The Lorna Prieta, California, Eaahquake of 

October 17, 1989-Tectonic Processes and Models 

ROBERT W. SIMPSON, Editor 

EARTHQUAKE OCCURRENCE 

WILLIAM H. BAKUN and WILLIAM H. PRESCOTT, Coordinators 

UoSo GEOLOGICAL SURVEY PROFESSIONAL PAPER 1550-F 

- -- 

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1994 

CONTENTS 

Relations between folding and faulting in the Loma Prieta 

epicentral zone: Strike-slip fault-bend folding---------- 

By John H. Shaw, Richard E. Bischke, and John Suppe 

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 ----- ------ ----- ------ -------- ---- --- 

By Gianluca Valensise 

Complex fault interactions in a restraining bend on the 

San Andreas fault, southern Santa Cruz Mountains, 

California --------------- - .................................... 

By Susan Y. Schwartz, Daniel L. Orange, and 

Robert S. Anderson 

By Robert W. Simpson and Paul A. Reasenberg 

Cumulative slip along the peninsular section of the 

San Andreas fault, California, estimated from 

two-dimensional boundary-element models of 

historical rupture - ---- ----- ----- ------ ----- ---- ----- - - 

By Paul Bodin and Roger Bilham 

Three-dimensional lithospheric kinematics in the 

Loma Prieta region, California: Implications for the 

cycle ................................. --- ------- 

Bv Kevin P. Furlong and David Verdonck 

Page 

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THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAKE OCCURRENCE 

TECTONIC PROCESSES AND MODELS 

INTRODUCTION 

By Robert W. Simpson, 

U.S. Geological Survey 

If there is a single theme that unifies the diverse papers in 

this chapter, it is the attempt to understand the role of the 

Loma Prieta earthquake in the context of the earthquake 

"machine" in northern California: as the latest event in a 

long history of shocks in the San Francisco Bay region, as 

an incremental contributor to the regional deformation pattern, and as a possible harbinger of future large earthquakes. 

One of the surprises generated by the earthquake was 

the rather large amount of uplift that occurred as a result 

of the reverse component of slip on the southwest-dipping 

fault plane. Preearthquake conventional wisdom had been 

that large earthquakes in the region would probably be 

caused by horizontal, right-lateral, strike-slip motion on 

vertical fault planes. 

In retrospect7 the high topography of the Santa Cruz 

Mountains and the elevated marine terraces along the 

coast should have provided some clues. With the observed 

ocean retreat and the obvious uplift of the coast near Santa 

Cruz that accompanied the earthquake, Mother Nature was 

finally caught in the act. Several investigators quickly saw 

the connection between the earthquake uplift and the longterm evolution of the Santa Cruz Mountains and realized 

that important insights were to be gained by attempting to 

quantify the process of crustal deformation in terms of 

Loma Prieta-type increments of northward transport and 

fault-normal shortening. 

Three papers in this chapter explore how the geometry 

of the Loma Prieta fault plane and the oblique slip recorded 

during the earthquake can be used to explain the structural 

and topographic features of the Santa Cruz Mountains. Shaw 

and others present a detailed, three-dimensional kinematic 

model7 based on repeated earthquakes on a nonplanar Loma 

Prieta rupture surface, that explains the location and evolution of synclines mapped in the southern Santa Cruz Mountains. Their method allows them to infer the depth and 

position of fault bends in the subsurface from surface geologic structures. The inferred geometry compares favorably 

with the locations of aftershocks and is consistent with the 

observed main-shock slip direction. They suggest that Loma 

Prieta-type events should recur every 132k26 years. Their 

approach shows promise for inferring information about deformation modes at depth in regions where earthquakes have 

not been recorded during historical time. 

Valensise uses the present elevations of the first and third 

marine terraces near Santa Cruz and the geometry on the base 

of the Upper Miocene and Pliocene Purisima Formation to 

explore the relative contributions of strike-slip and reverseslip earthquake offsets to the northward transport and uplift 

of the Santa Cruz region. From his models7 he concludes that 

the location of Loma Prieta-type events has remained stationary relative to the North American plate over the past million 

years and that only a fraction of the topography in the Santa 

Cruz Mountains can be explained by such events. He suggests 

that the remaining uplift may have been generated by distributed deformation in the upper 5 km of crust caused by regional 

compression perpendicular to the plate boundary. 

Schwartz and others point out that although deformation 

associated with a restraining bend can explain many of the 

topographic features in the bay region, Loma Prieta-type 

events cannot be the only source of topographic change because Loma Prieta, the highest point in the southern Santa 

Cruz Mountains, actually subsided in the earthquake. This 

observation suggests that motion on other faults, notably 

the nearby Sargent-Berrocal fault zone, must occur periodically to complement the uplift accompanying the Loma 

Prieta main shock. If these motions occur as earthquakes, 

then there may be a part of the seismic cycle in the bay 

region that we have not yet witnessed. 

These attempts to relate geologic structures and topography, 

generated over hundreds of thousands to millions of years, 

to the deformations produced by a single earthquake have 

proved most enlightening for understanding the place of the 

1989 Loma Prieta earthquake in the larger scheme of things. 

By using quantitative models, discrepancies have been identified in the regional deformation budget, and hypotheses 

have been presented to explain these discrepancies. Although 

the final word on the subject has probably not yet been 

heard, the results from these initial efforts are quite exciting. 

Three additional papers in this chapter examine the interactions of the various faults in the San Francisco Bay 

region and the interplay of stresses on these faults7 using 

rather different approaches and presenting results that span 
F2 TECTONIC PROCESSES AND MODELS 

different time intervals. In the short term, the Loma Prieta 

rupture changed the static-stress loads on other bay-region 

faults. Simpson and Reasenberg calculate these changes, 

using dislocation theory in an elastic half-space. Sections 

of the San Andreas fault to the north and south of the Loma 

Prieta rupture zone now have greater stress loads as a result 

of the earthquake, whereas the Hayward fault has been slightly relaxed in most models. If the earthquake pairs in 1836138 

and 1865168 on the Hayward and San Andreas faults were 

caused by triggering across the bay7 the most likely way 

for the 1989 earthquake to trigger an event on the Hayward 

fault during the next several years would be through extensional normal stresses applied at the south end of the 

Hayward fault. If pore fluids are present, the full effect of 

this unclamping might not be felt for several years as the 

fluids reequilibrate. 

Looking at the record of historical earthquakes7 Bodin 

and Bilham use two-dimensional dislocation models to investigate the overall slip budget on the San Andreas fault 

since 1800. They load an elastic plate at an azimuth representing the relative motion between the North American 

and Pacific plates, and allow faults, represented as vertical 

cuts in the plate, to slip frictionlessly along segments corresponding to the estimated rupture lengths of historical 

earthquakes. Slip from the 1989 Loma Prieta earthquake is 

underestimated by their model, suggesting either higher 

failure strain for this event or limitations of a two-dimensional approach. The concept of using geometrically realistic mechanical models that include fault interactions to 

account for slip and stress budgets for earthquake-prediction purposes is an important advance over simple time- or 

slip-predictable models of earthquake recurrence. 

Taking the very long view, Furlong and Verdonck use 

finite-element modeling to explore how bay-region faults* 

including the Loma Prieta rupture surface, interact. Their 

preferred model uses a viscously deforming shear zone in 

the lower crust to connect the San Andreas fault with the 

Hayward and Calaveras faults in the east bay. Most of the 

deep plate-boundary motion occurs under these east-bay 

faults in this model, and motion is transferred to the San 

Andreas fault in the Loma Prieta region via a horizontal 

shear zone. Their model suggests that Loma Prieta-type 

events may represent decoupling of the Santa Cruz crustal 

block from its underlying mantle in response to stress accumulation after large, 1906-type earthquakes. 

Although these modeling efforts are still limited in 

scope and complexity7 they do suggest that useful insight 

can be gained with relatively simple models, and they 

offer the hope that someday we may know enough about 

the Earth's crust and mantle beneath the San Francisco 

Bay region to devise models able to do justice to the 

earthquake "machine." 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAmOCCUmNCE 

Tl2CTONIC PROCESSES AND MODELS 

RELATIONS BETWEEN FOLDING AND FAULTING IN 

THE LOMA PRIETA EPICENTRAL ZONE: 

STRIKE-SLIP FAULT-BEND FOLDING 

By John H. Shaw, Richard E. Bischke, and John Suppe, 

Princeton University 

Introduction ............................................................... 

Folding and faulting in the epicentral zone-------------------------- 

Surface relations between folds and faults .................... 

Three-dimensional balanced models of strike-slip folding-- 

Predicting subsurface fault geometry--------------------------- 

Subsurface fault geometry inferred from Loma Prieta 

%ismicity ........................................................ 

Fault slip .................................................................. 

Fault-slip directions and regional stress------------------------ 

Recurrence intervals, long-term slip, and uplift rates-------- 

Motion on the Byante fault ..................................... 

Summaq and conc~u~ion~ .............................................. 

Acknowledgments ..................................................... -- References cited .......................................................... 

Page 

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ABSTRACT 

We present balanced kinematic models of strike-slip faultbend folding that demonstrate how synclines in the 1989 

Loma Prieta epicentral zone grow in transpression. Rightlateral motion along left-stepping restraining bends in the 

San Andreas and Zayante faults results in transpression and 

uplift of rocks adjacent to the fault bends. Uplift is caused 

by thrusting over nonplanar fault surfaces, causing folding 

of the hanging-wall block. We model fold growth by kinkband migration, with deformation of the overriding block 

localized along active axial surfaces, which are pinned to 

subsurface fault bends. Applied to the epicentral zone, these 

balanced models yield predictions of the subsurface fault 

geometry. The orientation of the Glenwood syncline, which 

emanates in map view from a restraining bend in the San 

Andreas fault, suggests a steepening-upward subsurface bend 

in the underlying fault at a depth of about 8 km. The Scotts 

Valley syncline, which emanates in map view from a bend 

in the nearby Zayante fault, suggests a similar steepeningupward bend in the underlying fault at a depth of about 15 km. 

We test our predictions of the subsurface fault geometry in 

the Loma Prieta epicentral zone by examining hypocenters 

of the earthquake and its aftershocks. A contour map and 

series of cross sections of the fault surface, based on aftershock locations, confirm the existence of a steepening-upward 

subsurface bend in the San Andreas fault at 8-krn depth. 

Furthermore, the geometry of this fault bend agrees with the 

fold orientation. The consistency between the fault geometry 

predicted by our models applied to surface data and the shape 

of the subsurface fault rupture outlined by aftershocks confirms the relation between fold and fault shape. These results 

suggest that fault-bend-folding theory is a viable explanation 

for the origin of folds that lie adjacent to strike-slip faults. 

We further test our models by comparing their predicted 

slip directions with slip vectors inferred from seismology and 

regional stress. Our predicted slip directions are found to be 

consistent with both the slip vector of the main shock and 

shear-stress directions resolved onto the various fault segments from regional stresses. Assuming that these favorable 

slip directions approximate the long-term slip directions, the 

12-mdyr slip rate on the San Andreas fault southeast of the 

rupture zone must increase to 15.2 mmlyr onto the rupture 

surface. This increase in slip rate within restraining bends 

may explain why the 1989 Loma Prieta and, possibly, 

other strike-slip earthquakes originate at fault bends. This 

15.2-dyr slip rate resolves to a 11.6-dyr strike-slip, 

9.8-dyr dip-slip, and 9.2-dyear uplift rate above the 

inclined fault rupture. This uplift rate, once it is corrected for 

isostatic compensation, falls within the range of uplift rates in 

the Loma Prieta epicentral zone predicted from dated marine 

terraces along the nearby Santa Cruz coastline. This result 

suggests that most slip on the adjacent San Andreas fault is 

transferred onto the inclined ruptpre surface, and if this slip is 

released in Loma Prieta-type events (2M.4 m of slip), a major 

earthquake should recur every 132k26 yr. In addition, a study 

of syntectonic sediment deposited along the adjacent Zayante 

fault indicates large motions before deposition of the Pliocene section. More recent strike-slip motion that began during the middle Pliocene appears to continue into the present. 

F3 
TECTONIC PROCESSES AND MODELS 

INTRODUCTION 

The 1989 Loma Prieta earthquake occurred along a leftstepping bend of the San Andreas fault in the Santa Cruz 

Mountains of central California (fig. 1). In analogy with the 

Transverse Ranges north of the Los Angeles Basin (Crowell, 1974a, b), right-lateral motion on the San Andreas fault 

into a left-stepping restraining bend has resulted in transpression, uplift, and deformation of the hanging-wall rocks 

adjacent to the fault. In support of these conclusions, (1) 

earthquake focal-mechanism solutions of the Loma Prieta 

main shock suggest a combination of reverse and strike-slip 

motion on a 7O0&1O0 SW.-dipping fault (Oppenheimer, 

1990), and (2) modeling of geodetic data by Lisowski and 

others (1990) indicates that 1.6 m of right-lateral slip and 

1.2 m of reverse-slip occurred during the earthquake. 

In this paper, we examine young geologic structure in 

the Loma Prieta epicentral zone, which includes deformed 

Pliocene to Holocene syntectonic (growth) sedimentary 

deposits adjacent to bends in the San Andreas and nearby 

Zayante faults (fig. 2). Right-lateral motion along these 

faults into left-stepping bends in the Loma Prieta epicentral zone generates synclines within recently deposited 

sediment. Material entering the restraining bends is thrust 

upward, causing monoclinal folding of the hanging-wall 

block. Quaternary sedimentary deposits and the upper Miocene and Pliocene Purisima Formation have been deformed into the Glenwood syncline as material has moved 

past a restraining bend in the San Andreas fault (fig. 2). 

Another syncline that folds the Purisima Formation runs 

through Scotts Valley, formed as material passed through a 

similar restraining bend in the nearby Zayante fault. 

We present balanced models of strike-slip fault-bend 

folding that show how these folds grow in restraining 

bends. Fold growth is modeled by kink-band migration, 

with deformation of the overriding block localized along 

axial surfaces pinned to subsurface fault bends. Application of these models to the folds in the Loma Prieta epicentral zone predicts the subsurface fault geometry, 

including the orientation of fault surfaces and depth to 

subsurface fault bends. To test our predictions of subsurface fault geometry, we examine hypocenters of the 1989 

Loma Prieta aftershock sequence. A contour map of the 

fault-surface rupture, a series of cross sections, and fault 

models confirm the existence of a subsurface bend in the 

San Andreas fault system, consistent with that predicted 

by the location and orientation of the Glenwood syncline. 

The subsurface geometry of the Zayante fault is also inferred from the location and orientation of the Scotts Valley syncline and other available data. 

Surface geology and aftershocks of the earthquake suggest that the Loma Prieta epicentral zone is characterized 

not by a single active throughgoing fault but by active 

segments of the San Andreas, Zayante, and Sargent(?) 

faults, which compose the San Andreas fault system. To 

test our model of the subsurface fault system, we compare 

the slip direction of the M~7.1 main shock (Oppenheimer, 

1990) and slip directions inferred from our models with 

shear-stress directions resolved onto the various fault segments from components of the regional stress tensors of 

1 22OOO' 121 '40' 

San Jose 

Restraining Bend 

1 22OOO1 1 21 '40' 

San Jose 

MONTEREY BA Y 

Figure I.-Lorna Prieta area, Calif., showing location of epicenter of 

1989 earthquake (M). A, Location of a restraining bend in the San Andrea~ fault. B, Epicenters of selected aftershocks (from Dietz and 

Ellsworth, 1990). 0, offset in seismicity between events along the San 

Andreas fault to southeast and shallow events east of fault to northwest. 

Shading marks area of figure 2. 
RELATIONS BETWEEN FOLDING AND FAULTING IN THE LOMA PRIETA EPICENTRAL ZONE 

Michael and others (1990). In addition, we use these slip 

directions, the subsurface fault geometry, and long-term 

slip rates on the San Andreas fault southeast of the Loma 

Prieta rupture zone to calculate Pliocene and Quaternary 

uplift rates above the San Andreas fault and the Loma Prieta fault segment. We compare the results with uplift rates 

in the Loma Prieta epicentral zone predicted by several 

investigators from marine-terrace elevations along the 

Santa Cruz coastline. 

To constrain past movements on the Zayante fault, 

which did not rupture in the earthquake, we examine 

electric logs from wells located on opposite sides of the 

fault. We apply a new technique to examine syntectonic 

(growth) strata, and we demonstrate that more recent motions initiated on the Zayante fault during the late Pliocene have continued into the Quaternary and, possibly, 

into the present day. 

FOLDING AND FAULTING 

IN THE EPICENTRAL ZONE 

, SURFACE RELATIONS 

BETWEEN FOLDS AND FAULTS 

Both the San Andreas and Zayante faults have major leftstepping or restraining bends in the vicinity of the Loma 

Prieta epicentral zone. The surface trace of the San Andreas 

fault changes trend from 320Â in the southeast to 310Â 

in the northwest in the study area (figs. 1, 2); a minor 

right-stepping bend marks this transition. The Glenwood 

syncline emanates in map view from this left-stepping restraining bend in the right-lateral San Andreas fault. The 

surface trace of the axial surface of the Glenwood syncline 

diverges from the fault trace, reaching a maximum distance 

of about 4 km and maintaining this distance it parallels the 

0 

- 

2 KILOMETERS 

Figure 2.4eoIogic map of Loma Prieta epicentral zone (modified from C-C' in figures 6, 9, 10, 15, and 18. A minor right-stepping bend marks 

Brabb, 19891, showing orientations of synclinal-axial surfaces that fold left-stepping change in trend of the San Andreas fault from 320' in southPliocene and younger strata emanating from restraining bends in the San east to 310' in northwest. Axial surfaces queried where inferred or uncerAndreas and Zayante faults and locations of cross sections A-A' through tain. Fault blocks: D, downthrown; U, uplifted. 
F6 'IECTONIC PROCESSES AND MODELS 

Andreas fault to the northwest for more than 17 km. The 

axial surface separates a gently southwest dipping panel to 

the south from a more steeply southwest dipping panel to 

the north, as shown by bedding dips at the surface (Brabb7 

1989) and well-log correlation data (Muir, 1972). At the 

surface, the Glenwood syncline folds semiconsolidated 

Quaternary sedimentary deposits and parts of the upper Miocene and Pliocene Purisima Formation. 

The Zayante fault also has a restraining bend in the 

Lorna Prieta epicentral zone due west of a similar bend in 

the San Andreas fault (fig. 2). Southeast of this bend, the 

most active branch of the Zayante fault trends 320' 

through Pleasant Valley and the Freedom-Watsonville, 

Calif., areas (see subsection below entitled "Motion on the 

Zayante FaultY7). Northwest of this bend, the surface trace 

of the Zayante fault trends approximately 310' for about 

13.5 km, subparallel to the adjacent San Andreas fault. 

Clark and Rietman (1973) interpreted the Zayante fault to 

be a large, near-vertical fault active during the Oligocene. 

More recent, Pliocene and Quaternary motion on the Zayante fault offsets the upper Miocene and Pliocene Purisima 

Formation (Clark* 1981). In addition, recent motion is indicated by deformed Quaternary horizons and a fault scarp 

of probable Holocene age (Hall and others, 1974; Clark 

and others, 1984). We suggest that Pliocene and Quaternary motions are predominantly strike slip in the Loma 

Prieta epicentral zone, causing local thrusting and uplift in 

a restraining bend of the Zayante fault (fig. 2). Consistent 

with this interpretation, (1) Clark and others (1984) reported oblique-reverse, right-lateral offsets across the fault; 

and (2) the surface trace of the near-vertical Zayante fault 

south of the bend parallels and merges with the San Andreas fault along the Vergeles fault (Clark, 1981). 

The Scotts Valley syncline emanates in map view from a 

left-stepping bend in the Zayante fault, similar to the relation between the nearby Glenwood syncline and the San 

Andreas fault (fig. 2). The axial-surface trace of the Scotts 

Valley syncline runs 2 to 4 km southwest of and subparallel to the Zayante fault for 8 km northwest of the fault 

bend. Farther to the northwest, the distance between the 

axial surface and fault trace decreases as the Zayante fault 

trace curves sharply to trend nearly due west (Clark, 

1981). The synclinal-axial surface separates a near-horizontal southern limb from a gently south dipping limb to 

the north. 

Eocene and Oligocene rocks adjacent to the San Andrea 

and Zayante faults are more strongly folded. The age and 

intense folding of these rocks suggest that they may have 

been deformed before the development of the modem San 

Andreas fault system during the late Miocene, associated 

with opening of the Gulf of California (Curray and Moore, 

1984). These rocks may also have been folded while passing through other restraining bends in the modern San Andreas and Zayante faults southeast of the study area. To 

model deformation solely associated with the restraining 

fault bends in the Loma Prieta epicentral zone, we concentrate on the more recent Pliocene and Quaternary growth 

sediment deposited while the faults were active. These 

younger strata are less likely to have been intensely deformed before entering the restraining bends, an interpretation consistent with areas of near-horizontal strata south 

of the axial surfaces. Locally steeper dips very close to the 

fault traces (Brabb, 1989) are attributed to minor restraining bends or to other local fault-zone processes. 

THREE-DIMENSIONAL BALANCED MODELS 

OF STRIKE-SLIP FOLDING 

Balanced models of strike-slip deformation that illustrate 

how folds grow in restraining fault bends are shown in 

figure 3. Construction of these models has been governed 

by the two basic assumptions of Suppe's (1983) faultbend-folding theory; (1) at depth, rocks are too weak to 

support large voids opened by movement of rigid blocks 

over nonplanar fault surfaces; and (2) rock volume is conserved during deformation. As focal-mechanism and 

ground-motion studies of the 1989 Loma Prieta earthquake 

have demonstrated, movement of material into a left-stepping bend in the San Andrea fault system has caused 

thrusting. This thrust component of motion results in folding of the hanging-wall block as it moves over bends in 

the underlying fault. Rich (1934) and Suppe (1983) demonstrated that rigid-block translation over nonplanar fault 

surfaces generates unreasonable "overlap7' or subsurface 

voids in the underlying rock between fault surfaces (fig. 

4). At depth, these voids cannot be supported, assuming 

reasonable rock strengths. As detailed in fault-bend-folding theory (Suppe, 1983), collapse of these voids and removal of the "overlap" may be accommodated by 

deformation of the overriding block localized along active 

axial surfaces pinned to subsurface fault bends (fig. 4). 

Folds develop as material shears through active axial surfaces, and grow by kink-band migration during progressive fault slip. The quantitative relations between fold 

shape and fault shape are those derived for fault-bend 

folding by Suppe (1983). In cases of oblique slip, which 

may arise in transpression, the limb lengths or kink-band 

widths of the folds, measured normal to the active and inactive axial-surface pairs, are minimum estimates of the 

dip slip on the underlying faults. Additional constraints on 

slip direction and subsurface fault geometry are required 

to determine the total slip vector. 

The four models shown in figure 3 all illustrate folds 

developed within restraining bends along left-stepping, 

right-lateral fault systems. The progression of models, presented in order of increasing complexity, shows how specific changes in fault geometry affect fold growth and 

fault slip. In this and the following sections, we test aspects of these simplified models and apply them to the San 
ELATIONS BEmEN FOLDING AND FAULTING IN THE LOMA PRETA EPICENTRAL ZONE F5' 

Andreas and Zayante fault systems. All the models consist kink-band migration, in which active axial surfaces are 

of vertical, dominantly strike-slip faults connected by dip- pinned to subsurface bends in the underlying thrust or 

ping thrust or oblique-slip faults. Thrusting causes uplift oblique-slip faults. In these models, axial surfaces bisect 

of material above the connecting fault plane between the mechanical-bedding units, and bed thickness and volume 

vertical faults. Uplift is accomplished with fold growth by are conserved. These balanced models therefore represent 

Overlap / 

Kink band 

Figure 4.-Balanced fault models. A, Rigid-block translation over nonplanar fault surfaces results in unreasonable "overlap" (hatched pattern) 

or subsurface voids between fault surfaces. B, Folding of hanging-wall 

block, localized along active axial surfaces (A) pinned to fault bends, 

accommodates fault slip without resulting in "overlap" or voids. 

Figure 3.-Balanced three-dimensional models of fold growth adjacent 

to restraining bends in right-lateral strike-slip fault systems, showing 

uplift and fold growth by kink-band migration above a thrust or 

oblique-slip fault that connects vertical strike-slip faults. Dark surface 

layer represents mechanical bedding; arrows indicate directions of relative motion. A, Horizontal detachment surface ramps upward and strikes 

normal to adjacent vertical faults. Width of kink band equals fault slip. 

B, Oblique-slip right-lateral thrust ramp strikes oblique to trend of 

strike-slip faults. Kink-band width represents only dip slip on underlying ramp. C, Dipping thrust with steepening-upward ramp strikes normal to adjacent vertical faults. Dip of thrust results in relative uplift of 

hanging-wall block relative to footwall, and kink-band width above 

ramp is less than slip on underlying fault. D, Dipping oblique-slip, 

right-lateral thrust with steepening-upward ramp strikes oblique to adjacent vertical fault. Only dip-slip component of motion on connecting 

faults results in uplift and kink-band growth. 
TECTONIC PROCESSES AND MODELS 

geometrically and kinematically reasonable solutions to 

fold growth in transpression. 

In model A, the connecting thrust ramps to the surface 

from a horizontal detachment at depth. This ramp is perpendicular to the strike of the adjoining vertical faults. The 

orientation of mechanical bedding is represented in all of 

the models in figure 3 by a dark surface layer. The horizontaldetachment fault at depth is bedding parallel and contains 

a slip vector parallel and equal in magnitude and direction 

to that on the adjoining strike-slip faults. During progressive 

fault slip, a dipping kink band forms above the ramp, with 

its inclined surface parallel to the underlying thrust ramp. 

Because this surface (bedding) parallels the underlying fault 

plane, the kink-band width, measured normal to the axial 

surfaces along bedding, is equal to the fault slip. 

Model B differs from model A in that the strike of the 

connecting fault ramp is not perpendicular to the strike of 

the adjoining vertical faults. The inclined surface of the 

fold again parallels the underlying fault ramp, although the 

kink-band width represents only the dip-slip component of 

motion on the oblique-slip fault ramp. Thus, for a given 

amount of slip entering a restraining bend, fold-limb width 

and uplift decrease as the strike of the connecting ramp 

approaches that of the adjacent vertical faults. In places 

where the subsurface fault geometry is known and the slip 

direction can be inferred, the magnitude of fault slip can 

be calculated from the kink-band width by resolving the 

vector triangle on the fault surface. 

In model C, the horizontal detachment in models A and 

B is replaced by an inclined connecting thrust that has a 

steepening-upward bend as it approaches the surface. The 

slip vector on the deeper segment of the thrust is again 

equal to the slip on the oblique-slip vertical faults. Unlike 

in models A and B, however, this inclined slip vector results 

in uplift of the hanging-wall block relative to the footwall 

above the deeper thrust-fault segment. Mechanical bedding 

(dark surface layer, fig. 30 does not parallel the lower 

thrust-fault segment, and so fault slip must increase slightly 

onto the steepening-upward thrust ramp (Suppe, 1983). 

Moreover, the inclined surface of the fold limb dips less 

than the underlying thrust ramp because bedding does not 

parallel the deeper thrust segment. Because only the dipslip component of motion generates the folds in these models, 

the relations between fold shape and fault shape are those 

derived for fault-bend folding by Suppe (1983). In this model 

where the fold limb dips less than the underlying thrust, 

the kink-band or fold-limb width represents a minimum 

estimate of dip slip on the fault. In places where the subsurface fault geometry is known, fault slip can be calculated. 

In places where the subsurface fault geometry is poorly 

constrained, however, fold-limb width provides a reasonable 

estimate (generally within 20 percent) of fault dip slip (Suppe 

and others, 1992). 

Model D, which combines aspects of models B and C, is 

presented as a simplified representation of fold growth in 

the Loma Prieta epicentral zone along the San Andreas and 

Zayante faults. As in model C, the dipping lower segment 

of the thrust fault ramps upward toward the surface. The 

strikes of the connecting thrusts, however, are not perpendicular to the adjacent vertical faults, as in model B. The 

dip-slip component of motion on the lower segment of the 

oblique thrust results in uplift of the hanging-wall block 

relative to the footwall. Because bedding does not parallel 

the lower connecting fault segment, slip slightly increases 

in magnitude onto the thrust ramp. Also, the inclined surface of the kink band, which develops as material shears 

through the active axial surface, dips more shallowly than 

the underlying ramp. Thus, the kink-band width in this 

model represents only a minimum estimate of the dip-slip 

component of motion on the underlying oblique-thrust 

ramp. As for the previous models, in places where the subsurface fault geometry is known and the slip direction can 

be inferred, fault-slip magnitude can be calculated. 

PREDICTING SUBSURFACE FAULT GEOMETRY 

Application of the relations between folds and faults illustrated in the models (fig. 3) to natural transpressive environments allows detailed predictions of the subsurface 

fault geometry along strike-slip fault systems. Axial surfaces that emanate from bends in strike-slip faults can be 

projected to depth if their orientations are known or are 

assumed to bisect adjacent fold limbs. The intersections at 

depth of faults and active axial surfaces predict the positions of subsurface fault bends. In addition, the acute angles between (1) bedding and the axial surface (y) and (2) 

bedding and the upper fault segment (p) can be used to 

predict the change in dip of the fault across the bend ((b) 

and the lower hanging-wall cutoff (6), using fault-bendfolding equations (fig. 5; see Suppe, 1983). 

Applying these models to the Loma Prieta epicentral zone, 

the location of the Glenwood synclinal-axial surface, which 

emanates in map view from a restraining bend in the San 

Andreas fault (fig. 2), predicts a steepening-upward subsurface bend in the underlying fault. The 72' E. dip of this axial 

surface, estimated from the dip of adjacent strata mapped by 

Brabb (1989), predicts an intersection of the fold hinge with 

the near-vertical San Andreas fault (which dips >75O from 

surface geology) at 7- to 12-kin depth (fig. 6). This depth 

estimate is refined and the change in dip across the fault 

bend predicted in the next subsection, where the dip of the 

San Andreas fault is more accurately determined. The Scotts 

Valley synclinal-axial surface, which in map view emanates 

from a restraining bend in the Zayante fault (fig. 2), suggests 

a similar steepening-upward subsurface bend in the underlying fault. The intersection of the 83' E.-dipping axial surface with the vertical Zayante fault should occur at about 

15-km depth. Alternative subsurface geometries for the Zayante fault are discussed below in the next subsection. 
RELATIONS BETWEEN FOLDING AND FAULTING IN THE LOMA PRIETA EPICENTRAL ZONE F9 

SUBSURFACE FAULT GEOMETRY INFERRED 

FROM LOMA PRIETA SEISMICITY 

Because seismicity can provide important constraints on 

fault geometry, we examined the hypocenters of the earthquake (fig. l), as located by Dietz and Ellsworth (1990) 

and provided by the U.S. Geological Survey, to test our 

predictions of the subsurface fault geometry in the Loma 

Prieta epicentral zone. The sequence that we used consists 

of the 1,173 best constrained aftershocks (from a total of 

3,750) processed by October 1989. The hypocenters were 

located using two one-dimensional velocity models separated by the San Andreas fault. Horizontal standard errors 

<0.5 km and vertical standard errors <1.0 km were assigned 

to the selected hypocenters, although relative locations are 

thought to be more accurate (average relative epicentral 

error, M.3 km; average relative vertical error, M.6 km). 

Fault-surface contour maps generated from subsurface 

data have proved to be an effective first step toward developing reasonable structural interpretations of faulted terFigure 5.-Synclinal-axial surface emanating from a steepening-upward 

bend in underlying fault. Fold shape is related to fault shape by faultbend-folding equations of Suppe (1 983). Arrow indicates direction of slip. 

Note that axial surface bisects fold limbs, conserving layer thickness. 

rains (Tearpock and Bischke, 1991). To create a contoured 

fault-surface map of the Loma Prieta rupture from the seismicity in the epicentral zone, we divided hypocenters into 

horizontal sections corresponding to 2-km-depth intervals. 

Contour lines of the rupture surface were drawn freehand 

through the hypocenters for each horizontal section. Typically, this technique has proved to yield the most accurate 

Glenwood 

syncline 

Figure 6.-Preliminary cross section B-B' across the Glenwood syncline 

and San Andreas fault (see fig. 2 for locations). Ball and bar indicates local 

dip of bedding. Orientation of synclinal-axial surface (dashed line), which 

bisects bedding, predicts a steepening-upward subsurface bend beneath the 

steeply dipping San Andreas fault at a depth of 7 to 12 km. True dip of 

upper segment of the San Andreas fault, to be determined from hypocentral locations of 1989 Loma Prieta earthquake, further constrains depth to 

fault bend. P, projected Blake well. Arrow indicates direction of slip. 
F10 TECTONIC PROCESSES AND MODELS 

representation of subsurface fault geometry (Tearpock and 

Bischke, 1991). Contour lines were assigned depths equal 

to the depth of the center of their corresponding horizontal 

sections, and were projected vertically to the surface to 

form a contour map of the fault (fig. 7). Vertical cross sections were then constructed through the contour map to 

highlight fault bends and to show changes in the subsurface 

fault geometry along strike. 

37'20' A I I I I 

San Jose 

0 

Sea 

level 

+ Hypocenter 

20 0 Fault geometry from contour map 

Figure 7.-Contour map (A) and cross sections (B) of Loma Prieta rupture zone, derived from hypocentral locations reported by Dietz and 

Ellsworth (1990). Change in trend of contours from southeast to northwest highlights restraining bend in fault system. Boxes outline areas 

within which hypocenters are plotted around profiles 1 through 3, showing dipping fault segments and locating a steepening-upward fault bend 

in central part of rupture zone (profile 2). 

Changes in the relative spacing and trends of contour 

lines in the fault-surface map indicate that the Loma Prieta 

rupture occurred not on a single planar fault but on a complex system comp~sed of multiple fault segments. The 

subsurface fault geometry outlined by the contour map 

and cross sections (fig. 7) is illustrated by the models in 

figure 8. The contour map and cross section 3 in figure 7 

suggest that the southeastern part of the aftershock zone 

defines a steeply dipping plane beneath the surface trace 

of the San Andreas fault, consistent with the observation 

of Dietz and Ellsworth (1990). This segment of the San 

Andreas fault strikes 320' and dips 82' W. (fault segment 

1, fig. 8A). Focal-mechanism solutions of selected aftershocks along this fault segment, which lies to the southeast of the restraining bend, show large components of 

right-lateral slip (Oppenheimer, 1990). 

The main shock and aftershocks in the deep central and 

northwestern parts of the Loma Prieta rupture zone outline 

a different planar fault segment (2, fig. 8A) that strikes 

310' and dips 70' SW.. The orientation of this fault segment coincides with that of the preferred nodal plane of 

the focal-mechanism solution of the main shock reported 

by Oppenheimer (1990). The change in strike between this 

northwestern fault segment and the fault rupture to the 

south forms the restraining bend that caused the thrusting 

in Loma Prieta seismicity. 

Shallow hypocenters at the northwest edge of the aftershock zone suggest that the Loma Prieta rupture in this 

area projects eastward of the surface trace of the San Andreas fault (fig. 1A; cross sec. 1, fig. 7). The northwestward extension of the 78' W.-dipping San Andreas fault 

(fault segment 3, fig. 8A) apparently did not rupture during 

the earthquake. The 70' W.-dipping fault rupture is therefore addressed in the following discussion as the Loma 

Prieta fault segment, a component of the San Andreas fault 

system. Schwartz and others (1990) suggested that shallow 

slip may have been transferred from the Loma Prieta fault 

b Figure 8.-Fault-bend fold models of the Loma Prieta epicentral 

zone. A, Subsurface fault geometry derived from contour map and cross 

sections shown in figure 7. Fault system is composed of multiple fault 

segments that include (1) the San Andreas fault southeast of restraining 

bend; (2) the west-dipping Loma Prieta fault segment (completely buried), which corresponds to main-shock preferred nodal plane of Oppenheimer (1990); and (3) a segment of the San Andreas fault northwest of 

restraining bend that forms an active steepening-upward bend above the 

underlying Loma Prieta fault segment. The Glenwood syncline emanates 

at depth from this fault bend. Northwest of rupture zone, above the Loma 

Prieta fault segment, long-term slip may be transferred to shallower dipping thrusts in the eastern Santa Cruz Mountains. B, Balanced three-dimensional model of hanging-wall deformation above fault geometry 

shown in figure 8A. Thrusting results in growth of the Glenwood syncline by kink-band migration, with shearing of materials through axial 

surface pinned to an underlying subsurface fault bend. Formation of the 

Scotts Valley syncline is attributed to a similar steepening-upward bend 

beneath the Zayante fault. 
RELATIONS BETWEEN FOLDING AND FAULTING IN THE LOMA PRIETA EPICENTRAL ZONE Fll 

segment to the Sargent-Berrocal fault zone east of the San term slip on the Loma Prieta fault segment may in part be 

Andreas fault (fig. 1). Seeber and Armbruster (1990) re- transferred onto a series of shallowly dipping thrusts beported that seismicity in the 20-yr period before the earth- neath the eastern Santa Cruz Mountains (fig. 8A). 

quake and faults mapped to the east of the San Andreas The fault rupture outlined by aftershocks breaks approxfault (McLaughlin and others, 1988) indicate that long- imately due east of the main-shock epicenter (fig. 15). 

