripod over the bench mark. The antenna was 

leveled by using a sensitive bubble in a rotating carrier 

that clamps into the tribrach. To center and level the antenna, both Caltrans and USGS used bayonets, with bull'seye leveling bubbles, that extended from the top of the 

tripod directly down to the bench mark. We determined 

the antenna height by measuring the slant height from the 

station marker to the top of the antenna ground plane. As 

a check, we also measured the vertical height from the 

bench mark to the base of the antenna adapter, Adding the 

height between the antenna adapter and the top of the 

ground plane (0.355 m) yields an independent measure of 

the antenna height (fig. 2). Vertical height and slant height 

were measured in both inches and meters. Caltrans measured antenna height by using a Wild height hook, whereas 

the USGS measured the slant height in both inches and 

meters before and after the data collection. 

GPS measurements determine the intersite vector between the electrical phase centers of the two antennas. 

These phase centers commonly are offset vertically from 

the physical top of the antenna and may also be offset 

horizontally from the antenna center. If identical antennas 

are used, the phase-center offsets cancel; however, if different antennas are used, the relative phase-center offset 

must be known. The preearthquake survey used Trimble 

4000SL antennas except at station LPl (fig. I), which 

was occupied by a TI-4100 antenna. The postearthquake 

survey used Trimble 4OOOSDT antennas except at station 

LPl, which was again occupied by a TI-4100 antenna. 

Thus, the displacement of station LPl relative to the Santa 

Cruz network stations will depend on the phase-center 

offsets. We have used the vertical offsets reported by 

Gurtner and others (19891, with the following exception: 
COSEISMIC DISPLACEMENTS MEASURED WITH THE GLOBAL POSITIONING SYSTEM A265 

We assume that the Ll and L2 phase centers of the TI4100 antenna are 0.227 and 0.212 m, respectively, above 

the antenna base (Prescott and others, 1989). Because we 

recorded the antenna height to the top of the antenna 

ground plane for the Trimble antennas, we obtain an Ll 

vertical offset of -0.007 m and an L2 offset of +0.011 m 

for the dual-frequency Trimble 4000SDT antenna, and an 

Ll offset of -0.015 m for the single-frequency Trimble 

4000SL antenna. We make no correction for horizontal 

phase-center offsets because these offsets are considerably smaller and less well determined. The tie between 

Loma Prieta (sta. LP1) and the Santa Cruz sites is sensitive to the relative offset between the TI-4100 and Trimble 

antennas, whereas the displacements between the Santa 

Cruz sites are independent of the antenna offsets. 

DATA ANALYSIS 

The preearthquake data were processed together in a 

network solution. The USGS data collected at station LP1 

(fig. 1) on March 1, 1989, and all of the Caltrans data 

-3 \ '\ ' 

3 , MONTEREY BAY, 1, 

<-rt \ 

\ \ ' \ s 

EXPLANATION 

Magnitude 

00 o+ 

Figure 1.-Loma Prieta region, Calif., showing locations of major faults (thin irregular lines, dashed where inferred, queried where uncertain) and 

Global Positioning System stations (triangles) used to determine coseismic displacements near epicenter of 1989 earthquake (star). Solid triangles, 

stations occupied by California Department of Transportation (Caltrans) before earthquake and by us after earthquake. Stations Moe and H36A were 

occupied by Caltrans and used to strengthen preearthquake solution but were not reoccupied after earthquake; station LP1 was occupied by U.S. 

Geological Survey (USGS) during preearthquake and postearthquake surveys, and data from station LP1 were used to tie Santa Cruz network to 

USGS network. Numbers denote number of times baselines were measured during preearthquake survey; lines without numbers were measured only 

once. 
MAIN-SHOCK CHARACTERISTICS 

Table 1 .-Preearthquake Global Positioning System data collected by the California Department of Transportation with single-frequency Trimble 4000SL receivers 

[Sampling interval, 15 s. Antenna height is vertical distance measured form bench mark to antenna's electrical phase center] 

Date JL$ Station Start time Stop time Number of (fig. 1) (G.m.t.) (G,m.t.) satellites 

Fcb. 27, 1989 

Fcb. 28, 1989 

Mar. 1, 1989 

Mar. 2, 1989 

Mar. 3, 1989 

Mar. 8, 1989 

Mar. 9, 1989 

Mar. 10, 1989 

Mar. 1 1, 1989 

Crowell 

H3 6A 

Pajaro3 

Porter 

H3 6A 

Leon 

Porter 

Traill 

Crowell 

Leon 

Pajaro3 

Traill 

H3 6A 

R121 

H3 6A 

R121 

Leon 

R121 

Leon 

Leon 

Porter 

Moe 

Porter 

Moe 

Porter 

Moe 

Crowell 

Traill 

Crowell 

R5 7 

Traill 

Crowell 

R57 

Traill 

Crowell 

Traill 

Cliff 

Crowell 

Cliff 

Crowell 

Cliff 

Crowell 

Cliff 

Crowell 

Cliff 

Crowell 

Porter 

Traill 

Cliff 

Crowell 

Moe 

Traill 

Cliff 

Crowell 

Traill 

Cliff 

Crowell 

Cliff 

Crowell 
COSEISMIC DISPLACEMENTS MEASURED WITH THE GLOBAL POSITIONING SYSTEM 

Table 2.-Postearthquake Global Positioning System data collected by Stanford University with dual-frequency Trimble 4000SDT receivers 

[Sampling interval, 15 s. Antenna height is vertical distance measured from bench mark to top of antenna ground plane] 

Date Juan Station St time St ti height Number of 

day (fig. 1) (G.m.t.) (G.m.t.) (m) satellites 

Mar. 28, 1990 8 6 

8 6 

8 6 

8 6 

Mar. 29, 1990 8 7 

8 7 

8 7 

8 7 

Mar. 30, 1990 88 

88 

88 

88 

Leon 

Pajar03 

Porter 

R121 

Crowell 

Porter 

R5 7 

Traill 

Cliff 

Crowell 

Porter 

Traill 

Table 3.-Global Positioning System data collected by U.S. Geological Survey with dual-frequency TI-400 

receivers 

[Sampling interval, 30 s. Antenna height is vertical distance measured from benchmark to base of antenna preamplifier] 

Date Julan Station St time St time 'Eight Number of 

day (fig. 1) (G.m.t.) (G.m.t.) (m) satellites 

Mar. 1, 1989 60 LP1 3:34 11:ll 1.7579 7 

Mar. 30, 1990 88 LP1 2: 12 7:49 1.4926 8 

Antenna phase center 

Antenna ground plane 

Antenna 

height 

Bench mark 

* - Antenna er correction ground plane 

height 

Vertical 

P? S.,nt 

/ height 

Antenna radius 

correction Hei@t F 

I 'slant 

Vertical ' height 

height I / 

Figure 2.-Diagram showing how antenna height was determined in postearthquake survey. Both slant height and vertical height were measured, and 

height correction was added to field-measured height to give height to top of antenna ground plane. Vertical distance from bench mark to antenna 

ground plane was used as antenna height. Phase-center correction, which is included in processing, is defined as offset between center of antenna 

ground plane and antenna's electrical phase center. 
A268 MAIN-SHOCK CHARACTERISTICS 

were used, except those collected at station Pajaro3 during session 581, the results from which yield unreasonable height changes at station Pajaro3, and so we believe 

that the antenna height (2.913 m) may be in error. For the 

postearthquake solution, all of the Stanford data plus the 

USGS data collected at station LP1 on March 30, 1990, 

were combined in a single network solution. In both solutions, the coordinates of station LP1 were fixed, and the 

coordinates of the other stations were estimated relative 

to station LP1. 

We processed the GPS data from the preearthquake and 

postearthquake surveys by using the Bernese GPS analysis software, version 3.2, with broadcast orbits. Because 

the scale of the Santa Cruz network is less than 35 km 

and broadcast orbits are believed to have a precision of 

-5 parts in lo7 or better (Hager and others, 1991), the 

error in the longest baselines due to orbital error should 

be 517.5 mm. We show below that the coseismic displacements in the epicentral region are approximately hundreds of millimeters, and so the error introduced by using 

broadcast orbits is comparatively small. 

The satellite clock errors are approximated by polynomials in time by using the coefficients sent as part of the 

navigation message from the satellite. Receiver clock corrections were determined at each epoch by using CIA 

code pseudorange, and residual satellite and receiver clock 

errors were eliminated by double-differencing the carrier 

phase. In processing the postearthquake survey, receiver 

clock corrections and initial coordinates were determined 

simultaneously from the CIA code pseudorange data. Because the short sessions of the preearthquake Caltrans data 

did not provide enough information to estimate position 

and receiver clock errors simultaneously, we estimated 

the clock corrections while constraining the receiver coordinates to the postearthquake survey positions. The 

coseismic displacements are negligible relative to the error in the pseudorange-determined coordinates and may 

safely be neglected in determining receiver clock corrections. 

Before further parameter estimation, single-difference 

phase files were created and cleaned of carrier-beat-phase 

cycle slips and outliers, using both automatic and manual 

programs. All the single-difference files were visually inspected to ensure that they were "clean." The station coordinates, tropospheric zenith delay, and integer-phase 

ambiguities were estimated by using double-differenced 

carrier-phase observations. During these estimations, a 20' 

elevation cutoff angle was used to minimize antenna 

multipath effects. The propagation delay due to the troposphere, which depends on temperature, humidity, and pressure, was estimated in the solution by using the 

atmospheric-zenith-delay model of Saastamoinen (1972). 

Zenith-delay parameters were estimated at each station 

for each day. Each integer-phase ambiguity was estimated 

as a real number and fixed to the closest integer if one 

and only one integer was within 30 of the estimate, where 

CJ is the larger of either the formal error of the estimated 

ambiguity or 0.05 cycle. Then, the remaining parameters 

(station coordinates and tropospheric parameters) were reestimated. Fixing ambiguities to their integer values can 

significantly strengthen the solution (for example, Davis 

and others, 1989). 

The ionosphere affects the GPS results in two ways: as 

a differential delay when the GPS signals pass through 

ionosphere with a different free-electron density, and as a 

systematic shortening due to an overall lensing effect of 

the ionosphere. First-order ionospheric effects can be eliminated by forming a linear combination of the two carrier 

frequencies. Because the Caltrans data had been collected 

with single-frequency receivers, the ionospheric delay 

could not be removed in the preearthquake survey. 

Georgiadou and Kluesberg (1988) found the lensing effect of the ionosphere to be 0.6 ppm for baselines ranging 

in length from 10 to 30 km. Because the longest baselines 

in the Caltrans network are 30 km long, the error in the 

baselines due to the ionosphere might be -18.0 mm. Although the 1989 Caltrans survey was close to a solar maximum, the data were collected during the night, when the 

ionosphere is more stable and the electron density is low. 

This circumstance suggests that variations in the ionosphere may have been small across the network and that 

the lensing effects may have been minimal. Indeed, the 

difference between single- and dual-frequency results from 

an 8-km-long permanent GPS baseline across the Hayward 

fault are very small when the observing sessions are at 

night (N. King, oral commun., 1991). 

The short station occupations used by Caltrans (15-90 

minutes) makes it difficult to resolve the integer-phase 

ambiguities. To strengthen the network solution for the 

preearthquake survey, data from two additional stations 

(Moe, H36A, fig. 1) were incorporated into the analysis, 

even though they were not occupied after the earthquake. 

Including stations Moe and H36A in the network solution 

allowed us to include more data and to form shorter singledifference baselines. 

Repeated GPS measurements into Loma Prieta indicate 

that during the March 1, 1989, survey, the antenna was 

set up -2.8 cm to the east of the bench-mark center (Mark 

Murray, oral commun., 1991). We have corrected for this 

offset in our analysis. 

The postearthquake data were degraded by the implementation of selective availability (SA) by the U.S. Department of Defense. SA involves the addition of random 

noise and offset in the clocks of Block I1 satellites. In 

differential GPS, the SA effects are eliminated as long as 

the two receivers simultaneously sample the phase. All 

the stations, except LP1 (fig. I), were occupied with 

Trimble 4000SDT receivers. Station LP1 was surveyed 

with a TI-4100 receiver, and so the tie to station LP1 was 

degraded by SA effects. In the processing, we eliminated 
COSEISMIC DISPLACEMENTS MEASURED WITH THE GLOBAL POSITIONING SYSTEM A269 

the data from satellite PRN 19, the only Block I1 satellite 

observed at station LP1. We also did not use any data 

from satellite PRN 13 on March 29, 1990, because the 

satellite was repositioned on this day. 

Despite the problems in both surveys, nearly all of the 

integer-phase ambiguities were resolved, and the rms residuals of single differences were less than 1 cm. From 

the preearthquake survey, 136 of the 137 ambiguities were 

fixed to integers, and for the postearthquake survey, 53 of 

the 54 could be fixed to integers. The rms residual of 

single differences for the preearthquake survey was 6.3 

mm with 25,73 1 double-difference phase observations, and 

for the postearthquake survey, 4.0 mm with 32,216 phase 

observations. 

GPS MEASUREMENT ERRORS 

PREEARTHQUAKE SURVEY 

Uncertainties in the Caltrans preearthquake survey dominate the errors in the estimated coseismic displacements 

because the data are single frequency and the observation 

sessions were short. Fortunately, Caltrans reoccupied some 

of their stations (fig. 1) many times. When more than two 

stations were occupied simultaneously, the shortest 

baselines were used to form the single differences. We 

note that the baselines in the northwestern part of the 

network were measured many more times than those in 

the southeastern part, and so the southeastern stations are 

not so well tied into the network. 

Two baselines were measured many more times than 

the rest: Crowell to Cliff and Crowell to Traill (fig. 1). 

The baseline Crowell to Cliff was measured nine times, 

whereas the baseline Crowell to Traill was measured eight 

times. Each of these observations was reprocessed independently in special single-difference solutions. The scatter of the repeated measurements about the preearthquake 

network solution was utilized to determine the precision 

of the data. Each measurement was processed in two ways: 

once by estimating the integer-phase ambiguities, and a 

second time by fixing the ambiguities to those determined 

in the network solution. Because many of the observation 

sessions were so short, not all of the integer-phase ambiguities could be resolved for individual sessions. Therefore, when integer-phase ambiguities are estimated, the 

session solutions show a larger scatter about the network 

solution and have larger formal errors. 

The network and session solutions for the repeated measurements of the baselines Crowell to Cliff and Crowell 

to Traill are plotted in figure 3. The scatter in the sessiondetermined-ambiguity solutions is a pessimistic estimate 

of the precision of the final network solution because far 

fewer data were utilized in the parameter determinations. 

In figure 3B, the session-determined-ambiguity solution 

for session 583 has very large error bars because so few 

data were obtained during this session and few of the 

integer-phase ambiguities were resolved. Also in figure 

3B, the session-determined-ambiguity solution for session 

671 is an obvious outlier in all components except the 

vertical. Examining the scatter in the session-determinedambiguity solutions gives a good estimate of the precision 

of the baselines that were repeatedly measured only a few 

times and for which few data are available, such as the 

baselines in the southeastern part of the network, 

Most of the integer ambiguities were fixed in the network solution, and so it is much stronger. Fixing the ambiguities to those determined by the network solution 

should give a reasonable estimate of the precision of the 

network solution. In this case, the scatter about the network solution is smaller, and the formal errors are generally smaller, than with the other technique (fig. 3). 

However, because uncertainties in the coordinates are 

scaled by the fit to the data, the formal errors may actually increase if the session data are incompatible with the 

network-determined ambiguities. For example, a suspected 

setup error during session 701 on the baseline Crowell to 

Cliff might have cause those session data to be incompatible with the rest of the data and would account for the 

large uncertainties in the coordinates of the network-determined-ambiguity solution. 

The formal errors computed by the GPS analysis software appear to have underestimated the true errors, probably owing to neglect of the effect of errors in the broadcast 

orbits and failure to model signal multipathing. To estimate by what factor these errors have been underestimated, a reduced x2 value was calculated, according to 

the relation 

(Bevington, 1969), where N is the number of measurements, ri is the difference between the session solution 

and the network solution, and oi is the formal standard 

deviation of the session solution. Assuming that none of 

the stations moved during the 13-day period when Caltrans 

collected their data and that the formal uncertainties are 

correct, then y2 should e ual 1.0. The square root of the 

reduced y^, value, (x$) ^ 2, provides an estimate of the 

factor by which we need to scale the formal errors. The 

(x$)^2values calculated for the baselines Crowell to Cliff 

and Crowell to Traill determined with both processing 

techniques are listed in table 4. From these calculations, 

we determined 11.0 to be a reasonable scaling factor for 

the formal errors in the horizontal components and 7.75 

for the formal errors in the vertical components; the error 

bars in figure 3 have been scaled by these factors. When 

the formal errors in the network solution for the baselines 
A270 MAIN-SHOCK CHARACTERISTICS 

Crowell to Cliff and Crowell to Traill are scaled by these 

factors, they fall in the range 0.4-0.8 cm for the horizontal components and in the range 3.2-4.7 cm for the vertical components. 

U.U3 

Baseline length 

-0.05 ' 

681 682 683 684 691 692 693 701 702 

SESSION 

0.05 

North component 0 

4 

0.00 - *& YAAQ *. 

0 t' 

-0.05' ' I 1.1 

681 682 683 684 691 692 693 701 702 CD SESSION 

-0.151 1 1 

Baseline length 

SESSION 

0.05 

North component 

SESSION 

To estimate the precision of the preearthquake network 

solution, we used the weighted rms misfit of individual 

baseline solutions about the network solution given by the 

expression 

-0.05' ' I I. 

681 682 683 684 691 692 693 701 702 CD SESSION 

0'10 

0.05 

0.00 

0.10 

Up component 

SESSION 

East component 

- 

SESSION 

0 

East component 

0.30 

0.25 Up component 

^ 

- , 0 v*:?~ 

. 

SESSION 

11 

Figure 3.-Scatterplots of repeated measurements along baselines Crowell to Cliff (A) and Crowell to Traill (B) (see fig. 1 for locations). Circles, 

solutions obtained with estimation of integer-phase ambiguity for each session; solid squares, solutions obtained using preearthquake-networkdetermined ambiguities. Differences in individual session solutions with respect to preearthquake network solution are plotted for baseline length and 

north, east, and up components. CD, coseismic displacement for baseline, that is, difference between preearthquake and postearthquake network 

solutions. Error bars represent scaled lo formal errors from Bernese software; no error bar is shown where error is smaller than size of plotted symbol. 
COSEISMIC DISPLACEMENTS MEASURED WITH THE GLOBAL POSITIONING SYSTEM 

Table 4.-Square root of the reduced y2 of repeated measurements of baselines Crowell 

to Cliff and Crowell to Traill 

[Reduced x2 calculated using equation 1 (see text). Values in parentheses were determined excluding 

data from session 67 1, an obvious outlier] 

Baseline Source of North East 

ambiguity component component 

UP 

(fig. 1) component 

Crowell to Cliff Session 21 .O 14.5 10.2 

Crowell to Trail1 Session 15.6 (11.1) 20.1 (9.0) 6.9 (7.4) 

Crowell to Cliff Network 18.5 5.5 8.5 

Crowell to Trail1 Network 9.9 9.3 6.8 

weighted rms misfit = 

where 0.13s the weighted-average variance (Bevington, 

1969), given by 

where a; is the variance of the ith measurement determined by the Bernese software and <s2 is the average 

variance, given by 

POSTEARTHQUAKE SURVEY 

(Bevington, 1969). The results of these calculations for 

the baselines Crowell to Cliff and Crowell to Traill are 

listed in table 5. The estimations for the baseline Crowell 

to Traill were calculated both including and excluding the 

outlier in session 67 1. When individual sessions were used 

to determine the ambiguities, the unweighted rms misfit 

for the baselines is 10 to 40 mm in the horizontal components and -45 mm in the vertical components. Because 

the outliers tend to have large uncertainties, the weighted 

rms misfit is less than the unweighted values. The weighted 

rrns misfit for the baselines is 5 to 9 mm in the horizontal 

components and -40 mm in the vertical components. Using the network-determined ambiguities, the unweighted 

rms misfit is 6 to 14 mm in the horizontal components 

and -40 mm in the vertical components, whereas the 

weighted rms misfit is 5 to 8 mm in the horizontal components and 30 to 35 mm in the vertical components. 

Conservatively, these calculations indicate that the horizontal measurements are reproducible to within 1 to 2 cm, 

whereas the vertical measurements are slightly less reproducible to within -3.5 cm. 

The postearthquake survey included very few repeated 

measurements. During the 3-day period of data collection, 

the baselines Crowell to Traill and Crowell to Porter were 

both measured twice. The baselines lengths were repeatable to within 0.6 to 5.9 mm, whereas the north, east, and 

up components were repeatable to within 0.5 to 1.1, 0.8 to 

5.9, and 5.1 to 17.2 mm, respectively. Repeated measurements with the same receivers in a 60-km-wide network 

with 10-km-long baselines suggest that the horizontal measurements are repeatable to within 0.5 cm and the vertical 

measurements to within 2 to 3 cm (Biirgmann and Segall, 

1991). For the error level in the postearthquake survey to 

be comparable to the repeatability, scaling factors of 11 

in the horizontal components and 5 in the vertical components were used. 

COSEISMIC DISPLACEMENTS 

We calculated coseismic displacements by differencing 

the station coordinates estimated from the preearthquake 

and postearthquake network solutions. In both solutions, 

the station coordinates were estimated relative to station 

LP1 (fig. 1). The coseismic displacement of station LP1 

was calculated from GPS measurements, made before and 

after the earthquake, at stations LP1 and Brush2 (Fort 

Ord) (Michael Lisowski, oral commun., 1992). The 

coseismic displacement of Fort Ord relative to "stable" 

North America was determined by VLBI (Clark and others, 1990). By combining these measurements, station LP1 

was found to have moved 17.6k0.8 cm to the south, 

3.7kl.O cm to the east, and 10.435.0 cm down. The calculated horizontal coseismic displacements are mapped in 

figure 4A, with 95-percent-confidence error ellipses determined by using the formal errors of the network solutions scaled as described in the preceding section; the 

uncertainties in the displacement of station LP1 have been 

propagated into the confidence ellipses of the Santa Cmz 
A272 MAIN-SHOCK CHARACTERISTICS 

Table 5.-Statistical analysis of scatter in repeated measurements of the baselines Crowell to Cliff and 

Crowell to Traill 

[Unweighted rms misfit calculated using equation 2 (see text) with co:=l; weighted rms misfit calculated using equation 2. 

Values in parentheses were determined excluding data from session 671, an obvious outlier] 

Baseline 

(fig. 1) 

Source of North East UP 

ambiguity Len component component component (mm) (mm) (mm) (mm) 

Unweighted rms misfit 

Crowell to Cliff Session 17.9 18.8 42.5 48.7 

Crowell to Trail1 Session 65.3 (8.8) 17-5 (5.9) 86.0 (10.0) 42.8 (43.8) 

Crowell to Cliff Network 6.4 6.0 14.2 39.3 

Crowell to Trail1 Network 8.1 5.7 9.3 42.1 

Weighted rms misfit 

Crowell to Cliff Session 9.3 9.0 6.9 37.9 

Crowell to Trail1 Session 13.2 (5.5) 8.9 (6.3) 13.2 (5.9) 37.2 (39.9) 

Crowell to Cliff Network 7.8 7.2 4.8 30.7 

Crowell to Trail1 Network 7.0 4.7 5.3 33.6 

stations. The calculated coseismic displacements are listed 

in table 6. These uncertainties are relative; that is, they do 

not include uncertainties associated with the displacement 

of station LP1 relative to sites external to the earthquake. 

Note that the inferred displacements are as large as 41 cm 

at station Traill (fig. 1). 

The displacements were determined relative to station 

LP1 (fig. I), which is not strongly tied to the Caltrans 

stations. Station LP1 is tied to the Caltrans network through 

three repeated measurements at station Leon (sessions 602- 

604) and through one session to station R121. Two of the 

measurements of the baseline LP1 to Leon (sessions 602, 

603) agree to within 1.5 to 3.0 cm. Session 604 has large 

uncertainties because it involves only 30 minutes of data, 

using a maximum of four satellites. The postearthquake 

survey data for station LP1 are also weak because only 

five Block I satellites were observed. The large error ellipses observed for the horizontal coseismic displacements 

in figure 4A primarily result from the poor tie to station 

LP1. The error ellipses that result if the scaled formal 

errors are determined relative to station Porter instead of 

station LP1 are mapped in figure 45, which shows that 

the relative displacements within the Caltrans network are 

much better determined than are the absolute motions. 