QtB 

8 

4 LU 

s 

0 

0 ^ 

z 

1% fc 0 Ms = 7.1 main shock--arrow w n 

denotes direction of slip * 

(Oppenheimer, 1990) 
F12 TECTONIC PROCESSES AND MODELS 

This break represents a change from shallow rupture in 

the northwest that occurs east of the San Andreas fault 

(cross sec. 3, fig. 7), to rupture in the southeast primarily 

beneath the surface trace of the San Andreas fault (cross 

sees. 1, 2, fig. 7). Southeast of this break, in the central 

part of the aftershock zone, the fault rupture steepens upward from the Loma Prieta fault segment (cross sec. 2, 

fig. 7). The seismicity defines a 78' W.-dipping fault segment (3, fig. 8) beneath the surface trace of the San Andreas fault. This segment, thought to be part of the San 

Andreas fault, and the underlying Loma Prieta fault segment form an active flat-to-ramp system, or steepeningupward fault bend, that slipped during the earthquake. 

This inferred fault geometry is similar to that suggested by 

Dietz and Ellsworth (1990), who also reported a concaveupward shape of the Loma Prieta rupture surface in the 

vicinity of the restraining bend. 

As discussed in the preceding section, dip slip across 

this fault bend, formed by the Loma Prieta fault segment 

(2, fig. 8A) and the San Andreas fault (segment 3, fig. 8A), 

must result in deformation of the overriding block (see fig. 

4). As illustrated in the models in figure 3, deformation 

should be localized along active axial surfaces pinned to 

subsurface fault bends. Similarly, movement of the hanging-wall block over the subsurface fault geometry shown 

in figure 8A results in fold growth above the fault bends 

(fig. 85). 

Applying the balanced models in figure 3 to the Loma 

Prieta epicentral zone, the location and orientation of the 

Glenwood syncline predict an underlying bend at 7- to 12- 

km depth in the San Andreas-Loma Prieta fault system 

(fig. 6). The seismicity, contour maps, and cross section 2 

in figure 7 confirm the existence of a steepening-upward 

bend at 8-krn depth. The geologic cross section in figure 9 

combines the surface geology with subsurface fault data 

provided by the seismicity. This steepening-upward fault 

bend is located at the intersection of the projected Glenwood syncline and the steeply dipping San Andreas fault. 

Using fault-bend-folding theory (fig. 5; Suppe, 1983), the 

47' cutoff angle (6) between the fault and adjacent strata, 

and the 77' angle between strata and the Glenwood syncline (y), an 8' change in fault dip is predicted across the 

bend ((b). This predicted 8' bend corresponds to the 78'- 

70' change in fault dip across the bend inferred from the 

seismicity (fig. 9). 

During past slip on the San Andreas-Loma Prieta fault 

system and growth of the Glenwood syncline, the inactive 

axial surface, or other end of the kink band, has probably 

been uplifted and eroded. In addition, the rupture of the 

steepening-upward fault bend only in the central part of 

the aftershock zone (fig. 7) suggests that the Glenwood 

syncline grew only in this region during the earthquake. 

Past ruptures that involved slip on the steeply dipping San 

Andreas fault northwest of the restraining bend, which did 

not rupture in the 1989 earthquake, as well as on the 

Loma Prieta fault segment, are most likely responsible for 

the northwestward extension of recent deformation along 

the syncline. 

The consistent fault geometry inferred from the applied 

balanced models, surface geology, and the seismicity 

confirms the predicted relations between subsurface fault 

bends and folds observed at the surface. These consistent 

relations suggests that fault-bend folding is, indeed, a 

folding mechanism of transpressional environments. Furthermore, fault-bend-folding theory may be used to predict subsurface fault geometry and slip directions in other 

transpressive structures without the aid of seismicity. 

Glenwood 

-1 

Sea level 

Figure 9.Ã‘Geologi cross section B-B' across the Glenwood syncline, 

the San Andreas fault, and the Loma Prieta fault segment (see fig. 2 for 

locations). Syncline emanates from steepening-upward bend in fault surfaces outlined by hypocentral locations (see fig. 7). Ball and bar indicates 

local dip of bedding. Using fault-bend-folding theory (Suppe, 1983), 

angle between bedding and axial surface (y) and upper hanging-wall cutoff (b) are consistent with 8' fault-dip change (@) and lower hanging-wall 

cutoff (9) determined from seismicity (see figs. 5, 6). P, projected Blake 

well. Arrows indicate directions of dip-slip motion: A, lateral motion 

away; T, lateral motion toward. 
RELATIONS BETWEEN FOLDING AND FAULTING IN THE LOMA PRIETA EPICENTRAL ZONE F13 

The similarities in the shape and location of the Scotts 

Valley and Glenwood synclines in restraining bends along 

strike-slip faults (fig. 2) suggest that the theories and models that explain the development of the Glenwood syncline 

should be applicable to the Scotts Valley syncline and 

Zayante fault. If the Zayante fault is near-vertical within 

its restraining bend, as indicated by Clark and Rietman 

(1973), then the fault should intersect the projected eastdipping Scotts Valley syncline at a depth of approximately 

15 krn (fig. 10). Alternatively, if the Zayante fault dips 

west, similar to the Loma Prieta fault segment, the fault 

and fold intersection should occur at a shallower depth. 

The 80' cutoff angle between strata and the vertical fault, 

and the 83.5' interlimb angle of the syncline, suggest only 

a few-degree change in dip of the fault across the subsurface bend. We note that this potential fault-bend and fold 

intersection occurs near the main-shock hypocenter, which 

lies on the adjacent Loma Prieta fault segment (fig. 10). If 

I 

Scotts Valley 

syncline 1 

\ 

\ 

\ 

\ 

\ 

\ 

- 1 

- Sea 

-- -2 

-- -4 

- -6 

- -8 

- -10 

-- -12 

-- -14 

-- -16 

- -18 

level 

main shock 

Figure 10.Ã‘Geologi cross section C-C' across the Scotts Valley syncline and the Zayante and San Andreas (Loma Prieta) faults (see fig. 2 

for locations). Orientation of synclinal-axial surface (assumed to bisect 

bedding) predicts a few-degree steepening-upward bend in the underlying 

Zayante fault at 15-km depth. This predicted subsurface fault geometry 

suggests that Loma Prieta main shock initiated in a complex region of 

multiple fault-fold intersections. Arrows indicate directions of dip-slip 

motion: A, lateral motion away; T, lateral motion toward. 

this predicted subsurface fault geometry is correct, then 

this geometrically complex region with multiple fault and 

fold intersections may have acted to concentrate stress, localizing the initial main-shock rupture on the Loma Prieta 

fault segment. We suggest that further development and 

application of this technique of modeling subsurface faults 

and folds holds promise in locating future hypocenters 

along other strike-slip fault systems. 

FAULT SLIP 

The transpressive fault-bend-folding model for the Loma 

Prieta epicentral zone may also be compared with faultslip data. Focal-mechanism solutions from the Loma Prieta seismicity yield important constraints on slip within this 

complex, multiple-fault system. The Me =7.1 main shock 

was reported to have oblique-reverse, right-lateral slip directed 40' from southeast (rake) on a fault plane striking 

310' and dipping 70' SW. (Oppenheimer, 1990). Focalmechanism solutions of selected aftershocks, however, 

suggest that other fault segments with different orientations also slipped. The model of subsurface fault geometry 

and fold development discussed in the preceding section 

(see fig. 8) also provides insight into slip direction on the 

various fault segments. To conserve rock volume during 

long-term fault slip, both dip-slip and strike-slip components of motion must be resolved between the adjacent 

fault segments illustrated in figure 8A. Slip directions are 

also constrained to avoid opening large subsurface voids 

between fault surfaces. 

In the following subsections, we combine fault-slip information provided by the regional seismicity with reasonable slip directions inferred from our balanced models 

to describe slip along the San Andreas fault system during 

the Loma Prieta rupture. To test the validity of our 

inferred slip directions on different fault segments, we 

compare these slip directions with shear-stress directions 

resolved onto the fault planes from regional stresses. The 

regional stresses were derived by Michael and others 

(1990) by using an inverse method from preearthquake 

and postearthquake seismicity. In the following subsec- . 

tion, assuming that these coseismic-slip directions approximate the long-term slip directions, we calculate 

long-term slip rates on the San Andreas fault and uplift 

rates above the Loma Prieta fault segment. We then compare the results with the uplift rates calculated by Anderson (1990) and Valensise and Ward (1991) from dated 

marine terraces on the nearby Santa Cruz coastline. Finally, we calculate uplift rates for the Zayante fault, which 

did not rupture in the earthquake, by analysis of syntectonic (growth) sediment. Electric logs from wells located 

on opposite sides of the fault record different stratal 

thicknesses that have resulted from uplift of one side of 

the fault relative to the other. 
TECTONIC PROCESSES AND MODELS 

FAULT-SLIP DIRECTIONS 

AND REGIONAL STRESS 

It has long been proposed that the direction of slip is 

equivalent to the direction of resolved shear stress on a 

fault plane (Bott, 1959). Thus, a straightforward test of the 

validity of the slip directions inferred from our models in 

the Loma Prieta epicentral zone is to compare them with 

the applied shear-stress directions calculated from the regional stress field. Michael and others (1990) examined 

events before and during the earthquake, using an inverse 

method (Michael, 1987a, b) to estimate the relative magnitudes and directions of the three principal stress axes. 

They calculated tensor components for the southern, the 

shallow and deep central, and the northern parts of the 

Loma Prieta rupture zone. We test whether our inferred 

slip directions (determined from fault geometry and models, not first motions) agree with the shear-stress directions 

resolved on the various fault segments by the regional 

stresses estimated by Michael and others (1990). This 

analysis simply confirms that the slip directions in our 

model (fig. 8) are reasonable within the inferred stress 

field. We used the Fortran program FMSI of Gephart 

(1990) to resolve shear-stress directions on the fault segments from regional stresses. 

Our fault-bend-folding model has right lateral strike-slip 

motion along the San Andreas fault (fault segment 1, fig. 

8A) in the southern part of the Loma Prieta rupture zone, 

which is consistent with focal-mechanism solutions of local 

aftershocks (Oppenheimer, 1990) and strong motions (Beroza, 1991). We find that components of the inferred regional 

stress tensor (0, trends 000Â° u2 is vertical, <(>*=0.39, R=0.61, 

XPLANATION 

Figure 1 1 .-Equal-area stereonets showing 95-percent-confidence limits 

of principal stress directions (q through 03) in Lorna Prieta epicentral 

zone calculated by Michael and others (1990). Symbols (dots, stars) 

mark principal stress directions that yield shear-stress parallel to the slip 

directions we infer on various fault segments shown in figure 8A. Components of stress tensors were inverted by using preearthquake seismicity 

in south (A) around fault segment 1 in figure 8A and shallow aftershocks 

in center of Loma Prieta rupture (B) around fault segment 3 in figure 8A. 

fig. 11A; Michael and others, 1990)' resolve into a shear 

stress on the southern segment of the San Andreas fault 

(320Â° 82' W.), directed essentially parallel to the inferred 

horizontal strike-slip vector 1. The angle between the resolved shear stress and the fault-slip direction measured in 

the fault plane, which is an accepted measure of error between 

slip and a predicted stress state, is here less than lo. Pure 

right-lateral strike slip on the San Andreas fault southeast 

of the restraining bend at Loma Prieta, as inferred from 

geologic evidence, is therefore consistent with regional seismicity and the inferred stress field. 

Michael and others (1990) reported a stress tensor within the 95-percent-confidence limit of their inversion, yielding a 25O discrepancy between the applied shear-stress 

direction and the slip direction of the main shock on the 

Loma Prieta fault segment (310Â° 70' W.; rake, 40' from 

SE.; Oppenheimer, 1990). They indicated that this discrepancy is less than the average variance in the data used in 

the inversion and that the main-shock slip direction is 

therefore consistent with their predicted regional stresses. 

The main-shock slip direction inferred from the seismicity 

(Oppenheimer, 1990) is also consistent with the subsurface 

fault geometry that we derive by analysis of the hypocentral locations (fig. 8A). The slip vector very closely approximates the line of intersection between the Loma 

Prieta fault segment and the southeastern section of the 

San Andreas fault (fig. 12). In fact, slip on two simultaneously active fault planes must be in the direction of the 

line of intersection of the two faults to avoid subsequent 

deformation of the fault blocks. Slip in any other direction 

on the Lorna Prieta fault segment would require additional 

deformation along the faults to close subsurface voids or 

to alleviate "room" problems. Similarly, we suggest a slip 

direction on a shallow segment of the San Andreas fault 

(310Â° 78O W.; fault segment 3, fig. 8A) above the Loma 

Prieta fault segment, parallel to the intersection of this 

fault with a bounding segment of the San Andreas fault 

(fault segment 1, fig. 8A). We calculate that another stress 

tensor (0,=029~, O3 is vertical, <(>*=0.6, R=0.4) within the 

95-percent-confidence limit of Michael and others (1990) 

applies a shear-stress direction parallel to the inferred slip 

direction on this shallow fault segment (fig. 115). 

These results suggest that the slip directions in the Loma 

Prieta epicentral zone calculated from our balanced models and the fault geometry defined by hypocentral locations are generally consistent with the inferred regional 

stresses. Slip directions on the San Andreas fault southeast 

and northwest of the restraining bend parallel the shearstress directions applied by stress tensors that lie within 

the confidence limit of inferred regional stresses (fig. 11). 

([)*=(O~<~)/(G,<~), where 01, 02, and o3 are the three principal 

stresses, from most compressional to most tensional (Angelier, 1979). and 

/?=I -<))*=(02-'Â¥< l)l(03-ol) (Etchecopar and others, 198 1 ). Note that <j)*?"<j), 

the change in fault dip of the fault-bend-folding equations in figure 5. 
RELATIONS BETWEEN FOLDING AND FAULTING IN THE LOMA PRIETA EPICENTRAL ZONE F15 

Slip during the main shock on the Loma Prieta fault segment, although it does not agree as well with the applied 

shear-stress direction, is consistent with the inferred regional stresses (Michael and others, 1990). Moreover, the 

main-shock slip direction is consistent with the subsurface 

fault geometry in the Loma Prieta epicentral zone (fig. 

12). The line of intersection of the San Andreas fault and 

the Loma Prieta fault segment may have set a geometric 

boundary condition controlling the direction of slip during 

the earthquake. These faults, acting as discontinuities, may 

have locally modified the regional stress field, resulting in 

the geometrically favorable slip direction of the main 

shock. 

The continuous lateral extent and similar dips of the 

limbs of the Glenwood syncline (fig. 2) suggest that the 

subsurface fault geometry in the Loma Prieta epicentral 

zone has remained essentially uniform throughout the Quaternary. Significant changes in this fault geometry would 

produce irregular fold limbs and offsets in the synclinalaxial surface. Therefore, we suggest that the geometrically 

favorable slip directions of the Loma Prieta rupture may 

provide a reasonable estimate of the long-term slip direction on these fault segments. In the following section, we 

explore this suggestion, using these inferred slip directions 

and estimates of the long-term slip rate on the San Andreas 

fault to calculate slip and uplift rates in the Loma Prieta 

epicentral zone. 

' San Andreas '. fault 

Figure 1 2.-Equal-area stereonet showing orientation of 

the Loma Prieta fault segment (solid curve) and a segment 

of the San Andreas fault (dashed curve) southeast of 

restraining bend (fault segments 2 and 1, respectively, 

fig. 8A). Line of intersection of fault planes closely corresponds to orientation of main-shock slip direction calculated from first-motion studies by Oppenheimer 

(1 990). 

RECURRENCE INTERVALS, LONG-TERM SLIP, 

AND UPLIFT RATES 

The long-term motion inferred by geologic and seismic 

(Hall, 1984) and geodetic (Prescott and others, 198 1) data 

is consistent with the predominantly right lateral strike-slip 

motion derived from focal-mechanism solutions of aftershocks located on the San Andreas fault in the southeastern 

part of the Loma Prieta rupture zone (Oppenheimer, 1990). 

Geologic and geodetic estimates of the long-term slip rate 

on the San Andreas fault in this area are reported at 12 

dyr (Hall, 1984) and 12.2 mm/yr (Prescott and others, 

1981). Slip on the Loma Prieta fault segment inferred from 

first-motion studies, however, is oblique-reverse, right-latera1 motion (Oppenheimer, 1990). Geodetic data suggest 

that 1.6M.3 m of strike slip and 1.2M.3 m of reverse slip 

(total slip, 2M.4 m) took place during the earthquake 

(Lisowski and others, 1990), resulting in a ratio of strike 

slip to dip slip of 1.3. Similarly, Marshall and others (1991) 

reported a best-fit model to vertical deformation with 

2.1M.1 m of total slip. As discussed in the preceding subsection, the slip direction of the Loma Prieta main shock 

parallels the intersection of the San Andreas fault with the 

Loma Prieta fault segment (fig. 12). Therefore, as modeled 

in figure 3, rigid-block translation over these faults would 

produce parallel slip on the Loma Prieta fault segment 

(vector C, fig. 13) and on the adjacent segment of the San 

Andreas fault (vector B). If long-term slip on this small 

segment of the San Andreas fault were not equivalent to 

slip on the Loma Prieta fault segment, then a large amount 

of unrecognized hanging-wall deformation would have to 

occur to conserve volume during deformation and to collapse large subsurface voids. Similarly, the long-term-slip 

vector on the small segment of the San Andreas fault (vector B) must contain a strike-slip component equivalent to 

the long-term slip rate on the San Andreas fault farther to 

the southeast of the restraining bend (vector A, fig. 13). 

Using the 12-mmlyr rate (vector A) and simply solving the 

slip-vector triangle yields a 15.2-mrnlyr long-term slip rate 

on the small segment of the San Andreas fault (vector B) 

and the adjacent Loma Prieta fault segment (vector C). This 

change in the long-term-slip vectors from predominantly 

strike slip in the southeast to oblique-reverse, right-lateral 

slip in the northwest is consistent with the slip directions of 

the earthquake inferred from strong motions (Beroza, 199 1 ; 

Steidl and others, 1991) and vertical deformation (Marshall 

and others, 1991). The 15.2-dyr long-term slip rate on 

the Loma Prieta fault segment (310Â° 70' W.) resolves to a 

dip-slip rate of 9.8 mm/yr and a strike-slip rate of 11.6 

mdyr that correspond to the estimated 1.3 slip ratio of the 

Loma Prieta main shock (Lisowski and others, 1990). In 

addition, this increase in slip rate on the Loma Prieta fault 

segment in the restraining bend may explain why the Loma 

Prieta and, possibly, other strike-slip earthquakes initiate at 

fault bends. 
F16 \ TECTONIC PROCESSES AND MODELS 

Resolution of the slip-vector triangle that includes the 

9.8-mmlyr dip-slip rate on the 70' SW.-dipping Loma Prieta fault segment yields an uplift rate above the fault of 

9.2 mm/yr (fig. 13). However, using dated, uplifted marine 

terraces along the Santa Cruz coastline, several investigators calculated much smaller average uplift rates of 0.77 

mm/yr (Valensise and Ward, 1991) and 0.8 mm/yr (Anderson, 1990) adjacent to the fault in the Loma Prieta epicentral zone. They suggested that repeated Loma Prieta-type 

events, which encompass all the slip on the adjacent San 

Andreas fault, would produce higher uplift rates than they 

calculated. They also suggested that ruptures similar to the 

1989 earthquake alternate with events on the fault that 

consist of greater amounts of strike slip relative to reverse 

motion. They contended that this alternation would allow 

all of the long-term slip on the San Andreas fault to be 

transferred to the Lorna Prieta fault segment, yet produce 

lower uplift rates consistent with their results. Alternatively, we suggest that slip in the 1989 earthquake parallel to 

the line of intersection of the two fault segments that form 

the restraining bend (fig. 12) was not fortuitous. Slip in 

any other direction on the Loma Prieta fault segment 

would necessitate additional deformation, as yet unrecognized, to conserve volume and close subsurface voids 

caused by slip over this fault-segment intersection. Furthermore, as Crowell (1974a, b) recognized, strike-slip 

motion in this restraining bend necessitates uplift or lateral 

motion of material away from the fault bend to conserve 

rock volume. That is, pure strike-slip motion on the Loma 

Prieta fault segment cannot cause uplift. Lateral motion of 

material away from the restraining bend would require additional reverse or thrust faulting in the western block in 

the vicinity of the fault bend, which has not been observed 

(fig. 2). Strike-slip motion on a near-vertical San Andreas 

fault that bends and passes below the Loma Prieta fault 

segment does not avoid these conservation-of-volume restrictions. Therefore, we suggest that when motion occurs 

on the San Andreas-Loma Prieta fault system, slip likely 

occurs parallel to the line of intersection between the two 

fault segments. 

Several effects may explain the discrepancy between 

the uplift rates calculated by Anderson (1990) and Valensise and Ward (1991) and the higher uplift rates that we 

calculated by assuming repeated Loma Prieta-type events. 

Foremost, the geometrically constrained values that we 

calculated are uncorrected for isostatic compensation. Presumably, repeated thrusting in Loma Prieta-type events 

would produce crustal thickening that would lead in turn 

Figure 13.-Subsurface fault model of Loma Prieta epicentral zone (see fig. SA), with long-term-slip vectors 

calculated by using inferred slip directions and 12 mrnlyr (vector A) estimate of long-term slip rate on the San 

Andreas fault southeast of rupture zone (Hall, 1984). Slip rates on the Loma Prieta fault segment (vector C) 

and the adjacent San Andreas fault (vector B) are equal (both 15.2 mdyr) and in direction of 1989 main 

shock. 15.2 mmlyr rate was calculated by assuming that slip on small segment of the San Andreas fault 

(vector B) must account for 12 mdyr of right-lateral strike slip southeast of rupture zone (vector A). 15.2 

mm/yr rate on the Loma Prieta fault segment (vector C) resolves to a 9.8-mdyr dip-slip and 11.6-mdyr 

strike-slip component and a 9.2-mdyr uplift rate above fault (uncorrected for isostatic compensation). 
RELATIONS BETWEEN FOLDING AND FAULTING IN THE LOMA PRIETA EPICENTRAL ZONE F17 

to downward vertical displacements of the lithosphere to 

achieve stable density distributions within the crust and 

upper mantle (Bott, 197 1 ; Suppe, 1985). Therefore,, uplift 

rates measured at the surface would be only a fraction of 

those summed from slip in repeated Loma Prieta-type 

events. Using the equations of pointwise isostqsy, 

and 

where AÂ is the total change in elevation, hc is the thickness of the crust, hm is the thickness of the mantle lithosphere, ha is the thickness of the mantle asthenosphere, pc 

is the density of the crust, pm is the density of the mantle 

lithosphere, and pa is the density of the mantle asthenosphere. Using the reasonable average densities of Bott 

(1971) and Suppe (1985), and assuming no change in the 

thickness of mantle lithosphere, 

and 

Therefore, for each 9.2 mm/yr of uplift and thickening of 

the crust, only 0.8 mmlyr of total elevation change occurs 

above the fault after isostatic compensation: 

and 

Solving for A/L and AÂ£ 

and 

AÂ = 0.8~10-~ m = 0.8 mm. 

This corrected uplift rate (0.8 mm/yr) falls within the 

range of uplift rates (0.77-0.8 rnrnlyr) reported by Valensise and Ward (1991) and Anderson (1990), which also account for elasticity and isostatic compensation of the crust. 

Although we cannot exclude the possibility of other types 

of slip events in the Loma Prieta epicentral zone, we suggest that the uplift rates calculated in these other studies 

are generally consistent with the rates we derive by assuming that all long-term slip on the San Andreas fault is 

released in repeated Loma Prieta-type events. It is therefore plausible that the 1989 earthquake was a typical rupture along this part of the San Andreas fault system and 

that long-term slip rates on the San Andreas fault can be 

used to estimate earthquake-recurrence intervals. 

To consume slip on the San Andreas fault at a rate of 12 

mmlyr, oblique slip must occur on the Loma Prieta fault 

segment at an average rate of 15.2 mm/yr (fig. 13). Assuming that this slip rate is correct, if all of this slip occurs during earthquakes similar to the 1989 Loma Prieta 

main shock, which released 2k0.4 m of slip (Lisowski and 

others, 1990), then an earthquake should recur every 

132k26 yr. The 1865 Santa Cruz Mountains earthquake 

may therefore be a viable candidate for the previous break 

on this fault segment (Toppozada and others, 1981). In accordance, McNutt and Toppozada (1990) reported that the 

1865 earthquake had an estimated magnitude (M=6.6) and 

epicentral location similar to those of the 1989 earthquake. 

MOTION ON THE ZAYANTE FAULT 

We have presented evidence that the Glenwood syncline 

developed by slip over a subsurface fault bend between 

the San Andreas fault and the Loma Prieta fault segment. 

Similarly, we suggest that the deformed Purisima Formation along the Scotts Valley syncline indicates that motion 

has occurred along a restraining bend in the Zayante fault 

in the Loma Prieta epicentral zone since the early Pliocene. Deformed Pliocene and Quaternary horizons (Hall 

and others, 1974; Clark and others, 1984) and several surface fault breaks through Quaternary sedimentary deposits 

to the south of this bend (fig. 2) suggest recent activity on 

the Zayante fault. To constrain fault-motion history and to 

identify active fault segments without the aid of recorded 

seismicity, we apply the technique of Bischke and Suppe 

(1990) and Bischke (in press) to analyze growth sediment 

coevally deposited with fault motion. Thickness changes 

in growth sedimentary sequences measured in electric logs 

from wells that straddle the fault record rates of uplift 

across splays of the Zayante fault. Only the differential 

dip-slip component of motion between any two wells is 

recorded. A brief description of the method follows. 

The vertical-displacement method (AD14 identifies expanded or syntectonic sedimentary sections that record the 

local tectonic history. An assumption of this method is that 

the sedimentation rate is greater than or nearly equal to the 

uplift rate (Bischke, in press). For example, the method may 

consider two wells located on opposite sides of a fault (fig. 

14). If sedimentary sequences can be correlated between 

these two wells, then the vertical distance that the sequences 

have been displaced relative to one another (AD) can be 

determined. A convenient graphical method of determining 

growth section in the two wells is to plot the relative vertical 

displacement between the sequence boundaries (AD) versus 
F18 TECTONIC PROCESSES AND MODELS 

the depth to the same horizons in the structurally higher well 

(4. In a plot of strata deposited before fault motion, data 

points that correspond to correlated horizons of pregrowth 

strata lie along a near-horizontal line (fig. 14A). However, 

in a similar plot of strata deposited coevally with fault motion, growth horizons lie along sloping lines or curves (fig. 

145). The steep slope of the lines results from thickness 

changes in strata on opposite sides of the fault brought on 

by the accumulation of thicker sediment on the downthrown 

side of the fault. Using this plotting convention, large positive slopes on these diagrams represent expanded growth 

sections, whereas large negative slopes represent reduced or 

condensed sections. This technique, applied to strata on opposite sides of a fault, therefore provides an easy method of 

distinguishing between growth and pregrowth strata that 

identify periods of fault motion and quiescence. 

In wells located across splays of the Zayante fault (fig. 

2) we are able to correlate 17 stratal sequences within the 

Pliocene and Pleistocene section (fig. 15). Motion along 

splays of the Zayante fault between Pierce, Light, and 

Blake wells (fig. 2) are recorded in growth-sedimentary 

sections. Lacking significant onlap, the well section 

Oddl 

depth in well 1 

0- dl 

depth in well 1 

Figure 14.-Schematic diagrams of stable (A) and unstable (5) tectonic 

environments where stratigraphic sequences can be correlated between 

wells, with plots of vertical displacement AD of correlated pregrowth (A) 

and growth (5) horizons versus depth d to horizons in structurally higher 

well. In figure 14.4, shallow slope of ADId curve establishes a pregrowth 

section; in figure 145, steep slope of AD/d curve indicates growth sedimentation, whereby section expansion is attributed to differential tectonic 

motion between wells, with thicker strata accumulating on downthrown 

fault block. 

(fig. 15) indicates no substantial bathymetryltopography 

across these fault splays during deposition of the Pliocene 

and Pleistocene sediment. Therefore, the sedimentation 

rate exceeded the rate of tectonic uplift during this period. 

A vertical-displacementldepth (AD/^) diagram generated 

from Pierce and Light well-log data shows that growth (in 

the form of an expanded section) was initiated during the 

late Pliocene, between the deposition of horizons 5 and 6 

(fig. 16). The sloping, linear growth above horizon 5 

shows that section expansion has continued into the Quaternary. This expansion rate, continuing into the Holocene, 

also appears to account for the present terrace relief across 

the fault (fig. 16), suggesting that the Pleasant Valley splay 

of the Zayante fault may still remain active. 

A AD/d plot of horizons recorded in Light and Blake 

wells (fig. 17) shows a slightly different growth history 

across the central splay of the Zayante fault (fig. 2). The 

negative slope of the growth phase between horizons 1 to 9 

indicates a condensed section that is contemporaneous with 

the expanded section between Pierce and Light wells (fig. 

16). This west-to-east transition from an expanded section 

across the western splay of the Zayante fault to the condensed section across the central splay suggests that a delta 

may have prograded away from the western, uplifted block 

of the Pleasant Valley fault (fig. 18). The condensed section 

above horizon 9, and the slightly expanded section between 

horizons 9 and 17 between Light and Blake wells (fig. 17), 

suggest that motion on the central splay of the Zayante fault 

was initiated before that on the western splay. The 670-m 

expanded section below 950-m in Blake well (figs. 15, 17) 

records early (pre-Pliocene) motion on the central splay of 

the Zayante fault. Motion on this ancestral Zayante fault 

created the basin between the Zayante and San Andreas 

faults (fig. 15; Clark and Rietman, 1973). 

The surface breaks and expanded and condensed sections 

across these two splays of the Zayante fault, which merge 

both to the north and south (fig. 2), suggest that these 

splays have moved during the Quaternary. Although there 

is no confirmed historical seismicity on the Zayante fault, 

the available evidence is consistent with its activity. Therefore, the Zayante fault may pose an earthquake hazard to 

the adjacent populated area. If this fault is active, our estimated average uplift rate of the west side relative to the 

east side of the fault splays has been small (4.07 rnmlyr) 

since the beginning of the Pleistocene (~1.8 Ma). This 

0.07-mm/yr uplift rate falls within the range of preferred 

uplift rates (0.06-0.1 mm/yr) along the Zayante fault reported by Clark and others (1984). However, the location of 

the Scotts Valley syncline in the restraining bend and the 

orientation of this near-vertical fault (fig. 2) with respect to 

the regional stress field (Michael and others, 1990) and the 

San Andreas fault suggest that most recent fault motion is 

strike slip. Further analysis of geologic data, or future seismicity, is required to constrain more precisely the slip rate 

and earthquake hazard posed by the Zayante fault. 
RELATIONS BETWEEN FOLDING AND FAULTING IN THE LOMA PRIETA EPICENTRAL ZONE F19 

SUMMARY AND CONCLUSIONS 

Right-lateral motion along left-stepping restraining 

bends in the San Andreas and Zayante faults has resulted 

in thrusting and uplift of the hanging-wall rocks. Thrusting 

over nonplanar fault surfaces within these restraining 

bends has folded the hanging-wall strata into synclines. 

Fold growth is illustrated in geometrically and kinematically reasonable balanced models constructed by using 

fault-bend-folding theory (Suppe, 1983). Application of 

these models to the Loma Prieta epicentral zone yields 

predictions of the dip and location of subsurface bends in 

the fault segments. We have confirmed these predictions 

for the San Andreas fault and the Loma Prieta fault segA >> 

- 2 >> (0 JO Light Pierce a. I!! 

ment by using the hypocenters of aftershocks to determine 

subsurface fault geometry. The consistent subsurface fault 

geometry inferred by these two independent methods suggests that fault-bend folding is a viable theory for the origin of the folds that lie adjacent to strike-slip faults. 

The seismicity, the surface geology, and the subsurface 

models indicate that the Loma Prieta epicentral zone consists 

of several active fault segments that compose the San Andreas fault system. Slip on the various fault segments, inferred from seismicity, geodesy, and the subsurface fault 

geometry, is found to be consistent with regional stresses, 

assuming that the slip directions on the faults parallel the 

applied shear-stress directions. Furthermore, the subsurface 

fault geometry of the Lorna Prieta epicentral zone suggests 

Blake 

- Sea level 

- Tpc 

- - ^Ã Tpa (shale) - - 

base of 

Tpa-Pufiima Fm. 

Figure 15.Ã‘Correlatio section A-A' of electric-resistivity and spontaneous-potential logs from wells located 

on opposite sides of strands of the Zayante fault (see fig. 2 for locations). A total of 17 Pliocene and Pleistocene stratigraphic sequences are correlated between wells, with expanded or growth section defining periods 

of fault motion. Units: 1 through 17, Pliocene and Pleistocene stratigraphic sequences; A and B, horizons in 

Miocene section; Tpa through Tpc, Purisima Formation (upper Miocene and Pliocene), units a through c; 

Tm?, Monterey(?) Formation (middle Miocene). 
F20 TECTONIC PROCESSES AND MODELS 

that long-term slip must increase in this restraining bend. 

The 12-mmlyr long-term slip rate on the San Andreas fault 

southeast of the Loma Prieta rupture zone must increase to 

a 15.2-rnm/yr slip rate on the Lorna Prieta fault segment. 

, Beginning of growth 1 

11 

Ã -^- UÃ‘ . 9 Pregrowth 

Change in terrace 

elevations across fault 

u ACKNOWLEDGMENTS -300 0 300 600 

DEPTH IN PIERCE WELL, IN METERS 

Figure 16.-Vertical displacement of correlated stratigraphic horizons between Pierce and Light wells versus depth to horizons in Pierce well (see 

fig. 15 for locations). Horizontal least-squares best-fit curve through data 

marks an early period of pregrowth, below 200-m depth, followed by 

expanded section (growth) above 200-m depth. Pliocene and Quaternary 

expanded section is attributed to coeval motion on splay of the Zayante 

fault between wells. Fault motion continuing to present may account for 

change in terrace elevations across fault. 

200 600 1000 

DEPTH IN LIGHT WELL, IN METERS 

This increase in slip rate in the restraining bend may explain 

why the 1989 Lorna Prieta and, possibly, other strike-slip 

earthquakes initiate at fault bends. In addition, long-term 

uplift rates calculated by using our observed fault geometry 

and reported long-term slip rates on the San Andreas fault 

in the region agree with the rates calculated by Anderson 

(1990) and Valensise and Ward (1990) from marine-terrace 

elevations along the Santa Cruz coastline, once they are 

corrected for isostatic compensation. Moreover, this result 

suggests that the 1989 earthquake may have been a typical 

rupture for this section of the San Andreas fault system. 

Furthermore, if slip on the San Andreas fault is released in 

repeated Loma Prieta-type events, then an earthquake should 

recur every 132k26 yr. Expanded sedimentary sections deposited across splays of the Zayante fault suggest that this 

fault is also presently active. Therefore, faults in the Santa 

Cruz Mountains continue to pose a significant earthquake 

hazard to the adjacent populated area. 

Figure 17.-Vertical displacement of correlated stratigraphic horizons between Blake and Light wells versus depth to horizons in Light well (see 

fig. 15 for locations). Inclined least-squares best-fit curves through data 

mark early (below 960-m depth) and more recent (above 600-m depth) 

periods of growth. Early Miocene growth is attributed to motion on the 

ancestral Zayante fault. 

This research was supported by National Earthquake 

Hazards Reduction Program (NEHRP) grant 14-08-000 1 - 

G1827 from Princeton University and by Texaco, Inc. We 

thank Chris Connors, Paul Genovese, Stephen Hook, 

Craig Nicholson, David Pollard, and Leonardo Seeber for 

helpful discussions and comments. Thanks go also to 

Daniel Tearpock for reviewing well-log correlations, and 

to John Gephart for providing his program FMSI, which 

we used to resolve shear-stress directions on the fault segments from regional stresses. In addition, we are grateful 

for beneficial reviews of the manuscript by Joseph Clark, 

Oona Scotti, Robert Simpson, and George Havach. 

Pierce Light 

Figure 18.-Schematic diagram showing thicker accumulation of deltaic 

sediment on downthrown side of the Zayante fault system along line AA' (see fig. 2 for locations). Arrows indicate directions of dip-slip motion. 
RELATIONS BETWEEN FOLDING AND FAULTING IN THE LOMA PRIETA EPICENTRAL ZONE F2 1 

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5, p. 1694-1704. 
This page intentionally left blank
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAmOCCUmNCE 

TEXTONIC PROCESSES AND MODELS 

GEOLOGIC ASSESSMENT OF THE RELATIVE CONTRIBUTION OF 

STRIKE-SLIP FAULTING, WVERSE-SLIP FAULTING, 

AND BULK SQUEEZING IN THE CREATION OF' 

THE CENTRAL SANTA CRUZ MOUNTAINS, CALIFORNIA 

CONTENTS 

By Gianluca Valensise, 

Istituto Nazionale di Geofisica, Rome 

ABSTRACT 

To deduce the tectonic history of the central Santa Cruz 

Mountains in relation to the activity of the San Andreas 

fault, I have investigated the state of deformation of three 

geologic datums: the first (1 25 ka) and third (320 ka) Santa 

Cruz Terraces, and the base of the Upper Miocene and Pliocene Purisima Formation. Terrace data were taken from 

published work, whereas the Purisima Formation was investigated by reconstructing its structural contours on the 

basis of the elevations of its contact with underlying formations. The shape and elevation of these three datums were 

compared to explore the relative importance of two major 

tectonic processes: uplift of the Santa Cruz region by repeated Loma Prieta-type events, and progressive northwestward advection of the Pacific plate. The main conclusions 

of this study are that (1) the source of Loma Prieta-type 

events is stationary relative to the North American plate and 

in motion relative to the Pacific plate over time scales of =l 

m.y.; (2) the central Santa Cruz Mountains have been uplifted at an average rate of <0.5 dyr after repeated obliquereverse slip at a rate of =3 dyr on the Loma Prieta fault 

and northwestward motion of the Pacific plate at a geologic 

rate of 5 to 20 dyr; (3) only a fraction of the topography 

in the Santa Cruz Mountains is explainable by motion along 

the Loma Prieta fault; and (4) geologic evidence shows that 

much of the observed topography is generated by a process 

which dissipates plate-boundary-normal compression in the 

upper 5 km of the crust. 

INTRODUCTION 

Only a few hours after the earthquake, many scientists 

realized that more than one misconception existed regarding the Santa Cruz Mountains section of the San Andreas 

fault. The large and unexpected reverse-slip component of 

the earthquake's fault motion made clear that more complex processes are active along that section of the fault 

than only relative right-lateral motion of the Pacific and 

North American plates. Before 1989, however, the only evidence that could be used to foresee an anomalous behavior 

of this stretch of the plate boundary was a hypothesized 

slip deficit after the 1906 San Francisco earthquake 

(Thatcher, 1975) and the existence of several bends and 

other complexities in the local fault trend (Pampeyan, 

1979) in some cases associated with anomalously high topography (Scholz, 1985). Among these complexities, the 

40-km-long double restraining bend formed by the San 

Andreas fault in the southern Santa Cruz Mountains was 

universally thought to have played an important role in the 

tectonic evolution of the region. 

Nonetheless, there was abundant geologic evidence of recent compression and uplift requiring a source of tectonic 
F24 l'ECTONIC PROCESSES AND MODELS 

strain other than pure lateral shear along the San Andreas 

fault. For example, Vanderhurst and others (1982) and 

Aydin and Page (1984) documented the extreme state of 

deformation of lower Pleistocene coastal and fluvial deposits along the foothills of the southern Santa Cruz 

Mountains east of the San Andreas fault; Clark and Rietman (1973), Greene and Clark (1979), Clark (1981), 

Crouch and others (1984) recognized the progressive transition from a marine to a subaerial environment of the =3- 

Ma-old top of the Tertiary sequence in the Santa Cruz 

Basin; and Harbert and Cox (1989) and Harbert (1991) 

correlated the onset of compression across the plate 

boundary and uplift of the Santa Cruz Mountains with a 

sharp change in Pacific-plate motion 4-3 Ma. Along the 

coast, more youthful records of sustained uplift were described as early as the 1890's by the first investigators of 

California geology, and later by Rode (1930), Alexander 

(1953), and Bradley and Griggs (1976). As many as five 

distinct wave-cut platforms composing one of the most 

spectacular flights of marine terraces in California were 

accurately described and mapped, but no one was able to 

identify the source of their uplift or to explain why their 

elevation differed so drastically from place to place. 

LARGE-SCALE TECTONIC 

DEFORMATION ASSOCIATED 

WITH THE EARTHQUAKE 

As soon as preliminary instrumental data on the earthquake became available, various investigators of its geologic impact focused on the coastal uplift that should have 

resulted from the large reverse-slip component shown by 

,the focal mechanism. Compelling evidence of sudden uplift of the coastline in association with the earthquake 

came from several individuals who witnessed an impressive ocean retreat at different locations between Santa 

Cruz and Aptos (fig. 1). Early, rather old fashioned attempts to assess the extent of coseismic uplift were based 

on readings from two tidal gages located in downtown 

Santa Cruz and on the height of barnacles on the piers of 

the Capitola wharf. However, the only fact that could be 

ascertained was that the coseismic uplift was smaller than 

the uncertainty associated with nontidal fluctuations in 

ocean level (4.3 m) and with the height distribution of 

the barnacles with respect to the mean higher high water 

(4.5 m). 

From a wider standpoint, McNally and others (1989) argued that the similarity between the region's landforms and 

the predicted pattern of coseismic uplift reflected a close 

relation between the seismic source and the recent evolution of the Santa Cruz Mountains. Their hypothesis was 

frustrated, however, by the observation that even though 

the general trend of uplift mimicked fairly well the gentle 

seaward slope of the southern Santa Cruz Mountains west 

of the San Andreas fault, subsidence was predicted for 

Lorna Prieta, the highest point in the study area (1,155 m; 

LP, fig. 1). Other investigators used various types of evidence to hypothesize that the 1989 earthquake was not a 

characteristic San Andreas event (Kanamori and Satake, 

1990) or that hma Prieta-type events may be repetitive but 

do not represent the only active tectonic process in the 

Santa Cruz Mountains (Dietz and Ellsworth, 1990). 

Subsequent investigators focused on the lowest emergent 

Santa Cruz terrace (figs. 1-3). Anderson (1990) and Valensise and Ward (1990) noticed that the pattern of elevation 

of the terrace's inner edge is reminiscent of the pattern of 

coseismic uplift predicted for the 1989 earthquake. Also, 

the elevation of a specific site on any of the best recognizable terraces appeared to be inversely proportional to the 

site's distance from the San Andreas fault-that is, from the 

source of tectonic strain. On the basis of a comparison between all the available terrace elevations and the predicted 

coseismic-uplift pattern, Anderson proposed a recurrence 

interval of =700 yr for a Loma Prieta-type event. Valensise 

and Ward (1991) performed a formal inversion to infer the 

full parameters of a fault that would raise the lowest terrace 

to its present elevation by repeated discrete slip events. The 

geometric parameters of their Geological Fault Model 

(GFM, fig. 4) turn out to be similar to those estimated for 

the earthquake, although the ratio of strike slip to reverse 

slip and the fault length were found to be significantly larger than those observed coseismically. Valensise and Ward 

(1991) also calculated a recurrence interval of =600 yr for a 

Loma Prieta-type event. Paradoxically, Anderson's and 

Valensise and Ward's solutions shared a similar estimate of 

recurrence interval, even though their proposed terrace ages 

and uplift rates differed completely. 

A second major object of scientific dispute was identification of the source of uplift of the marine terraces between 

Santa Cruz and Point Afio Nuevo (fig. I), a stretch of the 

coast where 1989 uplift was mild (Marshall and others, 

1991) but terrace elevations are comparable with those observed farther east. To account for the observed discrepancy, Anderson (1990) invoked the activity of a section of the 

San Andreas fault north of the 1989 rupture zone, whereas 

Anderson and Menking (1991) proposed a model based on 

oblique-reverse slip on the San Gregorio fault. In contrast, 

Valensise and Ward (1991) maintained that the existence of 

terraces west of Santa Cruz is consistent with repeated motion on the Loma Prieta fault alone, provided that the ratio 

of right-lateral to reverse slip is much larger than that observed in 1989, as predicted by the GFM. To reconcile the 

short-term (coseismic) and long-term (GFM) estimates of 

the fault rake, they hypothesized that what is shown in the 

geologic record is a combination of motion on the Loma 

Prieta fault as seen in 1989 and on the San Andreas fault 

proper. This hypothesis is further supported by the observation that the pattern of elevation of the first terrace between 
TIE CREATION OF THE CENTRAL SANTA CRUZ MOUNTAINS, CALIFORNIA F25 

Santa Cruz and Pajaro Valley requires a strong asymmetry out by K.R. Lajoie (unpub. data7 1991)* connecting innerin the distribution of uplift, regardless of the existence and edge positions with the same elevation (a*', fkF, y-yt7 

elevation of terraces west of Santa Cruz. As first pointed fig. 4) results in a series of widely divergent lines. This 

'\ MONTEREY BAY 

10 KILOMETERS 

Figure l.-Central Santa Cruz Mountains, Calif., showing location of 

major faults, marine terraces, and topographic domains associated with 

tectonic processes of varying nature and age. LP, Loma Prieta, highest 

point (elev, 1,155 m) in study area; SAFZ, San Andreas fault zone; 

SBFZ, Sargent-Berrocal fault zone (dashed where inferred); SGFZ, San 

Gregorio fault zone (dashed where inferred); ZAY, Zayante fault. Ia and 

Ib (diagonally ruled areas), western and eastern limbs, respectively, of 

First Terrace (RMe, 193Q Alexander, 19531, which Bradley and Griggs 

(1976) recognized as formed by three distinct platforms, highest of 

which coincides with platform of First Terrace as originally designated 

(two lower platforms not shown for simplicity); II (black areas) and 111 

(stippled areas), Second and Third Terraces, respectively, as originally 

defined by Alexander between Santa Cruz and the Pajaro Valley (see fig. 

2). Higher terraces recognized west of Santa Cmz do not correspond to 

those defined by Alexander and are not considered further here. A and 

B, culminations of First and Third Terraces, respectively; C, northwesternmost and highest outcrops of the Purisima Formation in the central 

Santa Cruz Mountains; D, southernmost outcrop of the Purisima Formation in the northern Santa Cmz Mountains. Stars, outcrops of base of 

the Purisima Formation (see fig. 7); contour interval, 100 m. Light shading indicates areas where elevation is above 300 m. On the basis of distribution of relief and gross geologic features, study area is divided into 

five topographic domains, extending original scheme by Aydin and Page 

(1984): (I) Laurel domain (elev, 0450 m, avg 250 m), a hilly terrain 

that includes drainage basins of main streams originating in the central 

Santa Cmz Mountains southwest of the Zayante fault and that directly 

overlies source region of 1989 earthquake; (2) Ben Lomond domain 

(elev, 0-750 m, avg 500 m), comprising a prominent coastal range corresponding to a structural high of Salinian basement (see fig. 5); (3) 

Summit domain (elev, 400-900 m, avg 600 m), a 5-km-wide band between the San Andmas and Zayante faults that forms a northwest-trending ridge overlooking the Pacific Ocean; (4) Loma Prieta domain (elev, 

600-1.155 m, avg 800 m), a 5- to 10-km-wide band comprising a series 

of slivers of the Franciscan Complex (see fig. 5) offset by a swarm of 

regional faults; and (5) Pajaro domain (elev, 0-100 m), which includes 

late Pleistocene and Holocene alluvial plain of the Pajaro River in foothills of the Santa Cruz Mountains but, unlike other coastal domains, has 

no marine terraces. 
TECTONIC PROCESSES AND MODELS 

model-independent approach yields an average spacing of 

the uplift contours that is twice as large near Santa Cruz as 

near the Pajaro Valley, in good agreement with the GM's 

predictions but in marked contrast with the nearly symmetrical pattern of 1989 vertical coseismic displacement (Marshall and others, 1991, fig. 4). 

Anderson's ( 1990) and Valensise and Ward's (1990, 199 1) 

results furnished convincing evidence for the generation of 

recent landforms by repeated earthquakes in the Santa Cruz 

region. The interpretations discussed above, however, are 

too different to be of much use-for example, to assess 

whether significant seismic potential remains in the area. In 

addition, none of them can satisfactorily explain the distribution of relief in the Santa Cruz Mountains and, in particular, 

the presence of high topography east of the San Andreas 

fault. Schwartz and others (1990) attributed the topography 

in this area to slip on one of the well-identified southwestdipping faults of the Sargent-Berrocal system or on a northeast-dipping, blind, undetected reverse fault (figs. 1,s). The 

main trace of the Sargent fault, however, lies to the southwest 

of Loma Prieta (McLaughlin and others, 1988), which would 

subside rather than be uplifted by the reverse component of 

slip. Although the existence of this undetected fault is suggested by limited seismologic observations (Olson, 1990), 

there is no evidence that it might significantly contribute to 

the generation of the Santa Cruz Mountains. The Monte Vista 

fault and the other frontal faults bounding the north flank of 

the southern Santa Cruz Mountains (Pampeyan, 1979) would 

be the best candidates to explain the uplift of Loma Prieta, 

but it is uncertain whether these faults are active, what the 

rate of their activity could be, and whether the orientation 

of the slip vector would imply a significant component of 

vertical motion. Davis and Namson (1991) invoked the 

growth of two late Cenozoic anticlinoria to explain the 

present configuration of the central and southern Santa Cruz 

Mountains in relation to the San Andreas fault and the 1989 

earthquake; the first anticlinorium is centered about halfway 

between the San Andreas fault and the coastline, whereas 

the axis of the second anticlinorium runs parallel and to the 

east of the Sargent-Berrocal fault system (fig. 1). Both of 

these structures are interpreted as fault-bend or fault-propagation folds. Although Davis and Namson's model easily 

accounts for uplift of the western anticlinorium as a result 

of repeated Loma Prieta-type events, uplift of the eastern 

anticlinorium would require the action of a shallowly dipping, northeast-verging thrust fault extending from 12- to 

17-km depth and overlying a southwest-dipping subduction 

zone. However, owing to the presence of a regional detachment at 16- to 17-km depth, no direct link is envisioned 

between the occurrence of the earthquake and the structure 

of the upper crust. If such a condition proved correct, this 

highly suggestive model would indeed impose major changes 

in the way we investigate seismogenic faults on the basis of 

surface geologic data, starting with the approach described 

in this paper. 
THE CFEATION OF THE CENTRAL SANTA CRUZ MOUNTAINS, CALIFORNIA 

To address these different models and issues and to verify 

whether repeated Loma Prieta-type events may be responsible not only for uplift of the lowest Santa Cruz terrace 

but also for the creation of the entire central Santa Cruz 

Mountains, I decided to investigate and compare the tectonic 

deformation recorded at different levels of the local geologic 

history. Because we are dealing with a partially or occasionally blind faulting seismogenic source, that of the 1989 

earthquake, as well as processes of continuous deformation 

associated with motion of the Pacific plate relative to a 

stable frame of reference, we cannot rely on such traditional 

approaches as evaluating fault displacements or identifying 

reliable piercing points. Instead, we locate and describe geologic features that may have kn areally deformed after 

the onset of compression across the central California basins. 

For this purpose, we select extended and reliable geologic 

datum spanning the 3 to 4 may. since the major platereorientation event that conceivably marks the inception of 

uplift in the Santa Cruz Mountains, and treat them as instantaneous pictures of cumulative deformation to infer the 

principal traits of the local tectonic history. 

GEOLOGIC DATUMS IN THE 

CENTRAL SANTA CRUZ MOUNTAINS 

Suitable geologic datums belong to two main categories: 

The first category includes wave-cut platforms, whereas 

the second category includes sedimentary deposits composing major members of a regional marine sequence. Because wave-cut platforms approximate palm-sea levels 

within a few meters, these datums represent the most 

faithful record of subsequent tectonic uplift. A commonly 

overlooked property of emergent coastal-erosional features 

is that they may also supply a reliable record of horizontal 

strain, especially when the sense of tectonic transport does 

not align with the coastline. Assuming that the carving of 

wave-cut platforms proceeds at about the same rate in 

comparable rock types, residual or anomalous offsets between strandlines of different age could be interpreted as a 

response to progressive advection of the land through the 

source of uplift. In contrast, datums of the second category 

carry large uncertainties related to the geometric characteristics of the depositional environment (for example, when 

deposition occurs on a sloping sea floor), to the depth of 

deposition, and to difficulties in identifying and dating the 

contact with underlying deposits (for example, when the 

bottom of the investigated unit is time transgressive). 

These combined uncertainties may result in a global inaccuracy of approximately a few hundred meters in the determination of the total uplift. 

The accuracy in dating each datum depends directly on 

its genetic characteristics. Wave-cut platforms can be indirectly dated on the basis of the age of the erosional events 

by which they were generated, which, in turn, reflect independently established global fluctuations of sea level, or 

by direct radiometric dating of fossils found in the terrace 

deposits. Dating by the first approach can be extremely 

Figure 3.4uter edge of First Terrace along West Cliff Drive, Santa Cruz (see fig. 5 for location and orientation). Upper part of wave-cut platform is carved in the uppr Miocene and Pliocene Purisima Formation, 

which, in turn, overlies unconfonnably the upper Miocene Santa Cmz Mudstone. East and southeast of this 

site, First Terrace is consistently carved in the Purisima Formation (see fig. 7). whereas to the west it is 

carved in the Santa Cruz Mudstone. Purisima beds dip =3O SSE., whereas terrace slopes =30Â mom westerly, 

consistent with prediction from Geological Fault Model (see fig. 4). In itself, this discrepancy indicates that 

orientation of strain field has rotated since onset of uplift at this site. 
F28 TECTONIC PROCESSES AND MODELS 

precise, but because major episodes of sea-level fluctuation 

occur every 100 ka or so, correlation with the wrong highstand may result in a dating inaccuracy comparable to the 

age itself. An incorrect correlation may have an even larger 

effect, considering the fact that each highstand is associated 

with a different formation elevation (difference in elevation 

between sea level at the time of the incision and modem 

sea level), which implies that the cumulative uplift between 

the original and present height of a specific platform also 

varies with the age assignment. Therefore, tectonic rates 

calculated in a region subject to moderate uplift (<0.5 mmlyr) 

may change by as much as 100 percent in response to an 

age uncertainty of 20 percent. Dating by the second approach 

is more straightforward in principle but is subject to the 

availability of suitable fossil species and to analytical limpreserved platforms and associated deposits all over the 

world, reliable dating of at least one terrace is generally 

possible everywhere, more so in central California. Higher 

platforms, which are normally depleted of datable fossils, 

owing to their age and to greater erosion, can then be dated 

by extrapolating backward the rate of uplift calculated for 

the younger terrace. 

The ages of generic marine units are obtained directly 

from the deposits, following standard stratigraphic criteria. 

Direct radiometric dating of specific minerals or magnetostratigraphic correlation is sometimes possible when dealing with clastic sedimentary deposits. Unlike datums of 

the first category, datums of this category should be considered for their ability to illustrate processes of continuous deformation at time scales of =1 m.y. rather than for 

itations. Because the last major highstand has left well- assessing instantaneous tectonic rates. 

Figure 4.Ã‘Centra Santa Cruz Mountains, Calif., showing predicted elevations (contour interval, 10 m) and uplift rates (contour interval, 0.08 

mmlyr) from Geological Fault Model (GFM) of Valensise and Ward 

(1991). GFM strikes 134' and dips 65' SW. Fault length, width, and minimum depth are 60, 13, and 5 km, respectively; rake is 162', corresponding 

to ratio of right-lateral to reverse slip of 3:l. Triangles, 28 inner-edge 

positions along Alexander's (1953) First Terrace (see fig. 2); dots, inneredge positions along Bradley and Griggs' (1976) Highway 1 platform; 

straight solid line ending in triangles, surface trace of GFM, which matches 

fairly well trend and extent of 1989 aftershock zone (Dietz and Ellsworth, 

1990); dotted area, surface projection of GFM; irregular solid line ending 

in circles, path of leveling line in figure 13; star, Loma Prieta main shock 

(McNally and others, 1989). Dashed lines connect sites marked by a-a', 

bp, and y-y' in figure 2; divergent trends of these lines suggest that longterm pattern of uplift is not symmetrical along strike of fault, as detailed by 

contours of GFM. Irregular long-dashed lines, San Gregorio fault zone. 
THE CREATION OF THE CENTRAL SANTA CRUZ MOUNTAINS, CALIFORNIA F29 

The following sections discuss in detail two datums of 

the first category, the first and third Santa Cruz terraces 

(figs. 1, 3; table I), and one datum of the second category, 

the upper Miocene and Pliocene Purisima Formation (figs. 

5, 6). Even though in recent literature the two terraces 

have been renamed, for simplicity I prefer to use the nomenclature of Alexander (1 953) (fig. 2). Common features 

of these three datums are: (1) the exceptional extent and 

continuity throughout the investigated region; (2) their 

conspicuous characteristics, which make them easy to 

identify; and (3) the availability of nearly a century of 

descriptions, field maps, and studies on specific aspects. 

Finally, the ratio among the ages of the three datums 

(=0.1:4.3:=3.0), which is comparable to the ratio among 

the uncertainties discussed above, should ensure a correct 

quantitative appraisal of the contribution of the identified 

agents of long-term tectonic strain to the final geologic 

structure. 

FIRST TERRACE 

The first Santa Cruz terrace was described as "First Terrace" by Rode (1930) and Alexander (1953), respectively 

for the coastline west (Ib, fig. 1) and east (la, fig. 1) of 

Santa Cruz. The stretch of this terrace between Santa Cruz 

Figure 5.-Simplified geologic map of the central Santa Cruz Mountains, 

Calif., based on published data of Clark (1981), Aydin and Page (1984), 

and Brabb (1989). Numbered squares denote locations, and arrows orientations, of photographs in figures 3 and 6. Units: 1, alluvial and coastal 

deposits (Holocene and P1eistocene)Ã‘include the Aromas Sand; 2, nonmarine sedimentary rocks (late Miocene to Pleistocene)-primarily the 

Santa Clara Formation; 3. Purisima Formation (late Miocene and Pliocene); 

4, marine sedimentary rocks (Tertiary)Ã‘exclude the Purisima Formation; 

5, sandstone (Upper Cretaceous); 6, plutonic and metamorphic rocks (Cretaceous)~consists of granitic plutonic and metamorphic rocks of the Salinian block; 7, Franciscan Complex (Cretaceous and Jurassic). BA, Butano 

anticline; BLF, Ben Lomond fault; CAL, Calaveras fault; DS, Davenport 

syncline; GS, Glenwood syncline; MVFZ, Monte Vista fault zone; SAFZ, 

San Andreas fault zone; SBFZ, Sargent-Berrocal fault zone; SGFZ, San 

Gregorio fault zone (dashed where inferred); SLS, San Lorenzo syncline; 

SVS, Scotts Valley syncline; ZAY, Zayante fault (dashed where inferred). 
TECTONIC PROCESSES AND MODELS 

Table 1 .-Nomenclature and ages of Santa Cruz marine terraces 

[All ages (in parentheses) in thousands of years. A given terrace may or may not 

correlate with adjacent terraces described by other investigators. The nomenclature 

of Valensise and Ward is the same as that introduced by Alexander (1953)J 

Bradley and Hanks and Anderson Valensise and Lajoie 

Griggs (1976) others (1984) (1990) Ward (1991) (1991) 

Santa Cruzl --- Santa Cruz --- --- (81-105). 

Davenport 

(102). 

Highway I 112 

(125). 

Highway 1 1 

(105). 

Highway 1, Highway 1 

First (125). (124). 

Gre yhound112 

(160) 

Cement1 Cement Second3 

(1 24). (120). (212). 

Western Third3 

(212). (3 20). 

Wilder 1 Wilder' 

(370). (330). 

Cement' 

(3 20). 

Western 

(430). 

Wilder 

(800). 

lhvestigated only between Santa Cruz and Point Afio Nuevo. 

originally identified as a separate platform within the terrace. 

3hvestigated only between Santa Cruz and the Pajaro Valley. 

and Point Aiio Nuevo (Ib, fig. 1) was later reanalyzed in 

great detail by Bradley and Griggs (1976), who divided it 

into three distinct platforms that together form what they 

named "Santa Cmz Terrace" (table 1). The inner edge of 

the highest and best developed of these three platforms, 

which they named "Highway 1 platform," coincides with 

that of First Terrace of the previous investigators. 

The incision of First Terrace was correlated (table 1) 

with the Sangamon (125-85 ka) global sea-level highstand 

by Alexander (1953), with the 125-ka highstand (correspending to stage 5e of the oxygen-isotope time scale) by 

Bradley and Griggs (1976), with the 105- to 103-ka highstand (oxygen-isotope stage 5c) by Hanks and others 

(1984) and Lajoie (1986), with either the 81-ka (oxygenisotope stage 5a) or the 105-ka (oxygen-isotope stage 5c) 

highstand by Anderson (1990), and again with the 125-ka 

highstand by Valensise and Ward (1991). As discussed 

above, the assignment to the 125-ka or a subsequent highstand implies significantly different estimates for the formation elevation and, thus, of the cumulative tectonic 

uplift undergone by a specific platform. For example, 

Anderson's (1990) assignment to the 8 1- or 105-ka highstand (formation elevation, -19 and -9 m, respectively) 

implies an uplift rate in the range 0.3-0.9 mm/yr. In contrast, accepting the 125-ka assignment of Valensise and 

Ward (1991) and the formation elevation of 8.9Â± m obtained by inversion as a free parameter of their GFM (fig. 

4) implies a significantly slower uplift rate in the range 

Figure 6Ã‘Purisi1m in seacliff at New Bf&ton State Beach, about 5 km west-northhest of Aptos 

(see fig. 5 for location and orientation). Seacliff is much higher than in (do~town Santa Cruz (fig. 3), consistent with lange @fence in uplift fata predicted -or these twft sites by Geological Fault Model (@%; see fig. 

4). As &saws@ in figure 3, east-southeastward dip of Tertiary bedrbck is inconsistent with local terrace 

slope, which is perpendicular to northwestward trend of shoreline, and with orientation of gradient of uplift 

predicted by QPM. At this site, however, disocepancy is SOe, suggesting that majot reorientation of strain 

field has occurredsince onset of compression in this area. 
THE CREATION OF THE CENTRAL SANTA CRUZ MOUNTAINS, CALIFORNIA F3 1 

0.13-0.35 mmlyr, corresponding to a tilt rate in the range 

0.7'-2S0/m.y. These results would change by & 10 percent 

or less if we replaced the GFM's 8.9-m formation elevation with the widely accepted 6- to 10-m estimate from 

studies of coastal geology. 

Direct dating of the Santa Cmz terraces has been attempted 

by many investigators, but owing to the absence of suitable 

fossils, the results are dispersed within the fairly wide range 

68-130 ka. However, on the basis of a reevaluation of the 

field data, a new scheme of correlation with the global sealevel history, and the observation that none of the dated 

fossils was collected on the highest platform, K.R. Lajoie 

(unpub. data, 1991) changed his own age assignment from 

105-103 ka (Hanks and others, 1984; Lajoie, 1986) to 125 

ka for Highway 1 platform of First Terrace. 

THIRD TERRACE 

As anticipated above, this section describes Third Terrace as originally defined by Alexander (1953). This higher terrace is far less continuous and generally narrower 

than First Terrace, reflecting a combination of erosional 

degradation and different formation conditions. It was initially described as "Second Terrace" by Rode (1930) but 

then renamed "Third Terrace" by Alexander (1953), who 

updated the local nomenclature after recognizing another, 

more subdued terrace (which he named "Second Terrace") 

emerging from the inner edge of the First Terrace and extending for a few kilometers around the mouth of the 

Aptos River (figs. 1, 2). 

Third Terrace (table 1) appears to continue west of the 

San Lorenzo River (fig. 1) with Western Terrace of Bradley and Griggs (1976). On the basis of the results from 

First Terrace, Valensise and Ward (1991) assigned the incision of the part of this surface lying east of Santa Cruz to 

the 320-ka (ox ygen-isotope stage 9) highstand, whereas 

west of Santa Cruz it was dated at 450 ka by Bradley and 

Griggs (1976). In fact, the carving of Western Terrace during the 320 ka highstand is incompatible with the 0.13- to 

0.21-dyr uplift rate calculated for the part of the 125-ka 

terrace west of Santa Cruz. Thus, Third Terrace may reflect the reoccupation of a platform carved during the 

Western Terrace highstand, a hypothesis seemingly suggested also by Alexander (1953) (fig. 2), or the 320-ka terrace west of Santa Cmz may have been removed by 

subsequent highstands. 

Though not used in our analysis, Alexander's (1953) 

Second Terrace deserves special attention because it provides strong evidence to constrain the age assignments 

proposed by Valensise and Ward (1991) for First and 

Third Terraces. Alexander noticed that Second Terrace 

does not parallel First Terrace but is, instead, cut by it, and 

that it is found only where the uplift rate is highest. Simple analytical arguments (Lajoie, 1986) indicate that these 

two conditions are evidence that Second Terrace was cut 

at a substantially lower elevation than First Terrace. Assuming that First and Second Terraces merge into a single 

wave-cut platform at an elevation of 40 to 45 m (sites a', 

a", fig. 2), and assuming that First Terrace is 125 ka old, 

we conclude that a minimum uplift rate of 0.26 to 0.29 

dyr is required to compensate for this difference in formation elevation. Therefore, any estimate for the age of 

Second Terrace will translate directly into a formation elevation, which, in any case, will be lower than that of First 

Terrace. Assuming that Second Terrace formed during the 

2 12-ka highstand (oxygen-isotope stage 7; Valensise and 

Ward, 1991), the formation elevation would be -15 m. 

Because global sea level is generally believed to have 

been lower during the 212-ka highstand (oxygen-isotope 

stage 7) than during the 125- and 320-ka highstands (oxygen-isotope stages 5e and 9, respectively), this conclusion 

indirectly supports the age assignments proposed by 

Valensise and Ward (1991) for Second and Third Terraces, 

although these results also imply that Second Terrace is 

not a suitable datum for the purposes of our investigation. 

PURISIMA FORMATION 

The Purisima Formation is the youngest and, probably, 

most extensively exposed marine unit of the Tertiary sequence in the central Santa Cruz Mountains west of the 

San Andreas fault (Greene, 1977; Greene and Clark, 1979; 

Clark, 1981; Stanley, 1985, 1990). The unit consists of 

thick, yellowish-gray, tuffaceous and diatomaceous siltstone beds, with thick andesitic sandstone interbeds. 

Abundant glassy debris, presumably from the Sierra Nevada and Cascades volcanoes, differentiates the Purisima 

from older marine formations. Its age is constrained by 

various sets of paleontologic, radiometric, and paleomagnetic observations to the range late Miocene to late Pliocene (Stuart and others, 1982). 

Overall, the Purisima Formation records a rapid late Miocene transgression followed by slow regression and basin 

filling during the Pliocene. The coincidence between the 

onset of compression and uplift across the Coast Ranges 

(4-3 Ma; Harbert and Cox, 1989; Harbert, 199 l), the end 

of volcanism, and the end of marine sedimentation during 

the late Pliocene (Crouch and others, 1984; Clark and others, 1991) suggests that the Purisima Formation bears a 

complete record of all the tectonic processes leading to the 

post-Pliocene creation of the Santa Cruz Mountains. To 

extract this information, we must select a structural surface for which both the present configuration and a reasonable hypothesis on the original shape and elevation are 

available. The contact between the Purisima Formation 

and the underlying middle to late Tertiary units is generally unconformable and marked by a characteristic glauconitic sandstone, which makes it one of the most reliable 
F32 TECTONIC PROCESSES AND MODELS 

landmarks in central California stratigraphy. I reconstructed the structural contours of the base of the Purisima Formation by interpolating elevations of its contact with the 

underlying formations (fig. 7; tables 2, 3), using published 

geologic maps (McLaughlin and others, 1988; Brabb, 

1989), geologic maps in preparation (R.J. McLaughlin, 

written commun., 1990), and well data (Clark and Rietman, 1973; E.E. Brabb, written comrnun., 1990). 

A precise age for this datum is difficult to assess because the basal part of the Purisima Formation is time 

transgressive from northwest to southeast (Greene and 

Clark, 1979). For our purposes, however, all we need to 

know is the timing of the latest major regression in the 

study area, which we will infer on the basis of plate-tectonic arguments, assuming that deformation has since proceeded rather uniformly until the present. 

With respect to the original shape of this datum, the 

simplest and most convenient assumption is that it was a 

flat, horizontal surface. Alternatively, we should prove that 

the present-day departure from planarity and horizontality 

is large in comparison with that inferred for the depositional environment of the Purisima Formation. Not much 

0 

u 

5 KILOMETERS 

Figure 7.Ã‘Structura map of base of the Purisima Formation in the central Santa Cruz Mountains. Calif., constructed by using elevations of contact between the Purisima and underlying formations from published and 

unpublished geologic maps and well data (see fig. 5; tables 2, 3). Elevations in meters above or below sea level; contour interval. 50 m. Stars, 

data points; straight solid line, surface trace of Geological Fault Model 

(fig. 4); large plus and minus signs, location of highest and lowest parts 

of datum, respectively; lined area, part of datum currently within 50 m of 

present sea level. A and B. culminations of First and Third Terraces, respectively (Alexander, 1953); C, northwesternmost and highest outcrops 

of the Purisima Formation in the central Santa Cruz Mountains. The 

Purisima is gently warped west-northwestward against Ben Lomond 

Mountain and tightly warped northeastward against the San Andreas 

fault. In both directions, edge of contoured area marks places where extrapolated base of the Purisima is higher than present topography-in 

other words, where all of the Purisima has been removed by erosion and 

older rocks are exposed. To east, the Purisima is buried beneath as much 

as 600 m of Pleistocene sedimentary deposits of the Aromas Sand and 

other coastal units marking end of marine cycle. Away from the mountains, Purisima datum can be approximated by a surface dipping about 3' 

ESE. SAFZ, San Andreas fault zone; SBFZ, Sargent-Berrocal fault zone 

(dashed where inferred). 
THE CREATION OF THE CENTRAL SANTA CRUZ MOUNTAINS, CALIFORNIA 

Table 2.-Elevations of the base of the Purisirna Formation from outcrop data 

[a.s.l., above sea level; SC, Santa Cruz] 

No. Latitude Longitude Elevation Location No. Latitude Longitude Elevation Location 

West Cliff Drive I, SC 

West Cliff Drive 11, SC 

City Hall, SC 

High Street E., SC 

Harvey West, SC 

Laurel and Escalona Streets, SC 

Water and Branciforte Streets, SC 

DeLaveaga Golf Course S., SC 

DeLaveaga Golf Course N., SC 

Branciforte Creek E., SC 

Branciforte Creek W., SC 

Highway 17, Pasatiempo Drive 

Highway 17, Sims Road 

Highway 17, Brook Knoll School 

Graham Hill Road 

Camp Evers S. 

Highway 17 and Mount Hermon Road 

Carbonera Creek S. 

Glen Canyon Road 

Carbonera Creek N. 

Redwood Drive 

N. Delaveaga I 

N. Delaveaga I1 

Highway 17, San Augustin 

Scotts Valley 

Highway 17 and Scotts Valley Drive 

Bean Creek Road 

Glenwood Drive 

Redwood Glen Camp 

Mackenzie Creek and Bean Creek 

Nelson Road 

Mission Springs 

Bean Creek Fault 

Scotts Valley syncline I 

Scotts Valley syncline I1 

Zayante Creek 

Lockhart Gulch I 

Zayante 

Lockhart Gulch I1 

Lockhart Gulch 111 

Mackenzie Creek I 

Mackenzie Creek I1 

Bethany Park 

Highway 17 and Vinehill Road 

Bethany Bible College 

Highway 17 and Carbonera Creek W. 

Highway 17 and Carbonera Creek E. 

is known, however, about the paleobathymetry and paleoecology of this formation. A compilation by Stanley 

(1985) suggests a depositional depth of <500 m below 

present-day sea level. Clark (1981) reported fossils indicative of inner neritic depths (GO m) collected a few kilometers north of Santa Cruz (fig. I), and suggested that the 

Purisima Formation was deposited in a continental-shelf 

Vinehill Road 

Vinehill Road and Jarvis Road 

Branciforte Drive N. 

Granite Creek N. 

Granite Creek S. 

Granite Creek E. 

Branciforte Drive and Crystal Creek 

Crystal Creek 

Happy Valley School N. 

Happy Valley School S. 

Happy Valley Conference Ground 

Blackburn Gulch S. 

Soquel Creek 

Jarvis Road 

Blackburn Gulch N 

Glenwood Basin 

Hester Creek 

Olive Spring Quarry 

Bridge Creek 

Old San Jose Road 

Mountain Charlie Road S. 

Mountain Charlie Road N. 

St. Mary's Girl Camp 

Laurel Tunnel 

Glenwood Basin N. 

Soquel Creek W. Branch 

Glenwood Basin S. 

Hester Creek Church 

Sugarloaf Mountain 

Amaya Creek 

Soquel Creek and Amaya Creek 

Olive Springs 

Bridge Creek 

Hinckley Creek N 

Hinckley Creek S. 

China Ridge 

San Lorenzo syncline 

Mountain Charlie Gulch 

Camp Wasibo 

Aptos Creek W. 

Aptos Creek E. 

Buzzard Lagoon Road W. 

Buzzard Lagoon Road E. 

Eureka Gulch 

Eureka Canyon W. 

Eureka Canyon E. 

94 37.039 121.809 427 Eureka School 

environment. All investigators agree that the formation 

was deposited in a tectonically active basin, possibly 

owing to the vicinity of such major faults as the San Andreas and San Gregorio, and that localized uplift occurred 

within the basin well before the end of marine sedimentation, as evidenced by internal disconformities and by rapid 

vertical and lateral variations. Sedimentologic arguments 
F34 TECTONIC PROCESSES AND MODELS 

Table 3.-Elevations of the base of the Purisima Formation from well 

data 

(a.s.1.. above sea level] 

MODES OF TECTONIC DEFORMATION 

IN THE CENTRAL SANTA CRUZ 

MOUNTAINS 

-- 

No. Latitude Longitude Elevation Welllyear 

N. W. (m a.s.1.) 

1 37.043 121.894 8 8 Lorna Prieta 1 (1949) 

21.877 1 9 5 Lorna Prieta 2 (1949) 

21.847 - 1 5 8 Bean Hill Hihn 1 (1946) 

21.853 2 9 Union Oil Hihn 1 (1951) 

21.857 -3 9 1 Union Oil Hihn 2 (1952) 

21.814 - 9 5 3 Blake 1 (1954) 

21.821 -830 Light 1 (1951) 

21.841 -7 1 7 Pierce 1 (1950) 

9 36.902 121.834 -7 15 Blake 1 (1953) 

10 36.938 121.821 - 8 3 5 Carpenter 1 (1953) 

11 36.987 121.954 c-320 Sequel County (1977) 

As pointed out earlier, the generation of coastal landforms by repeated Loma Prieta-type events is established 

by more than 2 years of investigations since 1989, although 

important ambiguities and discrepancies in major aspects of 

this process are still unresolved. To address these aspects, I 

selected three geologic datums, each of which supplies an 

instantaneous picture of cumulative tectonic deformation at 

different periods of the geologic history. The following section describes how the interplay between the information 

contained in each picture can be used to investigate processes undetected by studies on the deformation of First Terrace, and to extend backward the record of tectonic events 

in the central Santa Cruz Mountains. 