The greatest uncertainties are at stations LP1 and Pajaro3, 

both of which were occupied only a few times during the 

initial survey. The absolute displacements of the Santa 

Cruz stations, together with those of the other sites in the 

area determined by Segall and Lisowski (1990) from a 

combination of GPS, EDM, and VLBI data, are mapped 

in figure 5. 

The vertical coseismic displacements were determined 

by differencing the two solutions relative to station Cliff 

(fig. I), which is near a leveling bench mark that was 

uplifted 2.5k1.2 cm during the earthquake relative to more 

distant stations (Marshall and others, 1991). The coseismic 

uplift of the GPS stations, assuming that station Cliff 

moved up 2.5 cm, is mapped on figure 6; the largest uplift, 34.1k2.7 cm, was observed at station Traill. The vertical displacements determined by GPS are qualitatively 

consistent with the results from repeated leveling (Marshall 

and others, 1991). From the VLBI results at Ford Ord and 

the GPS measurements connecting stations LP1 and Brush2 

(Fort Ord), station LP1 was determined to have subsided 

-10.4k5.0 cm. Using the uplift at station Cliff estimated 

from leveling, we obtain 9.5k5.6 cm of subsidence at station LP1. The two results agree to within 1 cm, well within 

the uncertainties of the measurements. 

By comparing the solutions from two GPS surveys that 

were made 1 year apart, we have been able to resolve 

horizontal and vertical coseismic displacements due to the 

earthquake that are relatively unbiased by interseismic deformation (table 6). In contrast, the leveling data (Marshall 

and others, 1991) and the geodetic data examined by Snay 

and others (1991) span several decades and so are potentially biased by interseismic deformation. Snay and others 

(199 1) determined displacements by comparing 

preearthquake triangulationltrilateration data with 

postearthquake GPS data. In particular, they calculated 

displacements at three stations at or near stations for which 

we have estimated displacements: Traill, Crowell, and 

Pajaro3 (figs. 1, 7). The horizontal displacements calcu- 
COSEISMIC DISPLACEMENTS MEASURED WITH THE GLOBAL POSITIONING SYSTEM 

Table 6.-Coseismic displacements at Global Positioning System stations, with scaled formal error 

[Formal errors calculated by multiplying lo Bernese formal errors by scaling factor (see text). Displacements of horizontal 

(north, east) components computed by using the displacement of station LP1 (fig. I), as determined by Michael Lisowski 

(oral cornmun., 1992); uncertainty in the displacement of station LP1 is omitted in uncertainties at other stations. Displacement of vertical (up) components computed by using the vertical displacement of station Cliff (fig. I), as measured by 

leveling survey (Marshall and others, 1991); uncertainty in the uplift of station Cliff is omitted in uncertainties at other 

stations] 

North East UP 

Station Latitude N. Longitude W. component component component 

(m) (m) (m) 

Cliff 

Crowcll 

Leon 

LP 1 

Pajar03 

Porter 

R57 

R121 

Traill 

\ Leon \ \ 

Figure 4.-Loma Prieta region, Calif., showing horizontal coseismic displacements at Global Positioning System stations 

relative to station LP1. Error ellipses are 95-percent-confidence interval computed relative to stations LP1 (A) and Porter (B), 

Irregular thin lines, faults (dashed where inferred, queried where uncertain). In figure 4A, uncertainties in station LP1 vector 

propagate into those of other stations. 
A274 MAIN-SHOCK CHARACTERISTICS 

lated by Snay and others (1991) agree reasonably well 

with those estimated here; their displacements are somewhat larger than ours, possibly owing to their incomplete 

correction for interseismic deformation. 

CONCLUSIONS 

We have measured the horizontal and vertical coseismic 

deformation resulting for the 1989 Lorna Prieta earthquake, 

using GPS data. The horizontal displacements fill in a gap 

in the USGS geodetic network (Lisowski and others, 1990) 

in the epicentral region on the hanging-wall side of the 

fault. These data provide useful constraints in determining the characteristics of the seismic source. The calculated vertical displacements agree quite well with leveling 

observations in the Santa Cruz Mountains area. 

ACKNOWLEDGMENTS 

This research was supported by U.S. National Science 

Foundation grant EAR-9003575. We thank Richard Snay 

for bringing the Caltrans network to our attention, and 

John Fundus and Steven Bourn of the California Department of Transportation for providing the raw GPS data 

and field sheets. Thora ~rnadbttir, Roland Burgmann, 

Lanbo Liu, Mark Matthews, Cleavy McKnight, and Sarah 

Saltzer assisted in the fieldwork. The USGS GPS data 

collected at station LP1 were provided by Mike Lisowski 

and Jerry Svarc. 

REFERENCES CITED 

Bevington, P.R., 1969, Data reduction and error analysis for the physical sciences: San Francisco, McGraw-Hill, 336 p. 

Figure 4.-Continued. 
COSEISMIC DISPLACEMENTS MEASURED WITH THE GLOBAL POSITIONING SYSTEM 

Biirgmann, Roland, and Segall, Paul, 199 1, Postseismic GPS monitoring NW of the 1989 Loma Prieta rupture zone [abs.]: Eos (American Geophysical Union Transactions), v, 72, no. 44, p. 119. 

Clark, T.A., Ma, Choppo, Sauber, J.M., Ryan, J.W., Gordon, David, 

Shaffer, D.B., Caprette, D.S., and Vandenberg, N.R., 1990, Geodetic measurement of deformation in the Loma Prieta, California, 

earthquake with very long baseline interferometry: Geophysical 

Research Letters, v. 17, no. 8, p. 1215-1218. 

Davis, J.L., Prescott, W.H., Svarc, J.L., and Wendt, K.J., 1989, Assessment of Global Positioning System measurements for studies of 

crustal deformation: Journal of Geophysical Research, v. 94, no. 

B10, p. 13635-13650. 

Dietz, L.D., and Ellsworth, W.L., 1990, The October 17, 1989, Loma 

Prieta, California, earthquake and its aftershocks; geometry of the 

sequence from high-resolution locations: Geophysical Research Letters, v. 17, no. 9, p. 1417-1420. 

Georgiadou, Yola, and Kluesberg, Alfred, 1988, On the effect of ionospheric delay on geodetic relative GPS positioning: Manuscripta 

Geodaetica, v. 13, no. 1, p. 1-8. 

Gurtner, Werner, Beutler, Gerhardt, and Rothacher, Markus, 1989, Combination of GPS measurements made with different receiver types: 

International Geodetic Symposium on Satellite Positioning, 5th. Las 

Cruces, N. Mex., 1989, Proceedings. 

Hager, B.H., King, R.K., and Murray, M.H., 1991, Measurement of 

crustal deformation using the Global Positioning System: Annual 

Review of Earth and Planetary Sciences, v. 19, p. 351-382. 

Lawson, A.C., chairman, 1908, The California earthquake of April 18, 

1906; Report of the State Earthquake Investigation Commission: 

Carnegie Institution of Washington Publication 87, 2 v. 

Lisowski, Michael, Prescott, W.H., Savage, J.C., and Johnson, M.J.S., 

1990, Geodetic estimate of coseismic slip during the 1989 Loma 

Prieta, California, earthquake: Geophysical Research Letters, v. 17, 

no. 9, p. 1437-1440. 

Marshall, G.A., Stein, R.S., and Thatcher, Wayne, 1991, Faulting geometry and slip from co-seismic elevation changes; the 18 October 

1989, Loma Prieta, California, earthquake: Seismological Society 

\ 

CENTIMETERS ', \ 

Figure 5.-Loma Prieta region, Calif., showing horizontal coseismic displacements at stations in Santa Cruz 

network (diamonds) and displacements estimated by Segall and Lisowski (1990) (triangles). Error ellipses 

are 95-percent-confidence intervals. Irregular thin lines, faults (dashed where inferred, queried where uncertain). 
A276 MAIN-SHOCK CHARACTERISTICS 

of America Bulletin, v. 8 1, no. 5, p. 1660-1693. 

Olson, J.A., 1990, Seismicity in the twenty years preceding the Loma 

Prieta, California earthquake: Geophysical Research Letters, v. 17, 

no. 9, p. 1429-1432. 

Prescott, W.H., Davis, J.L., and Svarc, J.L., 1989, Height of L2 phase 

centers for TI antennas: International Coordination of Space Technology for Geodesy and Geodynamics, Commission VIII Bulletin, 

v. 2, no. 2, p. 13. 

Saastarnoinen, J., 1972, Atmospheric correction for the troposphere and 

stratosphere in radio ranging of satellites, in Henriksen, S.W., 

Mancini, Armando, and Chovitz, B.H., eds., The use of artificial 

satellites for geodesy: American Geophysical Union Geophysical 

Monograph 15, p. 247-25 1. 

Segall, Paul, and Lisowski, Michael, 1990, Surface displacements in the 

1906 San Francisco and 1989 Loma Prieta earthquakes: Science, v. 

250, no. 4985, p. 1241-1244. 

Snay, R.A., Neugebauer, H.C., and Prescott, W.H., 1991, Horizontal 

deformation associated with the Loma Prieta earthquake, Seismological Society of America Bulletin, v. 81, no. 5, p. 1647-1659. 

\ \ 

\ \ \ 

0 \ 10 20 KILOMETERS 

lllllll~l~ lllilllll \ \ 

Figure 6.-Loma Prieta region, Calif., showing observed uplift (in centimeters) relative to station Cliff, determined by 

assuming that station Cliff was uplifted 2.5 cm in 1989 Loma Prieta earthquake. Irregular thin lines, faults (dashed where 

inferred, queried where uncertain). 
COSEISMIC DISPLACEMENTS MEASURED WITH THE GLOBAL POSITIONING SYSTEM A277 

122'10' 122'00' 12 1'50' 121'40' 121'30' 

Figure 7.-Loma Prieta region, Calif., showing vectors of observed displacement at Global Positioning System stations (with 

error ellipses that are 95-percent-confidence interval) and displacements calculated by Snay and others (1991). Irregular thin 

lines, faults (dashed where inferred, queried where uncertain). 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAKE OCCURRENCE 

MAIN-SHOCK CHARACTERISTICS 

ESTIMATION OF THE RUPTURE VELOCITY OF THE MAIN SHOCK 

FROM THE LOVE-WAVE GROUP VELOCITY 

CONTENTS 

By Francis T. Wu, 

State University of New York, Binghamton 

Page 

A279 

279 

280 

280 

282 

282 

282 

282 

284 

285 

286 

288 

288 

288 

ABSTRACT 

The group velocity of a surface wave measured from a 

large earthquake is perturbed by the dynamic rupture 

propagation of the seismic source. Using a moving-source 

model, the deviation of this group velocity from the intrinsic group velocity can be shown to depend on the 

rupture velocity, the fault length, the direction of rupture 

propagation, and the distance from the source. If this deviation can be measured, then the rupture parameters can 

be determined. The group velocity of a surface wave from 

an earthquake whose source dimension is much smaller 

than the wavelengths of the surface wave being studied is 

essentially the same as the intrinsic group velocity. The 

differential group velocities determined for a large and a 

small earthquake (say, more than two magnitude units 

smaller) can then be readily used to determine the rupture 

parameters. I apply this method to calculate the rupture 

velocity of the 1989 Loma Prieta earthquake (Me7.1), 

using broadband, wide-dynamic-range seismograms recorded at a station in Pasadena, Calif. The intrinsic group 

velocities of Love waves were obtained from the records 

of an Me4.5 foreshock. The locations of this foreshock 

and the Loma Prieta main shock are assumed to be known, 

and the rupture length of the main shock is estimated 

from the aftershock distribution. For a rupture half-length 

of 25 km, the rupture velocity thus calculated ranges from 

1.85 to 2.45 km/s. The upper limit is obtained by assuming that the rupture was initiated 1.8 s after a weak 

foreshock, and the lower limit by assuming that a slow 

rupture was initiated at the time of the foreshock. 

INTRODUCTION 

The direction of rupture propagation, the rupture velocity, and the fault length are important earthquake source 

parameters to be determined because they control the amplitude of ground motion as a function of azimuth (BenMenahem, 1961) and are probably related to the stress 

intensity (Wu and others, 1972). Ben-Menahem (1961) 

and Ben-Menahem and Toksoz (1962) used the spectral 

ratios of long-period surface waves to calculate the rupture velocities of several large earthquakes. Kanamori 

(1970), Kanamori and Given (1981), and Zhang and 

Kanamori (1988) used mantle surface waves to study the 

source mechanisms of many large events; the long-period 

waves used in these studies generally are insensitive to 

the source finiteness. 

In teleseismic body-wave or near-field source studies 

for the Loma Prieta main shock (Beroza, 1991; Hartzell 

and others, 1991; Steidl and others, 1991; Wald and others, 199 1) the rupture-propagation parameters mentioned 

above are either held fixed (Beroza, 1991; Wald and others, 1991) or treated as variables (Hartzell and others, 

199 1 ; Steidl and others, 199 1). With variable parameters, 

the amplitude residuals are used as criteria for choosing a 

particular rupture velocity; the results of these studies are 

summarized in table 1. As Hartzell and others (1991, table 

3) and Steidl and others (1991, table 3) showed in their 

source modeling, the results are nearly insensitive to rupture velocity. Although Steidl and others chose 3 km/s as 

their preferred rupture velocity, a value of 2.5 km/s and a 

different set of rise-time and slip functions actually give a 

smaller residual. 
MAIN-SHOCK CHARACTERISTICS 

Table 1.-Rupture velocity of the Loma Prieta main shock 

Author Method (2,s) Range 

Beroza (1 991)----------- Inversion using data from 20 2.7-3.1 Fixed. 

strong-motion stations. (80 percent 

of v,) 

Hartzell and others Inversion of teleseismic P and 2.5 2.1-3.1 

(1991). SH waves. 

Wald and others Joint inversion of teleseismic 2.7 Fixed. 

(1 99 1). body waves and strongmotion data. 

Steidl and others Inversion using strong-motion 3.0 2.5,2.8, 

(1 99 1). data from 38 stations. 3.0 

Press and others (1961, p. 3484) described earlier methods for determining fault length and rupture velocity, noting that the finiteness of a seismic source can affect the 

group velocities measured at a single station. They presented a formula relating the group velocity to rupturepropagation parameters and estimated that for a fault length 

of 1,000 km, the effect may be as large as 10 percent. 

Although they did not so state, if the "intrinsic group 

velocity" of the medium is measurable, then the group 

velocities measured from a large earthquake clearly can 

be used to determine the rupture-propagation parameters. 

In this paper, I apply this concept to a study of the rupture 

process of the Loma Prieta main shock. This study was 

made possible by the installation of a broadband, widedynamic-range station in Pasadena, Calif. (PAS, fig. I), 

in 1988. Regional events of Mp4.5 can be recorded with 

high signal-to-noise ratio, and events of Mp7 can remain 

on scale. Because M~4.5 events have a fault length of 

about 1 km and an Mc=7 event may have a fault length of 

several tens of kilometers, the group velocity measured 

from smaller events, Us, can be viewed as the intrinsic 

velocity, and the group velocity measured from larger 

events, Ur, can then be used for rupture-propagation studies. Because only one appropriate station was available 

for such studies of the Loma Prieta main shock, accurate 

epicentral locations and origin times are important because they are used directly in estimating group velocities. With the dense telemetered U.S. Geological Survey 

network in central California and the availability of reasonably detailed velocity models, the locations are probably as good as can be obtained. Whereas the rupture 

velocity is one of the model parameters in other Loma 

Prieta main-shock studies, it is determined more directly 

in this work and can therefore provide an independent 

assessment of this important quantity. 

GROUP VELOCITY OF SURFACE 

WAVES FROM A MOVING SOURCE 

THEORY 

The group velocity is well defined when the source is a 

point in space and impulsive in time. For a large earthquake on a finite fault formed from rupture propagation, 

the group velocity measured is not the intrinsic velocity , 

of the medium. Assuming a unilaterally propagating point 

source, Ben-Menahem (1961) showed that the surface 

waves radiated from the source can be written as 

where co is the frequency; t is the time; k is the wave 

number; A is the epicentral distance; cQ is the velocity of 

source propagation; en is the azimuthal angle of the station, measured clockwise from the direction of source 

propagation; b is the fault length; and c(co) is the phase 

velocity. For a stationary phase 

After differentiation, we obtain 

where U=dw/dk is the intrinsic group velocity appropriate 

for the path and U'=A/t is the velocity that would be mea- 
ESTIMATION OF THE RUPTURE VELOCITY OF THE MAIN SHOCK FROM THE LOVE-WAVE GROUP VELOCITY A28 1 

sured for a source propagating at the velocity CQ. This 

expression was first derived by Press and others (1961), (3) When 0=*/2, AU = - 

2t [^-I, c', who emphasized the necessity of correcting the group velocity when the effect of source finiteness is strong. Con- In this case, AU<0, but its value will be smaller than in 

sider a few special cases: special case 2. 

(1)when9=0, 

If Ux0, AU < 0; 

if U=c0, AU = 0; 

and if U<c0, AU > 0. 

In this case, AU<0 is always true. 

The limitation of this method comes from (1) the difficulty in obtaining the intrinsic group velocity along the 

path between the source and the receiver, and (2) the fact 

that AU depends on bit; in other words, short fault length 

or large distance could make the difference AU too small 

to be used in this method. For the 1989 Loma Prieta earthquake, the circumstances were such that both obstacles 

can be overcome. For the intrinsic group velocity, we can 

use seismograms from a foreshock that is at least two 

magnitude units smaller. In comparison with the main 

shock, the dimensions of the fault associated with this 

Figure 1 .-California, showing locations of Loma Prieta main shock, station PAS, and major faults (irregular dashed lines). Notice that line from station to main shock lies nearly along strike of the San Andreas fault 

in the Loma Prieta region. Surface-wave propagation path almost coincides with trace of the San Andreas 

fault in northern California; surface-wave velocities along this path are very low. 
A282 MAIN-SHOCK CHARACTERISTICS 

foreshock are so small that it can be approximated as a 

point source. For example, using the relation of Slemmons 

and DePolo (1986, p. 55), for an event of Me4.5, the 

fault is about 1 km long; and for the main shock, the fault 

is 40 to 60 km long. 

Note that, in contrast to other methods involving matching synthesized waveforms with observations, only phase 

information is used here, as shown in the derivation above. 

Nonetheless, this method assumes an unilateral fault propagating at an uniform velocity-clearly an approximation. 

This question is addressed in the section below entitled 

"Discussion." 

EXPERIMENTAL DETERMINATION 

The determination of the group velocity is well established; the main quantity to be determined is the group 

delay 

where Vo(a) is the initial phase and the prime indicates 

differentiation with respect to the frequency co (for example, Keilis-Borok, 1989, p. 137). For waves with periods much longer than the source rise time, the far-field 

source-time function can be considered impulsive, and 

the rate of change of the initial phase can be neglected. 

Thus, for foreshocks with a source time of about 1 s, the 

group delay can be ignored. For the main shock, the finiteness of the source-time function is assumed to be the 

result of a moving source; in other words, the rise time at 

each source point is still very short. This assumption is 

consistent with the conclusion from near-source modeling 

(Steidl and others, 1991) that the rise-time function is 

very short at each source element. 

To obtain the group velocity at one period, we can 

design a filter that isolates the energy within a narrow 

band centered on the period, and so the arrival time of the 

peak of the envelope represents the group delay. The filtering techniques used in this design were described in 

detail by Dziewonski and Hales (1972). Once AU is obtained, we can solve equation 1 for c0: 

OBSERVATIONS 

It is fortuitous that not long before the 1989 Loma Prieta 

earthquake, the establishment of broadband stations began. One of the first such stations was located in southern 

California (sta. PAS, fig. 1). As shown in figure 1, the 

path from the epicenter to station PAS is nearly along the 

strike of the San Andreas fault near Loma Prieta. Two 

foreshoc ks and the main shock, which were recorded 

clearly at station PAS, were used in this study; the location parameters are listed in table 2. The foreshock locations are from the USGS' central California network 

(Calnet; Jean Olson, written commun., 1992). The main 

shock location, which is from the USGS' Preliminary Determination of Epicenters, is essentially the same as that 

of Dietz and Ellsworth (1990, p. 141 8). By relocating the 

known shotpoints, Dietz and Ellsworth (1990, p. 1417) 

estimated a bias in the epicentral locations of about 1 km, 

due to the differences in velocity on both sides of the 

fault; the relative error of the epicentral locations is estimated to be much less, about 0.3 km. An rms error in 

arrival time of less than 0.1 s is indicated for the solutions 

(Jean Olson, written commun., 1992). 

FORESHOCKS 

The August 8, 1989, foreshock was one of two Lake 

Elsman earthquakes that were recognized as unusual 

(Olson, 1990) and most probably precursory to the Loma 

Prieta main shock (Seeber and Ambruster, 1990). The event 

is located 11 km to the north of the Loma Prieta epicenter, at nearly 14-km depth, and has Mr=5.1 (table I), 

mb=4.9, and Mp4.5 (Preliminary Determination of Epicenters). Because of its location and source mechanism, 

this foreshock is generally thought to have occurred along 

a buried fault east of the fault associated with the Loma 

Prieta main shock. Unfiltered and filtered seismograms of 

the Love waves from the August 8, 1989, foreshock recorded at station PAS (fig. 1) are plotted in figure 2B. 

Records of the June 13, 1988, foreshock north of the 

Lake Elsman area are used to estimate how well group 

velocities can be determined in this area. Unfiltered and 

filtered seismograms of Love wave from this event recorded at station PAS (fig. 1) are plotted in figure 2B. 

Notice the similarity of the first few cycles of the filtered 

seismograms in figures 2A and 2B (solid curves). 

Since U is a function of frequency, whereas c0 is assumed 

to be constant, we can calculate c0 from equation 2 by 

averaging over values at different frequencies or leastsquares inversion when data at several azimuths are available. 

MAIN SHOCK 

The Loma Prieta main shock is well located (table 1). 

The origin time of the main rupture, however, is an interesting question and most relevant to this study. Wald and 
ESTIMATION OF THE RUPTURE VELOCITY OF THE MAIN SHOCK FROM THE LOVE-WAVE GROUP VELOCITY A283 

Table 2.-Location parameters of the events used in this study 

[RMS, root-mean-square error in arrival time; ERH, standard error in horizontal 

location; ERZ, standard error in vertical location] 

Date Time Latitude Longitude Depth RMS ERH ERZ 

N. W. (km) (s) (km) (km) 

others (1991) deciphered a foreshock or slow rupture nucle- main shock was bilateral. The length of the rupture used 

ation about 1.8 s before the main rupture. This difference by various investigators differs; for example, Hartzell and 

will directly affect the rupture velocity determined here. others (1991) used a fault half-length of 30 krn, Wald and 

As far as the rupture process is concerned, it is commonly others (1991) a fault half-length of 20 km, Steidl and 

agreed that the rupture associated with the Loma Prieta others (1991) a fault half-length of 19 km, and Beroza 

TIME, IN SECONDS 

Figure 2.-Unfiltered (dashed curve) and filtered (solid curve) seismograms of Love wave from two Loma Prieta foreshocks: (A) June 13, 1988, Lake 

Elsman earthquake, which was located about 18 km north of main shock; and (B) August 8, 1989, Lake Elsman earthquake, which was located about 

11 km north of main shock. Unfiltered seismogram was obtained by rotating two original horizontal (north-south and east-west) components of 

velocity into transverse direction (positive is counterclockwise from radial direction); filtered seismogram was obtained from two passes of a lowpass, four-pole Butterworth filter with a comer frequency at 0.06 Hz. 
A284 MAIN-SHOCK CHARACTERISTICS 

(1991) a fault half-length of 20 km in their waveform 

modeling based on strong motion and (or) teleseismic data. 

Judging from the distribution of aftershocks within the 

first 24 hours after the main shock (Dietz and Ellsworth, 

1990) and assuming that they occurred within the region 

of main-shock rupture, the fault half-length could range 

from 20 to more than 30 km. 