LATERAL MIGRATION OF THE SHORELINES 

also suggest that the sea floor on which the Purisima Formation was being deposited was not everywhere regular; 

for example, its contact with the underlying formations is 

generally conformable throughout the central Santa Cruz 

Mountains but unconformable in the vicinity of Ben 

Lomond Mountain (figs. 1, 5). In combination with other 

lines of evidence, this observation suggests that Ben 

Lomond Mountain was already delineated topographically 

by the middle Miocene, well before initial deposition of 

the Purisima Formation. 

To test more quantitatively whether the Purisima Formation was deformed during or after deposition, I compared 

(fig. 8; table 4) actual attitudes of the Purisima Formation 

from geologic maps or directly collected in the field with 

local gradients of the base of the formation inferred from 

the structural map (fig. 7). Correspondence between the attitudes observed at the surface and those inferred for the 

base of the formation can be taken as evidence that the 

formation was originally deposited in flat, subhorizontal 

layers and subsequently deformed as a whole. If this were 

true throughout the study area, then the present dip of the 

Purisima Formation could be taken as representative of 

postsedimentary tectonic processes, rather than as reflecting irregularities of the sea floor or peculiar depositional 

conditions (for example, clinostratification associated with 

the evolution of a delta). An upper limit on the departure 

from purely horizontal deposition is set by the observation 

that the Purisima Formation dips <3O over the entire 

southernmost part of the study area, both from outcrop 

data and from the structural map (fig. 7). 

Observations from rising coastlines around the world indicate that shorelines migrate over time in the same direction as the gradient of local uplift and that they tend to 

parallel each other if the source of uplift remains fixed (for 

example, Woodring and others, 1946; Chappell, 1974; 

Muhs, 1983; Keraudren and Sorel, 1987). Minor lateral 

fluctuations in the rate at which a coastline migrates away 

from the source of uplift can generally be accounted for 

by the varying interaction among the parameters controlling coastal evolution. However, if such fluctuations persist through two or more subsequent complete climatic 

and sea-level cycles, some form of tectonic control becomes more plausible. For example, we could invoke the 

action of a second, more localized tectonic force contrasting the positive movement or simply shifting the land 

away from the source of uplift. The first and third Santa 

Cruz terraces parallel each other southeast of Aptos and 

northwest of Sand Hill Bluff (halfway between Santa Cmz 

and Davenport, fig. I), where they are perpendicular to the 

local gradient of uplift, whereas between these two sites 

they diverge, describing a sigmoidal gap (fig. 9). This gap 

is centered on the region where the characteristic curvature 

of the Santa Cruz coastline is tightest and where both 

shorelines align nearly parallel to the gradient of uplift 

predicted by the GFM (fig. 4). Comparison of the 125-ka 

strandline with the modem shoreline shows a similar, 

though more pronounced pattern. If the tendency of a 

coastline subjected to pure uplift is to move forward (that 

is, away from the source of uplift), then the formation of 

these gaps-that is, the migration of the shoreline in a direction nearly perpendicular to the local gradient of uplift-requires that the pattern of vertical strain be modified 

over time, either by simple shifting of the source of uplift 
THE CREATION OF THE CENTRAL SANTA CRUZ MOUNTAINS, CALIFORNIA F35 

relative to the land or by the action of an additional source 

of vertical strain which disrupts the pattern of uplift 

caused by the main source. 

We test these hypotheses with a graphical restoration 

procedure to calculate the amount of motion required to fit 

shorelines of different ages one on top of the other (fig. 

10). Our approach considers only tectonic deformation and 

disregards possible lithologic inhomogeneities and other 

conditions leading to differential erodibility, which simply 

serve as additional sources of uncertainty. The limited 

breadth fluctuations of First and Third Terraces away from 

Santa Cruz (fig. 9), and the observation that both of these 

terraces are carved into rocks of the Purisima Formation 

all along the above-described gap (figs. 3, 6), suggest that 

the contribution of such effects is modest in comparison 

with the main tectonic effect. 

The first step in the restoration (figs. 10A, 105) indicates 

that the shoreline has migrated apay from the source of uplift 

by about 1.5 krn in the interval between the age of First and 

Third Terraces (300-200 ka). This result has no direct tectonic meaning but simply indicates that the shoreline has 

advanced by "1,500 m for every 50 to 70 m of uplift (assuming 0.24 mmlyr as an average uplift rate for the Santa 

Cruz coastline; see fig. 4) and thus that the average gradient 

of the offshore part of a typical Santa Cmz platform ranges 

from 30 to 50 m/km, in agreement with the 7- to 40-m/km 

gradients measured on modem platforms in the same area 

by Bradley and Griggs (1976). These simple calculations 

and their match with field observations indicate that the 

breadth of a marine terrace is strongly controlled by the seafloor slope, which, in turn, is controlled by the geometry of 

the uplift pattern and by the rate of offshore sedimentation. 

- 0 5 KILOMETERS 

Figure 8.-Sketch map of southern Santa Cruz Mountains, Calif., corn- that the Purisima was deposited on a fairly flat, subhorizontal surface 

paring observed attitudes of the Purisima Formation (heavy arrows) and thus that its present setting is largely an effect of true tectonic deforfrom published geologic maps and field data (table 4), with local gradi- mation. Dips of 0'4' ESE. on Purisima strata just seaward of Soquelents of the formation inferred from structural map (fig. 7). Length of Aptos area (fig. 1; Greene and Clark, 1979) are also consistent with 

arrow is proportional to dip angle. Good agreement supports hypothesis expected attitudes. 
F36 TECTONIC PROCESSES AND MODELS 

Table 4.-Attitudes of outcrops of the Purisima Formation 

No. Latitude Longitude Dip Dip 

N. W. angle direction 

I also considered fitting the modem shoreline to the shoreline of First Terrace. This would have required a slightly 

larger offset for a considerably shorter time interval than 

in the previous fit. The evolution of the modem shoreline, 

however, is far from complete (in fact, it is actively receding 

at a rate of a few centimeters per year), and so the comparison 

with the fully mature shoreline of First Terrace would be 

distorted. 

Unlike the previous step, what is left after removal of 

the contribution of simple forward migration appears to 

have an interesting tectonic meaning. Restoration of the 

coastline-perpendicular component has turned the sigmoidal gap into two separate rectangular gaps (shaded area, 

fig. 10). Fitting the two shorelines (figs. 105, 10C) now 

requires 1.5 to 2.0 km of apparent northwestward (parallel 

to the San Andreas fault) motion of the land, a process 

reminiscent of the generation of pullapart basins that could 

reflect progressive northwestward advection of the Pacific 

plate through the source region of the 1989 earthquake at 

a rate of 5 to 10 mrnlyr. Quite surprisingly, this result implies that the local source of uplift is stationary with respect to the North American plate over time scales of a 

fraction of a million years, a hypothesis that should be 

verifiable on the basis of the setting of our oldest datum. 

LATERAL MIGRATION OF THE PATTERN OF 

LONGITUDINAL WARPING 

The hypothesis that the local source of uplift is stationary with respect to the North American plate can also be 

tested by using the trend of vertical warping of our daturns, rather than their shape in map view. A simple observation is that the site where Third Terrace is highest is 

situated to the northwest relative to the culmination of 

both First and Second Terraces (figs. 2, 9). As pointed out 

earlier, the broad upwarping of an individual terrace reflects its varying distance from the Loma Prieta fault. The 

highest point on Third Terrace (site marked with "136 m" 

in figs. 2, ll), however, is not observed at the inner-edge 

position that falls closest to the fault but is shifted =3 km 

to the northwest of this site. The highest point on First 

Terrace ("57 m", figs. 2, 11) is one of the closest to the 

fault, but it is also the southeastemmost of a series of four 

positions whose heights fall within 4 m of the peak elevation. (Owing to the quality of available inner-edge observations, Second Terrace is omitted from this analysis.) 

A possible explanation for the existence of such 

"bumps" along the inner-edge trends may be found in a 

notable characteristic of the 1989 earthquake. To account 

for discrepancies among its main source parameters, Wallace and others (1991) hypothesized that a significant 

amount of "slow slip" could have been released from the 

hypocentral region of the fault, where little aftershock activity was observed but no moment release was detected 

by conventional seismometric analyses. Marshall and others' (1991) fit of coseismic elevation changes (see line 2 
THE CREATION OF THE CENTRAL SANTA CRUZ MOUNTAINS, CALIFORNIA F37 

in fig. 7 of Marshall and others, 1991) also shows some 

unmodeled uplift along the leveling line that runs closest 

to the earthquake epicenter. Both of these observations 

may reflect a concentration of moment release near the 

hypocenter, which would translate into excess uplift in the 

area between the epicenter and the shoreline. If this uplift 

were a permanent characteristic of the Loma Prieta source 

region, the "bumps" in the elevation trend of First and 

Third Terraces might simply record a cumulative effect of 

the passage of the Pacific plate through the epicenter of 

the 1989 earthquake. Again, different terraces would 

record different positions of the source of uplift relative to 

the land, thus allowing the rate of northwestward shifting 

to be evaluated on the basis of the time interval between 

subsequent highstands. However, quantifying this process 

is made difficult by the following observations (fig. 11): 

(1) There is a 3-km-wide data gap around the apex of 

Third Terrace; (2) the culminations occur along =2-kmlong sections of the terraces rather than at well-identified 

sites; and (3) identification of the culminations is subject 

to an additional uncertainty related to the fact that the 

strandlines do not perfectly parallel each other but instead 

indent more or less deeply the pattern of long-term uplift, 

implying that part of the difference in elevation between 

adjacent inner-edge positions on the same terrace simply 

reflects varying distance from the fault. Figure 11 shows 

that for First Terrace we can expect elevations to fluctuate 

by k4 m in response to variations of k1 krn in the distance between the inner edge and the fault. Because the 

average difference in elevation between adjacent positions 

on First Terrace is <3 m, this effect must be carefully 

considered. 

Figure 9.-Santa Cruz, Calif., area, showing reconstructed inner edges of 

two best expressed late Pleistocene marine terraces, First (125 ka) and 

Third (320-450 ka) Terraces, based on data of Alexander (1953) and Bradley and Griggs (1976). A and B, culminations of First and Third Terraces, respectively (see figs. 1, 2, 7). Arrows denote local direction of 

gradient of uplift along 0.5-mrnlyr contour, as predicted by Geological 

Fault Model (fig. 4). Shaded area (detailed in fig. 10) includes region 

where both modern shoreline and paleoshorelines may reflect migration 

of land relative to source of uplift. Double-headed arrows indicate how 

land may have migrated northwestward by 1.5 to 2.0 km during 200- to 

300-ka interval between incision of Third and First Terraces (corresponding to migration rate of 5-10 mrnlyr). Distance of ~3.0 km between culminations of First and Third Terraces also suggests that land has moved 

relative to source of uplift that has created elevated coastal features in 

Santa Cruz area. Dotted line (approximately corresponding to 90-ft depth 

contour) marks expected position of shoreline during a hypothetical future highstand 100 ka from present. SAFZ, San Andreas fault zone; 

SBFZ, Sargent-Berrocal fault zone (dashed where inferred). 
F38 TECTONIC PROCESSES AND MODELS 

Our preferred pick for the culmination of First and Third with the rate independently obtained from the map shape 

Terraces (sites A and B, respectively, fig. 11) implies a of the inner edges. What I believe to be extremely importotal shift of about 3k1 km. Because this part of Third tant, however, is that if the process of progressive uplift 

Terrace was assigned to the 320-ka highstand, we can cal- and advection has continued for time scales of 21 m.y., we 

culate a shift rate of 10 to 20 rnm/yr. Although the associ- should see large accumulation of topography at a considerated uncertainty is very large, this estimate is consistent able distance northwest of Santa Cruz, a hypothesis that 

91rd lerrace - 

Figure 10.Ã‘Coasta area near Santa Cruz, Calif. (see fig. 9 for location), 

showing migration of shoreline and subsequent modifications of landscape 

in response to tectonic forces and processes during interval enclosed by 

ages of First and Third Terraces (Alexander, 1953). A, Present setting, 

showing location of modem, First Terrace, and Third Terrace shorelines. 

Small arrows on First Terrace shoreline point in direction opposite to that 

of forward migration of shoreline after pure uplift, as predicted by Geological Fault Model (fig. 4); length of lower large arrow indicates amount of 

motion (-1.5 km) necessary to match visually shorelines of First and Third 

Terraces. Rate of forward migration is controlled by uplift rate and a combination of elements controlling original slope of sea floor. B, Paleoshorelines of First and Third Terraces after backmigration of younger shoreline 

parallel to gradient of uplift. Small arrows on First Terrace shoreline point 

in a direction opposite to that of its apparent lateral migration; length of 

0 

w 

1 2 KILOMETERS 

upper large arrow indicates amount of motion ("1.5 km) necessary to 

match visually shorelines of First and Third Terrace. For simplicity, younger shoreline is moved rigidly, in contrast to field evidence that uplift rate 

and, thus, rate of forward migration double between east and west ends of 

figure, possibly partly explaining gaps and overlaps observed at both ends. 

Two main gaps (lined areas) remain in central part of figure between sharp 

bends where orientation of shoreline changes from northwestward to southwestward, suggesting that shoreline may also have migrated laterally. C, 

Paleoshorelines of First and Third Terraces after backmigration illustrated 

in figure 1OB and lateral migration parallel to orientation of Pacific-North 

American plate boundary. Visual match of two shorelines requires 1.5 to 

2.0 km of motion in direction indicated by arrows in figure 105. Because 

shorelines are farther from source of tectonic strain than in figure 105, 

match should not be affected by assumption of rigid-body translation. 
THE CREATION OF THE CENTRAL SANTA CRUZ MOUNTAINS, CALIFORNIA F39 

we can test on the basis of the state of deformation of our 

oldest datum. 

It would have been interesting to test the other end of our 

record of tectonic uplift, that is, verify whether the peak of 

1989 coseismic uplift is centered to the southeast of the 

culmination of First Terrace (site A, fig. I), as expected. 

However, the leveling line that extends from Santa Cruz to 

Pajaro Gap through the Pajaro Valley (see Marshall and 

others, 1991, fig. 1) does not parallel the fault or the pattern 

of coseismic uplift and cuts the inner edge of First Terrace 

at an angle of "30'. The peak uplift (~0.13 m) is observed 

at the bench mark located closest to the fault, which lies 

within 1 km of the culmination of First Terrace. 

PROGRESSIVE UPLIFT OF THE 

CENTRAL SANTA CRUZ MOUNTAINS 

The structural maps in figure 7 and 8 provide convincing 

evidence that the Purisima Formation has been highly deformed since its deposition. In general, the formation has 

been warped quite gently toward the northwest and against 

Ben Lomond Mountain, and tightly warped and locally 

folded in the narrow corridor between the San Andreas 

and Zayante faults, and has subsided several hundred 

meters beneath the Pajaro Valley and the inner part of 

Monterey Bay. Assuming a depositional depth in the range 

50-500 m and assuming that the deformation process 

started 23 Ma, as suggested by studies of plate motion 

(Harbert and Cox, 1989) and regional geology (Clark and 

others, 199 I), we can calculate individual maximum rates 

of long-term uplift and tilt for two of the topographic domains defined in figure 1. Assuming an earlier date for the 

inception of uplift (or assuming that the datum had been 

deformed by previous tectonic phases when uplift started 

3 Ma) would proportionally reduce all the estimates. In the 

Laurel domain, the Purisima Formation has been tilted 

southeastward at a maximum rate of 1Â°/m.y. The upper 

part of the domain records uplift at a maximum rate of 

0.15 to 0.30 mmlyr, whereas its coastal part records subsidence at a rate of 0.10 to 0.25 rnrnlyr. This motion is 

pivoted along a northeast-trending line running through 

Santa Cmz, where the base of the Purisima Formation is 

exposed near sea level. In contrast, south-southwestward 

tilting at much more severe rates is observed in the Summit domain. Tilting at an average 5OIm.y. is observed close 

Figure 11 .-Santa Cruz, Calif., area, showing locations of 28 positions of and Third Terraces, respectively (same as in figs. 1, 2, 7, 9). Dashed lines 

First Terrace (triangles) and 20 positions of Third Terrace (squares) as connect sites marked by a-a', &-r, and yy' in figure 2, indicating that 

mapped by Alexander (1953). 57 m and 136 m, highest inner-edge posi- for a comparable distance from the Loma Prieta (LP) fault, long-term 

tions of First and Third Terraces, respectively (see fig. 2 for elevations of uplift is higher near Santa Cruz than near the Pajaro Valley (see fig. 1). 

other positions). A and B, preferred positions of culminations of First Star, epicenter of 1989 earthquake. 
F40 TECTONIC PROCESSES AND MODELS 

to the Zayante fault, whereas closer to the San Andreas 

fault the Purisima Formation has been folded in a series of 

tight synclines and anticlines. Throughout this domain, the 

Purisima Formation records uplift at a maximum rate of 

0.2 to 0.4 mrn/yr. Note that the peak Summit domain rates 

are, in fact, minimums for this domain, considering that 

the Purisima has been completely removed from much of 

the Santa Cruz Mountains northwest of the study area. 

Although the uplift and tilting recorded by the Purisima 

Formation are generally comparable in magnitude to those 

recorded by late Pleistocene marine terraces, the distribution 

of uplift and the pattern of tilting displayed by the older 

datum differ substantially from those inferred for the younger features. For example, the culmination of First Terrace 

(site A, figs. 1, 7, 1 I), where uplift proceeds at 0.35 rndyr, 

sits above a section of the Purisima Formation that records 

net subsidence of a few hundred meters, and the site where 

the growth of First Terrace has been slowest locates where 

long-term deformation has been modest. Even considering 

that the actual elevation of the Purisima Formation is not 

well constrained in the area where late Pleistocene uplift is 

largest, these observations testify to drastic changes not only 

in the intensity but also in the polarity of the displacement 

field. Indeed, these changes may simply indicate that the 

tectonic agent responsible for the deformation of the Purisima Formation differs from that causing such oblique-reverse 

slip earthquakes as the 1989 main shock and, thus, modem 

uplift along the coast (figs. 3,6). Whether the regional strain 

field can be assumed constant for time scales of 1 m.y. is 

a fascinating issue of enormous potential for earthquakeprediction studies (Gordon and Stein, 1992), but extrapolation of modem deformation rates to the 3- to 4-m.y. history 

of the Purisima Formation seems against common sense. 

Nonetheless, two issues raised in the previous paragraphs-the northwestward shift of the land relative to the 

source of uplift and possibly progressive accumulation of 

much of the topography to the northwest of Santa Cruzsuggest that the Purisima Formation furnishes an extended 

version of what we have seen recorded by the marine terraces. The base of the formation culminates at 4-00 m 

about 15 km north-northwest of Santa Cruz and about 19 

km northwest of site A in figure 1, along the same trend of 

northwestward shift delineated by a comparison of the pattern of elevation of late Pleistocene marine terraces. To the 

northwest (site C, figs. 1, 7), the extrapolated base of the 

Purisima Formation is higher than the topography, and 

older rocks are exposed for a length of about 18 km. The 

formation appears again at elevations <350 m near Portola 

Park in the La Honda quadrangle (site D, fig. 1; Brabb and 

Pampeyan, 1983), at the northwest end of the central 

Santa Cruz Mountains, suggesting that its true culmination 

along an axis parallel to the plate boundary occurs somewhere between there and site C, 28k9 krn away from the 

culmination of First Terrace (site A, fig. 1). Similarly to 

our comparison of terrace elevations, we interpret this distance as evidence for progressive northwestward advection 

of the Pacific plate through the source region of the 1989 

earthquake at an average rate of 5.4 to 10.6 mrn/yr. 

TOPOGRAPHIC DOMAINS IN THE 

CENTRAL SANTA CRUZ MOUNTAINS: 

EVIDENCE FOR MULTIPLE 

TECTONIC PROCESSES 

After the earthquake, many seismologists wondered 

whether it had been a characteristic earthquake and, if so, 

what its recurrence interval would be. For most investigators, the large reverse-slip component in the earthquake 

mechanism was a convincing argument in favor of a relatively infrequent occurrence, in contrast to most pre-1989 

opinions envisioning a ~100-yr recurrence interval for 

large earthquakes rupturing this section of the San Andreas 

fault. Even accounting for significant interseismic relaxation of the lower crust and for fast erosional degradation, 

the repetition of 50-cm-high jolts with a frequency of 

about a century would have produced a 3,000- to 4,000-mhigh ridge, comparable to the Swiss Alps and much higher 

than the Santa Cruz Mountains. Therefore, when Anderson 

(1990) and Valensise and Ward (1990) provided geologic 

evidence that a Loma Prieta-type event may occur as rarely as every 600 to 700 yr, most of the seismological community agreed that this estimate was reasonable. The 

results reported here, however, indicate that even such an 

infrequent rate would produce significantly more topography than observed. For instance, the GFM (fig. 4) predicts 

0.7 to 0.9 mdyr of uplift and 5O-7OIm.y. of tilting in the 

upper part of the Laurel domain (fig. I), which would ultimately produce at least 400 rn1m.y. of topography. Field 

evidence (fig. 7), however, shows that, on average, the deformation recorded by the Purisima Formation within this 

domain cannot be more than 0.15 to 0.30 mmlyr of uplift 

and 1Â°/m.y of tilting. In addition, the Purisima Formation 

is tilted south-southeastward, almost perpendicular to the 

southwestward direction predicted by the GFM for modem 

tilt. Anderson's (1990) rates of coastal uplift and tilting are 

2 to 3 times higher than those predicted by the GFM and 

thus would at least double this 1:3 discrepancy. 

In the previous sections, I have discussed different lines 

of evidence suggesting that what we see in the Santa Cruz 

Mountains is a process not only of creation but also of 

progressive passive transport of the topography parallel to 

the San Andreas fault. We can envision the geologic structure that should result from such a process as an arch elongated parallel to the plate boundary and culminating at a 

distance from the source of uplift proportional to the time 

elapsed since the onset of compression. Anderson (1990) 

developed this concept on the basis of purely topographic 

arguments, concluding that the present configuration of the 
THE CREATION OF THE CENTRAL SANTA CRUZ MOUNTAINS, CALIFORNIA F4 1 

Santa Cruz Mountains can, in fact, be reproduced simply 

by repeating a Loma Prieta-type event at the same time 

that the land is moved northwestward at the rate normally 

assumed for strike slip on this section of the San Andreas 

fault. However, many important features of the Santa Cruz 

Mountains are not explained by Anderson's model, and so 

I present here an alternative analytical forward model by 

combining the effects of repeated Loma Prieta-type faulting (expressed by the GFM, fig. 4) and progressive northwestward advection of the crust along the plate boundary 

(fig. 12). 

Our computer algorithm can be summarized as follows: 

(1) The source of the 1989 earthquake is initially shifted 

northwestward by a distance corresponding to the San Andreas slip rate multiplied by the time of slipping (for example, 12 mm/yrx3 m.y.=36 km); (2) the source of the 

1989 earthquake is shifted back southeastward in steps 

corresponding to the right-lateral slip accumulated during 

1,000 yr (for example, 12 dyrxl ka=12 m); (3) the 

Loma Prieta fault is assumed to have slipped by an 

amount corresponding to the oblique-reverse slip accumulated during 1,000 yr (for example, 3 mm/yrxl ka=3 m), 

and the expected vertical displacement field is calculated; 

and (4) steps 2 and 3 are iterated as many times as needed 

to bring the source of the 1989 earthquake back to its 

present position (for example, 3 m.y.11 ka=3,000 cycles). 

This algorithm allows the center of uplift to migrate relative to the land from its hypothesized position beneath the 

central Santa Cmz Mountains at the time of inception of 

uplift, to its present position beneath the San Lorenzo Valley-Santa Cmz area (fig. 1). To reduce the uncertainty associated with the evaluation of rates of erosional 

degradation, we refer all our predictions to an arbitrary 

horizontal datum and all our interpretations to a real 

datum, represented here by the Purisima Formation. To account at least in part for the reduction of topography by 

relaxation of the lower crust and mantle, we set the rigidity of the half-space equal to zero (Ward, 1986). 

The main conclusions of our modeling are as follows: 

(1) the model (fig. 12A) appears to reproduce the elevation 

and, to some extent, the shape of the datum in the Laurel 

domain (fig. 1); (2) the model also seems to reproduce 

quite well the overall topography of the Santa Cmz Mountains, at least in the Laurel domain and along its northwestward extension; and (3) the site where the model 

predicts the peak long-term uplift of the datum falls about 

halfway between its northernmost outcrop in the central 

Santa Cmz Mountains and its southernmost outcrop in the 

northern Santa Cruz Mountains (sites C, D, figs. 1, 12). 

Therefore, in parallel with what we inferred from the 

younger datums, our first conclusion is that the present morphology of the Purisima datum records the overprint of at 

least two simultaneously active tectonic processes. Our second conclusion concerns the rate of lateral advection of the 

Pacific crust around the Santa Cruz Mountains bend of the 

San Andreas fault. We find this rate to be compatible both 

with short-term estimates of 12.2k3.9 mm/yr from conventional geodesy (Prescott and others, 1981) and 10 dyr 

from very long baseline interferometric observations (Ward, 

1990); with long-term geologic estimates of "14 dyr 

from displacement of early Pleistocene sedimentary deposits 

(Cumrnings, 1968), "14 dyr from displacement of late 

Pliocene sedimentary deposits (Addicott, 1969), and >\1 

dyr from paleoseismology (Hall, 1984); and with the 

multidisciplinary estimate of 19 dyr proposed by the 

Working Group on California Earthquake Probabilities 

(1990). Our third conclusion concerns a further constraint 

on the slip rate of the Loma Prieta fault. A comparison 

between figures 12A and 125 demonstrates that increasing 

by fourfold the 3-mm/yr average oblique-reverse slip rate 

of Valensise and Ward (1991) for the Loma Prieta fault, 

which implies reducing the expected recurrence interval of 

a Loma Prieta-type event to "150 yr, will produce uplift of 

the Purisima Formation up to 1,000 m in the Laurel domain 

(fig. I), in strong contrast to field evidence (fig. 7). Including 

figure 12C in the comparison indicates that even changing 

the rate of lateral advection by 50 percent does not alter 

substantially the predicted elevation of the Purisima Formation in the Laurel domain, where control is best. A final 

conclusion concerns the model fit in the Pajaro domain (fig. 

I), where Pleistocene subsidence is well documented (Dupre, 

1990) and the Purisima Formation is found at its lowest 

elevation in the study area (down to -800 m, fig. 7). Both 

our model and the GFM predict long-term subsidence in 

this domain, but even considering the uncertainty in the 

original elevation of the Purisima Formation, the expected 

displacement is substantially smaller than observed. 

Indeed, the depth of the Purisima Formation beneath the 

Pajaro Valley represents a major morphologic feature that 

is only part accounted for by our model. Another obvious 

misfit is represented by Ben Lomond Mountain (figs. 1, 

7), an island of crystalline rocks embedded in the Tertiary 

sequence of the Santa Cmz Mountains. Both our model 

and the GFM show that Ben Lomond Mountain has undergone only a fraction of the long-term uplift sustained by 

the adjacent Laurel domain (fig. I), which, in contrast, exhibits an average elevation about half that of the Coast 

Ranges. However, the observation that Ben Lomond 

Mountain is an inherited topographic feature-that is, a 

structural high of Salinian basement uplifted at least 15 

Ma along the now-inactive Ben Lomond fault (fig. 7; 

Stanley and McCaffrey, 1983)~convincingly explains this 

discrepancy. The example of Ben Lomond Mountain underscores the role played by large inherited structural features in determining the topographic setting of an active 

region. The GFM predicts that "1 m.y. will be necessary 

to compensate for the 250-m average elevation contrast 

between the Ben Lomond and Laurel domains. At the 

same time, however, the contrast will be rejuvenated by 

the differential erodibility between the Salinian basement 
F42 TECTONIC PROCESSES AND MODELS 

of Ben Lomond Mountain and the Tertiary sequence A second major and potentially more worrisome examunderlying the Laurel domain, and so complete compensa- ple of a topographic or geologic feature unaccounted for 

tion may never take place before the next major reori- by both our and Anderson's (1990) models is the elevation 

entation of the strain field. of the Purisima datum in the Summit domain (fig. 1). The 

- .- ---- 

Right lateral: 12 mm/yr 
THE CREATION OF THE CENTRAL SANTA CRUZ MOUNTAINS, CALIFORNIA F43 

GFM predicts no to moderate uplift within this domain, 

consistent with leveling observations after the 1989 earthquake (Marshall and others, 1991). An even more difficult 

task is to explain the state of extreme deformation of the 

Purisima Formation in the corridor between the San Andreas and Zayante faults (McLaughlin, 1990), a feature 

unexplained by either the modest coseismic shortening observed in 1989 (Snay and others, 1991) or by a reevaluation of the 1906 earthquake slip vector (Segall and 

Lisowski, 1990). 

Having considered all the known sources of tectonic 

strain, we must conclude that the generation of high topography in the Summit domain is driven by a separate 

and unknown process. The absence of surface faulting 

after the 1989 earthquake, the unusual upper depth of fault 

slip (4 km), and the comparability of this depth to the 

width of the Summit domain suggest that deformation of a 

5- by 5-km parallelepiped of crust elongated parallel to the 

Pacific side of the San Andreas fault cannot be simply described by slip on regional faults. Instead, evidence from 

repeated pre- 1989 leveling surveys showing a possible rate 

of uplift of 1 to 2 rnrnlyr (fig. 13) in the absence of significant coseismic release suggests that this domain undergoes 

continuous and, probably, aseismic deformation. This deformation could represent a form of bulk squeezing of the 

shallow cmst as a result of the plate-boundary-perpendicular compression predicted by Harbert and Cox (1989), the 

Figure 12.-Models of topography generation due to combination of 

oblique-reverse motion along Loma Prieta fault plane (simulated by repeated dislocation in a totally relaxed half-space) and right-lateral motion across 

Pacific-North American plate boundary (simulated by simple aseismic 

northwestward advection of the Pacific plate) for different combinations of 

oblique-slip and strike-slip rates, assuming that the Loma Prieta fault is 

stationary with respect to the North American plate. Process iterates by 

small, discrete slip increments for an equivalent duration of 3 m.y., estimated age of present compressional tectonism. Contour intervals (80,400, and 

80 m, respectively, in figs. 124, 125, and 12C) represent cumulative deformation of an arbitrary horizontal datum originally at sea level. Stars, outcrops of base of the Purisima Formation (see fig. 7); irregular thin lines, 

faults, dashed where inferred. Predictions can be directly compared with 

structural map in figure 7 (after correction for depth of deposition of the 

Purisima Formation), whereas a comparison with actual topography requires assumption about rate of erosional denudation of range. BLD, Ben 

Lomond domain; LD, Laurel domain; PD, Pajaro domain; SD, Summit 

domain. Solutions in figures 125 and 12C are largely unrealistic (topography is too high in fig. 125; too much topography is predicted in the northern 

Santa Cruz Mountains in fig. 12C), whereas figure 124 produces a reasonable approximation to observed and extrapolated morphology of the Purisima Formation. Note that site where figure 12A predicts culmination of 

datum is about halfway between northwestemmost outcrop of the Purisima 

Formation in the central Santa Cruz Mountains (C) and southernmost outcrop of the Purisima in the northern Santa Cruz Mountains (D). In all three 

models, however, no topography is predicted in area corresponding to the 

Summit domain (and the Loma Prieta domain, not shown), indicating that 

complete modeling of topography generation in the central Santa Cruz 

Mountains requires at least one more agent of long-term tectonic strain (see 

fig. 13). A and B, culminations of First and Third Terraces, respectively. 

same process that is ultimately responsible for Loma Prieta-type events at greater depths. This process could be invoked to account for at least part of the topography of the 

adjacent Loma Prieta domain, where it would represent a 

shallow-seated alternative to Davis and Namson's (1991) 

deep-thrusting model to explain the uplift of the Santa 

Cruz Mountains east of the San Andreas fault. Extreme 

deformation in the vicinity of the San Andreas fault could 

also be invoked to explain the discrepancy between the 

observed and predicted directions of tilting of the Purisima 

Formation in the Laurel domain. Diffuse compressional 

deformation of the shallow cmst in the Summit and Loma 

Prieta domains is suggested by an analysis of the local 

pre- 1989 seismicity (Seeber and Armbruster, 1990) that 

shows several small earthquakes with P axes almost perpendicular to the San Andreas fault. 

OPEN QUESTIONS AND CONCLUSIONS 

Analysis of three well-identified geologic datums has allowed the identification of different but coexisting processes of tectonic deformation and the quantification of 

their average rates. This section summarizes the main findings concerning each of these processes, emphasizing 

what I believe is reasonably ascertained and what instead 

requires further investigation. 

The first process we analyzed is responsible for the creation of the Santa Cruz terraces. Although broad agreement exists about the causal relations between slip on the 

Lorna Prieta fault and coastal uplift in the area between 

Santa Cruz and the Pajaro Valley, uncertainty still remains 

concerning two aspects of this relation: (1) the presence of 

elevated coastal features to the west of Santa Cmz and (2) 

the rates at which deformation proceeds throughout the 

study area. The first aspect was addressed by Anderson 

and Menking (1991), who proposed that uplift of the 

coastal region west of Santa Cruz could be driven by a 

component of reverse motion on the San Gregorio fault 

(figs. 4, 5), and by Valensise and Ward (1991), who invoked slip on the San Andreas fault proper to explain the 

existence and pattern of elevation of First Terrace between 

Santa Cruz and Point Afio Nuevo. Not much is known, 

however, about the slip rate and sense of motion of the 

San Gregorio fault, and the only available estimates diverge quite drastically (1 mmlyr: Hamilton and others, 

1979; 611 1 mrnlyr: Weber and Cotton, 1981). However, 

various lines of geologic evidence contradict Anderson 

and Menking's (1991) hypothesis. (1) The local orientation 

of the San Gregorio fault is =lo0 more northerly than the 

local direction of plate motion (N. 34Ok2' W.; Ward, 

1990), suggesting that a dip-slip component of motion on 

the right-lateral San Gregorio fault would more likely be 

normal than reverse. (2) The largest uplift from motion on 

the San Gregorio fault should be recorded closest to the 
F44 TECTONIC PROCESSES AND MODELS 

fault itself, in contrast with field observations showing a 

local culmination of Bradley and Griggs' (1976) Highway 

1 platform "5 km southeast of the site where the fault cuts 

the terrace's inner edge (fig. 4). This pattern would be 

consistent with burial of the San Gregorio fault at "3-km 

depth, in contrast with the observation that it clearly is not 

a blind fault. (3) Coastal uplift by reverse motion on the 

San Gregorio fault would produce terraces dipping inland, 

in contrast with field evidence (particularly for the older 

terraces) that the Santa Cruz terraces display a progressive 

seaward tilting (see Bradley and Griggs, 1976, fig. 14). In 

any case, the mechanism envisioned by Valensise and 

Ward (1991) is not substantiated by the results of the 

present study, and so the dissimilarity between the pattern 

of 1989 coseismic elevation changes and the pattern of elevation of the Santa Cruz terraces is still an open question. 

Reducing the scatter in the timing of terrace formation 

(table 1) and, thus, the uncertainties in the rate of coastal 

uplift is also a difficult task. Addressing this second aspect 

requires the availability of reliable direct ages on fossils 

collected from at least one of the best expressed terraces, a 

condition that may never be fulfilled in the Santa Cruz region. Nevertheless, the lowest uplift rates among all those 

published (Bradley and Griggs, 1976; K.R. Lajoie, unpub. 

data, 1991; Valensise and Ward, 1991) are substantially 

higher than the rates of deformation recorded by the 

Purisima Formation and likely represent upper limits for 

the average rate of vertical strain in the study area, at least 

during the late Pleistocene. 

Comparison of the map shape and the elevation of 

strandlines of different ages fully supports the fascinating 

hypothesis that the elevated coastal features in the Santa 

Cruz region also bear a strong imprint of the relative horizontal motion between the North American and Pacific 

plates. The rates of right-lateral motion that we calculated 

are comparable to both short- and long-term estimates of 

the rate of right-lateral slip on the Santa Cruz Mountains 

section of the San Andreas fault. This hypothesis leads to 

the prediction that most of the topography created by 

Lorna Prieta-type reverse faulting should be found a few 

tens of kilometers northwest of the present position of the 

fault. Although this prediction is, indeed, supported by observations, obtaining precise estimates of the rate of lateral 

advection is made difficult by the erosion of key parts of 

the Purisima datum and by the interference of other, more 

efficient modes of topography generation, such as the bulk 

squeezing described previously. 

An intriguing problem revealed by the model of topography generation shown in figure 12 is the excess subsidence detected in the Pajaro Valley. None of the tectonic 

processes considered in the present study can be invoked 

to explain why the Purisima datum has dropped in this 

area at a rate of 0.10 to 0.25 rnrnlyr since its deposition 

(fig. 7). Indirect evidence for continuing subsidence is 

supplied by a comparison of the present bathymetry of 

northern Monterey Bay and the coastal topography 

between Santa Cruz and Aptos (fig. 1). Extrapolating the 

present uplift rate forward to a hypothetical highstand 

DISTANCE, IN KILOMETERS 

Figure 13.-Elevation changes along leveling line across south end of the Loma Prieta rupture zone (see fig. 