Unfiltered and filtered seismograms of the Love wave 

from the Loma Prieta main shock recorded at station PAS 

(fig. 1) are plotted in figure 3. The filtered seismogram is 

nearly identical to that of the August 8, 1989, foreshock 

(inset). The main shock evidently is richer in low-frequency signal content, as shown in figure 4. 

GROUP VELOCITIES 

The Love-wave group velocities of the two foreshocks 

of June 13, 1988, and August 8, 1989, are plotted in figure 5. At periods beyond 32 s and below 20 s, the group 

velocities of the two foreshocks begin to crisscross. The 

phase spectra of the main shock and the August 8, 1988, 

foreshock (fig. 4) are most stable within the period range 

22-30 s. The dispersion curves for the two foreshocks 

(squares and triangles, fig. 5) have a discrepancy of less 

than 0.02 kmls, slightly larger than the 2s that could arise 

from the relative errors in epicentral location (0.3 km) 

and origin time (0.1 s). A systematic error in location or 

origin time cannot be ruled out. 

The Love-wave group velocities of the Loma Prieta 

main shock are also plotted in figure 5, both assuming a 

1.8-s delay in origin time (circles) and without such a 

delay (diamonds). As expected, the group velocities computed with the delay are higher than those without the 

delay; the average difference is 0.035 kmls. 

The measured group velocities are quite low. The path 

between Loma Prieta and station PAS follows quite closely 

the San Andreas fault in central California, a region of 

200 400 600 

TIME, IN SECONDS 

Figure 3.-Unfiltered (dashed curve) and filtered (solid curve) seismograms of Love wave from Loma Prieta main shock. Unfiltered seismogram 

clearly shows long-period (>lo s) signal, in contrast to unfiltered seismograms of foreshocks plotted in figure 2; this contrast evidently reflects 

differences in source spectra. Filtered seismogram, however, is nearly identical to that for August 8, 1989, foreshock (inset). Seismograms obtained as 

described in figure 2. 
ESTIMATION OF THE RUPTURE VELOCITY OF THE MAIN SHOCK FROM THE LOVE-WAVE GROUP VELOCITY A285 

known low velocity (fig. 1). Tanimoto (1990), for example, observed that surface waves propagating between 

the epicenter of the 1987 Whittier Narrows, Calif., earthquake and station SAO or MHC in the San Francisco Bay 

region show a delay of 25 s relative to a station in eastern 

California at about the same distance. He found that group 

and phase velocities for surface waves traveling along the 

Coast Ranges are 20 percent lower than those traveling 

through eastern California. Thus, the low group velocities 

calculated here, though not heretofore reported, are not 

unexpected. 

RUPTURE-VELOCITY DETERMINATION 

Because the group velocities measured from the main 

shock are lower than those for the two foreshocks (fig. 5) 

calculated from equation 2, we can ascertain that U>c0 

(otherwise, Auk0). On the basis of previous modeling, 

the main-shock rupture is assumed to propagate bilaterally from the epicenter. For the reasons presented in the 

next section, only the southeastward-propagating source 

is taken into account. Therefore, the half-length of the 

fault is used. 

The rupture velocity of the main shock for several fault 

half-lengths, calculated from equation 2 with or without 

the delays discussed by Wald and others (1991), are plotted in figure 7. Only the results for the period range 22- 

30 s are used; at longer or shorter periods, the values 

fluctuate rapidly. Assuming a fault half-length of 25 krn, 

as suggested by the aftershock distribution within the first 

24 hours after the main shock, the rupture velocity would 

be 2.35 krnls, with the 1.8-s delay of rupture propagation 

after the origin time (table 2) incorporated. Without this 

delay-in other words, with a surface-wave-radiating, slow 

rupture propagation beginning at the origin time-the rupture velocity would be as low as 1.8 km/s. If the fault 

half-length is increased, the calculated rupture velocity 

will increase, as shown in equation 2; and the converse is 

also true. For example, assuming a fault half-length of 30 

km (Hartzell and others, 1991, p. 153 I), a rupture velocity of about 2.45 kmls is obtained. 

FREQUENCY, IN HERTZ 

Figure 4.-Relative spectral densities of Loma Prieta main shock (solid curve) and August 8, 1989, foreshock 

(dashed curve). Notice relatively steep spectral slope above 0.055 Hz (or below a period of 18.2 s), above 

which phase spectra become rather unstable, especially for foreshock. 
A286 MAIN-SHOCK CHARACTERISTICS 

By incorporating a 1.8-s delay in main shock rupture 

propagation, the group-velocity method yields a rupture 

velocity of 2.35 to 2.45 kds, at the low end of the values 

calculated by other investigators (table 1). The significance of these values is discussed below. 

DISCUSSION 

The rupture velocity calculated here is an average, obtained on the basis of a unilaterally propagating source. It 

may not be too surprising that the source appears to be 

unilateral at station PAS (fig. I), with the source propagating toward it. This appearance is consonant with the 

fact that in this direction the radiated wavelets from successive sources interfere constructively; when the rupture 

velocity and the surface-wave velocity are equal, maximum constructive interference occurs. For a source propagating in the opposite direction, however, the waves from 

later sources will not catch up with the waves that had left 

the previous source points, and constructive interference 

will not occur. As shown in figure 3, the Loma Prieta 

main shock show no significant energy at the trailing end 

of the Love wave, in contrast to the August 8, 1989, 

foreshock-a phenomenon that should be seen if the 

northwestward-propagating rupture contributes significantly to the waveform. This dominance of the rupture 

propagating toward a station is also seen in strong-motion 

modeling (fig. 11 in Wald and others, 1991). 

The determination of rupture-propagation parameters by 

this method would be much more robust if the seismograms at several stations around a source were available. 

The distance between station PAS and the source (fig. 1) 

was ideal for this application, and with the establishment 

of more broadband stations in northern and southern California, this method can be used to study the rupture characteristics of future Mp>6 events in this region. The reason 

why this method can be used at all in a study of the Loma 

Prieta main-shock rupture is that the epicenters of the two 

foreshocks and the main shock were well located by 

I I 1 I I I I I I I I I -i 

22 24 26 28 30 

PERIOD, IN SECONDS 

Figure 5.-Group velocities versus period for Love waves from Loma Prieta main shock (circles, triangles) and two foreshocks 

of June 13, 1988 (squares), and August 8, 1989 (triangles). Two curves for main shock assume 1.8-s (circles) and 0.0-s 

(diamonds) delay in origin time (see table 2). Inset shows data plotted over period range 17-45 s. 
ESTIMATION OF T RUT VELOCITY 0 T MAIN SHOCK OM T LOVE-WAVE GROUP VELOCITY A287 

TIME, IN SECONDS 

cure - 6.-Bandpass-filtered seismograms for Loma Prieta main shock (solid curve) and August 8, 1989, foreshock (dashed curve). Seismogram of 

foreshock precedes that of main shock by a fraction of a second (inset). 

t I I I I i 

2 2 24 26 2 8 30 

PERIOD, IN SECONDS 

I I I I i 

2 2 24 2 6 28 30 

PERIOD, IN SECONDS 

Figure 7.-Rupture velocities versus period for Loma Prieta main shock. Rupture velocity was calculated from group velocity, using fault lengths of 

20 km (circles), 25 km (triangles), and 30 km (diamonds) and assuming delay times of 1.8 s (A) and 0.0 s (B) from origin time. 
A288 MAIN-SHOCK CHARACTERISTICS 

Calnet; many of the sources of errors in event location 

and timing have been removed. With more stations, we 

could ideally solve for the fault length, b, as well as the 

rupture velocity. 

The source duration calculated from a rupture velocity 

of 2.45 kmls and a fault half-length of 30 krn is 12.2 s, or 

10.6 s with a rupture velocity of 2.35 km/s and a fault 

half-length of 25 km. Note that the time function obtained 

from teleseismic-waveform or near-source modeling of 

the earthquake has source durations of 7.5 to 15 s (Wallace 

and others, 1991, p. 1628). In this regard, the results presented here are consistent with those of other models. 

CONCLUSION 

This study is a first attempt at determining the rupture 

velocity of a large earthquake by using the difference between the group velocity measured from the earthquake 

and the intrinsic group velocity, which is defined here as 

the group velocity measured from an event more than two 

magnitude units smaller. As the number of broadband, 

wide-dynamic-range stations increases, such a determination can be routinely made for many events. When more 

than one station around an earthquake epicenter is used, 

both the fault length and the rupture velocity could also 

be determined. 

The method used in this paper depends only on the 

phase information contained in the waveforms. Because 

this information does not involve the amplitude spectrum, 

the tradeoffs between slip amplitudes and rupture velocity 

used by Steidl and others (1991) may be avoided. As the 

method is presently formulated, however, only average 

rupture properties can be calculated. 

ACKNOWLEDGMENTS 

This research was supported by U.S. National Science 

Foundation grant EAR-901 1449. Alan Jones' assistance 

in editing is appreciated. My study was made possible by 

the timely data-retrieval service provided by Marcie Palmer 

of Incorporated Research Institutions for Seismology's 

Data Management Center in Austin, Tex. I also thank 

Jean Olson of the USGS for providing updated hypocentral locations for the events studied. 

REFERENCES CITED 

Ben-Menahem, Ari, 1961, Radiation of seismic waves from finite moving sources: Seismological Society of America Bulletin, v. 51, no. 

2, p. 401-435. 

Ben-Menahem, Ari, and Toksoz, M.N., 1962, Source-mechanism from 

spectra of long-period seismic surface-waves. 1. The Mongolian 

earthquake of December 4, 1957: Journal of Geophysical Research, 

v. 67, no. 5, p. 1943-1955. 

Beroza, G.C., 1991, Heterogeneous slip at Loma Prieta: Seismological 

Society of America Bulletin, v. 8 1, no. 5, p. 1603-1621. 

Dietz, L.D., and Ellsworth, W.L., 1990, The October 17, 1989 Loma 

Prieta, California, earthquake and its aftershocks; geometry of the 

sequence from high-resolution locations: Geophysical Research Letters, v. 17, no. 9, p. 1417-1420. 

Dziewonski, A.M., and Hales, A.L., 1972, Numerical analysis of dispersed seismic waves, in Bolt, B.A., ed., Computational physics: 

New York, Academic Press, v. 11, p. 39-85. 

Hartzell, S.H., Stewart, G.S., and Mendoza, Carlos, 1991, Comparison 

of L, and L, norms in a teleseismic waveform inversion for the slip 

history of the Loma Prieta, California, earthquake: Seismological 

Society of America Bulletin, v. 81, no. 5, p. 1518-1539. 

Kanarnori, Hiroo, 1970, Synthesis of long-period surface waves and its 

application to earthquake source studies, Kurile islands earthquake 

of October 13, 1963: Journal of Geophysical Research, v. 75, no. 

26, p. 501 1-5027. 

Kanamori, Hiroo, and Given, G.W., 1981, Use of long-period surface 

waves for rapid determination of earthquake-source parameters: 

Physics of the Earth and Planetary Interiors, v. 27, no. 1, p. 

8-3 1. 

Keilis-Borok, V.I., ed., 1989, Seismic surface waves in a laterally inhomogeneous earth: Boston, Kluwer Academic Publishers, 293 p. 

Olson, J.A., 1990, Seismicity in the twenty years preceding the Loma 

Prieta, California earthquake: Geophysical Research Letters, v. 17, 

no. 9, p. 1429-1432. 

Press, Frank, Ben-Menahem, Ari, and Toksoz, M.N., 1961, Experimental determination of earthquake fault length and rupture velocity: 

Journal of Geophysical Research, v. 66, no. 10, p. 3471-3485. 

Romanowicz, B.A., and Lyon-Caen, Helene, 1990, The Loma Prieta 

earthquake of October 18, 1989; results of teleseismic mantle and 

body-wave inversion: Geophysical Research Letters, v. 17, no. 9, p. 

1191-1 194. 

Seeber, Leonardo, and Ambruster, J.G., 1990, Fault kinematics in the 

1989 Loma Prieta rupture area during 20 years before that event: 

Geophysical Research Letters, v. 17, no. 9, p. 1425-1428. 

Slernrnons, D.B., and DePolo, C.M., 1986, Evaluation of active faulting 

and associated hazards, in Active tectonics: Washington, D.C., National Academy Press, p. 45-62. 

Steidl, J.H., Archuleta, R.J., and Hartzell, S.H., 1991, Rupture history 

of the 1989 Loma Prieta, California, earthquake: Seismological Society of America Bulletin, v. 81, no. 5, p. 1573-1602. 

Tanimoto, Toshiro, 1990, Modelling curved surface wave paths; membrane surface wave synthetics: Geophysical Journal International, 

v. 102, no. 1, p. 89-100. 

Wald, D.J., Helmberger, D.V., and Heaton, T.H., 1991, Rupture model 

of the 1989 Loma Prieta earthquake from the inversion of strongmotion and broadband teleseismic data: Seismological Society of 

America Bulletin, v. 81, no. 5, p. 1540-1572. 

Wallace, T.C., Velasco, A.A., Zhang, Jiajun, and Lay, Thorne, 1991, A 

broadband seismological investigation of 1989 Loma Prieta, California, earthquake; evidence for deep slow slip?: Seismological Society of America Bulletin, v. 81, no. 5, p. 1622-1646. 

Wu, F.T., Thompson, K.C., and Kuenzler, H., 1972, Stick-slip propagation velocity and seismic source mechanism: Seismological Society 

of America Bulletin, v. 62, no. 6, p. 1621-1628. 

Zhang, Jiajun, and Kanamori, Hiroo, 1988, Source finiteness of large 

earthquakes measured from long-period Rayleigh waves: Physics 

of the Earth and Planetary Interiors, v. 52, no. 1, p. 56-84. 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAmOCCURRENCE 

MAIN-SHOCK CHARACTERISTICS 

USE OF STRESS-DROP MODELS TO INTERPRET GEODOLITEIGLOBAL 

POSITIONING SYSTEM AND LEVELING MEASUREMENTS AT 

LOMA PRIETA 

CONTENTS 

By Mingdong Wu and John W. Rudnicki, 

Northwestern University 

[fid]=l. 1 m. The rupture area inferred from the leveling 

data is slightly smaller than that inferred from the 

GeodolitelGPS data (408 versus 518 km2), and so AT^, 

 AT^, Mo, and Gmm in the model fitting the leveling data 

are all slightly larger. The Gmm value in both models is 

near the upper end of the range inferred for crustal faults, 

a result consistent with other evidence suggesting that 

Loma Prieta-type events are relatively infrequent. 

INTRODUCTION 

ABSTRACT 

We interpret the coseismic surface deformation associated with the 1989 Loma Prieta earthquake by approximating the rupture as a planar elliptical zone embedded 

within an elastic half-space. In contrast to dislocation models, in which the slip is prescribed, the stress change in 

our model is prescribed on the fault surface. The stress 

drop is assumed to be uniform, with a component AT^ 

along the strike direction and a component AT^ along the 

dip direction of the fault. The stress drop and rupturezone geometry are adjusted until the calculated surface 

deformation agrees as closely as possible with that observed, As in simple dislocation models, stress-drop models of this type are found to fit the GeodolitelGlobal 

Positioning System (GPS) and leveling data separately 

much better than the combined data. The main differences 

between the models fitting the GeodolitelGPS and leveling data are the dip on the fault surface (73' versus 65O, 

respectively) and a fault center 2 km farther northeast, as 

inferred from the GeodolitelGPS data. The discrepancies 

between the two models suggest that both of these models 

are too simple to capture fully the actual rupture-zone 

geometry and stress-drop distribution. The alongstrike and 

alongdip stress-drop components, geodetic moment, and 

maximum energy-release rate, respectively, inferred from 

the GeodolitelGPS data are as follows: A~~=1.5 MPa, 

A~~=1.4 MPa, ~~=2.5~10~~ N-m, and ~~~=5.5~10~ Jl 

m2. The average slip amplitudes in the strike and (reverse) dip direction, respectively, are [iis]=1.3 m and 

Surface displacements associated with the 1989 Loma 

Prieta earthquake (Ms=7. 1) have been interpreted as due 

to slip on an oblique fault plane with subequal components of strike-slip and reverse faulting (Lisowski and 

others, 1990; Marshall and others, 1991). Lisowski and 

others inferred the coseismic slip on the fault surface by 

comparing the line lengths measured by a Geodolite and a 

few vector-component changes detected by Global Positioning System (GPS) observations at Loma Prieta with 

those calculated from a model of uniform slip over a rectangular region embedded in an elastic half-space 

(Mansinha and Smylie, 1971). Marshall and others used 

the same modeling approach but focused on the vertical 

deformation measured by leveling surveys of the Loma 

Prieta leveling network before and after the earthquake. 

Although the geometries of the model faults inferred from 

these two data sets differ moderately, both models predict 

similar values for the coseismic strike and reverse dip 

slip. 

In this paper, we analyze the data of Lisowski and others (1990) and Marshall and others (1991) but use a stressdrop model (Wu and others, 1991); that is, the stress drop, 

rather than the slip, is specified on the fault surface and 

adjusted (along with the geometry) to fit the measured 

surface deformation. Although dislocation models are convenient and widely used for inferring the geometry of the 

rupture zone and the amplitude of slip, one limitation of 

this approach is that it is purely kinematic: It relates the 
A290 MAIN-SHOCK CHARACTERISTICS 

surface deformation to slip at depth but only indirectly 

yields information about the stresses that produced the 

slip and the conditions for propagation and termination of 

the rupture. Typically, dislocation models approximate the 

slip as uniform over the entire fault surface or in elements, and so the slip amplitude drops to zero discontinuously near the edge of the rupture zone. Therefore, the 

average stress change and the strain-energy changes in 

volumes containing the rupture-zone edge are unbounded. 

The stress-drop method of Wu and others (1991) provides an alternative approach. Though computationally demanding, this method constrains the stress drop directly 

by using it as a model parameter to fit the surface deformation. Because their method uses the exact asymptotic 

form for the slip distribution near the edge of the rupture 

zone, it is mechanically consistent: Although the stresses 

near the rupture-zone edge are singular, with the characteristic dependence on the inverse square root of distance 

from the edge, the strain-energy changes in volumes containing the edge are finite. Therefore, the distribution of 

the energy-release rate along the rupture front, which Wu 

and others used to estimate the critical energy-release rate 

at the termination of rupture, can be calculated. Furthermore, comparison of the fault geometries inferred by this 

method with those inferred from dislocation models provides information about the resolving power of the data 

among solutions. 

In this study, we apply the stress-drop method of Wu 

and others (1991) to the coseismic-deformation data associated with the 1989 Loma Prieta earthquake. In particular, we assume an elliptical rupture zone, with uniform 

stress drops in the strike and dip directions. The dimension and orientation of the rupture zone and the magnitude of stress drops are determined by comparing predicted 

with observed surface displacements. Once the rupturezone geometry and stress drops are determined, the slip 

distribution, geodetic moment, and critical energy-release 

rate at the termination of rupture can be calculated. Then, 

we compare our estimated rupture-zone geometry, slip 

amplitude, and geodetic moment with those calculated by 

Lisowski and others (1990) and Marshall and others 

(1991), and discuss the implications of our results. 

DATA 

Coseismic surface deformation associated with the 1989 

Loma Prieta earthquake has been observed by geodetic 

measurements in the San Francisco Bay region. The deformation data used in this paper consist of electronic 

distance measurement (EDM), a few Global Positioning 

System (GPS) relative-position changes (fig. lA), and elevation changes along seven leveling lines (fig. 1B). The 

characteristics of the EDM and GPS systems were described by Lisowski and others (19901, and the leveling 

data by Marshall and others (1991). We briefly review the 

data quality and uncertainty below. 

The distances between the geodetic stations shown in 

figure 1A have been measured by the U.S. Geological 

Survey (USGS) since the early 1970's (Prescott and others, 1981). The precision of measurements made by a 

Geodolite, a laser distance-measuring instrument, is about 

0.2 ppm (Savage and Prescott, 1973); some lines measured with a short-range distancemeter (model HP3808) 

have a precision of 2 ppm. GPS observations of the position vectors between Loma Prieta and stations Eagle Rk, 

Allison, Hamilton, and Brush 2 have been obtained since 

1985; the data precision is about 0.2 ppm, depending on 

the orientation of the line and the data-processing techniques used (Prescott and others, 1989). Specifications of 

the observed coseismic offsets in the relative positions of 

the geodetic stations and the associated data uncertainties 

are discussed by Lisowski and others (this chapter) and 

listed in table 1. 

Preearthquake surveys of the Loma Prieta leveling network (fig. 1B) were performed by both the U.S. National 

Geodetic Survey (NGS) and the USGS between 1947 and 

1989. Postearthquake leveling surveys were conducted 

from February through June 1990 (Marshall and others, 

1991). Because little postseismic slip was observed between October 1989 and June 1990 (Behr and others, 1990; 

Langbein, 1990), the elevation changes between the 

preearthquake and postearthquake surveys are treated as 

coseismic, following Marshall and others. Errors in leveling measurements accumulate with the square root of the 

distance; the observed errors in the leveling data can be 

expressed as oo = ,/=, where the tii are the relative 

uncertainties and LC (=lo km) is the characteristic length 

scale for the leveling network (Marshall and others, 1991). 

Specific absolute elevation changes and relative uncertainties were reported by Marshall and others. A constant 

can be freely added to these elevation-change observations; Marshall and others determined a constant of +28 

mm for their modeling. In this paper, we adopt the same 

constant, and so we add a datum shift of +28 mm to the 

absolute elevation changes listed by Marshall and others 

(1991, table 2A). 

STRESS-DROP MODEL 

The presence of two adjacent faults, the San Andreas 

and Sargent faults (fig. I), in the Loma Prieta rupture 

zone and the aftershock sequence of the earthquake (Dietz 

and Ellsworth, 1990) suggest that the rupture may have 

involved complex fault interactions. Nevertheless, 

Lisowski and others (1990) and Marshall and others (1991) 

showed that most of the coseismic surface deformation 
STRESS-DROP MODELS TO INTERPRET GEODOLITWGLOBAL POSITIONING SYSTEM AND LEVELING MEASUREMENTS A29 1 

can be modeled adequately with buried oblique slip on a 

single planar fault surface. We follow a similar approach 

and attempt to model the surface deformation as due to a 

single planar zone of prescribed stress drop. Although our 

procedure can accommodate arbitrary-shape rupture zones 

and spatially distributed stress drops, we assume that the 

rupture zone is elliptical and the stress drop is uniform. 

We make these simplifying assumptions because insufficient information is contained in the geodetic data to constrain the details of slip (Lisowski and others, 1990; 

Marshall and others, 1991). We also ignore the possibility 

of fault interaction suggested by the topographic model of 

Schwartz and others (1990) and the seismicity study of 

Olson (1990). 

The uniform-stress-drop model of an elliptical rupture 

zone is illustrated in figure 2. The procedure for calculating the displacements and stresses due to a zone of prescribed stress drop embedded within an elastic half-space 

was described in detail by Wu and others (1991) and is 

briefly summarized here. Wu and others begin with an 

expression for the stress in the half-space due to a prescribed displacement discontinuity. When this expression 

is evaluated on the surface of discontinuity, it becomes an 

integral equation for the unknown distribution of displacement discontinuity arising from the prescribed stress drop. 

This integral equation is then solved by converting it to a 

set of linear algebraic equations. Once the appropriate 

distribution of displacement discontinuity is determined, 

:XPLANATION 

-& Geodolite 

1 KILOMETERS I 1 

Figure 1.-Loma Prieta region, Calif., showing locations of major faults (dotted where buried, dashed where 

inferred) and of (A) Geodolite, electronic distance measurement, and Global Positioning System stations 

(station names are shown only selectively for simplicity; for more details, see Lisowski and others, 1990) 

and (B) leveling network of 211 bench marks (after Marshall and others, 1991). Star, epicenter of 1989 

Loma Prieta earthquake. Inset in figure 1B shows locations of leveling lines 1 through 7; circled dots 

correspond to first stations of leveling lines in figure 3. 
A292 MAIN-SHOCK CHARACTERISTICS 

other quantities of interest, such as the surface displacements and the stresses near the edge of the rupture zone, 

can be calculated. An important feature of this solution is 

that the exact asymptotic form of the displacement field 

near the edge of a crack (rupture zone) in elastic solids is 

used to approximate the kernels of the integral equation. 