4 for locations), using data of Marshall and others (1991). SAF and SAR, crossings of the San Andreas and 

Sargent faults, respectively. Note that measured elevation changes are relative to an arbitrary, not absolute, 

datum. Anomalous signal observed in distance range 62-65 km was interpreted by Marshall and others (1991, 

fig. A2) as nontectonic subsidence associated with ground-water withdrawal. Profile suggests uplift of the 

southern Santa Cruz Mountains relative to adjacent plains at a rate of 1 to 2 mrntyr during interval 1972-89. 

Observed pattern suggests same bulk-squeezing deformational style recorded by the Purisima Formation in 

vicinity of the San Andreas fault (see Summit domain, fig. 1). Even though area is affected by persistent 

microseismicity, no earthquake of M>4 has occurred since 1972 (Olson, 1990). suggesting that observed strain 

is result of diffuse deformation rather than of slip on regional faults. 
THE CREATION OF THE CENTRAL SANTA CRUZ MOUNTAINS, CALIFORNIA F45 

100 ka from now shows that the shoreline should then appear nearly rectilinear (dotted line, fig. 9), in contrast to 

the curved shape of First, Second, and Third Terraces and 

of the modem shoreline. The action of an unknown tectonic force causing subsidence centered near Aptos would locally counteract the uplift, with the final effect of giving 

the new shoreline the same shape as that of its fossil counterparts. This unknown force producing subsidence at a 

rate of ~0.25 dyr appears as the mirror image of the 

previously discussed, yet unexplained, force that causes 

coastal uplift at c0.20 dyr between Santa Cruz and 

Point Ano Nuevo (figs. 1, 4). Interestingly, the bipolar arrangement of these two forces has a reverse correspondence on the opposite side of the San Andreas fault, where 

uplift of the Loma Prieta domain (fig. 1) is balanced by 

documented late Pleistocene subsidence of southern San 

Francisco Bay at 0.2 to 0.4 dyr (Atwater and others, 

1977). At this time, we can only speculate that this quadrupole of forces producing deformation of opposite sign at 

comparable rates owes its existence to the geometric and 

dynamic complexities associated with the Santa Cruz 

Mountains bend in the San Andreas fault. 

Possibly the most important conclusion of this study 

concerns the process responsible for the generation of high 

topography in the vicinity of the San Andreas fault, which 

also represents the highest relief in the entire Santa Cruz 

Mountains. In addition to the geodetic evidence discussed 

above (fig. 13), geologic evidence is now available in the 

form of a series of terraces on the Pajaro River that have 

been uplifted several hundred meters as they cross the San 

Andreas fault around Pajaro Gap (fig. 1). Hall and others 

(1991) reconstructed these terraces, showing that the 

strongest upwarping has a wavelength of 5 to 10 km and 

that late Pleistocene uplift has locally proceeded at 20.2 to 

0.3 rnmlyr. To account for the absence of substantial vertical displacement across the main faults in the study area, 

Hall and others (1991) hypothesized that the Pajaro River 

terraces, along with most of the southern Santa Cruz 

Mountains, have been uplifted by the activity of a southwest-dipping, low-angle, buried thrust fault rooted in the 

San Andreas fault near 8-km depth. Hall and others' 

model compares directly with other previously discussed 

hypotheses for explaining the presence of high topography 

east of the San Andreas fault, such as (1) activity of the 

Sargent-Berrocal fault system (Schwartz and others, 1 NO), 

(2) activity of a shallowly northeast dipping thrust fault 

extending from 12- to 17-km depth (Davis and Namson, 

1991), and (3) the bulk-squeezing deformational style proposed in this paper. The third hypothesis, however, is the 

only one that may also account for uplift in the Summit 

domain (fig. I), an area where mild subsidence is expected 

on the basis of the other models. Paradoxically, although 

the bulk-squeezing deformational mode should sooner or 

later bring to light all the main faults in the study area, 

none of them would necessarily be active seismic sources; 

instead, each of them would be required to relieve some of 

the stress accumulated in the top few kilometers of the 

crust, a task that would be made easier by large nearby 

earthquakes, as seen in 1906 and 1989. The accumulation 

of sympathetic slip would make these faults appear active 

in the geologic record, but the individual long-term slip 

rates would be negligible in comparison with the rate of 

other plate-boundary-related processes. Once the activity 

of these faults has been established, deciding whether they 

act as independent sources of seismicity or as passive participants in broader scale plate-boundary events becomes 

the key question for seismic-hazard assessment in the 

densely populated San Francisco Bay region. We believe 

that this question could be fruitfully addressed by extending the concepts and methodology of the present study to 

the region east of the San Andreas fault. 

ACKNOWLEDGMENTS 

This research was performed while I was a Visiting Scientist at the U.S. Geological Survey in Men10 Park, Calif. 

I am indebted to Earl Brabb, Jo Clark, Bob McLaughlin, 

and Ross Stein of the U.S. Geological Survey and to Bob 

Anderson and Steve Ward of the University of California, 

Santa Cruz, for providing valuable data and suggestions 

about central aspects of this work. In particular, I thank 

Earl Brabb for supplying the original well data, and Bob 

McLaughlin for making available a preprint of his geologic map of the Laurel quadrangle. I am especially grateful 

to Ross Stein for his help in obtaining financial and logistic support for this research and for his encouragement, 

and to Enzo Boschi for the continuing opportunity to extend my research to different parts of the world. Critical 

reviews by Bob Anderson, Bob Simpson, and Ross Stein 

substantially improved the manuscript. 

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Stuart, R.M., Madrid, V.M., and Verosub, K.L., 1982, Late Neogene tectonics and sedimentation, Santa Cruz Mountains, California [abs.]: 

Geological Society of America Abstracts with Programs, v. 14, 

no. 4, p. 237-238. 

Thatcher, Wayne, 1975, Strain accumulation on the northern San Andreas 

fault zone since 1906: Journal of Geophysical Research, v. 80, 

no. 35, p. 4873-4880. 

Valensise, Gianluca, and Ward, S.N., 1990, Recurrence interval of Loma 

Prieta-type earthquakes based on long-term uplift patterns along the 

Santa Cruz coastline [abs.]: Seismological Research Letters, v. 61, 

no. I, p. 23. 

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. 

Vanderhurst, W.L., Cumming, J.C., and Andersen, D.W., 1982, The Santa 

Clara Formation as a record of late Cenozoic uplift of the Santa 

Cruz Mountains, Santa Clara County, California, in Ingersoll, R.V., 

and Woodburne, M.O., eds., Cenozoic nonmarine deposits of California and Arizona: Los Angeles, Society of Economic Paleontologists and Mineralogists, Pacific Section, p. 23-33. 

Wallace, T.C., Velasco, Aaron, Zhang, Jiajun, and Lay, Thome, 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. 

Ward, S.N., 1986, A note on the surface volume change of shallow earthquakes: Royal astronomical Society Geophysical Journal, v. 85, 

no. 2, p. 461-466. 

1990, Pacific-North America plate motions: new results from very 

long baseline interferometry: Journal of Geophysical Research, 

v. 95, no. B 13, p. 21965-21981. 

Weber, G.E., and Cotton, W.R., 1981, Geologic investigation of recurrence intervals and recency of faulting along the San Gregorio fault 

zone, San Mateo County, California: U.S. Geological Survey OpenFile Report 81-263, 99 p. 

Woodring, W.P., Bramlette, M.N., and Kew, W.S.W., 1946, Geology and 

paleontology of the Palos Verdes Hills, California: U.S. Geological 

Survey Professional Paper 207, 145 p. 

Working Group on California Earthquake Probabilities, 1990, Probabilities of large earthquakes in the San Francisco Bay region, California: U.S. Geological Survey Circular 1053, 51 p. 
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THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAmOCCUmNCE 

TECTONIC PROCESSES AND MODELS 

COMPLEX FAULT INTERACTIONS IN A RESTRAINING BEND 

ON THE SAN ANDREAS FAULT, 

SOUTHERN SANTA CRUZ MOUNTAINS, CALIFORNIA 

By Susan Y. Schwartz, Daniel L. Orange, and Robert S. Anderson, 

University of California, Santa Cruz 

CONTENTS 

ABSTRACT 

The unusual oblique-thrust mechanism of the earthquake 

focused attention on the complex tectonic setting of the Santa 

Cruz Mountains section of the San Andreas fault. Near the 

main-shock epicenter, the San Andreas fault curves to the 

left, defining a restraining bend. The large thrust component 

of the main-shock focal mechanism is consistent with the 

horizontal compression expected across restraining bends. 

However, repeated Loma Prieta-type events cannot exclusively produce the observed topography of the southern Santa 

Cruz Mountains, the highest point of which subsided during 

the earthquake. In this paper, we integrate seismic, geomorphic, and tectonic data to investigate the possibility that 

motions on faults adjacent to the San Andreas fault play an 

important role in producing the observed topography. The 

three-dimensional geometry of active faults in this region is 

imaged using the Loma Prieta foreshock and aftershock 

sequences. The most conspicuous features of the fault geometries at depth are: (1) the presence of two distinct zones 

of seismicity corresponding to the San Andreas and SargentBerrocal fault zones; (2) the concave-upward shape of the 

~oka Prieta rupture surface; (3) the reduction in dip of the 

deepest parts of the rupture plane as the main-shock hypocenter is approached; (4) the apparent transfer of shallow 

slip in some areas from faults in the San Andreas fault zone 

to those in the Sargent-Berrocal fault zone; and (5) the 

presence of a deep, northeasterly dipping plane associated 

with the Sargent-Berrocal fault zone. We find that a model 

of fault interactions that involves displacement on faults in 

both the San Andreas and Sargent-Berrocal fault zones is 

consistent with Loma Prieta coseismic displacements, foreshock and aftershock seismicity, and observed topography. 

INTRODUCTION 

Several major transcurrent fault systems compose the diffuse transform boundary between the Pacific and North American plates. Although the faults that form this boundary (fig. 

1) crudely parallel the direction of relative plate motion, minor 

changes in fault strike are evident that introduce geometric 

complexities which result in local tension or compression. 

Sibson (1986) termed these bends in strike-slip faults "releasing" or "restraining" bends, respectively. Although the 

predominance of right-lateral strike-slip motion in this region 

has been recognized since the great 1906 San Francisco 

earthquake, only recently has the prevalence of compressional 

features been appreciated (Aydin and Page, 1984). 

In the vicinity of the 1989 Loma Prieta earthquake, the 

San Andreas fault curves to the left, describing a restraining 

bend here called the Santa Cruz bend. The horizontal compression expected across this restraining bend is consistent 

with the large thrust component of the Loma Prieta main 

shock and with the abundant observed compressional features in the southern Santa Cruz Mountains, such as folds 

and reverse faults (Aydin and Page, 1984). The highest topography lies on the east side of the San Andreas fault, a 

region that subsided during the earthquake (Lisowski and 

others, 1990). In this paper, we investigate the complex fault 

interactions that occur within the Santa Cruz bend. We are 

particularly interested in the development of high topography on the North American plate, which coincides with the 

middle of the restraining bend (fig. 1). If Loma Prieta-type 

events are characteristic of this region on any time scale, the 

vertical-displacement field associated with these events requires that fault motions resulting in diverse uplift patterns 
F50 TECTONIC PROCESSES AND MODELS 

must also occur in this region to produce the topographic 

relief. We evaluate the Sargent-Berrocal fault zone as a 

possible candidate to produce the observed topography. 

Here, we include the Berrocal, Sierra Azul, and Sargent 

faults (inset, fig. 1) in our definition of the Sargent-Berrocal 

fault zone. We find that a model which involves displacement on faults in both the San Andreas and Sargent-Berrocal fault zones can satisfy the available data. 

TECTONIC SETTING 

The complexity of the fault system composing the Pacific-North American plate boundary in this region of central 

California is illustrated in figure 1. Although the San Andreas and Hayward faults have both produced large earthquakes in 1838 and 1906 (San Andreas fault) and 1836 

and 1868 (Hayward fault), several other near-parallel 

faults in the area have shown observable late Quaternary 

activity. Of these faults, the Sargent-Berrocal fault zone 

has been the most seismically active in recent years. Aside 

from abundant microseismicity along the southern section 

Contour interval, 200 m starting at 300 m 

Figure 1.-Topographic and tectonic map of the San Francisco Bay region, central California, showing locations of major faults (dashed where * inferred) and Global Positioning System stations (stars). Inset shows locations of faults composing Santa Cruz bend of the San Andreas fault, 

main shock of 1989 earthquake (large star), and recent M>5 earthquakes 

(small stars). A, Allison; ER, Eagle Rock; LP, Lorna Prieta; MtH, Mount 

Hamilton; SBFZ, Sargent-Berrocal fault zone. 

of the Sargent-Berrocal fault zone before the 1989 Loma 

Prieta earthquake and along the northern section during 

the aftershock sequence (U.S. Geological Survey locations 

of seismicity between 1969 and 1989; Bakun and 

McLaren, 19841, an Mz5.0 earthquake followed by more 

than 100 aftershocks occurred on the Sargent-Berrocal 

fault zone (inset, fig. 1) in November 1964 (McEvilly, 

1966). In addition, Olson (1990) interpreted the two largest events before the Loma Prieta main shock as rupturing 

the Sargent fault (inset, fig. 1). Owing to the abundant 

seismic activity along the Sargent-Berrocal fault zone both 

before and immediately after the Loma Prieta main shock, 

we believe that careful examination is warranted to establish the possible role of this fault zone in elevating the 

southern Santa Cruz Mountains. 

Field geologic studies indicate a range of surface dips 

from 20' SW. to vertical for the faults within the SargentBerrocal fault zone (McLaughlin, 1974; McLaughlin and 

others, 197 1, 1988), although good surface outcrops of the 

fault are rare. McLaughlin (1974) interpreted the Sargent 

fault as a thrust fault over much of its length. Hay and 

others (1980), however, presented geologic evidence indicating that the faults of the Sargent-Berrocal fault zone 

have components of both strike-slip and thrust motion. 

They inferred a predominance of strike-slip motion on 

fault strands oriented parallel to the San Andreas fault and 

large thrust motion on strands oriented oblique to the San 

Andreas fault. A 5-year geodetic survey across the southern section of the Sargent-Berrocal fault zone near Hollister, Calif. (fig. 1; Prescott and Burford, 1976), indicated a 

present right-lateral-slip rate of 3 mdyr. The next step toward understanding the interactions between the San Andreas fault and the Sargent-Berrocal fault zone is to obtain 

an accurate image of the these faults at depth. 

LOMA PRIETA 

AFTERSHOCK SEISMICITY 

AND FAULTING GEOMETRY 

The aftershock sequence of the 1989 Loma Prieta earthquake provides the best information on the three-dimensional geometry of the active faults in the region. A series 

of cross sections through the aftershock seismicity perpendicular to the strike of the San Andreas fault is shown in 

figure 2. The earthquakes shown were relocated by the 

U.S. Geological Survey, using the same velocity model as 

that used to locate the main shock (Dietz and Ellsworth, 

1990). The topography and surface traces of the San Andreas and Sargent faults are superimposed on each cross 

section. The domainal analysis presented in figure 2 clearly indicates two distinct zones of seismicity in cross sections B-B' and D-D' that may correspond to separate 

activity on the San Andreas and Sargent-Berrocal fault 

zones. In contrast, cross section C-C' shows only one 
COMPLEX FAULT INTERACTIONS IN A RESTRAINING BEND ON THE SAN ANDREAS FAULT F5 1 

zone of seismicity, indicating a significant change in the 

Loma Prieta rupture geometry along its strike. 

The most conspicuous feature revealed by the aftershock 

seismicity is the striking change in fault-plane geometry as 

the San Andreas fault enters the Santa Cruz bend. In the 

bend region, the deepest parts of the fault reduce in dip to 

approximately 65', whereas the shallower parts of the 

fault remain near-vertical, resulting in a concave-upward 

shape to the Loma Prieta rupture surface. Other interesting 

features of the seismicity are (1) the overall reduction in 

the depth of earthquakes to the south; (2) the apparent 

transfer of shallow slip from the San Andreas fault to the 

Sargent-Berrocal fault zone in cross section C-C'; and (3) 

the location of the main-shock hypocenter along the most 

shallowly dipping and deepest part of the rupture plane. 

The location of the hypocenter in the most contorted part 

of the fault plane is consistent with the notion that asperities may represent geometric complexities in fault planes. 

FAULT GEOMETRY AND TOPOGRAPHY 

OF' THE SANTA CRUZ MOUNTAINS 

Anderson (1990) suggested that the northern Santa Cruz 

Mountains owe their elevation to repeated Loma Prieta-type 

events and northwestward advection of the resulting topography. As he pointed out, however, a similar argument cannot 

be made for the southern Santa Cruz Mountains, which lie 

on the opposite side of the San Andreas fault from the 

northern part of the range (fig. 1). Measurements of coseismic 

vertical displacements after the earthquake indicate that 

Loma Prieta (LP, fig. 1) subsided 14, 15, and 20 cm, respectively, relative to stations at Allison (A), Mount Hamilton 

(MtH), and Eagle Rock (ER) (Lisowski and others, 1990). 

Allison and Mount Hamilton, which are located more than 

30 km from Loma Prieta, should have undergone very little 

coseismic elevation change during the earthquake. Therefore, 

the 14 to 15 cm of subsidence of Loma Prieta relative to 

these stations should approximate an absolute elevation 

change for this peak. Because the highest point in the southern Santa Cruz Mountains subsided during the earthquake, 

how might this topography have developed? 

The images of the faulting geometry presented in figure 2 

suggest a possible answer to this question. Cross sections BB' through D-D' clearly show that the Sargent-Berrocal fault 

system was active during the aftershock sequence. Apparently, when the San Andreas and Sargent-Berrocal fault zones 

are close to one another, shallow slip may be accommodated 

on either or both fault zones. In cross section C-C', all of the 

shallow slip occurred on the Sargent-Berrocal fault zone and 

almost no shallow slip on the San Andreas fault. The complex 

geometry of these two fault zones beneath Loma Prieta (cross 

sec. D-D') accommodated shallow displacement during the 

earthquake, primarily on the more nearly vertical San Andreas fault west of the peak, resulting in subsidence of Lorna 

Prieta. If more shallow displacement had occurred on the 

Sargent-Berrocal fault zone, as in cross section C-C', it 

would have produced uplift rather than subsidence. 

Evidence for yet-another fault oriented favorably to result in uplift northeast of the San Andreas fault comes 

from fault-plane solutions of several large deep earthquakes with epicenters located east of the fault. Olson 

(1990) determined northwesterly striking and 65' northeasterly dipping fault planes with reverse motion for six 

earthquakes before the 1989 Loma Prieta earthquake. 

These earthquakes, which are located in the Sargent-Berrocal fault zone near its intersection with the San Andreas 

fault, include the two largest events (Mz5.2, 5.0) to have 

occurred here since 1969 (inset, fig. 1). In addition, similar 

fault-plane solutions have been obtained for moderate 

deep earthquakes on the southern section of the SargentBerrocal fault zone (Olson, 19901, including an Mz5.0 

event in November 1964 (McEvilly, 1966). The occurrence of large deep earthquakes with northeasterly dipping 

planes at several places along the Sargent-Berrocal fault 

zone suggests that these events occurred on a deep nearcontinuous plane that extends along this fault zone. If substantial displacement occurs on this fault plane, it would 

result in uplift east of the San Andreas fault, thereby contributing to the present high elevations observed there. 

Thus far, we have discussed evidence for seismic activity 

on four fault planes in the Santa Cruz bend of the San Andreas 

fault, as shown schematically in figure 3C. Although seismic 

activity on these planes may be greatest at different positions 

along-strike of the San Andreas and Sargent-Berrocal fault 

zones, we present an along strike synthesis to best illustrate 

their possible interactions. Our hypothetical fault structure 

consists of plane 1, a deep (10-18 km), 65' SW.- dipping 

plane (activated in the main shock); plane 2, a shallow (5- 

10 lun), vertical plane beneath the surface trace of the San 

Andreas fault (also activated in the main shock); plane 3, a 

shallow (5-10 km), -6S0 SW.-dipping plane that is part of 

the Sargent-Berrocal fault zone (cross sec. C-C, fig. 2); and 

plane 4, a deep, 65' NE.-dipping plane also associated with 

the Sargent-Berro~al fault zone (the plane generating the 

largest events preceding the main shock). Vertical surface 

displacements predicted for 1.3 m of reverse slip on each of 

these four fault planes were calculated by using a twodimensional elastic-dislocation model (fig. 3B). Reverse motion on planes 1 and 2 would characterize the 1989 Loma 

Prieta earthquake, predicted displacements for which can be 

estimated by summing curves 1 and 2 in figure 3B. The 

observation of -14 cm of subsidence at Loma Prieta that 

accompanied this earthquake (star, fig. 3B) agrees well with 

the 15 cm of subsidence predicted by this model. Motion on 

planes 1 and 3 or on plane 4 would result in vertical surface 

displacements consistent with the observed topography. Figure 3B shows that repeated events on rupture planes 1 and 

2 cannot produce the high elevation of Lorna Prieta and its 

surrounding mountain peaks (fig. 3A). Rupture on planes 1 
TECTONIC PROCESSES AND MODELS 

0 DISTANCE, 

LOMETERS 
COMPLEX FAULT INTENACTIONS IN A ESTRAINING BEND ON THE SAN ANDEAS FAULT F53 

and 3 or on plane 4, however, would produce surface displacements that act to elevate this area of presently high 

topography. Thus, some combination of events that rupture 

planes 1 and 2 with those that rupture planes 1 and 3 and 

(or) plane 4 is consistent with the available data. 

DISCUSSION AND CONCLUSION 

Although the four-plane-fault model presented here is consistent with the available data, it undoubtedly oversimplifies 

what must be a more complex system of faults in the region. 

For example, there is some evidence that the vertical San 

Andreas fault imaged at shallow depths by the aftershock 

seismicity extends to greater depths. Seismicity during the 

10-yr period before the earthquake includes some deep events 

located directly below the surface trace of the San Andreas 

fault (Olson, 1990). Olson interpreted the difference in the 

apparent dip of the San Andreas fault at depth, imaged by 

seismicity before and after the earthquake, as representing 

two different fault planes: the vertical San Andreas fault and 

the southwest-dipping fault that ruptured in the Lorna Prieta 

main shock. Geodetic data, however, require that parts of both 

these fault planes ruptured in the main shock. There is little 

evidence for a deep vertical extension of the San Andreas 

fault in the Loma Prieta aftershock data (with the possible 

exception of four deep events in cross section C-C', fig. 2). 

Slip on a deep vertical extension of the San Andreas fault with 

primarily strike slip motion would produce less vertical displacement than slip on the fault planes with predominantly 

oblique motion. 

Repeated failure of the Loma Prieta rupture plane exclusively is inconsistent with the high topography observed in 

the southern Santa Cruz Mountains. The transfer of shallow 

slip from the vertical San Andreas fault to a southwestdipping fault of the Sargent-Berrocal fault zone provides 

evidence for seismic activity on a fault plane favorably oriented to uplift the southern Santa Cruz Mountains. Evidence 

for activity on another fault plane properly oriented to uplift 

these mountains comes from fault-plane solutions of the 

largest earthquakes to occur in the Loma Prieta aftershock 

zone since at least 1969 (Olson, 1990). The fault model 

shown in figure 3C is consistent with Loma Prieta coseismic 

displacements, both foreshock and aftershock seismicity, and 

can explain the high topography of the southern Santa Cruz 

Mountains. 

4 Figure 2.-Plan (bottom map) and cross-sectional (A-A' through GG') views of main shock and aftershock sequence of 1989 earthquake 

(from Dietz and Ellsworth, 19901, showing topography (vertical exaggeration, 3x1 and vertical projection of mapped traces of the Sargent and San 

Andrea faults above each cross section. Sizes of symbols are proportional to magnitude. SAF, San Andreas fault; SBFZ, Sargent-Berrocal fault 

zone. Irregular thin lines in plan view, faults, dashed where inferred, 

queried where uncertain. 

A 

Prieta 

W / Vertical exaggeration, 20x 

200 

HORIZONTAL DISTANCE, IN KILOMETERS 

Figure 3.-Hypothetical fault structure near Santa Cruz bend of the San 

Andreas fault in the southern Santa Cruz Mountains, Calif. (see fig. 1 for 

location). A, Maximum elevation. B, Vertical displacement from 1.3 m of 

vertical slip on each of four buried fault planes shown in figure 3C. Star, 

measured subsidence from Global Positioning System. C, Hypothetical 

fault planes 1 through 4. SAF, San Andrea fault; SBFZ, Sargent-Berrocal 

fault zone. 

IUCFERENCES CITED 

Anderson, R.S., Evolution of the northern Santa Cruz Mountains by 

advection of crust past a San Andrea fault knd: Science, v. 249, 

no. 4967, p. 397-40 1. 

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. I 1, p. 1303-1 3 17. 

Bakun, W.H., and McLaren, Marcia, 1984, Microearthquakes and the 

nature of the creeping-to-locked transition of the San Andrea 

fault zone near San Juan Bautista, California: Seismo1ogica1 Society of America Bulletin, v. 74, no. 1, p. 235-254. 

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

Prieta, California, earthquake and its aftershocks; geometry of the 
F54 TECTONIC PROCESSES AND MODELS 

sequence from high-resolution locations: Geophysical Research 

Letters, v. 17, no. 9, p. 1417-1420. 

Hay, E.A., Cotton, W.R., and Hall, N.T., 1980, Shear couple tectonics 

and the Sargent-Berrocal fault System in northern California, in 

"Streitz, Robert, and Sherburne, R.W., eds., Studies of the San Andreas fault zone in northern California: California Division of 

Mines and Geology Special Report 140, p. 41-5 1. 

Lisowski, Michael, Prescott, W.H., Savage, J.C., and Svarc, J.L., 1990, 

A possible geodetic anomaly observed prior to the Loma Prieta, 

California, earthquake: Geophysical Research Letters, v. 17, no. 8, 

p. 1211-1214. 

McEvilly, T.V., 1966, The earthquake sequence of November 1964 near 

Corralitos, California: Seismological Society of America Bulletin, 

v. 56, no. 3, p. 755-773. 

McLaughlin, R.J., 1974, The Sargent-Berrocal fault zone and its relation 

to the San Andreas fault system in the southern San Francisco Bay 

region and Santa Clara Valley, California: U.S. Geological Survey 

Journal of Research, v. 2, no. 5, p. 593-598. 

McLaughlin, R.J., Clark, J.C., and Brabb, E.E. 1988, Geologic map and 

structure sections of the Loma Prieta 7% quadrangle, Santa Clara 

and Santa Cruz Counties, California, U.S. Geological Survey OpenFile Map 88-752, scale 1:24,000, 2 sheets. 

McLaughlin, R.J., Simoni, T.R., Osbun, E.D., and Bauer, P.G., 1971, Preliminary geologic map of the Loma Prieta-Mount Madonna area, 

Santa Clara and Santa Cruz Counties, California, U.S. Geological 

Survey Open File Map, scale 1 :24,000. 

Olson, J.A., Seismicity in the twenty years preceding the 1989 Loma 

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

no. 9, p. 1429-1432. 

Prescott, W.H. and Burford, R.P., 1976, Slip on the Sargent fault: Seismological Society of America Bulletin, v. 66, no. 3, p. 1013- 

1016. 

Sibson, R.H., 1986, Rupture interaction with fault jogs, in Shamita, Das, 

Boatwright, John, and Scholz, C.H., eds., Earthquake source mechanics: American Geophysical Union Geophysical Monograph 37, 

p. 157-167. 
THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF' OCTOBER 17,1989: 

EARTHQUAKEOCCUmNCE 

TECTONIC PROCESSES AND MODELS 

EARTHQUAKE-INDUCED STATIC-STWSS CHANGES 

ON CENTRAL CALIFORNIA FAULTS 

By Robert W. Simpson and Paul A. Reasenberg, 

U.S. Geological Survey 

CONTENTS 

Abstract .................................................................. Introduction ------------------------------------------------------------- 

Regional stress changes caused by the earthquake ----------------- Calculated changes in static stress .............................. 

Calculated changes in Coulomb failure function ------------- Observed changes in microseismicity rates and fault-creep 

rates-------------------------------------------------------------- 

Microseismicity rates ------------------------------------- Fau1t-creep rates ............................................ 

Neglected variables that could be important ........................ Elastic heterogeneity ---------------------------------------------- Effect of dipping faults ........................................... Effect of other structures ....................................... 

Simulating time-dependent effects with dislocation models ------ Slip at depth in response to the earthquake ------------------- Afterslip on veflicai planes ------------------------------- 

Afterslip on horizontal detachment surfaces ------------ Plate-tectonic loading after the 1989 earthquake ------------- 

Plate-tectonic loading after the 1906 earthquake and the 

end to 73 years of seismic quiescence----------------------- 

Paired earthquakes on the San Andreas and Hayward faults? ---- Prerequisites for interactions .................................... me 1865168 pair -------------------------------------------------- me 1836138 pair -------------------------------------------------- 

simulating fault interactions ..................................... Conc~usions ............................................ -------------- 

Acknowledgments ------------------------------------------------------ 

References cited .......................................................... 

ABSTRACT 

We have calculated the static-stress changes caused by 

the earthquake on central California faults, using three-dimensional elastic-dislocation models in an elastic halfspace. We compare the results for three different models 

of the Lama Prieta rupture and explore the effects of nonvertical dips on several faults, as well as the long-term 

redistribution of stresses that might accompany deep aseismic slip on vertical and horizontal structures. Calculated 

changes in the Coulomb failure function (CFF) after the 

earthquake correlate with observed changes in microseismicity rates and surface-creep rates, suggesting that the 

CFF can be used to describe the proximity of these faults 

to failure. The correlation favors a low apparent coefficient 

of friction p'4.2. Such a low value could be explained by 

the combination of a normal laboratory value for the coefficient of friction (~4.75) moderated by pore-fluid effects, 

with a Skempton's coefficient B4.7. Our models suggest 

that the earthquake-induced stress changes are unlikely to 

trigger an earthquake on the Hayward fault unless a high 

value of apparent friction applies, so that the unclamping 

of the south end of the Hayward fault can bring it closer to 

failure. Over time, reequilibration of pore fluids in this area 

might increase the apparent coefficient of friction from its 

presently low inferred values, and we suggest that the microseismicity rates and surface-creep rates at the south end 

of the Hayward fault need to be monitored as possible precursors to a triggered event. stress-evolution models of 

central California faults after the 1906 San Francisco earthquake are consistent with the seismic quiescence in the bay 

region after 1906 and suggest that the 1989 earthquake effects described in this paper would be dwarfed by those 

accompanying a recurrence of the 1906 event. 

INTRODUCTION 

Should we expect the earthquake (M=7. I), with an average 

slip of 2 m over a 40-km-long rupture surface, to affect the 

probability of earthquakes on other faults in the San Francisco 

Bay region? As a possible example of such an effect, the 

1906 San Francisco earthquake (M=7.7) was followed by a 

73-yr period of unusual quiescence during which only one 

earthquake of M% occurred on bay-region faults (Ellsworth 

and others, 198 1; Sykes and Jaumk, 1990). 

About 17 days after the Lorna Prieta main shock, an M=3.4 

earthquake occurred on the Hayward fault about 85 km from 

the Loma Prieta epicenter (fig. 1). Although this earthquake 

was not large, it did cause some concern because on at least 

two occasions in the 18OO7s, large earthquakes on one side 
F56 TECTONIC PROCESSES AND MODELS 

of San Francisco Bay were followed within 3 yr by second 

large earthquakes on the opposite side of the bay (Louderback, 1947; Ellsworth, 1990; Sykes and Jaum6, 1990; Jaum6 

and Sykes, 1992). Because earthquakes on the San Andreas 

and Hayward faults were involved in both of these pairings, 

this Mz3.4 earthquake might have been the precursor to a 

larger shock, and the question arose as to how the Loma 

Prieta rupture might have affected stress levels on other bayregion faults. 

Long-term stress changes caused by fault offset are 

called static-stress changes, to distinguish them from the 

short-period dynamic-stress changes that accompany the 

passage of seismic waves. In this paper, static-stress 

changes on central California faults are calculated by 

using three different slip distributions that have been proposed for the Loma Prieta rupture. 

We also present simple models that attempt to assess, at 

least qualitatively, the importance of pore fluids, fault geometry, and nonlinear time-dependent relaxation on the 

distribution of stresses. Additional models are designed to 

help visualize the evolution of the regional stress field 

after the earthquake, as plate-tectonic-loading stresses accumulate on bay-region faults. We also present a similar 

evolutionary model for the years after the 1906 earthquake. The magnitude of the 1906 effects puts the 1989 

earthquake into sobering perspective. 

REGIONAL STRESS CHANGES 

CAUSED BY THE EARTHQUAKE 

CALCULATED CHANGES IN STATIC STRESS 

Although the Earth is far from being a perfectly homogeneous, elastic half-space, several lines of evidence suggest that static-stress changes calculated by using this 

assumption are a fair approximation to the true stress 

changes in the Earth. For example, the magnitudes of 

strain steps observed on sensitive strainmeters at the times 

of distant earthquakes agree well with magnitudes calculated from dislocation theory (for example, Johnston and 

others, 1987, 1990; Shimada and others, 1987). Some success has also been reported in attempts to correlate aftershock patterns, aftershock focal mechanisms, and creep 

perturbations with static-stress changes calculated for 

moderate earthquakes (for example, Das and Scholz, 1981, 

1983; Stein and Lisowski, 1983; Mavko and others, 1985; 

Kato and others, 1987; Li and others, 1987; Oppenheimer 

and others, 1988; Hudnut and others, 1989). 

Slip on a surface within an elastic medium produces 

stress changes throughout the medium that can be calculated mathematically from dislucation theory (for example, 

Steketee, 1958; Chinnery, 1963; Press, 1965). For most of 

the models presented in this paper, stress changes were 

calculated at the centers of 13-km-tall by approximately 

10-km-long vertical rectangular patches arrayed under the 

traces of major bay-region faults (figs. 1, 2). The 13-km 

height was selected because the midpoint coincides with 

the mean depth of seismicity in the bay region, which is 

estimated at 6 to 7 km. Three dipping fault patches (198- 

200, fig. 2) have also been included in the model to simulate nonvertical planes on which seismicity is occurring in 

two areas of special interest. 

We used two computer programs to perform the calculations. Our initial calculations were based on equations derived by Glen Converse for the elastic fields generated by 

uniform slip on rectangular dislocation surfaces in a halfspace. Scott Dunbar originally coded these equations as the 

program DIS3D, which Erickson (1986) subsequently improved and documented. Our later calculations used the 

Figure 1.4tudy area in central California, showing locations of selected faults. Large dot, epicenter of October 17, 1989, earthquake; small dot, 

epicenter of November 4, 1989, earthquake (M=3.4) on the Hayward fault. Tickmarks along faults indicate ends of vertical rectangular patches used in 

models to simulate faults; small rectangles are surface projections of dipping patches used in models (see fig. 2). 
EARTHQUAKE-INDUCED STATIC-STRESS CHANGES ON CENTRAL CALIFORNIA FAULTS F57 

subroutines of Okada (1992). In all the models, a Poisson's 

ratio of 0.25 and a shear modulus of 3x10~ bars were used. 

To calculate the stress changes, we must define a Loma 

Prieta slip surface and specify a slip distribution on it. For 

comparative purposes, we used three slip distributions inferred from different data sets (table 1). Although several 

others have been proposed, these three slip distributions 

serve to illustrate the range of static-stress changes resulting from reasonable solutions for the slip distribution and 

the geometry of the slip plane. 

In general, the results at large distances (min 80 km) 

from the Loma Prieta slip surface depend mostly on the 

total moment of the assumed slip distribution rather than 

on it$ finer details. The results at intermediate distances 

(approx 40-80 km) should be qualitatively similar, with 

some differences reflecting the details of the slip distribution used. Finally, the results at near distances (less than 

approx 40 km) may differ significantly. 

The first and simplest slip distribution we used is based 

on a single uniform-slip dislocation inferred from geodetic 

line-length changes by Lisowski and others (1990). The 

second, more complex slip distribution is the two-dislocation model of Marshall and others (1991), based on leveling data, which uses different rakes for the slip directions 

on the two parts of the slip surface. The strike of their 

model differs by 8O from that of the first model (table 1). 

The third and most complex slip distribution is that proposed by Beroza (1991) from strong-ground-motion 

records. He divided the fault surface into 280 separate elements with varying amounts of strike slip and dip slip. 

Paul Spudich (oral commun., 1991) emphasized that inversions based on strong-ground-motion records do not yield 

unique solutions. However, the common features predicted 

by all three slip distributions, at least in the intermediate 

and far field, suggest that nonuniqueness is not seriously 

biasing the stress calculations. 

The results from these three slip distributions are illustrated in figure 3 and plotted for selected bay-region faults 

in figure 4. Stresses are calculated at the centers of the 

rectangular fault patches. The decay in horizontal shear 

stress with distance for the slip distribution of Lisowski 

and others (1990) is plotted in figure 5. Static-stress 

changes in the study area range from less than 0.001 bar 

to a few tens of bars. In contrast, Earth tides on the Hayward fault during the year after the earthquake produced a 

maximum calculated range of approximately 0.01 bar in 

horizontal shear and 0.05 bar in normal stress; mean daily 

variations were about a fourth of this maximum range, or 

about 0.002 and 0.01 bar, respectively. 

All three slip distributions predict an increase in rightlateral shear stress on the San Andreas fault to the northwest aiid southeast of the Loma Prieta rupture zone. This 

is the result that we would intuitively expect: Failure of 

one fault patch increases the stress on adjacent coplanar 

fault patches that must now support more of the load. The 

magnitudes of the stress increases on the San Andreas 

fault adjacent to the Loma Prieta rupture zone show large 

differences for the three distributions, reflecting the differences in both orientation and slip distribution among the 

three slip surfaces. These intermodel differences suggest 

that given the present uncertainties in the models, staticstress changes close to the rupture zone cannot be reliably 

calculated. In the following discussion, we confine our interpretations mostly to static-stress changes at intermediate 

to far distances from the rupture zone. 