Therefore, the stress-intensity factors (coefficients of the 

6 singularity at the edge of the rupture zone, where r is 

the distance from the edge; see Rice, 1968) can be calculated accurately. Then, the energy-release rate G-that is, 

the amount of energy released per unit area of advance of 

the rupture-can be calculated by using the following expression (Rice, 1968): 

where p is the shear modulus, v is Poisson's ratio, and KI, 

KII, and KIII are the stress-intensity factors for modes I, 

11, and 111, respectively. A common and simple criterion 

for both quasi-static and dynamic modeling of rupture 

propagation is to assume that rupture propagation occurs 

when the local energy-release rate is equal to a critical 

value which reflects the material resistance to slip. Although this criterion is too simple to describe in detail the 

actual rupture process, it provides a good description when 

slip occurs in a region near the edge of the rupture zone 

on a length scale much smaller than other relevant lengths, 

for example, fault-rupture length, distance to the free surface, and so on (Rice, 1980, 1983; Rudnicki, 1980). If we 

assume that the rupture propagates according to the criterion that the energy-release rate is equal to a critical value, 

then the maximum G value, Gma,,, estimated here is a 

lower bound on the critical energy-release rate at the termination of rupture. If this critical energy-release rate varies strongly with position and (or) velocity, as is likely, 

then the Gmax value estimated here may differ from those 

calculated with dynamic rupture models (for example, 

Beroza and Spudich, 1988). 

Figure 1 .-Continued. 
STRESS-DROP MODELS TO INTERPRET GEODOLITWGLOBAL POSITIONING SYSTEM AND LEVELING MEASUREMENTS A293 

Table 1 .-Model fit of coseismic offset to Geodolite/Global Positioning System data 

[All values in millimeters. GPS, Global Positioning System] 

Beg-g Ending Coseismic offset 

station station Residual 

(fig. 1) (fig. 1) Observed Calculated 

Begeg Ending Coseismic offset 

station station Residual 

(fig* 1) (fig. 1) Observed Calculated 

Geodolite line-length changes Geodolite line-length changes-Continued 

Allison 

Allison 

Allison 

American 

American 

American 

Biel 

Biel 

Biel 

BMT FS 

BMT FS 

Butano 

Butano 

Butano 

Butano 

CROSSRMl 

Dump 

Eagle Rk 

Gilroy 

Gilroy 

Hamil Ec 

Hamil Ek 

Llagas 

Llagas 

LOMA USE 

Mindego 

BMTlO 

BMTlO 

BMT 1 ORM 1 

BMTll 

BMTll 

BMTll 

BMT8 

BMT8 

BMT9 

Pawt 

Pawt 

Allison 

Eagle Rk 

Hamilton 

LOMADWR 

LP 1 

LP 1 

Brush 2 

Brush 2 

Chamber 

Chamber 

Chamber 

Fairview 

Fremont 

Fremont 

Gilroy 

Hollis 

Juan 

Juan 

LP 1 

BMT RF 

Hamilton 

Mindego 

BMT RF 

Hamilton 

LOMA USE 

Eagle Rk 

LOMA USE 

Mindego 

LOMA USE 

Mindego 

Dump 

Eagle Rk 

Mindego 

Pom 

Mindego 

Pom 

Mindego 

Llagas 

LP 1 

Llagas 

SHEEPRM2 

LP 1 

SHEEPRM2 

Mindego 

Pom 

BMT9 

Pawt 

BMT9 

BMT8 

BMT9 

Pawt 

BMT9 

W5Reset 

SKY 1 

Wl 

SKY 1 

Lomancer 

Lomancer 

Lomancer 

PR6 

LP2 

LP4 

Fremont 

Mulligan 

Juan 

Mulligan 

Vqo 

Juan 

Juan 

Mulligan 

Juan 

Juan 

Mulligan 

Sargent 

vargo 

Fremont 

Canada 

Canada 

Fairview 

Gilroy 

Canada 

Gilroy 

Canada 

P 1 

P 1 

P 1 

P 1 

P2 

P2 

P2 

P2 

P2 

P 3 

P3 

P3 

P4 

P4 

P4 

P5 

P5 

P 7 

P 5 

P 5 

Sargent 

Fairview 

Sargent 

Gilroy 

Sargent 

SHEEPRM2 

SHEEPRM2 

Gilroy 

P2 

P3 

P4 

P6 

P3 

P4 

P5 

P6 

P7 

P4 

P5 

P6 

P5 

P6 

P7 

P6 

P7 

P8 

c 1 

Chamb 2 

GPS east 

LP 1 Allison 34.8k5.9 55.2 -20.4 

LP 1 Eagle Un 225.2k11.8 243.6 -18.4 

LP 1 Hamilton 65.6k7.0 66.0 -.4 

LP 1 Brush 2 41.3k15.6 78.4 -37.1 

GPS north 

LP 1 Allison -1 10.6k3.8 -103.7 -6.9 

LP 1 Eagle Un -205.455.6 -185.3 -20.1 

LP 1 Hamilton -106.6k2.6 -96.2 -10.4 

LP 1 Brush 2 -229.2k4.6 -205.1 -24.1 

GPS up 

LP 1 Allison -105.5k33.4 -129.1 23.6 

LP 1 Eagle Un -21 1.8k24.7 -202.6 -9.2 

LP 1 Hamilton -1 14.4k25.5 A, -131.4 17.0 

LP 1 Brush 2 -4O.Ok27.8 -93.4 53.4 

RESULTS AND DISCUSSION 

Marshall and others (1991) found that the fault model 

that best fits the leveling data is not fully consistent with 

the model used by Lisowski and others (1990) to fit the 

geodeticlGPS data. More specifically, Marshall and others found that using the parameters calculated by Lisowski 

and others to model the elevation changes produces a misfit 

twice as large as that for their best-fitting model. In our 

modeling, therefore, we search for the models that best fit 

separately the GeodolitelGPS data of Lisowski and others 

and the leveling data of Marshall and others. We then 

search for the model that best fits both the GeodolitelGPS 

and the leveling data. The best-fitting models are determined by trial and error. The starting fault surface is suggested by the main-shock and aftershock locations (Dietz 

and Ellsworth, 1990). 

Reasonable agreement with the EDM (line-length 

changes) and GPS vector changes of Lisowski and others 

(1990) is obtained with a model for which the strike, dip, 

depth to center, length, width, and area of the rupture 

zone are about 132O, 73O, 11 km, 44 ktn, 15 ktn, and 518 
MAIN-SHOCK CHARACTERISTICS 

Table 2.-Modeling of the Geodolite/Global Positioning System and Leveling Data 

[GPS, Global Positioning System] 

GeodoliteIGPS data Leveling data 

Dislocation Dislocation 

model of This model of This 

Lisowski and study Marshall and study 

others (1 990) others (1 99 1) 

Length (2L) (km) --------- ------- Depth to top (dsin a) (km)---- Width (D-d) (km) ----------- --- Rupture area (km2) -------------- Dip (a) (O) ....................... Slip amplitude along strike 

(m). Slip amplitude along dip 

6-4. 

Geodetic moment (Mo) 

(lo^ N-m). 

Alongstrike stress-drop 

component (AT,) (MPa). 

Alongdip stress-drop 

component (AT^) (MPa). 

Maximum energy-release 

rate (Gmax) (106 J/m2). 

Misfit-to-noise ratio ------------ 

44 

3.8 

15 

518 

73 

avg 1.3 

40 

3.6 

13 

408 

65 

avg 1.8 

avg 1.1 avg 1.5 

km2, respectively. The surface location of the rupturezone center is lat 37.07' N., long 121.83' W. The stressdrop components are A~=1.45 MPa (along strike) and 

Atd=1.35 MPa (along dip), and the calculated geodetic 

moment is 2.5x1019 N-m. The maximum energy-release 

rate, which occurs near the top of the model fault, is about 

5.5~10~ J/m2; the minimum energy-release rate is about 

2.0~10~ J/m2. In general, the location of the maximum 

energy-release rate depends on the aspect ratio of the rupture zone and the ratio of the stress-drop components (Wu 

and others, 1991). The distribution of slip over the fault 

surface would be elliptical for uniform stress drop on a 

planar elliptical zone embedded within an infinite space. 

Here, within the elastic half-space, the slip distribution is 

approximately elliptical but is skewed toward the free surface. More specifically, the peak slip amplitude does not 

occur at the geometric center but at a distance from the 

center equal to a fourth of the half-width closer to the free 

surface. The average slip amplitudes in the strike and (reverse) dip direction, respectively, are [u]=1.3 m and 

[>L,]=1.1 m. The fit of the best model to the Geodolitel 

GPS data is listed in table 1, and the model parameters 

are compared with those of Lisowski and others (1990) in 

table 2. The misfit-to-noise ratio is 2.4, and the largest 

misfit occurs on line LP1-LP2 (table 1). As pointed out 

by local movements accompanying the widespread surface cracking and secondary faulting observed in the epicentral area (U.S. Geological Survey staff, 1990). The 

geodetic moment, dip, rupture area, and strike-slip and 

dip-slip amplitudes are close to those (2.8x1019 N-m, 70Â° 

492 km2, 1.6 m, 1.2 m) obtained by Lisowski and others. 

Because our method is more computationally demanding 

than the conventional dislocation method, we tested the 

sensitivity of the model fit only approximately. Nevertheless, we found that the model fit can be degraded significantly for rupture zones with lengths (2L) less than 40 

km, although greater lengths are permitted by the 

GeodoliteIGPS data. In addition, the dip of the model 

fault can be varied between 70' and 75' without increasing the model misfit significantly. 

The best-fitting model for the leveling data of Marshall 

and others (1991) corresponds to a moderately different 

fault geometry. Specifically, the strike, dip, depth to center, length, width, and area of the rupture zone are about 

133', 65', 9.5 km, 40 km, 13 km, and 408 km2, respectively. In addition, the surface location of the rupturezone center (lat 37.06' N., long 121.88' W.) is about 2 

km southwest of that in the GeodoliteIGPS model. The 

rupture-zone area inferred here is slightly smaller than 

that inferred from the GeodoliteIGPS data, but the 

by Lisowski and others, this line probably was affected alongstrike and alongdip stress-drop components, geodetic 
STRESS-DROP MODELS TO INTERPRET GEODOLITWGLOBAL POSITIONING SYSTEM AND LEVELING MEASUREMENTS A295 

moment, and maximum energy-release rate are all slightly 

larger: Ats=l .7 MPa, Atd= 1.95 MPa, ~~=2.8xl0~~ N-m, 

and G~~=S. 8x 1 o6 ~lm~, respectively. The rupture-zone 

area is close to that (372 km2) obtained by Marshall and 

others (1991). The average slip amplitudes in the strike 

and (reverse) dip directions, respectively, are [iis]=1.8 m 

and [%]=IS m, and the misfit-to-noise ratio is 1.9. The 

fit of the best model to the leveling data is profiled in 

figure 3, and the model parameters are compared with 

those of Marshall and others in table 2. As shown in figure 3, the calculated elevation changes agree reasonably 

well with the observed data along the leveling lines (fig. 

lB), but, similar to the result of Marshall and others, notable misfits occur in several places along someleveling 

lines. Approximate sensitivity tests suggest that the leveling data are more sensitive to the length of the rupture 

zone than are the GeodoliteIGPS data. Specifically, the 

model fit to the leveling data can be degraded significantly for rupture-zone lengths greater than 44 and less 

than 34 km. The dip of the model fault here is about 5' 

greater than that obtained by Marshall and others, but 

Fault plane 

Figure 2.-Schematic sketch of rupture-zone model, showing a planar 

elliptical zone (shaded oval) embedded within an elastic half-space. x-y 

plane coincides with half-space surface, x-axis is parallel to strike of 

rupture zone and to semimajor axis of ellipse, and z-axis points downward into half-space. x-, y-, and z-axes are all orthogonal. Â£-axis which 

is intersection of vertical y-z plane and slip plane, is parallel to minor 

axis of ellipse. a, angle between Â£ and y-axes; d, depth to top of rupture 

zone (along x direction); D, depth to bottom of rupture zone (along 6 

direction); L, half-length of rupture zone. Orientation of stress drop AT 

is defined by angle o measured from Â direction; thus, vertical depth to 

top of rupture zone is dsin a, and width of rupture zone is D-d. Two 

stress-drop components along strike and dip directions are A~=Arsin (0 

and AT~=ATCOS o, respectively. 

decreasing the dip to 63' gives only a slightly larger misfit. 