Most of the Hayward fault and the northern and central 

sections of the Calaveras fault, which are subparallel to 

the Loma Prieta rupture zone, undergo a decrease in rightlateral horizontal shear stress (that is, an increase in leftlateral shear) in all three slip distributions. Although this 

result may be somewhat less obvious, it makes intuitive 

sense also: A failure on one of two parallel faults will tend 

to relax the shear stress on adjacent parts of the other fault 

if they are close enough together. (The actual geometry for 

relaxation to occur is illustrated in fig. 2 of Rybicki and 

others, 1985.) 

For the southern section of the Calaveras fault and the 

San Gregorio fault, which form larger angles with the 

Figure 2.4blique view of fault patches used in models. Most fault patches are vertical, except for large rectangle that is hma Prieta rupture surface 

of Lisowski and others (1990) and three small fault patches included for illustrative purposes. Coastline is shown for reference. 
F5 8 TECTONIC PROCESSES AND MODELS 

Table 1 .-Parameters for three LQ~ Prieta slip distributions 

[Some parameters are inferred from information in references. Height is veaical or updip width of rectangular surface] 

Overall Depth 

Slip distribution Number le:$by length by &pth to Center Center ::$ Reverse Moment 

height height $Ef bottom strike Dip (1atN.) (10ngW.) smkeslip 'lip (m) (lOl8 N-m) 

&m) m) m) (m) 

Lisowski and others 1 37 by 13.3 37 by 13.3 5.0 17.5 136' 70Â°SW 37.060' 121.906' 1.66 1.19 30 

(1990, model 3). 

Marshall and others 2 18.5 by 9 37 by 9 4.5 12.4 128' 62'SW. 37.046' 121.864' l.9212.01 l1.8910.61 2 1 

(1991, two-rake). Bema (1991) -------------- 280 1 by 2 40 by 14 5.8 18.9 130' 70Â°SW 37.055' 121.858' e) (3 24 

lFirst number refers to northwest rectangle, and second number to southeast rectangle. 

%lip varies over patches of the slip surface. 

Loma Prieta rupture surface, the horizontal shear is both 

right lateral and left lateral, depending on orientation and 

distance. Differences exist among the slip distributions between the boundaries separating domains of right- and 

left-lateral shear on these two fault segments. 

Some of the most dramatic stress changes occur in the 

normal component of traction. Under the sign convention 

used here, positive changes in the normal component represent unclamping (less compression) on the fault patches, 

whereas negative changes suggest clamping (increased compression). The reverse component of motion on the dipping 

Loma Prieta slip surface will tend to produce unclamping to 

either side of this surface. The most pronounced unclamping 

occurs on the southern section of the Hayward fault (fig. 

40, on adjacent sections of the Calaveras fault (fig. 4D), 

and on the section of the San Gregorio fault opposite the 

Lorna Prieta rupture zone (fig. 4E). If a Coulomb failure 

criterion is operating on these faults, then changes in normal 

stress acting on the fault patches, as well as changes in shear 

stress, could affect their proximity to failure. 

CALCULATED CHANGES 

IN COULOMB FAILURE FUNCTION 

To quantify the possibility of failure on nearby faults 

caused by static-stress changes after the earthquake, we 

use the Coulomb failure function (CFF'), defined by 

where fp is the shear traction on a plane P, op is the normal traction (positive for tension) on plane P, p is the 

pore-fluid pressure, S is the cohesion, and p is the coefficient of friction. This function is based on the Coulomb 

failure criterion, which applies to failure in unfractured 

rock, and on the mathematically identical Amonton's law 

for sliding on preexisting planes of weakness (for example, Jaeger and Cook, 1979; Scholz, 1990). 

If the CFF applies to seismogenic faults in the Earth, then 

failure would be expected to occur when CFF 2O.If a negative CFF increased (that is, became less negative) on a fault 

plane, then that plane would be expected to be closer to 

failure than before, with possibly greater consequent microseismicity, whereas fault planes for which a negative 

CFF decreased would be farther from failure, with possibly 

lower microseismicity. In the terminology of kmbruster 

and Seeber (1991), earthquakes might be encouraged or 

discouraged on a fault as a result of static-stress changes. 

If we assume that p and S are constant over time, then 

the change in CFF is given by 

Because the magnitude of the vector TP appears in this 

equation, ACFF as defined above is not readily calculated 

without knowledge of the absolute value of the preexisting 

stress field, or some simplifying assumptions. For vertical 

fault patches, we assume that A 1 AT^^^, where AT^^^ is 

the change in horizontal right-lateral shear, so that 

b Figure 3.4blique views of patches on central California faults, 

showing static-stress changes calculated by using slip distributions of (A) 

Lisowski and others (19901, (B) Marshall and others (1991), and (C) 

Beroza (1991). Top diagram, change in horizontal shear stress, where red 

indicates an increase and blue a decrease in right-lateral traction; middle 

diagram, change in updip shear stress, where red indicates an increase 

and blue a decrease in west-side-up traction; bottom diagram, change in 

normal stress, where red indicates an increase in tension (unclamping) 

and blue an increase in compression (clamping). Yellow patches represent Loma Prieta rupture. 
EARTHQUAKE-INDUCED STAmC-STRESS CHANGES ON CENTRAL CALFOm FAULTS 

2 3 

HORIZONTAL SHEAR STRESS, IN BARS - Lisowski 

12345 

UPDIP SHEAR STRESS, IN BARS - Lisowski 

4..' 

2345 

NORMAL STRESS, IN BARS - Lisowski 
TECTONIC PROCESSES AND MODELS 

345 

HORIZONTAL SHEAR STRESS, IN BARS - Marshall 

UPDIP SHEAR STRESS, IN BARS - Marshall 

Figure 3.Ã‘Continued 

2343 

NORMAL STRESS, IN BARS - Marshall 
EARTHQUAKE-INDUCED STATIC-STRESS CHANGES ON CENTRAL CALIFORNIA FAULTS 

I 7 

-5 -4 2* 

HORIZONTAL SHEAR STRESS, IN BARS - Beroza 

I-. 

3- 

UPDIP SHEAR STRESS, IN BARS - Beroza 

12 345 

NORMAL STRESS, IN BARS - Beroza 

Figure 3.Ã‘Continued 
TECTONIC PROCESSES AND MODELS 

SAN ANDREAS FAULT, NORTH c HAYWARD FAULT 

HORIZONTAL-SHEAMTRESS CHANGE HORIZONTAL-SHEAR-STRESS CHANGE 

""""""' 

cn 25 26 27 28 29 30 31 32 33 34 35 36 37 

a 

m a 

- UPDIP-SHEAR-STRESS CHANGE UPDIP-SHEAR-STRESS CHANGE 

z NORMAL-STRESS CHANGE cn """"""' 

NORMAL-STRESS CHANGE 

9b 91 B2 93 94 95 96 97 98 99 

FAULT PATCH FAULT PATCH 

B SAN ANDREAS FAULT, SOUTH CALAVERAS FAULT 

HORIZONTAL-SHEAR-STRESS CHANGE HORIZONTAL-SHEAR-STRESS CHANGE 

:: 

cn 103 104 105 106 107 108 109 110 111 112 113 114 

a 

$ UPDIP-SHEAR-STRESS CHANGE 8 UPDIP-SHEAR-STRESS CHANGE 

b 42 43 44 45 46 47 46 49 50 d 

z NORMAL-STRESS CHANGE rn 

I2 NORMAL-STRESS CHANGE cn 

FAULT PATCH FAULT PATCH 

Figure 4.-Static-stress changes on patches of the San Andreas fault (A) 

north and (B) south of hma Prieta rupture zone, (C) the Hayward fault, (D) 

the Calaveras fault, and (E) the San Gregorio fault. Solid line, slip distribution of Lisowski and others (1 990); short dashes, slip distribution of Marshall 

and others (1991); long dashes, slip distribution of Beroza (1991). Distance 

between fault patches is approximately 10 km. Top plot, change in horizontal 

shear stress, where positive values indicate an increase in right-lateral 

traction; middle plot, change in updip shear stress, where positive values 

indicate an increase in west-side-up traction; bottom plot, change in normal 

stress, where positive values indicate an increase in tension (unclamping). 
EARTHQUAKE-INDUCED STATIC-STRE~SS CHANGES ON CENTRAL CALIFORNIA FAULTS F63 

This assumption is similar to that made by Armbruster and 

Seeber (1991), who assumed in their analysis that induced 

earthquakes will always have the same slip directions as 

earlier earthquakes at a given site. Because most of our 

vertical fault patches represent faults expected to slip in 

predominantly right lateral earthquakes, the assumption is 

probably a good one. The alternative is to use information 

about the preearthquake state of stress acting on the fault 

patches to define the direction and magnitude of % before 

the static-stress changes are added, but with this approach, 

uncertainties introduced by the possible dependence of 

fault strength on the direction of slip cloud the issue. 

Three nonvertical fault patches were treated differently. 

For dipping patches 198 and 199 (fig. 21, which were intended to represent schematically some of the reverse-slip 

earthquakes on the San Francisco peninsula adjacent to 

the San Andreas fault (Olson and Lindh, 1985; Olson, 1986), 

the updip shear traction was used instead of the horizontal 

shear traction to calculate A in equation 2, equivalent 

to assuming a rake of 90'. Slipon dipping patch 200 was 

assigned an oblique (reverse plus right lateral) rake of 150Â° 

determined from nearby focal mechanisms, to calculate 

ACFF. 

Pore fluids seem to play an important role in the distribution of stress and in the failure process. Raleigh and others 

(1976) were able to control the occurrence of small earthE SAN GREGORIO FAULT 

HORIZONTAL-SHEAR-STRESS CHANGE 

121 122 123 124 125 1s 127 128 129 130 131 132 133 134 135 136 137 138 

0 K 

s UPDIP-SHEAR-STRESS CHANGE 

Q + 5 NORMAL-STRESS CHANGE 

quakes near Rangely, Colo., by changing fluid pressures in 

oil wells. Numerous reports describe seismicity induced by 

reservoir filling (for example, Roeloffs, 1988), with both 

load changes and pore-pressure changes probably contributing. The distribution of aftershocks over time after a main 

shock has been attributed to the reequilibration of pore fluids after the main shock (for example, Nur and Booker, 

1972; Li and others, 1987). Hudnut and others (1989) explained the Ms=6.6earthquake that occurred on the Superstition Hills fault 11 hours after an Ms=6.2 earthquake on 

the Elmore Ranch crossfault by appealing to static-stress 

changes and subsequent fluid flow. Segall (1989) modeled 

the generation of earthquakes in regions where pore pressures are decreasing because of fluid extraction. 

Although our dislocation models do not allow an incisive analysis of the role of pore fluids, we can obtain some 

impression of their potential importance. For example, in 

the undrained state immediately after the static-stress 

changes have been imposed, the change in pore pressure 

Ap in a homogeneous isotropic medium would be expected to be -BAod3, where B is Skempton's coefficient, 

which ranges from 0 to 1, and Aokk is the summation of 

the diagonal elements of the stress-change tensor (for example, Rice and Cleary, 1976; Roeloffs, 1988; Scholz, 

1990). Thus, equation 1 becomes 

or, simplifying for horizontal slip on vertical patches, 

ACFF A'ThrI + jl(Aop - BAokk/3). (3b) 

Tidal 

stresses 

DISTANCE, IN KILOMETERS 

FAULT PATCH 

Figure 4.4ontinued. 

Figure 5.4hange in horizontal shear stress as a function of distance 

from Lorna Prieta epicenter for slip distribution of Lisowski and others 

(1990). 
F64 TECTONIC PROCESSES AND MODELS 

We call this the homogeneous model. In this model, porepressure changes generally tend to counter normal-stress 

changes, resulting in a lower apparent coefficient of friction if pore-fluid effects are ignored, as discussed below. 

If the fault-zone materials are more ductile than the surrounding materials, then Rice (1992) has demonstrated 

that in the fault zone, and so Ao&3=AaP and 

or, again simplifying, 

where pt=p(1-B) is called the apparent coefficient of friction. We call this the Rice model. In this model, after the 

main shock but before pore fluids have had enough time to 

reequilibrate, the coefficient of friction would appear to be 

diminished by a factor depending on Skempton's coefficient over normal laboratory values, which range from 0.6 

to 0.9 (Byerlee, 1990; Zoback and Healy, 1984). 

If pore fluids are unimportant because Ap=O or B=O, 

then 

which would also be the result for finite permeabilities at 

t== after pore fluids have reequilibrated so that A@. We 

call this the dry or drained model. Note, however, that Byerlee (1990) and Rice (1992) have suggested mechanisms 

which might inhibit such reequilibration in a fault zone. 

The results from these three pore-fluid models are illustrated in figure 6 for the three slip distributions, assuming 

that p4.75 and B=l. This B value gives the maximum 

undrained-pore-fluid effect. B values ranging from 0.23 to 

0.99 have been reported for various rock types (Rice and 

Cleary, 1976; Roeloffs, 1988). Reasenberg and Simpson 

(1992) reported that the best correlation of changes in microseismicity rate with calculated static-stress changes 

after the earthquake is obtained for low apparent coefficients of friction (~'4.2). In the Rice model, for a coefficient of friction p. close to laboratory values of 0.75, this 

result implies a Skempton's coefficient B4.73. As before, 

the results for the three slip distributions are qualitatively 

similar beyond about 40-km distance from the rupture surface. Substantial differences exist for fault patches closer 

than 40 km, but such near-field results are unreliable in 

any event. 

A graphical comparison of the three pore-fluid models for 

selected bay-region faults, using the slip distribution of 

Lisowski and others (1990), is shown in figure 7, assuming 

that p4.75 and B=l. Comparison of the results suggests that 

pore-fluid effects can substantially shift patterns of encouraged and discouraged fault patches. For example, the south 

end of the Hayward fault is closer to failure in the dry1 

drained model than in either of the models for which porepressure changes are important. This section of the Hayward 

fault exhibited lower microseismicity rates (Reasenberg and 

Simpson, 1992) after the earthquake than before, a behavior 

consistent with pore fluids playing a role in the failure criterion. If, over time, the reequilibration of fluids leads to a 

result for ACFF closer to that in the dryldrained model, then 

microseismicity rates may increase on this section of the 

fault as it moves closer to failure. 

At several fault patches in the bay region, ACFF in the 

undrained state (homogeneous or Rice model) differs significantly from its value in the drained state. Fault patches 

97 through 99 on the Hayward fault (fig. 2) are more 

prone to failure in the drained state, whereas fault patches 

128 through 132 on the San Gregorio fault are less prone 

to failure. Changes in microseismicity rate on these fault 

patches over time may serve as an inplace test of the 

progress from undrained to drained states. The most definitive tests might be made in the near field, where the 

changes are largest but where our calculated results also 

depend most on the assumed slip distribution. 

Although these models oversimplify the pore-fluid effects, some generalizations are possible about the changes 

in CFF over time. Undrained models are strongly controlled by changes in shear stress, whereas dryidrained 

models are also controlled by changes in normal stress. In 

general, the dryldrained model yields ACFF values that are 

either the largest (most positive) or the smallest (most 

negative) of the three models (fig. 6); the Rice model 

tends to yield results that are least extreme. Thus, if the 

drainddry solution represents a t== end state, the largest 

changes in CFF over time after the earthquake will tend to 

occur if the appropriate starting model is the Rice model. 

Intermodel differences showing the direction of potential 

changes over time are plotted in figure 7. 

The role of pore fluids in the earthquake cycle has recently been highlighted by the realization that the regional compressive-stress field in much of California is oriented 

perpendicular to the San Andreas fault system (Mount and 

Suppe, 1987; Zoback and others, 1987). This realization 

would seem to require that the San Andreas fault have a 

Figure 6.4blique views of patches on central California faults, 

showing changes in Coulomb failure function for three pore-fluid models, calculated by using distributions of (A) Lisowski and others (1990), 

(B) Marshall and others (1991), and (0 Beroza (1991). Top diagram, 

homogeneous model; middle diagram, Rice model; bottom diagram, 

dryldrained model (see text for explanation). Coefficient of friction 

pO.75; Skempton's coefficient B=l. Red indicates changes that bring 

fault patches closer to failure, and blue changes that move fault patches 

farther from failure. Yellow patches represent the Loma Prieta rupture. 
EARTHQUAKE-INDUCED STAmC-STRESS CHANGES ON CEm CALEORNIA FAmTS 

3 4 

DELTA CFF, IN BARS I HOMOGENEOUS MODEL - Lisowski 

-- - 12345 

DELTA CFF, IN BARS I RICE MODEL - Lisowski 

7. . 2345 

DELTA CFF, IN BARS 1 DRY-DRAINED MODEL - Lisowski 
'IZCTONIC PROC$SSES AND MODELS 

I -3 -* -., 

DELTA CFF, IN BARS / HOMOGENEOUS MODEL - Marshall 

DELTA CFF, IN BARS / RICE MQREL - Marshall 

DELTA CFF, IN BARS I DRY-DRAINED MODEL - Marshall 
EARTHQUAKE-INDUCED STATIC-STRESS CHANGES ON CENTRAL CALIFORNIA FAULTS 

DELTA CFF, IN BARS / HOMOGENEOUS MODEL - Beroza 

DELTA CFF, IN BARS / RICE MODEL - Beroza 

DELTA OFF, IN BARS / DRY-DRAINED MODEL - Beroza 

Figure 6.Ã‘Continued 
TECTONIC PROCESSES AND MODELS 

SAN ANDREAS FAULT, NORTH c HAYWARD FAULT 

CHANGE IN CFF FOR THREE PORE-FLUID MODELS CHANGE IN CFF FOR THREE PORE-FLUID MODELS 

""""""' 

6 90 91 92 93 94 95 96 97 98 99 

2- 

Q DIFFERENCE: DRYIDRAINED - HOMOGENEOUS 

2- 

Q 

0 DIFFERENCE: DRYIDRAINED - HOMOGENEOUS 

2 

3"t' " " " " " ''1 uDIFFERENCE: DRYIDRAINED - RICE DIFFERENCE: DRYIDRAINED - RICE 

FAULT PATCH FAULT PATCH 

SAN ANDREAS FAULT, SOUTH 

CHANGE IN CFF FOR THREE PORE-FLUID MODELS 

CALAVERAS FAULT 

CHANGE IN CFF FOR THREE PORE-FLUID MODELS 

Ã‘Ã‘Ã‘Ã‘Ã‘ 

= 42 43 44' 45 46 47 48 49 50 

2 

Q 

& DIFFERENCE: DRYIDRAINED - HOMOGENEOUS 

5 103 104 105 106 107 108 109 110 111 112 113 114 

2 

0 DIFFERENCE: DRYIDRAINED - HOMOGENEOUS 

DIFFERENCE: DRYIDRAINED - RICE DIFFERENCE: DRYIDRAINED - RICE 

FAULT PATCH FAULT PATCH 

Figure 7.Ã‘Change in Coulomb failure function (top plot) on patches of 

the San Andreas fault (A) north and (B) south of Loma Prieta rupture 

zone, (C) the Hayward fault, (D) the Calaveras fault, and (E) the San 

Gregorio fault. Positive values for patches closer to failure. Short dashes, 

homogeneous model; long dashes, Rice model; solid line, dryidrained 

pore-fluid model. Middle plot, difference between dryidrained and homogeneous models; bottom plot, difference between dryidrained and Rice 

models. Positive values in middle and bottom plots may indicate changes 

over time that move fault patches closer to failure. All models calculated 

by using slip distributions of Lisowski and others (1990). 
EARTHQUAKE-INDUCED STATIC-STRESS CHANGES ON CENTRAL CALIFORNIA FAULTS F69 

low strength at seismogenic depths, so that if the Coulomb 

failure criterion is applicable at these depths, either a low 

coefficient of friction or a high pore-fluid pressure must 

obtain. Low shear stresses on the fault would also seem to 

be required by the absence of a heat-flow anomaly (Brune 

and others, 1969; Lachenbruch and Sass, 1980), although 

laboratory coefficients of friction for a wide variety of rock 

types are uniformly high (0.6-0.9). Maintaining high pore 

pressures in fault zones poses conceptual problems because 

the high pressures would be expected to hydrofracture the 

rock in simple models (Lachenbruch and McGarr, 1990), 

thereby releasing the pressure. Recent work by Byerlee 

(1990), Blanpied and others (1992), Rice (1 992), and Sleep 

and Blanpied (1992) has offered some new ideas for maintaining high fluid pressures in fault zones that circumvent 

the old problems. Changes in microseismicity rate may 

yield some inplace tests of the role of pore fluids. 

OBSERVED CHANGES 

IN MICROSEISMICITY RATES 

AND FAULT-CREEP RATES 

The calculated changes in stress and CFF presented in the 

preceding sections are theoretical results based on simple 

E SAN GREGORIO FAULT 

CHANGE IN CFF FOR THREE PORE-FLUID MODELS 

121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 

2- 

Q 

k DIFFERENCE: DRYIDRAINED - HOMOGENEOUS 

u 

0 

z DIFFERENCE: DRYIDRAINED - RICE 

FAULT PATCH 

Figure 7.Ã‘Continued 

models. Two data sets offer independent confirmation of 

these results: microseismicity rates and fault-creep rates. 

MICROSEISMICITY RATES 

About 3 months after the earthquake, the microseismicity rate on the Hayward fault was observed to have diminished in comparison with that for the 3-month period 

before the earthquake. This change was consistent with the 

results of models that assumed low apparent coefficients 

of friction, in which the Hayward fault was relaxed by the 

addition of left-lateral horizontal static stress. 

A detailed study of microseismicity rates on central 

California faults (Reasenberg and Simpson, 1992 and in 

press) subsequently revealed a correlation between calculated stress changes and microseismicity rates at the 95- 

percent-confidence level. Although the correlation works 

well for some faults, such as the Hayward fault and the 

parts of the San Andreas fault to the north and south of 

the Loma Prieta rupture zone, we note that other faults, 

especially the San Gregorio fault, do not fit the models 

well. The best correlation was observed for models with 

low apparent coefficients of friction p', on fault patches 

within 100 krn of the Loma Prieta epicenter. At epicentral 

distances greater than 80 to 100 krn, the response of seismicity to stress changes is statistically undetectable at the 

95-percent-confidence level. At these distances, the maximum absolute value of ACFF is approximately 0.1 bar or 

less (fig. 5). 

Although it seems extraordinary that such small stress 

changes could influence the occurrence of earthquakes, the 

levels of change are comparable to those calculated at 

seismogenic depths under water-filled reservoirs, for 

which the initial filling process and subsequent seasonal 

cycling of water levels are known to generate earthquakes 

(for example, Roeloffs, 1988). 

Stresses generated by Earth tides on the Hayward fault 

during the year after the earthquake were calculated to 

have a maximum range of 0.01 bar for horizontal shear 

stress and 0.05 bar for normal stress. (Mean daily variations were approximately 20 to 30 percent of these maximums.) Several investigators have looked for correlations 

of tectonic earthquakes with the tidal-stressing cycle, with 

only mixed success (for example, Heaton, 1975, 1982; 

Hartzell and Heaton, 1989, 1990; Rydelek and others, 

1992). In particular, a study of central California earthquakes by McNutt and Heaton (1981) failed to uncover a 

statistically significant correlation. M.J.S. Johnston (oral 

cornmun., 1990), however, reported that microseismicity 

on the San Andreas fault does show a correlation with 

peak tidal stresses. If he is correct, there is little doubt that 

static-stress changes of the size calculated in this paper 
F70 TECTONIC PROCESSES AND MODELS 

could alter microseismicity rates out to distances of 100 to 

150 km from the Loma Prieta epicenter. 

We tried to infer both p and B values in equation 3b from 

the microseismicity data, but the results were not statistically an improvement over simply inferring a p' value from 

equation 4b. Thus, the microseismicity data do not seem to 

contain information that would differentiate the homogeneous model from the other two models at a statistically significant level. The low inferred apparent coefficient of 

friction p' does argue for the presence of pore fluids and a 

non-zero value for Skempton's coefficient, because in the 

absence of pore-fluid effects, p values of 0.6 to 0.9 are 

favored by laboratory experiments on rock friction. 

FAULT-CREEP RATES 

A second data set that shows some correlation with the 

static-stress changes caused by the earthquake consists of 

slip rates measured over fault traces in the San Francisco 

Bay region by creepmeters and alignment arrays. Behr and 

others (1990) reported increased rates of right-lateral slip on 

several creepmeters spanning the San Andreas fault south of 

the Loma Prieta rupture zone in the days after the main 

shock, Galehouse (1990) reported triggered right-lateral slip 

at two alignment-array sites in Hollister, Calif. (fig. I), and 

McClellan and Hay (1990) reported right-lateral offsets at 

two sites on the Calaveras fault that occurred within hours 

or days of the earthquake. These right-lateral-slip observations are consistent with the stress changes predicted by the 

models, although faults can sometimes release an accumulated backlog of strain if they are triggered by shaking (for 

example, Allen and others, 1972; King and others, 1977; 

Fuis, 1979; Sieh, 1982; Simpson and others, 1988; Williams, 

1988; Sharp, 1989). 

Because of triggered slip, creepmeters or alignment arrays on right-lateral fault traces that show slowed or even 

reversed (that is, left lateral) motion offer potentially more 

reliable indicators of stress changes. The Hayward fault, 

which was relaxed in the low-apparent-coefficient-of-friction models described above, would seem like a good candidate for retarded slip motions. Galehouse (1992 and in 

press) reported lower rates at four of five alignment arrays 

on the Hayward fault during the 2-yr period after the earthquake. A new site at Camellia Drive in Fremont, Calif. 

(near fault patch 96, fig. 2), established by Galehouse after 

the earthquake shows a small amount of left-lateral slip, 

even though it is located at a site that has slipped at high 

right-lateral rates in the past, judging from curb offsets. 

Harsh and Burford (1982) reported a possible slowing of 

the creep rate at an alignment array on Prune Avenue (now 

South Grimmer Boulevard) in Fremont about 0.7 krn 

southwest of Galehouse's site at Camellia Drive (Lienkaemper and others, 1991) after the 1980 Livermore, 

Calif. (M=5.8), earthquake. A dislocation model constructed to calculate the static-stress changes from this earthquake yielded left-lateral shear stresses of less than 0.02 

bar at the Prune Avenue array, as well as tensional normal 

stresses of about 0.06 bar. The left-lateral shear stress 

might have helped to slow creep, whereas the tensional 

normal stress might be expected to accelerate it if frictional forces are important. It would be remarkable if such 

small stresses were to have an effect on the creep rate at 

this site. The site lies on an unusual 5- to 7-km-long 

stretch of the fault that has displayed the highest historical 

creep rates (8-9 mrnlyr), which Lienkaemper and others 

(1991) took to be an indication of slip rates at depth on 

the Hayward fault. 

In summary, it appears that a good correlation exists between our calculated stress changes and observed microseismicity rates for low assumed apparent coefficients 

of friction and that a possible correlation exists with retarded surface slip rates observed at alignment arrays on 

the Hayward fault. 

NEGLECTED VARIABLES 

THAT COULD BE IMPORTANT 

Several important variables have been ignored in the 

models presented above, including elastic heterogeneities, 

the possibility of nonvertical dips on some major faults, 

and the interactions of deep faults with other structures not 

included in the models. In this section, we estimate the 

possible magnitude and importance of these effects. 

ELASTIC HETEROGENEITY 

Eberhart-Phillips and Stuart (1992) demonstrated that 

slip models for the earthquake based on geodetic information could be rnislocated by as much as 2 krn because of 

changes in elastic moduli on the two sides of the rupture. 

Such changes could also bias the stress calculations presented here, especially in the near field. Although we have 

made no attempt to correct for this effect, we suspect that 

middle- and far-field results will not be much changed by 

shifting any of the distributions used by several kilometers 

in any direction. 

EFFECT OF DIPPING FAULTS 

The magnitudes of the stress changes induced on various 

fault planes in the San Francisco Bay region depend on the 

orientations as well as the distances of these planes relative 

to the Loma Prieta rupture surface. For example, a small 

dipping fault plane near the San Gregorio fault (fault patch 

200, fig. 2) can be seen in figure 6 to have a propensity for 
EARTHQUAKE-INDUCED STATIC-STRESS CHANGES ON CENTRAL CALIFORNIA FAULTS F7 1 

failure opposite to that of the adjacent vertical patches 

aligned under the San Gregorio fault trace. The DCFF 

value for this fault patch was calculated by assuming 

oblique (reverse plus right lateral) slip on the fault plane, 

with a rake of 150'. The presence of dipping faults undergoing oblique slip in this region is suggested by about 40 

reasonably well controlled local focal mechanisms that we 

examined, which also suggested the rake value used. 

Whether these events occurred on a dipping San Gregorio 

fault or on adjacent dipping faults is unclear. Jachens and 

Griscom (in press) report that aeromagnetic data suggest a 

50Â°-60 NE. dip for the onland section of the San Gregorio 

fault and its offshore extension to the south. 

Dipping fault patches 198 and 199 (fig. 2) adjacent to 

the San Andreas fault to the north of the Loma Prieta mpture zone were also added to the model in a region of 

known reverse-faulting mechanisms (Olson and Lindh, 

1985) to test the importance of geometric factors. These 

two fault patches come closer to failure as a result of 

Loma Prieta stress changes, as do the adjacent vertical 

fault patches (36, 37) under the San Andreas fault trace. 

Could the Hayward fault, though moved farther from failure in our low-apparent-coefficient-of-friction models based 

on vertical fault patches, be stressed closer to failure if it 

dipped east or west? Several investigators have pointed to 

compressional structures around the San Francisco Bay region (for example, Aydin and Page, 1984; Wentworth and 

Zoback, 1989), and Jones and others (1991) suggested that 

the Hayward fault itself may dip or have an associated dipping companion fault. The unexpected reverse component 

of slip on the Loma Prieta rupture surface does raise the 

possibility that other intermediate to large earthquakes which 

have occurred in the bay region may have had oblique (that 

is, both strike slip and reverse slip) motions to them. This 

conclusion would be consistent with the presence of faultnormal compression in California along the San Andreas 

fault, as noted by Mount and Suppe (1987), Zoback and 

others (1987), and Wentworth and Zoback (1989). 

To test the effect of a dipping Hayward fault, we tried 

two variations of the dislocation model based on the slip 

distribution of Lisowski and others (1990). In the first variation, the Hayward fault was assigned a dip of 45' E., 

and in the second variation, a dip of 45' W.; the results are 

plotted in figure 8. Although the stresses on dipping fault 

patches differ from those on a vertical fault, no real 

change occurs in the relaxation picture because the dipping model faults still show an increase in left-lateral horizontal stress, which is presumably relaxing, and the 

unclamping effect is translated into downdip tensional 

stress, which also would be expected to move the Hayward fault farther from failure in a regional fault-normal 

compressive-stress field. 

This result for the Hayward fault does not necessarily 

apply to other faults with other locations and geometries 

relative to the Lorna Prieta rupture zone. For example, the 

result for the San Gregorio fault described above suggests 

that in some places dip can be important in determining 

the change in the proximity to failure. Griscom and 

Jachens (1990), Jachens and others (1990), and Jachens 

and Griscom (in press) suggested that several of the principle faults in the San Francisco Bay region, including the 

San Andreas fault, have nonvertical dips, on the basis of 

the geometry of gravity and aeromagnetic anomalies. 

More work needs to be done to refine our models of the 

active tectonic elements in the bay region. 

EFFECT OF OTHER STRUCTURES 

In most of our models, the Hayward fault seems to be 

relaxed rather than stressed by the Loma Prieta staticstress changes. Could a Loma Prieta-type event trigger an 

earthquake on the Hayward fault in other ways? 

For example, a Loma Prieta-type event might trigger seismic or aseismic slip on an intermediate structure that would, 

in turn, trigger an earthquake on the Hayward fault. Andrews and others (1993) suggested that the Mission fault 

(fig. 1) could play a critical triggering role for earthquakes 

on the Hayward fault. Using the slip distribution of Lisowski and others (1990), we tried three models for a Mission 

DIPPING HAYWARD FAULT 

HORIZONTAL-SH EAR-STRESS CHANGE 

cn 90 91 92 93 94 95 96 97 98 99 

cc 

c0 UPDIP-SHEAR-STRESS CHANGE 

w 

0) -1 j-\--- w -2 

lr .3 U) 90 91 92 93 94 95 96 97 98 99 

0 

NORMAL-STRESS CHANGE w 

FAULT PATCH 

Figure 8.-Static-stress changes on patches of the Hayward fault, calculated by using slip distribution of Lisowski and others (1990). Long 

dashes, 45' E.-dipping fault; solid line, vertical fault; short dashes, 45' 

W.-dipping fault. Top plot, change in horizontal shear stress; middle plot, 

change in updip shear stress; bottom plot, change in normal stress. 
P72 TECTONIC PROCESSES AND MODELS 

fault dipping vertically, 45' NE., and 45O SW., assuming 

that the preexisting load on the fault is a combination of 

right-lateral horizontal shear and reverse updip shear. For all 

three dips used in our models, the Mission fault received a 

left-lateral horizontal shear-stress increment and, for the 

dipping models, a normal-faulting downdip shear increment 

as a result of the Loma Prieta rupture. Both shear components are therefore likely to relax the assumed state of shear 

stress on the Mission fault. Normal-stress changes for all 

three dips are tensional, tending to unclamp the fault, but 

the magnitudes of tension are mostly smaller than the shear 

components. Only with a vertical dip and a high coefficient 

of friction (0.8) does the Mission fault move closer to failure as a result of the earthquake. Thus, the Mission fault 

does not seem to be an effective intermediary for transferring Loma Prieta stress changes to the Hayward fault. 

Other candidates for intermediary triggering structures 

lie under San Francisco Bay between the Loma Prieta rupture zone and the Hayward fault. Gravity and magnetic 

data suggest the presence of several structures at depth 

under the bay (Griscom and Jachens, 1990). It is not yet 

known whether these structures are still active and, if so, 

whether aseismic or seismic slip on any of them might 

bring the Hayward fault closer to failure. 

SIMULATING 

TIME-DEPENDENT EFFECTS 

WITH DISLOCATION MODELS 

Regional adjustments that occur after large earthquakes 

may include aseismic slip on other nearby structures and 

on deeper parts of the fault that ruptured in the main 

shock; these adjustments may occur over periods of days 

to years. Without a model of the pertinent rheologies, 

time-dependent histories of the subsequent stress changes 

cannot be calculated. Directions and final states, however, 

can be estimated by solving the boundary-value problem 

for which the aseismically slipping structures are required to attain a zero shear-stress state. This state is presumed to approximate the final state (after infinite time 

has passed) of the time-dependent solution. A better approach is to actually construct a model of the lithosphere 

that incorporates appropriate rheologies and to calculate 

the resulting evolution over time. Linker and Rice (1991 

and in press) used this approach in a finite-element 

model. 

SLIP AT DEPTH 

IN RESPONSE TO THE EARTHQUAKE 

We consider two types of redistribution of stresses: (1) 

that which would result from deep afterslip, triggered by 

Loma Prieta static-stress changes, on vertical planes beneath the locked seismogenic layer; and (2) that which 

would result from slip on a horizontal-detachment surface 

under San Francisco Bay. Both types show that afterslip 

can change the magnitude and even the sign of Loma Prieta static stresses acting on other nearby faults. 

AFTERSLIP ON VERTICAL PLANES 

To evaluate the effect of the Lorna Prieta stress impulse 

on the vertical, aseismically slipping parts of bay-region 

faults, we added a second layer of 13-km-tall vertical 

patches extending from 13- to 26-km depth (yellow, fig. 

9A) that were free to slip in response to the static-stress 

changes. The top layer of fault patches was held locked, as 

in the previous models. The purpose of this exercise was 

to see how stresses acting on the top layer would be 

changed by slip at depth. 

The results are shown in figure 10, using the slip distribution of Lisowski and others (1990). The stresses acting 

on the top layer (0- to 13-km depth) in the model do 

change in response to the deep vertical-slip adjustments, 

but not by much. No substantial increase in the danger of 

failure on any bay-region faults occurs as a result of such 

afterslip on vertical s of the faults. 

AFTERSLIP ON HORIZONTAL DETACHMENT SURFACW 

Horizontal detachment surfaces might offer a more effective way to convey stresses efficiently over large distances. Although there is presently no direct evidence for 

such surfaces in the San Francisco Bay region, their presence has been hypothesized (see Furlong and Verdonck, 

this chapter), and so it is of interest to explore the utility 

of such a horizon in redistributing stresses. Both Furlong 

and Verdonck (this chapter) and Linker and Rice (in 

press) present models that use detachment surfaces to redistribute stresses. Our model is shown in figure 95. The 

horizontal floor of 10- by 10-km rectangular dislocations 

at a depth of 13 krn was free to slip so as to eliminate 

shear stresses. 

The results are shown in figure 10. As expected, the 

stress changes on the seismogenic layer are more striking 

than for vertical aseismic slip surfaces. In particular, normal-stress changes on the Calaveras and San Gregorio 

faults have changed by a factor of 2 or more in some places opposite the Loma Prieta model rupture. Shear stresses 

on the San Gregorio fault have also changed somewhat, 

and the boundaries between regions of increased relaxation and failure have shifted by about 10 km on these 

faults. 