As found by Marshall and others (1991), if we use the 

parameters of the best-fitting GeodoliteIGPS model to interpret the leveling data, the misfit-to-noise ratio increases 

to 3.4. Similarly, using the parameters of the best-fitting 

leveling model produces a misfit-to-noise ratio of 3.2 to 

the GeodoliteIGPS data. If we combine these two data 

sets, the best-fitting model suggests a fault geometry somewhat between those for the two best-fitting models obtained from the GeodoliteIGPS and leveling data. 

Specifically, the strike, dip, depth (to center), length, and 

width of the rupture zone are about 132O, 70Â° 10.5 km, 

42 km, and 13.5 km, respectively. However, then the misfit-to-noise ratio is 3.0, about 50 percent larger than the 

best-fitting GeodoliteIGPS and leveling models. 

The discrepancy between the two model fits indicates 

that our model does not capture fully the actual faulting 

behavior. Indeed, the aftershock locations of Dietz and 

Ellsworth (1990) suggest a kinked fault with a joint at 

about 6-km depth, rather than the simple planar surface 

we have assumed here. Future analysis of the mechanical 

behavior of a kinked rupture zone (of prescribed stress 

change) may lead to a better understanding of the groundsurface response to such a complex rupture. In addition, 

other modifications on the surface displacements may be 

introduced, owing to variations in stress drop and a 

nonelliptical shape of the rupture zone. Our model fits 

probably could be improved by allowing a nonuniform 

stress drop and shapes other than elliptical. However, because of the tradeoff between the stress-drop distribution 

and the configuration of the rupture zone, there is little 

point in doing so before additional constraints on the rupture-zone geometry are determined. 

Although the long-term rates of horizontal and vertical 

displacement in the Loma Prieta region differ substantially, the inferred stress-drop components (and average 

slip components) along strike and dip are approximately 

equal. Because the long-term horizontal-displacement rates 

exceed the vertical rates by more than a factor of 10 in 

the San Francisco Bay region (Bradley and Griggs, 1976; 

Prescott and others, 1981; Hanks and others, 1984), stress 

drops along the strike directions might be expected to be 

much larger than those along the dip directions for rupture zones in this region. As pointed out by many investigators (for example, Anderson, 1990; Segall and Lisowski, 

1990; Valensise and Ward, 1991), this result suggests that 

Loma Prieta-type events with subequal components of 

stress drop along strike and dip must be relatively infrequent. 

The maximum energy-release rate for the 1989 Loma 

Prieta earthquake is toward the upper end of the range of 

the critical energy-release rate inferred for crustal faulting 

(Rudnicki, 1980; Li, 1987): from loo to lo8 ~/m~, with

most values ranging from lo5 to lo8 ~lm~. Thisresult is 
MAIN-SHOCK CHARACTERISTICS 

consistent with the inferred infrequency of a Loma Prietatype event: High maximum energy-release rates suggest 

that the rupture propagated through relatively intact or 

largely rehealed rock. The recent study by Wu and others 

(1991) estimated critical values of 1 .5xlo6 J/m2 for the 

1966 Parkfield, Calif. (Ms=5.6), 1.2~10~ J/m2 for the 1983 

fiorah Peak, Idaho (Ms=6.9), and 2x10~ J/m2 for the 1987 

Whittier Narrows, Calif. (M=6.0), earthquakes. Among 

them, the critical value of 1.5~10~ J/m2 for the 1966 

Parkfield earthquake is consistent with the 2.0~10~ J/m2 

estimated by Beroza and Spudich (1988), using a dynamic 

rupture model, and with the 0.8~10~ J/m2 estimated by 

Aki (1978), using a barrier model for the same event. 

These values and the estimate for the 1989 Loma Prieta 

karthquake are about 100 times larger than those (of approx 

lo4) inferred from slip experiments on sawcut laboratory 

specimens, as collected by Wong (1982, 1986), and those 

(ranging from 5x10~ to 2x10~ J/m2) inferred from field 

20 40 60 80 

DISTANCE, 

IN KILOMETERS 

observations of slip along small faults in granite rock, as 

reported by Martel and Pollard (1989). Currently available estimates of the critical energy-release rate for crustal 

faulting exhibit considerable variation, and further efforts 

in estimating their values and variation throughout the 

crust are needed to better understand the mechanism of 

earthquake faulting. 

ACKNOWLEDGMENTS 

This research was supported by U.S. Geological Survey grant 14-08-0001-G1847 and U.S. National Science 

Foundation grants EAR-8707392 and EAR-9 105467. 

Thoughtful comments by Paul Spudich and the reviewers 

improved the manuscript. We thank Grant Marshall for 

checking our use of the data and pointing out a datumshift error. 

-200 ! I I I I 1 -200 

0 20 40 60 80 100 1 20 40 

DISTANCE, DISTANCE, 

IN KILOMETERS IN KILOMETERS 

t 

0 20 40 60 0 20 40 60 0 20 0 20 40 

DISTANCE, DISTANCE, DISTANCE, DISTANCE, 

IN KILOMETERS IN KILOMETERS IN KILOMETERS IN KILOMETERS 

Figure 3.-Profiles of model fault (solid curves) derived from observed coseismic elevation changes AH along leveling lines 1 through 7 (inset, fig. 

15). Error bars indicate relative uncertainty in leveling data. Note that vertical scale for leveling line 4 is about twice as larger as that for other 

leveling lines. , 
STRESS-DROP MODELS TO INTERPRET GEODOLITEJGLOBAL POSITIONING SYSTEM AND LEVELING MEASUREMENTS A297 

REFERENCES CITED 

Aki, Keiiti, 1978, Origin of the seismic gap; what initiates and stops a 

rupture propagation along a plate boundary?, in Proceedings of 

Conference VI; Methodology for Identifying Seismic Gaps and Soonto-Break Gaps: U.S. Geological Survey Open-File Report 78-943, 

p. 3-46. 

Anderson, R.S., 1990, Evolution of the northern Santa Cruz Mountains 

by advection of crust past a San Andreas Fault bend: Science, v. 

249, no. 4967, p. 397-401. 

Behr, Jeffrey, Bilharn, Roger, Bodin, Paul, Burford, R.O., and Burgmann, 

Roland, Aseismic slip on the San Andreas fault south of Loma 

Prieta: Geophysical Research Letters, v. 17, no. 9, p. 1445-1448. 

Beroza, G.C., and Spudich, Paul, 1988, Linearized inversion for fault 

rupture behavior; application to the 1984 Morgan Hill, California, 

earthquake: Journal of Geophysical Research, v. 93, no. B6, p. 

6275-6296. 

Bradley, W.C., and Griggs, G.B., 1976, Form, genesis, and deformation 

of central California wave-cut platforms: Geological Society of 

America Bulletin, v. 87, no. 3, p. 433-449. 

Dietz, L.D., and Ellsworth, W.L., 1990, The October 17, 1989, Loma 

Prieta, California, earthquake and its aftershocks; geometry of the 

sequence from high-resolution locations: Geophysical Research Letters, v. 17, no. 9, p. 1417-1420. 

Hanks, T.C., Bucknam, R.C., Lajoie, R.K., and Wallace, R.E., 1984, 

Modification of wave-cut and faulting-controlled landforms: Journal of Geophysical Research, v. 89, no. B7, p. 5771-5790. 

Langbein, J.O., 1990, Post-seismic slip on the San Andreas Fault at the 

northwestern end of the 1989 Loma Prieta earthquake rupture zone: 

Geophysical Research Letters, v. 17, no. 8, p. 1223-1226. 

Li, V.C., 1987, Mechanics of shear rupture applied to earthquake zones, 

in Atkinson, B.K., ed., Fracture mechanics of rock: London, Academic Press, p. 351-428. 

Lisowski, Michael, Prescott, W.H., Savage, J.C., and Johnston, M.J.S., 

1990, Geodetic estimate of coseismic slip during the 1989 Loma 

Prieta, California, earthquake: Geophysical Research Letters, v. 17, 

no. 9, p. 1437-1440. 

Mansinha, Lalatendu, and Smylie, D.E., 1971, The displacement fields 

of inclined faults: Seismological Society of America Bulletin, v. 

61, no. 5, p. 1433-1440. 

Martel, S.J., and Pollard, D.D., 1989, Mechanics of slip and fracture 

along small faults and simple strike-slip fault zones in granitic rock: 

Journal of Geophysical Research, v. 94, no. B7, p. 9417-9428. 

Marshall, G.A., Stein, R.S., and Thatcher, Wayne, 1991, Faulting geometry and slip from coseismic elevation changes; the 18 October 

1989, Loma Prieta, California, earthquake: Seismological Society 

of America Bulletin, v. 81, no. 5, p. 1660-1693. 

Olson, J.A., 1990, Seismicity in the twenty years preceding the Loma 

Prieta, California earthquake: Geophysical Research Letters, v. 17, 

no. 9, p. 1429-1432. 

Prescott, W.H., Davis, J.L., and Svarc, J.L, 1989, Global Positioning 

System measurements for crustal deformation; precision and accu~ 

racy: Science, v. 244, no. 4910, p. 1337-1340. 

Prescott, W.H., Lisowski, Michael, and Savage, J.C., 1981, Geodetic 

measurement of crustal deformation on the San Andreas, Hayward 

and Calaveras faults near San Francisco, California: Journal of Geophysical Research, v. 86, no. 11, p. 10853-10869. 

Rice, J.R., 1968, Mathematical analysis in the mechanics of fracture, in 

Liebowitz, Harold, ed., Fracture; an advanced treatise: New York, 

Academic Press, p. 191-3 1 1. 

1980, The mechanics of earthquake rupture, in Dziewonski, A.M., 

and Boschi, Enzo, eds., Physics of the Earth's interior: Amsterdam, 

North Holland, p. 555-649. 

1983, Constitutive relations for fault slip and earthquake instabilities: Pure and Applied Geophysics, v. 121, no. 3, p. 444-475. 

Rudnicki, J.W., 1980, Fracture mechanics applied to the Earth's crust 

Annual Review of Earth and Planetary Science, v. 8, p. 489-525. , 

Savage, J.C., and Prescott, W.H., 1973, Precision of Geodolite distance 

measurements for determining fault movements: Journal of Geqphysical Research, v. 78, no. 26, p. 6001-6007. 

Segall, Paul, and Lisowski, Michael, 1990, Surface displacements in the 

1906 San Francisco and 1989 Loma Prieta earthquakes: Science, vj 

250, no. 4983, p. 1241-1244. 

Schwartz, S.Y., Orange, D.L., and Anderson, R.S., 1990, Complex fault 

interactions in a restraining bend on the San Andreas fault, south* 

em Santa Cruz Mountains, California: Geophysical Research Letters, v. 17, no. 8, p. 1207-1210. 

U.S. Geological Survey staff, 1990, The Loma Prieta, California, earthquake; an anticipated event: Science, v. 247, no. 4940, p. 286-293. 

Valensise, Gianluca, and Ward, S.N., 1991, Long-term uplift of the 

Santa Cruz coastline in response to repeated earthquakes along the 

San Andreas Fault: Seismological Society of America Bulletin, v. 

81, no. 5, p. 1694-1704. 

Wong, Teng-fong, 1982, Shear fracture energy of Westerly Granite from 

post-failure behavior: Journal of Geophysical Research, v. 87, no. 

B2, p. 990-1000. 

1986, On the normal stress dependence of the shear fracture 

energy, in Das, Sharnita, Boatwright, John, and Scholz, C.H., eds., 

Earthquake source mechanics: American Geophysical Union Geophysical Monograph 37, p. 1-1 1. 

Wu, Mingdong, Rudnicki, J.W., Kuo, C.H., and Keer, L.M., 1991, Surface deformation and energy release rates for constant stress drop 

slip zones in an elastic half-space: Journal of Geophysical Research, 

v. 96, no. 10, p. 16509-16524. 

Â¥ U.S. GOVERNMENT PRINTING OFFICE: 1997 - 573-046 / 20064 REGION NO. 8