Overall, however, even slip on this simulated horizontal 

detachment surface does not change our results significant- 
EARTHQUAKE-INDUCED STATIC-STRESS CHANGES ON CENTRAL CALIFORNIA FAULTS 

ly for faults at middle and far distances (min 40 km) from PLATE-TECTONIC LOADING 

the Loma Prieta rupture. In particular, results for the Hay- AFTER THE 1989 EARTHQUAKE 

ward fault hardly change at all. A different geometry for 

the detachment surface, possibly with bounding edges The static-stress changes on other central California faults 

closer to the locations of major faults, might yield greater resulting from the Loma Prieta rupture are imposed coseiseffects. mically and essentially instantaneously (within seconds or 

-5 -4 -3 -2 -1 0 1 2 3 4 

NORMAL STRESS, IN BARS 

-5 -4 -3 -2 -1 0 1 2 0 't 

NORMAL STRESS, IN BARS 

Figure 9.Ã‘Obliqu views of patches on central California faults 

showing static-stress changes calculated by using slip distribution 

of Lisowski and others (1990). A, Oblique view of model, with 

freely slipping vertical layer (yellow patches) from 13- to 26-km 

depth under top layer of locked fault patches. B, Oblique view of 

model, with freely slipping horizontal detachment surface (yellow 

patches) at 13-km depth. Loma Prieta rupture, though shown in 

yellow, is not free to slip in either model. 
TECTONIC PROCESSES AND MODELS 

SAN ANDREAS FAULT, NORTH c HAYWARD FAULT 

HORIZONTAL-SHEAR-STRESS CHANGE 

""""""' 

HORIZONTAL-SHEAR-STRESS CHANGE 

w 25 26 27 26 29 30 31 32 33 34 35 36 37 

a 

s UPDIP-SHEAR-STRESS CHANGE is UPDIP-SHEAR-STRESS CHANGE 

a 90 91 92 93 94 95 96 97 98 99 ^ < NORMAL-STRESS CHANGE 

0 

I- < NORMAL-STRESS CHANGE 

90 91 92 93 94 95 96 97 98 99 

FAULT PATCH 

CALAVERAS FAULT 

HORIZONTAL-SHEAR-STRESS CHANGE 

FAULT PATCH 

SAN ANDREAS FAULT, SOUTH 

HORIZONTAL-SHEAR-STRESS CHANGE 

1 

103 104 105 106 107 108 109 110 111 112 113 114 

UPDIP-SHEAR-STRESS CHANGE 

42 43 44 45 46 47 48 49 50 

w K

2i UPDIP-SHEAR-STRESS CHANGE 

,+. . . . I. I I.. . ., 

3 42 

43 44 45 46 47 48 49 50 

I- ? NORMAL-STRESS CHANGE CO 10 ' 1 

NORMAL-STRESS CHANGE 

103 104 105 106 107 108 109 110 111 112 113 114 

FAULT PATCH FAULT PATCH 

Figure 10.Ã‘Static-stres changes on patches of the San Andreas fault (A) 

north and (B) south of Loma Prieta rupture zone, (Q the Hayward fault, 

(D) the Calaveras fault, and (0 the San Gregorio fault, calculated by 

using slip distribution of Lisowski and others (1990). Solid line, changes 

with no afterslip; short dashes, changes with afterslip on vertical layer 

from 13- to 26-km depth under top layer of locked fault patches; long 

dashes, changes with afterslip on a horizontal detachment surface at 13- 

km depth. Top plot, change in horizontal shear stress, where positive values indicate an increase in right-lateral traction; middle plot, change in 

updip shear stress, where positive values indicate an increase in westside-up traction; bottom plot, change in normal stress, where positive 

values indicate an increase in tension Cunclamoingl. 
EARTHQUAKE-INDUCED STATIC-STRESS CHANGES ON CENTRAL CALIFORNIA FAULTS 

Table 2.-Long-term deep slip rates on selected central California faults 

[Do., ditto] 

Fault Patches tgELd (fig. 2) (rnmlyr) References 

San Andreas: 

North-coastal section ----------------- 1-27 enin insular and southern sections---- 2849 

Central creeping section -------------- 50-71 

Prentice (1989), Niemi and Hall (1992). 

Working Group on California Earthquake 

Probabilities (1990), Lienkaemper and 

others (1991). 

Working Group on California Earthquake 

Probabilities (1990). 

Budding and others (1991). 

Lienkaemper and others (199 1). 

Do. 

Working Group on California Earthquake 

Probabilities (1990). 

Clark and others (1984). 

minutes). Additional changes may be added by continuing 

afterslip around the rupture zone (within days to months) 

that may for some earthquakes have a moment equal to that 

of the initial rupture (for example, Smith and Wyss, 1968). 

Over the longer term, the static-stress changes are modified 

by viscous relaxation and the ongoing increment of plateE SAN GREGORIO FAULT 

HORIZONTAL-SHEAR-STRESS CHANGE 

'"""~"'"""' 

3 UPDIP-SHEAR-STRESS CHANGE 

FAULT PATCH 

Figure 10.Ã‘Continued 

loading forces. Relaxation phenomena are discussed in the 

preceding section. 

The plate-tectonic loading can be approximated by using 

dislocations, as described below. This approach allows an 

estimate of how the earthquake-induced static-stress changes 

on a given fault segment compare with the yearly plateloading stress increments. For fault patches that were brought 

closer to failure by the Loma Prieta rupture, the ratio of these 

two quantities gives an estimate of by how may years failure 

on the patch has been advanced-assuming that the earthquake did not change the failure threshold. J.H. Dieterich 

(oral commun., 1992) pointed out that the dynamic effects of 

shaking accompanying the passage of the seismic waves 

might disrupt the healing process on a fault and induce it to 

fail earlier. 

For fault patches that have been relaxed by the addition 

of an increment of left-lateral shear stress, estimates of the 

plate-loading rate allow us to calculate how long it will 

take the fault patch to return to its state of loading before 

the earthquake. During the recovery period, we would not 

anticipate large earthquakes on the fault patch because it 

had already been at higher stress levels before the earthquake relaxed it, again assuming that the earthquake did 

not alter the failure threshold and that failure is a fairly 

deterministic, rather than chaotic, process. 

We assume that only the seismogenic upper layer is moving in stick-slip fashion and that the deeper layers are moving at steadier rates approximating observed long-term slip 

rates (table 2). These long-term slip rates are assigned to 

dislocations extending from 13- to 100-krn depth under the 

major faults, which are assumed to be vertical. The results 

are unlikely to be sensitive to the depth to the bottom of the 

second slipping layer. The assignment of long-term slip 
F76 TECTONIC PROCESSES AND MODELS 

rates to the various faults, however, also introduces some 

long-term inconsistencies. For example, faults that change 

in strike will accumulate normal stresses in the model that 

in the real world are presumably relieved by deformation 

adjacent to the fault (for example, thrusting and mountain 

building or basin formation). Alternative models of deformation at depth in the San Francisco Bay region are becoming available that could be utilized in these estimates (see 

Bodin and Bilham, this chapter; Furlong and Verdonck, this 

chapter). Furlong and Verdonck's models, in particular, are 

based on the presence of horizontal detachment surfaces 

connecting bay-region faults under San Francisco Bay, with 

most of the deep slip between plates occurring at depth 

under the Hayward fault. 

The results of our attempt to calculate long-term plateloading rates are plotted in figure 11, where stress-change 

rates are shown for the slip distribution of Lisowski and 

others (1990). In figure 12, long-term plate-loading rates 

and Loma Prieta static-stress changes have been converted 

into equivalent years of delay or advance in failure. On 

fault patch 37 (fig. 21, for example, north of the Loma 

Prieta rupture zone, the horizontal shear-stress increment of 

5.2 bars (fig. 4A) is nearly equal to 30 yr of loading (top 

plot, fig. 12A), with an assumed long-term slip rate of 19 

dyr (table 2) on this section of the San Andreas fault. On 

SAN ANDREAS FAULT, NORTH 

HORIZONTAL-SHEAR-STRESS CHANGE 

0.2 .-.-.-.-.-.-.-.-. .-.-. 

4.2 

a 

25 28 27 20 20 30 31 32 33 34 35 36 37 

UPDIP-SHEAR-STRESS CHANGE 

NORMAL-STRESS CHANGE 

FAULT PATCH 

Figure 11.-Annual plate-tectonic-loading rates on patches of the San 

Andreas fault (A) north and (B) south of Loma Prieta rupture zone, 

(C) the Hayward fault, (D) the Calaveras fault, and (0 the San Gregorio fault, calculated by using model described in text and deep slip 

rates listed in table 2. Top plot, change in horizontal shear stress, 

fault patch 99, on the southern section of the Hayward 

fault, the initial earthquake-induced relaxation in the horiB SAN ANDREAS FAULT, SOUTH 

a 4.J a 8 . 8 . . . a . J 5 42 43 U 45 46 47 48 49 50 

a 

w Q

3 UPDIP-SHEAR-STRESS CHANGE 

HORIZONTAL-SHEAR-STRESS CHANGE 

NORMAL-STRESS CHANGE 

0.4 

0.2 

0.0 

4.2 

FAULT PATCH 

' 

- .-.-.- .--.-,.-. -.-' 

- 

- 

c ' HAYWARD FAULT 

HORIZONTAL-SHEARSTRESS CHANGE 

a 2 1 a 1 9091 92930495W97W99 

a 

w a 

a UPDIP-SHEAR-STRESS CHANGE 

(j) -0.4 k 0 4 

Cn lu 9091 92S30495W97Wgg 

a 

t- 

!? NORMAL-STRESS CHANGE 

FAULT PATCH 

where positive values indicate an increase in right-lateral traction; 

middle plot, change in updip shear stress, where positive values indicate an increase in west-side-up traction; bottom plot, change in normal stress, where positive values indicate an increase in tension 

(unclamping). 
EARTHQUAKE-INDUCED STAmC-STRESS CHANGES ON CENTRAL CALIFORNIA FAULTS 

zontal shear stress of 1-34 bars (fig. 40 for the slip distribution of Lisowski and others (1990).is overcome in about 

10 yr (top plot, fig. 120 by the long-term plate-loading rate 

of 0.14 barlyr (fig. 110 calculated for an assumed longterm slip rate of 9 dyr at depth on the Hayward fault. 

CALAVERAS FAULT 

HORIZONTAL-SHEAR-STRESS CHANGE 

"""""" 

UPDIP-SHEAkSTRESS CHANGE 

"""""" 

NORMAL-STRESS CHANGE 

- 

103 104 105 106 107 lm 108 110 111 112 113 114 

FAULT PATCH 

SAN GREGORIO FAULT 

HORIZONTAL-SHEARSTRESS CHANGE 

UPDIP-SHEARSTRESS CHANGE 

"'"'""'"'~"' 

NORMAL-STRESS CHANGE 

""""""""" 

FAULT PATCH 

Figure 1 I .-Continued 

SAN ANDREAS FAULT, NORTH 

APPARENT COEFFICIENT OF FRICTION = 0.0 

APPARENT COEFFICIENT OF FRICTION = 0.4 

APPARENT COEFFICIENT OF FRICTION = 0.8 

-10 8-8-8-8-8 

-20 

FAULT PATCH 

SAN ANDREAS FAULT, SOUTH 

APPARENT COEFFICIENT OF FRICTION = 0.0 

I 

APPARENT COEFFICIENT OF FRICTION = 0.4 

1 

APPARENT COEFFICIENT OF FRICTION = 0.8 

I 

FAULT PATCH 

Figu~ 12.-Estimated delay (positive values) or advance (negative values) in time to failure introduced by 1989 hma Prieta earthquake on 

patches of the San Andreas fault (A) north and (B) south of hma Prieta 

rupture zone, (C) the Hayward fault, (D) the Calaveras fault, and (Q the 

San Gregorio fault, calculated by using slip distribution of Lisowski and 

others (IWO), assuming apparent coefficients of friction p' of 0.0 (top 

plot), 0.4 (middle plot), and 0.8 (bottom plot). 
W8 TJXTONIC PROCESSES AND MODELS 

We note that the times of advance or delay in failure are 

sensitive to the assumed long-term slip rates. Large delays 

on the San Gregorio fault, for example (fig. 12E), partly 

reflect the low plate-loading rate resulting from an assumed deep slip rate of 4 mm/yr (table 2). Changing this 

rate by just 1 dyr would substantially affect the time 

changes in figure 12E. 

The evolution of the horizontal shear stress over time on 

the Hayward and Calaveras faults after the Loma Prieta 

rupture is illustrated in figure 13. A return to light red indicates that the relaxation on a fault patch has ended and 

the horizontal shear stress has reached pre-1989 levels. 

Fault patches that were not relaxed by the earthquake continue to redden as they are loaded tectonically. 

HAYWARD FAULT 

APPARENT COEFFICIENT OF FRICTION = 0.0 

90 91 92 93 94 95 96 97,98 99 

APPARENT COEFFICIENT OF FRICTION = 0.4 

PLATE-TECTONIC LOADING 

AFTER THE 1906 EARTHQUAKE 

AND THE END TO 73 YEARS 

OF SEISMIC QUIESCENCE 

It is of some interest to calculate the static-stress changes caused by the 1906 San Francisco (M=8+) earthquake 

for comparison. We used the slip distributions inferred by 

Thatcher (1975) and Thatcher and Lisowski (1987) from 

surface slip and geodetic observations to calculate these 

static-stress changes. The dislocation model consists of 20- 

km-tall by 10-km-long vertical rectangular patches representing the major faults in the San Francisco Bay region. 

Thatcher (1975) suggested that coseismic slip during the 

APPARENT COEFFICIENT OF FRICTION = 0.8 

9091928394959697W99 

FAULT PATCH 

CALAVERAS FAULT 

APPARENT COEFFICIENT OF FRICTION = 0.0 

SAN GREGORIO FAULT 

APPARENT COEFFICIENT OF FRICTION = 0.0 

lw~""""~""""'~ 

APPARENT COEFFICIENT OF FRICTION = 0.4 APPARENT COEFFICIENT OF FRICTION = 0.4 

"""""" 

APPARENT COEFFICIENT OF FRICTION = 0.8 APPARENT COEFFICIENT OF FRICTION = 0.8 

FAULT PATCH FAULT PATCH 
EARTHQUAKE-INDUCED STATIC-STRESS CHANGES ON CENTRAL CALIFORNIA FAULTS F79

1906 earthquake extended to a depth of only 10 kIn but

that afterslip might have gone to depths as great as 30 kIn.

The static-stress changes in this model for bay-region

faults are plotted in figure 14, and the number of years of

delay or advance in failure after the 1906 rupture estimated from our dislocation model are plotted in figure IS.

The creeping section of the San Andreas fault south of San

Juan Bautista, Calif. (fig. 1), was more highly stressed,

whereas most other bay-region faults were relaxed in their

horizontal-shear component by the 1906 earthquake. We

suggest that this relaxation explains the 73-yr quiescence

for M>6 events on bay-region faults after the 1906 earthquake (except for the 1911 earthquake; Ellsworth and others, 1981; Sykes and Jaume, 1990).

103

The evolution of horizontal shear stress over time on the

Hayward and Calaveras faults after the 1906 earthquake is

illustrated in figure 16. The effect of the 1989 earthquake

can also be seen as a small perturbation at 1990 near the

south end of the Hayward fault (especially fault patch 98).

This perturbation helps place in perspective the relative

sizes of the static-stress changes from the 1906 and 1989

earthquakes.

The locations of M>5 earthquakes on the Calaveras fault

since 1906 (Oppenheimer and others, 1990, table 1) are

shown in figure 17. The onset of M>6 earthquakes in the

San Francisco Bay region after 73 yr of seismic quiescence began in a region near the intersection of the Hayward and Calaveras faults where the fault patches are

2002

2000

107

r--- 109

-.--r--- 111

r--- ....... _ r--JJ2.

r--- 115 117 119 -- r-- r-- r-- -r-- r--__ r--- ---r-- r--1--__ r--- ---to-- r--1--__ r---

---I--- --I-- r--- "

--r-I--- ---- 1--__ roo-- -- --- ~ ~ r-I-- I--

to--

--I"--I--

- ----- 1--__ t-- :"'1--_ --1--__ t-- ~~. 1"--- --I-- r---

I--- ~M-- -----

__r--_

it" . == ---~~ -to--~c

I---i ?!i "i,i, _ --I--'~;;

91 '-- --1--"- 93 95 97 - __ -..::tIi'

99 '---- ______

1998

1996

1994

1992

1990

1988

a:

«

w

>-

-5 -4 -3 -2 -1 o 2 3 4 5

STATIC-STRESS CHANGE, IN BARS

Figure 13.-Qblique view of patches on the Hayward fault (left block)

and the Calaveras fault (right block), showing changes in horizontal

shear from 1988 to 2002. Values for 1988 are all zero, taking that as a

reference year. Large changes introduced by 1989 Lorna Prieta earthquake are in some places left lateral (blue). As tectonic loading progresses (see text), additional right-lateral traction reloads sections of faults

that had been relaxed. By 2000, even sections of the Hayward fault that

sustained largest increments of left-lateral shear in this model are back to

pre- 1'989 stress levels. No provision for aseismic afterslip was made in

this model.
F80 TECTONIC PROCESSES AND MODELS 

calculated to have recovered earliest from the relaxation 

imposed in 1%. 

A note of caution needs to be applied to the results described in this subsection. Elastic-dislocation models may 

SAN ANDREAS FAULT CALAVERAS FAULT 

HORIZONTAL-SHEAR-STRESS CHANGE HORIZONTAL-SHEARSTRESS CHANGE 

UPDIP-SHEAR-STRESS CHANGE UPDIP-SHEAR-STRESS CHANGE 

"""""" 

NORMAL-STRESS CHANGE NORMAL-STRESS CHANGE 

~""'"''~' 

FAULT PATCH FAULT PATCH 

HAYWARD SAN GREGORIO FAULT FAULT 

HORIZONTAL-SHEAR-STRESS CHANGE HORIZONTAL-SHEAR4TRESS CHANGE 

UPDIP-SHEAR-STRESS CHANGE UPDIP-SHEAR-STRESS CHANGE 

N0RMAL;STRESS CHANGE NORMAL-STRESS CHANGE 

FAULT PATCH FAULT PATCH 

horizontal shear stress; middle plot, change in updip shear stress; bttom 

plot, change in normal stress. Coseismic slip was assumed to extend to 

20-km depth. Excumions at fault patches 26 and 43 in upper plot in figure 14A arise from discontinuities in slip estimates. Same sign conventions as in figure 4. 

Figure 14.4tatic-stress changes at 10-km depth after 1906 San Francisco earthquake on patches of (A) the San Andreas fault, (B) the Hayward 

fault, (0, the Calaveras fault, and (D) the San Gregorio fault, calculated 

by using simple model of 1906 rupture based on slip estimates of 

Thatcher (1975) and Thatcher and Lisowski (1987). Top plot, change in 
EARTHQUAm-INDUCED STATIC-STRESS CHANGES ON CENTRAL CALJFORNIA FAUL.TS F8 1 

become increasing inappropriate over time scales of tens 

or hundreds of years, during which nonelastic relaxation 

processes and off-fault nonelastic deformation could effectively change the stress distributions. 

SAN ANDREAS FAULT 

APPARENT COEFFICIENT OF FRICTION = 0.0 

mF"'"'"""'""""'""~ 

APPARENT COEFFICIENT OF FRICTION = 0.4 

mF""'"""'"""""""4 

APPARENT COEFFICIENT OF FRICTION = 0.8 

mk~""""""'""'"""'~ 

FAULT PATCH 

HAYWARD FAULT 

APPARENT COEFFICIENT OF FRICTION = 0.0 

APPARENT COEFFICIENT OF FRICTION = 0.4 

APPARENT COEFFICIENT OF FRICTION = 0.8 

FAULT PATCH 

Figure 15.-Estimated delay (positive values) or advance (negative values) in time to failure introduced by 1906 San Francisco earthquake on 

patches of (A) the San Andreas fault, (B) the Hayward fault, (0 the Calaveras fault, and (D) the San Gregorio fault, based on static-stress changes 

CALAVERAS FAULT 

APPARENT COEFFICIENT OF FRICTION = 0.0 

"""""" 

APPARENT COEFFICIENT OF FRICTION = 0.4 

APPARENT COEFFICIENT OF FRICTION = 0.8 

FAULT PATCH 

SAN GREGORIO FAULT 

APPARENT COEFFICIENT OF FRICTION = 0.0 

APPARENT QOEFFICIENT OF FRICTION = 0.4 

APPARENT COEFFICIENT OF FRICTION = 0.8 

FAULT PATCH 

calculated for 1906 San Francisco earthquake and on plate-tectonic-loading rates inferred from long-term slip rates listed in table 2, assuming 

apparent coefficients of friction p' of 0.0 (top plot), 0.4 (middle plot), and 

0.8 (bottom plot). 
TECTONIC PROCESSES AND MODELS 

PAIRED EARTHQUAKES 

ON THE SAN ANDREAS 

AND HAYWARD FAULTS? 

by a M=7 earthquake across the bay are not enough by 

themselves to generate a large earthquake-the fault must 

already be substantially loaded for triggering to occur. 

From our models, we estimate that static-stress changes 

PREREQUISITES FOR INTERACTIONS 

If large earthquakes on the San Andreas fault can trigger 

large earthquakes on the Hayward fault and vice versa, a 

preliminary loading stage is still required before such triggering can occur. Typical average stress drops in dislocation models of M=7 earthquakes are 20 to 40 bars, 

whereas the size of the stress change induced on the opposite side of San Francisco Bay by the 1989 Loma Prieta 

earthquake is at most a few bars. Thus, the stresses added 

from an M=7 earthquake might, at worst, trigger a second 

large earthquake on the other side of the bay that would 

have occurred anyway within ten or several tens of years. 

The occurrence of two earthquakes within a short timespan need not imply that one triggered the other at all. 

Reasenberg and Simpson (in press) point out that the 

crossbay-triggering hypothesis is not strongly supported 

by the existing historical record of earthquakes: The two 

pairings in the 1800's can be reasonably accounted for by 

randomly occurring, independent earthquakes. With this 

proviso in mind, we discuss below the geometry of the 

STATIC-STRESS CHANGE, IN BARS 

Figure 16.Ã‘Obliqu view of patches on the Hayward fault (left block) 

and the Calaveras fault (right block), showing changes in horizontal 

shear stress from 1905 to 2000. Values for 1905 are all zero, taking that 

as a reference year. Large changes appearing in 1910 after 1906 San 

Francisco earthquake are left lateral (blue) for both faults except at 

south end of the Calaveras fault. As plate-tectonic loading progresses 

(see text), right-lateral traction reloads sections of faults that had been 

relaxed. Effect of 1989 Loma Prieta earthquake is visible at 1990 on 

patches 97 and 98 as slight color changes. No provision was made for 

aseismic afterslip in this model, including aseismic creep on central 

California section of the San Andreas fault, and effects of all earthquakes other than 1906 and I989 are omitted. 
EARTHQUAKE-INDUCED STATIC-STRESS CHANGES ON CENTRAL CALIFORNIA FAULTS 

two historical pairings and consider how triggering might 

have occurred, if caused by static-stress changes. 

THE 1865168 PAIR 

In some scenarios, the 1865 earthquake would be an earlier version of the 1989 earthquake (Working Group on 

California Earthquake Probabilities, 1990). Here, the conclusions arrived at above regarding the triggering of an 

event on the southern section of the Hayward fault similar 

to the 1868 earthquake would still apply: The most obvious way to trigger an event on this section of the Hayward 

fault by static-stress changes would be through unclamp 

ing, which is most effective if coefficients of friction are 

high and pore-fluid pressure changes are small (or have 

had a chance to dissipate). This consideration suggests that 

the microseismicity rate along the southern section of the 

Hayward fault should be watched carefully for the next 

several years. 

Turtle and Sykes (1992) suggested that the 1865 earthquake was not a Lorna Prieta-type event but occurred on 

some other fault to the northeast of the San Andreas fault. 

Although we have performed no calculations for this 

eventuality, we expect that the results would be similar, 

especially if the 1865 earthquake occurred on one of the 

many reverse faults between the San Andreas and Hayward faults. Unclamping on the south end of the Hayward 

fault would probably once again be the best mode for triggering by static-stress changes. 

STATIC-STRESS CHANGE, IN BARS 

Figure 17.Ã‘Obliqu view of patches on the Calaveras fault, showing changes in horizontal shear stress after 1906. Effects 

of individual earthquakes after 1906 are omitted; each earthquake shown (M=5.1-6.5) would cause a small local relaxation 

if incorporated. Stress in red area at south end of fault would be relieved to some degree by aseismic creep on central 

California section of the San Andreas fault, which is also omitted. Earthquake magnitudes from table 1 of Oppenheimer 

and others (1990). from bottom to top: Md.5, 191 1 Morgan Hill; M=5.1, 1943 Alum Rock; M=5.2, 1949 Gilroy; M=5.5, 

1955 (no named location); M=5.9, 1979 Coyote Lake; M=6.2. 1984 Morgan Hill; M=5. I, 1988 Alum Rock. 
TECTONIC PROCESSES AND MODELS 

THE 1836/38 PAIR 

Even less is known about the locations and magnitudes 

of the 1836 and 1838 earthquakes (Ellsworth, 1990; Louderback, 1947; Lienkaemper and others, 1991). Most investigators suggest that the 1836 earthquake was an M=6- 

7 event on the northern section of the Hayward fault (for 

example, Lienkaemper and others, 199 1). The 1838 earthquake probably was also in the range M=6-7 and ruptured 

at least part of the peninsular section of the San Andreas 

fault. The northward and southward extents of the 1838 

rupture zone are quite uncertain. 

The static-stress changes calculated for a hypothetical 

1836-type event on the northern section of the Hayward fault 

are shown in figures 18 and 19. Right-lateral shear-stress 

increases near the north end of the San Francisco peninsula, 

and so nucleation might have occurred at this end, with the 

rupture progressing southward. The largest changes on the 

peninsula, however, occur in the normal component, and so 

unclamping might have triggered the 1838 rupture. One 

attractive aspect of the unclamping of normal stresses as a 

triggering mechanism is the built-in time delay if fluids are 

present. Full unclamping is attained only as the drained state 

is approached, a process that could take several years. 

SIMULATING FAULT INTERACTIONS 

Another reason for suggesting that unclamping might be 

more important than shear-stress changes comes from a 

simple interaction model based on the segmentation of 

bay-region faults proposed by the Working Group on California Earthquake Probabilities (1990). The model (fig. 

20) consists of large dislocations representing bay-region 

fault segments defined by the Working Group on California Earthquake Probabilities, plus a set of dislocations at 

depth under these segments that are forced to slip at observed long-term slip rates. The earthquake-prone segments were given strengths commensurate with the 

average recurrence intervals for characteristic earthquakes 

on these hypothetical segments. If the model is allowed to 

run through thousand of years of earthquakes and only 

shear interactions are accounted for, then earthquakes on 

the San Andreas and Hayward faults tend to alternate rather than to trigger each other. The reason for this "repulsive" behavior is that if the geometry is correct, an 

earthquake on one of two parallel faults tends to relax the 

shear stress on adjacent parts of the second fault (see Rybicki and others, 1985, fig. 2), thus retarding the next 

earthquake on the fault-pushing it farther into the future. 

Another model that includes normal-stress as well as 

shear-stress changes shows opposite behavior: Earthquakes 

on the two sides of San Francisco Bay tend to cluster in 

time. The reason for this clustering is that unclamping 

tends to advance the next earthquake, decreasing the interval between events. We] note that models incorporating 

normal-stress changes require some assumptions about the 

dissipation of this component over time. Although shear 

stress can be set equal to zero or some appropriate lower 

level after an earthquake, normal stress tends to keep accumulating in the models we have used, especially at fault 

bends. To avoid this bind, we simply required that the normal stress on a failed segment, as well as the shear stress, 

be reset to zero after an earthquake. A more realistic 

model would account for the nonelastic deformation occurring at such fault bends. 

Although these results are suggestive, the models are too 

simple to draw any definite conclusions. The use of long 

dislocations, with stress changes sampled at their centers, 

is also unrealistic because it can effectively insulate a 

model fault segment from the large stresses generated by 

an adjacent segment that has just slipped. 

CONCLUSIONS 

Static-stress changes calculated for central California 

faults at distances of 40 to 100 krn from the Loma Prieta 

rupture range from less than 0.1 bar to a few bars. These 

stress changes are large in comparison with the stresses 

generated by Earth tides (typical daily variations from 

about lo3 to lo2 bar) but commensurate with annual 

plate-tectonic-loading rates (typically, 0.1-0.3 barlyr for 

bay-region faults) and small in comparison with the average stress drops caused by M-7 earthquakes simulated in 

dislocation models (typically, 20-40 bars). 

,Calculated changes in CFF correlate with observed 

changes in microseismicity rates (Reasenberg and Simpson, 1992 and in press) and with measured surface creep 

rates (Galehouse, 1992 and in press). Low apparent coefficients of friction are favored by these correlations, suggesting that changes in normal stress are less important than 

b Figure 18.Ã‘Obliqu view of patches of central California faults, 

showing calculated static-stress changes induced by 1836 rupture of 

northern section of the Hayward fault (yellow patches) on other bayregion faults. Slip is 1 m on four 10-km-long by 13-km-tall patches, 

which approximately corresponds to an M4.8 earthquake. Top diagram, 

change in horizontal shear stress, where red indicates an increase and 

blue a decrease in right-lateral traction; middle diagram, change in updip 

shear stress, where red indicates an increase and blue a decrease in westside-up traction; bottom diagram, change in normal stress, where red 

indicates an increase in tension (unclamping) and blue an increase in 

compression (clamping). 
EARTHQUAKE-INDUCED STATIC-SWBSS CHANGES ON CENTRAL CALIFORNIA FAULTS 

123 

HORIZONTAL SHEAR STRESS IN BARS - 1836 

2 3 5 

UPDIP SHEAR STRESS. IN BARS - 1836 

12345 

NORMAL STRESS, IN BARS - 1836 
F86 TECTONIC PROCESSES AND MODELS 

changes in shear stress for triggering microearthquakes, at 

least until pore fluids have had enough time to reequilibrate. The low apparent coefficients of friction could be 

interpreted either as low rock friction (-0.2) or as normal 

rock friction (4.75) effectively decreased by pore-fluid 

pressure. 

We have explored the effect of nonvertical dips on some 

bay-region faults. A range in dip, both eastward and westward, on the Hayward and Mission faults (fig. 1) had no 

substantial effect on the conclusions arrived at for vertical 

orientations. One region adjacent to the San Gregorio fault 

HORIZONTAL-SHEAR-STRESS CHANGE 

2L.. 8 0 I................. . 1. .-I 

UPDIP-SHEAR-STRESS CHANGE 

NORMAL-STRESS CHANGE 

FAULT PATCH 

Figure 19.-Static-stress changes on the San Andreas fault corresponding 

to model of 1836 rupture shown in figure 18. Top plot, change in horizontal shear stress; middle plot, change in updip shear stress; bottom 

plot, change in normal stress. 

showed either a positive or negative change in CFF, depending on whether the fault was dipping or vertical. This 

result suggests that accurate dips on fault patches can be 

critical to correct CFF calculations. 

We have qualitatively investigated the possible longterm effects of aseismic slip in response to the 1989 

earthquake, first, for vertical faults at depths below the 

seismogenic layer and, second, on hypothetical horizontal 

detachment surfaces. Our models suggest that the resulting redistributions of load can alter the magnitudes of 

stress changes by as much as a factor of 2 in places on 

the bay-region faults studied but that such aseismic slip 

results in no important changes in the overall pattern of 

loading and unloading. 

Using estimates of the long-term slip rate for selected 

faults in central California, we calculated annual plate-tectonic-loading rates by using a simple dislocation model. 

By comparing these calculated annual stress changes with 

the Loma Prieta-induced stress changes, we can estimate 

by how many years future earthquakes on individual fault 

patches may have been advanced or retarded. Fault patches that were stressed closer to failure showed advances by 

as much as 30 yr; various relaxed fault patches showed 

retardations of nearly 50 yr. 

Similar calculations for the 1906 San Francisco earthquake suggest that most bay-region faults were relaxed by 

the static-stress changes accompanying this event. The 

segments of the Calaveras fault where M>5 earthquakes 

resumed in the 1940's are areas, in our models, that would 

recover soonest from this relaxation. Other bay-region 

faults may still be emerging from the 1906 relaxation 

shadow to the state of stress they were in just before 1906. 

The close pairing in time of earthquakes in 1836138 and 

1865168 on the San Andreas and Hayward faults raises the 

possibility of a major earthquake on the Hayward fault 

during the 1990's, although Reasenberg has demonstrated 

that given historical levels of seismicity, such pairings are 

likely to occur at random, without the aid of any physical 

triggering mechanism. In most of the models described 

Figure 20.Ã‘Geometr for interaction model based on segmentation of Mountains section of the San Andreas fault; 5, southern Santa Cruz 

bay-region faults proposed by Working Group on California Earthquake Mountains section of the San Andreas fault; 12, Rodgers Creek fault; 13, 

Probabilities (1990). 2, north-coastal section of the San Andreas fault; 3, northern section of the Hayward fault; 14, southern section of the Haypeninsular section of the San Andreas fault; 4, northern Santa Cruz ward fault. 
EARTHQUAKE-INDUCED STATIC-STRESS CHANGES ON CENTRAL CALIFORNIA FAULTS F87 

here, the Hayward fault is relaxed by the Loma Prieta 

rupture, arguing against any triggering by static-stress 

changes, except in the high-apparent-coefficient-of-friction 

models for which the south end of the Hayward fault becomes undamped, bringing it closer to failure. Although 

the correlations with microseismicity favor low-apparentcoefficient-of-friction models, these low apparent values 

could simply reflect pore-pressure effects temporarily 

masking a high coefficient of friction. 

If pore fluids are important, then the full impact of 

unclamping on the south end of the Hayward fault may 

become apparent over time only after the pore fluids have 

had a chance to reequilibrate. If so, then a possible triggered event on the Hayward fault during the 1990's cannot 

be ruled out. Monitoring microseismicity and surface 

creep rates at the south end of the Hayward fault for the 

next few years may yield some clues as to what is happening at depth. 

ACKNOWLEDGMENTS 

We thank Greg Beroza, Michael Lisowski, and Grant 

Marshall for providing detailed information about their 

slip distributions before they were published, and Ruth 

Harris and Ross Stein for helpful reviews. 

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THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAKEOCCUmNCE 

TEETONIC PROCESSES AND MODELS 

CUMULATIVE SLIP ALONG THE PENINSULAR SECTION 

OF THE SAN ANDREAS FAULT, CALIFORNIA, 

ESTIMATED FROM TWO-DMENSIONAL BOUNDARY-ELEmNT MODELS 

OF HISTORICAL RUPTURE 

CONTENTS 

By Paul Bodin and Roger Bilham, 

University of Colorado, Boulder 

page 

F91 

91 

93 

95 

97 

97 

98 

99 

100 

100 

ABSTRACT 

We use two-dimensional boundary-element methods to 

investigate the variation of slip along the San Andreas 

fault on the San Francisco peninsula during the period 

1800-1990. Faults are modeled in an elastic plate as frictionless, contiguous vertical cuts with the geometry of the 

mapped San Andreas system. Antisymmetric displacements are applied to edges of the elastic plate at azimuths 

corresponding to the relative plate motion between the 

North American and Pacific plates. Segments of faults corresponding to the locations of historical earthquakes since 

1800 are released sequentially to estimate the cumulative 

distribution of slip resulting from these earthquakes. Although the model slip distribution in the 1906 San Francisco earthquake agrees with the distribution inferred from 

geodetic data, slip and fault-normal convergence in the 

1989 Loma Prieta earthquake are underestimated by approximately 30 percent, suggesting that the failure strain 

may have been higher for this event. Another explanation 

for the underestimates may be that two-dimensional models do not adequately incoprate important three-dimensional boundary conditions, such as aseismic slip under 

the seismogenic layer. Our models suggest that the difference between the cumulative slip attributable to historical 

ruptures and the slip estimated from plate-tectonic motion 

in the San Francisco Bay region exceeds 1 m and in some 

places is as high as 3.5 m. Regions to the northwest and 

southeast of the Loma Prieta rupture zone currently exhibit 

the largest slip deficit, which may be sufficient to drive future M-6.5 earthquakes. Boundary-element models indicate 

that fault-normal convergence throughout the Santa Cruz 

Mountains reaches a maximum near the Loma Prieta rupture zone, where the amplitude of convergence may reach 

a third of the amplitude of dextral slip. This convergence is 

estimated to result in thickening of the crust at a rate of -2 

mrdyr as material is advected through the bend in the San 

Andreas fault where it traverses the Santa Cruz Mountains. 

INTRODUCTION 

Relative plate motion at the latitude of the San Francisco 

peninsula is partitioned among a system of faults ~onsisting 

of the single continuous San Andreas fault and apparently 

discontinuous fault strands represented by the Hayward, Calaveras, Rodgers Creek, and other faults. Geodetic and geologic data suggest that at this latitude, approximately 50 

percent of the total plate-boundary displacement is manifest 

on the principal trace of the San Andreas fault (Working 

Group on California Earthquake Probabilities, 1990). In this 

paper, we examine the spatial and temporal distribution of 

slip along the principal trace of the San Andreas fault between 

San Francisco and San Juan Bautista, Calif. (fig. 1). We 

assume a mean slip rate of 24 dyr on the fault north of 

San Francisco (Niemi and Hall, 1992) and examine the effect 

of the geometry of the San Andreas fatilt on the distribution 

of slip along strike to the southeast during an interval of 

approximately 200 yr. This interval, which represents the time 

period for which data on historical seismicity are available, 
F92 TECTONIC PROCESSES AND MODELS 

is equivalent in duration to the renewal time to generate 

1 906-size earthquakes from observed plate-boundary displacements. We assume that the strain field prevailing in 

1800 was uniform, although a complex strain field probably 

existed, generated by unknown prehistoric earthquakes and 

plate motions. As time progresses, the "memory" of this 

initial 1800 strain field decreases in importance. Because 

plate-boundary slip is distributed among several fault zones 

in the San Francisco Bay region, mutual interactions between 

fault segments affect the resulting slip rates on each segment. 

To estimate slip, we use boundary-element methods, which 

account explicitly for segment interactions that depend on 

the geometry of the fault system (Bilham and Bodin, 1992). 

Therefore, to estimate slip along the San Andreas fault, our 

models make use of information from other faults in the 

region, as well as from the San Andreas fault. 

Our goal in this paper is to estimate dextral-slip distributions for historical ruptures and for aseismic fault creep 

and to sum them to obtain the cumulative distribution of 

historical dextral slip along the San Andreas fault. Rupture 

data for earthquakes during the period 1800-1900 are not 

well established, and so our summations of cumulative 

slip and resulting slip deficits are somewhat speculative. 

Moreover, it is unclear whether the same failure conditions 

are applicable for all earthquakes on the San Francisco peninsula. We obtain some insight into this problem by constructing models that simulate the geodetically estimated 

slip distribution in the 1906 and 1989 earthquakes. 

To account for the influence of fault geometry and fault 

segmentation on slip in the Santa Cruz Mountains, we use 

the mapped fault trace as input in our elastic models. We 

digitized the mapped trace of the San Andreas fault from 

fault-strip maps (Sarna-Wojcicki and others, 1975) and 

simplified the mapped trace from the Golden Gate to San 

Juan Bautista as a set of 17 contiguous fault segments 

from 3.6 to 16.2 km long (Nishenko and Williams, 1985), 

with an average length of about 9.5 km (fig. 1; table 1). 

Where the surface breadth of the fault zone is greater than 

1 km, we determined a mean fault strike for all mapped 

strands of the fault. In subsequent analyses, we assume 

that historical earthquakes ruptured single segments or 

contiguous combinations of segments and that these ruptures terminated at bends between segments (King and 

Niibzlek, 1985). 

In the boundary-element models that follow, each fault 

segment is represented by a dislocation surface in a uniform elastic medium. The medium is assumed to be in a 

state of plane strain within which the vertical-strain components vanish. The model results simulate the response of 

frictionless vertical cuts in an elastic plate of uniform 

thickness (Bilham and King, 1989b). Seismicity suggests 

that the applicable elastic-plate thickness in the study area 

is approximately 10 km. Model results for isolated fault 

segments shorter than this assumed thickness would be invalid, and so the smallest isolated fault segment we used 

was approximately 12 km long (segment 16, fig. 1; table 

1). Rupture lengths used correspond to earthquakes of 

M26. The region is subjected to an antisymmetric dextralshear displacement at a mean azimuth appropriate to the 

Nuvel 1 pole of rotation for the North American and Pacific plates (N. 36' w.; DeMets and others, 1990). The 

effect of the change in azimuth along strike of the plate 

boundary due to the finite radius of the small-circle slipvector path is negligible. 

Figure 1.-San Francisco Bay region, Calif., showing locations of fault segments used in models. Segment numbers correspond 

to those listed in table 1. Segments 17 through 22 represent creeping section of the San Andreas fault south of San Juan 

Bautista. Arrows indicate direction of plate motion. 
CUMULATIVE SLIP ALONG THJ3 PENINSULAR SECTION OF 'IIE SAN ANDREAS FAULT 

Table 1 .-Model fault segments 

[See figure I for locations of segments. Origin of the coordinate system is lat 36.84' N., 121.54' W.; azimuth of the negative x-axis is N. 36' W. All coordinates in 

kilometers; angle of fault segment to plate vector in degrees anticlockwise from mean slip vector] 

-- -- 

starting starting ending ending Angle to 

Segment Name x-coordinate y-coordinate x-r.xmrdinate yardinate x-center y-center Length plate vector 

34 Southeast Glaveras extension- 25.50 -37.25 15.88 37.00 19.25 -1.50 

Combinations of fault segments that correspond to historical earthquake ruptures or creeping segments are permitted 

to slip freely (without friction) in response to imposed plateboundary displacements. The model yields the distribution 

of slip among those fault segments allowed to slip that 

minimizes the overall stress within the elastic plate. The 

resulting displacements, stresses, and strains within the region, including the strike-slip and fault-normal displacements along faults, are computed by using a two-dimensional 

boundary-element method (Crouch and Starfield, 1983; Bilham and King, 1989b). Freely slipping faults are simulated 

by displacement discontinuities with a zero tangential-shearstress constraint and a zero relative-normal-slip constraint. 

When a fault segment with fixed slip is used as a boundary 

condition, it is included as a single element with a specified 

relative displacement. Our models are thus free of the potential numerical artifacts in the boundary-element method 

described by Zeller and Pollard (1992). The slip distribution 

that results from subjecting a single uniform-stress-drop 

crack to antisymmetric shear is elliptical in form (for example, Crouch and Starfield, 1983). Therefore, slip is a maximum and varies smoothly and slowly at the center of the 

crack but decays rapidly to zero at each end (fig. 2). In our 

models for ruptures of historical earthquakes, we divide each 

dislocation segment into three to seven subelements, each 

with uniform slip, so that the computed slip distributions 

approximate this elliptical distribution of slip. 

STRAIN AT FAILUm 

Three parameters are important in determining the amount 

of displacement that occurs during the rupture of a vertical 

dislocation embedded within a uniform elastic plate subjected to applied shear strain: the length of the rupture, 

the azimuth of the rupture relative to the shear-strain field, 

and the magnitude of the strain at failure. If shear strain 

within the medium before the rupture is nonuniform, its 

spatial distribution influences the resulting slip. In our models, the mean slip on a rupture of length L subjected to 

uniform shear strain e is approximately d. Observed earthquake offsets, however, reveal almost a tenfold variation 
F94 TECTONIC PROCESSES AND MODELS 

in coseismic slip versus fault length (Slemmons, 1977; Bonilla and others, 1984); and the strain at failure, fault geometry, 

and frictional and dynamic effects clearly vary significantly 

among earthquakes. In the models that follow, we assume 

that the strain field which drives seismic rupture and creep 

is generated by relative plate motion and approximates simple shear at the azimuth of the plate slip vector (Lisowski 

and others, 1991). If friction and dynamic effects are ignored, 

numerical models of a dislocation of known length and 

orientation within the simple-shear plate boundary permit 

the magnitude of the applied strain field to be estimated 

from the magnitude of slip accompanying a rupture. Ruptures, however, take place on fault segments that interact 

with other previous ruptures and creeping fault segments, 

both of which alter the strain field. Our boundary-element 

models account for those interactions and allow us to explore 

hypotheses about the strain field from the distribution of 

slip among the ruptures in the plate boundary. Alternatively, 

if the strength and orientation of the applied strain field 

are known and the seismic history constrains estimates of 

the location of historical rupture and creep, we can account 

for the interactional effects among the faults and compute 

the distribution of slip on any given fault segment after a 

rupture. 

We apply this approach to the Santa Cruz mountains section of the San Andreas fault. The rupture lengths of earthquakes that are believed to have occurred in this region 

during the past 200 yr are plotted in figure 3. The locations 

and lengths of ruptures for pre-1906 events are speculative, 

and some may not even be on the San Andreas fault (for 

example, Tuttle and Sykes, 1992), but if we assume that the 

strain at failure is similar for all earthquakes in this region, 

we can estimate approximate slip distributions for these 

events. From these slip distributions, the cumulative slip 

along the fault may be summed to identify segments of the 

fault where slip may be overdue. 

The simplest assumption that can be made about failure is 

that all ruptures fail at approximately the same strain level. 

This assumption is motivated by the observation that scatter 

in the relation between slip and fault length for real earthA B 

Distance along fault 

Figure 2.-Coseismic displacements along a frictionless dislocation surface vary smoothly and slowly near its center and abruptly near its ends 

in an elliptical slip distribution. If rupture occurs in two separate events 

(lines AB, BC) instead of a single event (line AC), a slip deficit occum, 

especially near intersection of the two fault segments. 

quakes is commonly reduced by restricting the events included to those from a particular tectonic or geographic 

region (Slemmons, 1977; Bonilla and others, 1984). To test 

whether a single strain value at failure prevails in the Santa 

Cruz Mountains, we examine the distribution of slip during 

the 1906 and 1989 earthquakes. In our simple plate model, 

antisymmetric displacements (of hi m) are applied remotely from the fault. A shear-strain field of a given magnitude 

may be generated either by a large boundary displacement 

applied at a large distance or by a small displacement applied closer in. Displacements applied at &1,250 km were 

found to generate the slip distributions for both the 1906 

rupture and the creeping section of the San Andreas fault 

and to be consistent with known plate velocities. The magnitude of the shear-strain field (2d/2,500 microstrain) that 

best fits the observations is an estimate of the failure strain 

in each event. 

The 1906 and 1989 ruptures differ substantially in mechanism and may have occurred partly or completely on different faults. The most important geometric difference, 

apart from the length of the two ruptures, is the significant 

component of dip-slip motion during the 1989 earthquake 

(Segall and Lisowski, 1990). We simulate the dip-slip component of the 1989 earthquake in our two-dimensional 

models by permitting simultaneous convergence and dextral slip in the boundary-element specifications for these 

segments of the fault. We initially assume for simplicity 

that the 1906 and 1989 earthquakes occurred on the same 

fault but that convergence did not occur in the 1906 earthDISTANCE FROM SAN JUAN 

BAUTISTA, IN KILOMETE!RS 

Figure 3.-Space-time plot of moderate and large earthquakes on the San 

Francisco peninsula; horizontal lines indicate length of rupture. Locations 

of these events are poorly known and some may not have been on the 

San Andreas fault (Lindh and others, 1982; Working Group on California 

Earthquake Probabilities, 1990; L.R. Sykes, oral commun., 1992). Rupture lengths are adjusted to coincide with segment boundaries shown in 

figure 1 and listed in table 1. 
CUMULATIVE SLIP ALONG THE PENINSULAR SECTION OF THE SAN ANDREAS FAULT I35 

quake. The two ruptures are thus treated as isolated dislocations in an elastic plate and are both subjected to uniform 

shew-strain fields. In these tests, changes in the strain field 

caused by the earlier event are not applied to the later 

event. We find that to match geodetically observed displacements, the magnitude of applied strain for the 1989 

earthquake must be increased by a factor of 4 relative to the 

strain needed to model the 1906 earthquake. In figure 4 and 

table 2 (case I), we show strike-slip and fault-normal displacements on a model Loma Prieta rupture, assuming failure conditions similar to those of the 1906 rupture. Note 

that under these conditions, the synthetic 1989 displacements are smaller by a factor of 4 than estimates inferred 

from geodetic observations (case 9, table 2). 

This model, however, ignores several important changes 

in strain that occurred on the San Andreas fault system 

during the 1906 earthquake and in the following 83 years. 

There has been some debate concerning the existence of a 

significant slip deficit south of Black Mountain during the 

1906 earthquake (Scholz, 1985; Thatcher and Lisowski, 

1987). Our models agree well with geodetic estimates of 

slip in 1906 in this area (Bilham and King, 1989a; Segall 

and Lisowski, 1990). An elliptical decay of slip toward the 

south end of the 1906 rupture zone results in a reduction of 

slip on the fault relative to areas to the north. This slip 

Inferred 1906 slip 

DISTANCE FROM SAN JUAN BAUTISTA, 

IN KILOMErnRS 

Figure 4.-Synthetic and obsewed slip in 1906 San Francisco earthquake 

and synthetic slip in 1989 Loma Prieta earthquake versus distance from 

San Juan Bautista, Calif. (see fig. I), using similar plate-boundary geometry but with applied displacement increased by 83 years at a rate of 38 

mndyr inferred from geodetic data &isowski and others* 1991). Shaded 

area of curve shows range of slip predicted by 19% models normalized 

to maximum slips of 4 and 5 m, respectively7 on the San Andreas fault 

near Point Reyes (see fig. I)* about 180 km northwest of San Juan Bautista; vertical white lines are segment boundaries (bends in fault). Boxes, 

estimates for fault slip from geodetic obsewations (Thatcher and Lisowski7 1987); dots* surface obsewations of 1906 fault slip (Lawson, 1910). 

Synthetic dextral slip (patterned area) and fault-normal slip (black area) 

calculated for 1989 earthquake are evidently too small, suggesting that 

boundary conditions for 1906 and 1989 earthquakes differed, although 

limitations of two-dimensional modeling may also be responsible for 

some of the deficit. 

deficit influences the local strain field before the 1989 

earthquake. In the 83 years between the 1906 and the 1989 

ruptures, however, continued plate motion introduced additional strain. Strain was further concentrated in the Santa 

Cruz region because it is near the northwestward termination of steady-state creep on the San Andreas fault in central California. Moreover, strain on the San Francisco 

peninsula is presumably moderated by creep and seismic 

slip on the Calaveras and Hayward fault systems (fig. 1). 

We have included these effects on the strain field responsible for the modeled slip on the 1989 rupture in a succession 

of models (cases 2-6, table 2), which we discuss below. 

DEVELOPMENT OF 

THE STRAIN FIELD, 1906-89 

We first examine the development of strain during the 

period 1906-89. The full plate-displacement rate estimated 

from plate motions over the past several million years is 48 

Wyr (DeMets and others, 1990), which corresponds to 

plate-boundary displacements of 3.9 m during the 83 yr 

period since 1906. We believe, however, that more relevant 

estimates of the appropriate boundary displacements are 

provided by geodetic data obtained during the past two decades from a 100-lun-wide network on the San Francisco 

peninsula (Lisowski and others, 1991). These observations 

indicate that a displacement rate of 38 dyr is partitioned 

among faults in the San Francisco Bay region. The geodetic 

estimates correspond to 3.2 m of plate slip in 83 yr. In the 

following analysis, we use a strain increment of 32 microstrain (tensor shear) in 83 yr, derived from distributing the 

3.2 m of relative plate slip over the 100-km-wide zone of 

plate-boundary deformation observed by Lisowski and others (1991). Strain is increased in the Santa Cruz Mountains 

as a result of creep on the central California section of the 

San Andreas fault, which has its north end close to San 

Juan Bautista, and is influenced by creep and seismicity on 

the Hayward and Calaveras faults (fig. 1). To estimate the 

strain changes in the Santa Cruz Mountains, we assign appropriate offsets to these other faults, assuming that current 

creep rates have been constant for the past 83 yr. 

It is less obvious how to apply the strain field generated 

by the southward reduction of slip in the 1906 earthquake 

to models of subsequent ruptures in the Santa Cruz Mountains. We adopt the following strategy: We use the 1906 slip 

distribution in figure 4 for each segment of the San Andreas 

fault, except for those near Loma Prieta, as input to an 

elastic model in which we include the distribution of slip in 

the creep process south of San Juan Bautista (fig. 1). We 

then apply an antisymmetric shear strain similar to that 

used to best model the 1906 rupture (fig. 4) but increased 

by 32 microstrain (tensor shear), corresponding to 83 years 

of plate motion. In this model, slip is fixed on all segments 

of the fault except the Loma Prieta segments, which are 
TECTONIC PROCESSES AND MODELS 

Table 2.-Estimated slip from the 1989 Loma Prieta earthquake driven by different boundary conditions 

[Loma Prieta fault segments arc listed as segments 9 and 13 through 15 (fig. 1; table I)] 

Applied boundary Dextral Fault-normal Reverse slip on Reverse slip on 

Case conditions shear (cm) convergence (cm) 60' dipping fault 70' dipping fault 

Remote, suitable to reproduce 

slip of 1906 earthquake 

Remote, suitable for 1906 

earthquake plus 83 yr of plate 

motion 

Remote, plus 1906 earthquake 

and creep on the San Andreas fault, 

Remote, plus 1906 earthquake 

and creep on the San Andreas and 

east-bay faults 

Remote, plus modeled slip for 

1800,1838,1857,1860 

1890, and 1906 earthquakes, 

and creep on the San Andreas fault. 

No east-bay faults 

Remote, plus modeled slip for 

1800,1838,1857,1860 

1890, and 1906 earthquakes, 

and creep on the San Andreas fault, 

and east-bay faults Ill 

1989 on separate fault. 

Remote, plus modeled slip for 

1800,1838,1857,1860 

1890, and 1906 earthquakes, 

and creep on the San Andreas fault. 

No east-bay faults 

Slightly larger displacements are obtained if estimates of 

east-bay-fault displacements are excluded (case 3, table 2). 

The computed dextral slip is still less than observed, and 

fault-normal convergence is significantly larger than observed. If convergence occurred in 1906, it would reduce 

the value for 1989 convergence. Although geodetic data 

indicate that no convergence and, possibly, some extension 

may have occurred near Lorna Prieta in 1906 (Segall and 

Lisowski, 1990), triangulation points were not densely distributed in 1906, and off-fault convergence may have occurred undetected by the historical network. 

1989 on separate fault. 

Remote, plus modeled slip for 

1800,1838,1857,1860 

1890, and 1906 earthquakes, 

and creep on the San Andreas fault, 

and east-bay faults 

Inferred from geodetic 

data (Lisowski and others, 1990). 150 41 -- 120 

allowed to slip freely in both shear and fault-normal direction. That is, slip in the Loma Prieta region plotted in figure 

4 is driven both by displacement on contiguous fault segments and by applied displacements due to relative plate 

motion. The resulting estimate for fault-normal and dextral 

slip on the Loma Prieta segments exceeds the estimates we 

seek for 1989 slip by the amount that this section of the 

fault slipped in 1906. Subtraction of the 1906 synthetic 

displacement plotted in figure 4 from the total synthetic 

displacement yields 36 and 64 cm, respectively, for synthetic fault-normal and dextral slip in 1989 (case 4, table 2). 
CUMULATIVE SLIP ALONG THE PENINSULAR SECTION OF THE SAN ANDREAS FAULT F97 

DEVELOPMENT OF 

THE STRAIN FIELD, 1800-1989 

The calculations above assume that no slip occurred on 

the San Andreas fault before 1906; however, slip in the 

1906 event was driven by plate-boundary strains modified 

by earlier ruptures on or near the fault. We thus proceed to 

estimate slip in these earlier events and to estimate their 

contribution to cumulative slip. The seismic history of the 

San Francisco Bay region is probably complete to M-6 

since 1850 and to higher magnitudes since about 1800 

(Ellsworth, 1990). In this paper, we limit our consideration 

to the 189-year period from 1800 to the 1989 earthquake, 

with reasonable confidence that no large earthquakes have 

been ignored. Large earthquakes occurred in the region in 

1838 and 1865, and smaller earthquakes in 1800 and 1890 

(Lindh and others, 1982; Working Group on California 

Earthquake Probabilities, 1990; Tuttle and Sykes, 1992). 

Locations and rupture lengths for these events are poorly 

constrained by observation. Using historical records of 

damage and felt reports to constrain the magnitudes and 

locations of 19th-century events, Tuttle and Sykes concluded that the 1865 and 1890 earthquakes may not have 

ruptured the San Andreas fault; instead, they may have 

originated on faults close to but northeast of the San Andreas fault. Tuttle and Sykes also concluded that the 1838 

earthquake ruptured the San Andreas fault on the San 

Francisco peninsula northwest of and, possibly, including 

the Loma Prieta segment. These sparse observations, however, do not require the Loma Prieta segment to be included in the 1838 rupture. The rupture lengths and locations 

we use for 19th-century earthquakes differ somewhat from 

those presented by Tuttle and Sykes. We model the 1865 

and 1890 earthquake as ruptures on the San Andreas fault 

because even if they were off the fault, they were near 

enough that the volume of crustal strain release would 

have included the San Andreas fault. We model the 1838 

earthquake as a rupture abutting the Loma Prieta segment 

to the northwest. As discussed below, including the Loma 

Prieta segment in our models of the 1838 earthquake 

would nearly double its length and therefore approximately double the slip in our model of the 1838 rupture. Given 

these uncertainties, we model the 1800, 1838, and 1865 

earthquakes as simple dislocation offsets on the mapped 

trace of the San Andreas fault, with locations and lengths 

corresponding to multiples of the segments shown in figure 1. We assume that creep in central California occurred 

in the 18th and 19th centuries at rates similar to those 

today, although we recognize that the 1857 Fort Tejon and 

1906 San Francisco earthquakes may have changed or 

even initiated the creep process. 

We augment the strain field responsible for the slip plotted in figure 4 with strain resulting from creep on the fault 

to the south and with strain associated with the 1857 mpture for subsequent events. Under these conditions, the 

maximum modeled slip in these earlier events did not exceed 12, 65, and 40 cm, corresponding to model earthquakes of M=6, 6.8, and 6.6, respectively. The slip from 

these earthquakes is clearly small in comparison with the 

inferred slip during the 1906 rupture. We note, however, 

that the assumptions used in modeling these early historical 

ruptures are similar to those that yield apparent underestimates of slip for the 1989 earthquake, and we acknowledge 

that our model may underestimate the slip in these early 

events. We added modeled slip from these earlier ruptures 

to the modeled slip of the 1906 earthquake to obtain a more 

realistic pre-1989 slip distribution, but we did not attempt 

to estimate the influence of the pre-1906 strain field on the 

1906 rupture. Using the cumulative 1800-1906 slip distribution derived above increases the synthetic dextral slip for 

the 1989 earthquake to more than 1 m, with a ratio of 

convergence to shear of approximately 2 to 5 (cases 5, 6, 

table 2). These results underestimate the observed dextral 

displacements by about 30 percent but are close to the observed values for fault-normal convergence. 

We also performed a series of experiments in which an 

isolated fault, parallel and 5 krn SW. of the San Andreas 

fault, with the same location and length as those of the 

Loma Prieta rupture, was allowed to slip freely in shear 

and convergence. This fault approximates a source region 

off the San Andreas fault for the 1989 earthquake (for example, Segall and Lisowski, 1990). In these experiments, 

we imposed plate-boundary displacements equivalent to 

189 years of plate motion, and assigned the cumulative 

synthetic displacements inferred for all pre-1989 earthquakes on the San Andreas fault since 1800. The resulting 

dextral slip on the new fault was less than that for an 

equivalent-length mpture on the San Andreas fault. Mean 

synthetic dextral slip was approximately half that indicated 

by geodetic measurements in 1989 (cases 7, 8, table 2). 

SLIP DEFICIT 

ON THE SAN FRANCISCO PENINSULA 

Our models yield estimates for dextral slip in 1989 that 

are approximately 30 percent smaller than that observed. 

Uncertainties associated with preceding earthquake slip 

distributions may also be partly responsible for this discrepancy. For example, increased rupture length, change in 

location, or different style or amount of slip on the 1838 

rupture would tend to increase the synthetic slip we would 

calculate for a 1989 rupture, as would incomplete slip in 

the Loma Prieta region in 1865. Another plausible explanation is that the failure strain for reverse-slip earthquakes 

in the Santa Cmz Mountains (fig. 1) is greater than for 

pure-strike-slip earthquakes on faults of the San Andreas 

system. Also, the simplifications necessary in our two-dimensional approach may result in the discrepancy between 

synthetic and observed slip. 
F98 TECTONIC PROCESSES AND MODELS 

Despite the underestimated slip in 1989, our models 

clearly indicate that the 1989 earthquake occurred in a region of slip deficit and that smaller slip deficits still remain 

(fig. 5). In particular, small regions to the northwest and 

southeast of the Loma Prieta rupture zone appear overdue 

for additional slip. The lengths of these regions and the 

amplitude of the current slip deficit permit us to forecast 

probable magnitudes for future events. The upper surface of 

the black area in figure 5 represents the slip that would 

occur in our models on the San Andreas fault if it were to 

slip freely as a throughgoing fault terminating at San Juan 

Bautista (fig. 1). We consider this to be the potential slip 

developed on the fault since 1800. The slip distribution on 

the San Andreas fault is dictated by the geometry of the 

fault and the influence of slip on east-bay faults. The mean 

slip of more than 6 m is less than the 9.2 m of plateboundary slip since 1800 because some slip takes place on 

other faults within the plate boundary, and less than the 

7.3 m anticipated for the San Francisco Peninsula from current geodetic rates, presumably owing to slip on minor 

faults and off-fault folding. The gray areas in figure 5 show 

the cumulative synthetic slip associated with seismic and 

aseismic slip during the period 1800-1990. For the area 

south of San Juan Bautista we assume that the creep rate at 

the center of the creeping zone is 38 dyr, equal to the 

slip rate indicated by the current velocity field (Lisowski 

120 100 80 60 40 20 0 20 

DISTANCE FROM SAN JUAN BAUTISTA, 

IN KILOMETERS 

Figure 5.Ã‘Cumulativ slip from earthquakes and creep in the Santa 

Cruz Mountains (see fig. 1) since 1800. Upper dashed line, slip on the 

San Andreas fault since 1800 if slip were frictionless and continuous, 

driven by current plate-boundary displacements; lower shaded areas, estimated dextral slip from earthquakes and creep for period 1800-1906. For 

1989 earthquake, we use mean slip inferred from geodetic data (1.5 m; 

Lisowski and others, 1990). Black area above gray areas of cumulative 

slip represents current deficit of dextral slip, assuming that slip deficit in 

1800 was negligible. 

and others, 1991). The black area in figure 5 indicates the 

slip deficit-slip that has yet to occur on the fault. 

The mean slip deficit in figure 5 is approximately 1.5 m, 

but locally as much as 3.5 m of slip appears to be pending 

near San Juan Bautista, and as much as 2.5 m of slip may 

be overdue northwest of Loma Prieta (fig. 1). The upper 

bound of the potential slip area may be too high if we have 

underestimated slip on the adjoining Calaveras fault system or other faults in the region (fig. 1). The discrepancy 

between the mean slip on the fault and the upper bound for 

potential slip can be reconciled by assuming that approximately 10 dyr of dextral slip is absorbed outside the 

study area, lowering the mean slip deficit to leave small 

regions northwest and southeast of Loma Prieta. If these 

regions were to be filled now by earthquakes, their maximum rupture lengths would be 20 to 40 krn, with mean 

slips of more than 50 cm, corresponding to earthquakes in 

the range M=6.3-6.7. We note, however, that cumulative 

plate-boundary displacements exceed 7.5 m if the recent 

geodetic plate-boundary slip rate of 38 dyr on the 

southern San Francisco peninsula is extrapolated for the 

past 200 yr. Because it is unlikely that we are missing historical M>7 earthquakes in this period, the mean slip deficit indicated in figure 5 is probably applicable. 

FAULT-NORMAL SHORTENING 

IN THE SANTA CRUZ MOUNTAINS 

Intuitively, the slip on a throughgoing transform fault 

must be uniform along strike. Our models, however, indicate that a fault with complex geometry will generally exhibit reduced strike slip where the strike of the fault 

differs from the applied plate-slip direction (Bilham and 

King, 1989a). The resulting slip deficit results in fault-norma1 displacements that are manifest in thrust faulting and 

uplift in such a region as the Santa Cruz Mountains, where 

the fault undergoes transpression, and in normal faulting 

and subsidence in regions of transtension (Bilham and 

King, 1989b). Over geologic time, the fault geometry will 

change to more efficiently accommodate slip on the fault. 

We proceed to quantify the amplitude of fault-normal 

convergence that accompanies dextral slip on the peninsular section of the San Andreas fault. North of San Francisco, the fault approximately parallels the plate-slip vector 

(Bilham and Hurst, 1988), whereas south of San Juan 

Bautista (fig. 1) it is 6O oblique to it. The geometry of the 

San Andreas fault in the transition zone is a gentle Scurve, resulting in a reduction of strike slip accompanied 

by fault-normal convergence. If the fault zone were infinitely compliant, this fault-normal convergence would result in the extrusion of material from the fault zone. In 

practice, advection through the Santa Cruz Mountains results in uplift of a broad area (Anderson, 1990). 
CUMULATIVE SLIP ALONG THE PENINSULAR SECTION OF THE SAN ANDREAS FAULT F99 

To determine the maximum fault-normal convergence 

driving uplift and reverse faulting, we model the fault as a 

vertical, infinitely compliant dislocation and subject it to 

antisymmetric plate-boundary displacements, as before. 

The applied strain is adjusted to cause the central part of 

the 1906 rupture zone north of San Francisco to slip about 

5 m, which would take approximately 200 years if the 

fault slipped steadily (Niemi and Hall, 1992). The fault in 

these models is frictionless along strike and is permitted to 

close without friction, a process whose deformation field 

may be envisaged as the opposite of that resulting from 

dike injection. The boundary-element model yields an estimate of dextral and fault-normal slip in each fault segment 

(fig. 6). Dextral slip is approximately 4.6 m near the Loma 

Prieta segment, whereas maximum convergence is about 

1.3 m, leading to a ratio of dextral slip to convergence of 

approximately 3 to 1. From geodetic modeling, dextral 

slip during the 1989 earthquake was 1.5M.3 m, and reverse slip 1.LW.3 m, on a 70' dipping fault plane (case 9, 

table 2, Lisowski and others 1990) representing a ratio of 

dextral slip to convergence of about 3.75, with a range of 

uncertainty from 2.4 to 6. Thus, the rake of the 1989 

earthquake is similar to that expected if relative plateboundary displacements within the Santa Cruz Mountains 

(fig: 1) were entirely accommodated by ruptures of highangle-fault planes. Accounting for the dip of the Loma Prieta rupture, the fault-normal component of convergence 

during the 1989 earthquake was approximately 0.4 m. The 

difference between the convergence observed in the 1989 

earthquake and the 1.3 m indicated in figure 6 suggests 

that an additional 0.9 m of convergence remains, or has 

already occurred in previous events since 1800. In the 

1906 earthquake, however, convergence was not observed 

geodetically (Segall and Lisowski, 1990). We conclude 

that fault-normal convergence may have been accornrnodated by slip in earlier events or manifested as regional 

contraction within the southern Santa Cruz Mountains during the 1906 earthquake, but not well sampled by the distribution of geodetic control points. Off-fault folding and 

complex processes leading to crustal thickening must play 

a significant role in the morphologic development of the 

Santa Cruz Mountains, because reverse faulting tends to 

generate antisymmetric uplift and subsidence features unrepresentative of the current morphology of the range. 

DISCUSSION 

Our two-dimensional uniform-thickness elastic-plate 

model is adequate to estimate the broad features of deformation on the San Francisco peninsula because our 

models yield estimates for slip on faults within the body 

of the Santa Cruz Mountains (fig. l), whether these faults 

are contiguous segments of a single throughgoing fault or 

isolated segments. In studies of slip in specific historical 

events, the boundary-element method yields reasonable estimates for slip as long as faults are assigned reasonable 

azimuths and lengths. Moreover, this method permits the 

effect of interactions of fault segments with each other and 

with the causative strain field to be explicitly accounted 

for in the regional deformation. Slip during the Loma Prieta rupture was on an inclined fault, and the earthquake had 

Figure 6.-Dextral and fault normal displacements on the San Andreas fault through the Santa Cruz Mountains (see fig. 1 for locations) on a transverse Mercator projection centered on North American/Pacific pole of 

rotation. Length of white arrows indicates mean fault-normal convergence calculated for each fault segment; 

black arrows indicate average dextral slip at three points along fault. The Hayward and Calaveras fault zones 

do not slip in this model; maximum convergence occurs near Loma Prieta and is approximately a third of 

dextral-slip component. 
F100 TECTONIC PROCESSES AND MODELS 

a greater hypocentral depth relative to regions to the south 

(U.S. Geological Survey staff, 1990), suggesting that the 

rupture may have taken place within a plate of relatively 

increased thickness. Our method, however, yields estimates for mean dextral slip and convergence that are within 30 percent of those observed. 

The mean slip deficit along the peninsular section of the 

San Andreas fault (fig. 5) is surprisingly large; however, 

the size of the deficit reflects the fact that 86 yr (1906 to 

1992) represents a significant fraction of the renewal time 

between great 1906-type earthquakes (Niemi and Hall, 

1992). The cumulative slip distribution reveals regions of 

enhanced slip deficit to the northwest and southeast of the 

Loma Prieta rupture zone. The larger of these two regions 

of slip deficit is to the southwest, where an increase in 

creep rate has been reported near San Juan Bautista (fig. 

1) since the 1989 earthquake (Behr and others, 1990; 

Sylvester and others, 1990). Creep rates would have to increase to 2 cmlyr for about 50 to 75 yr to alleviate the 

current deficit in this region and thus would have to more 

than double to accommodate this deficit and the applied 

slip budget. Therefore, current increased surface slip rates 

are inadequate to relieve the slip deficit southeast of Loma 

Prieta (fig. 1). If the 1838 earthquake ruptured the Loma 

Prieta segment (Tuttle and Sykes, 1992), our estimate of 

the slip deficit on the peninsular section of the San Andreas fault would be reduced by approximately 80 cm, significantly reducing the inferred slip deficit northwest of the 

Loma Prieta rupture zone. 

The rate of convergence implied by the ratio of dextral 

slip to convergence in figure 6 is approximately 8 rnmlyr. 

Uniform distribution of this convergence across a 10-kmthick, 40-km-wide region would result in a crustal-thickening 

rate of 2 rnrnlyr, approximately 4 times the rate estimated 

from the elevation of coastal terraces (Segall and Lisowski, 

1990). We note, however, that the uplift rate is likely to be 

concentrated away from the coast in regions close to the fault 

and that isostatic adjustment will reduce this uplift rate. If 

we assume a mean slip rate of 24 mmlyr, the time taken for 

material to pass the fault bend is approximately 4 m.y. At a 

mean thickening rate of 2 mmlyr, this amount of slip would 

increase the thickness of the plate to 18 krn, consistent with 

observed seismicity and models for advection in the region 

(Anderson, 1990). 

CONCLUSIONS 

The 1989 Loma Prieta earthquake occurred on a part of 

the San Francisco peninsula where a dextral-slip deficit 

evidently existed before the event. The summation of slip 

in earlier events and the 1989 earthquake suggests that 

smaller deficits remain to the northwest and southeast of 

the Loma Prieta rupture zone, which could be the locus of 

future M<6.7 earthquakes, and that a substantial slip deficit may exist along most of the peninsula. The mean slip 

deficit on the San Andreas fault in the San Francisco Bay 

region exceeds 1.5 m, and locally the deficit is inferred to 

exceed 3.5 m. If the 1838 rupture included the Loma Prieta segment (Tuttle and Sykes, 1992), then the slip deficit 

to the northwest of the Loma Prieta rupture zone would be 

reduced by approximately 80 cm, resulting in the slip deficit in this region being the lowest on the peninsula. Creep 

occurring to the southeast of the Loma Prieta rupture zone, 

representing extended activity on the northwest end of the 

creeping section of the fault, is inadequate to relieve the 

slip deficit southeast of Loma Prieta (fig. 1). The absence 

of significant surface slip suggests that the potential for 

future earthquakes in this region remains high. 

Fault-normal convergence is a characteristic of deformation in the Loma Prieta region. The amount of convergence 

during the 1989 event was consistent with the component of 

dextral convergence expected from fault geometry. We estimate that over geologic time, this convergence results in 

crustal thickening at a rate of approximately 2 rnmlyr, consistent with observed depths of seismicity and rates of coastal 

uplift. 

One assumption in our models was that the pre-1800 

strain field was uniform, a consequence of our current ignorance concerning prehistoric earthquakes. Some idea of 

the inadequacies of this assumption may be obtained from 

the complex slip deficit that we calculated for events since 

1800 (fig. 5). 

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. 

Behr, Jeff, Bilham, Roger, Bodin, Paul, Burford, R.O., and Biirgmann, 

Roland, 1990, Aseismic slip on the San Andreas fault south of 

Loma Prieta: Geophysical Research Letters, v. 17, no. 9, p. 1445- 

1448. 

Bilham, Roger, and Bodin, Paul, 1992, Fault zone connectivity; slip rates 

on faults in the San Francisco Bay area, California: Science, v. 258, 

no. 5080, p. 281-284. 

Bilham, Roger, and Hurst, Kenneth, 1988, Relationships between fault 

zone deformation and segment obliquity on the San Andreas Fault, 

California: China-U.S. Symposium on Crustal Deformation and 

Earthquakes, Beijing, 1988, Proceedings, p. 5 10-524. 

Bilham, Roger, and King, G.C.P., 1989a, Slip distribution and oblique 

segments of the San Andreas Fault, California; observations and 

theory, in Schwartz, D.P., and Sibson, R.H., eds.. Proceedings of 

Conference XLV; a workshop on fault segmentation and controls of 

rupture initiation and termination: U.S. Geological Survey OpenFile Report 89-315, p. 80-93. 

1989b, The morphology of strike slip faults: examples from the 

San Andreas fault, California: Journal of Geophysical Research, 

v. 94, no. B8, p. 10204-1 021 6. 

Bonilla, M.G., Mark, R.K., and Lienkaemper, J.J., 1984, Statistical relations among earthquake magnitude, surface rupture length, and surface fault displacement: Seismological Society of America Bulletin, 

v. 74, no. 6, p. 2379-241 1. 

Crouch, S.L., and Starfield, A.M., 1983, Boundary element methods in 

solid mechanics: Winchester, Mass., Allen and Unwin, 322 p. 
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DeMets, Charles, Gordon, R.G., Argus, D.F., and Stein, Seth, 1990, Current plate motions: Geophysical Journal International, v. 101, no. 2, 

p. 425-478. 

Ellsworth, W.L., 1990, Earthquake history, 1769-1989, chap. 6 of Wallace, R.E., ed., The San Andreas fault system, California: U.S. Geological Survey Professional Paper 15 15, p. 153-1 87. 

King, G.C.P., and Nibelek, J.L., 1985, Role of fault beds in faults in the 

initiation and termination of earthquake rupture: Science, v. 228, 

no. 4702, p. 984-987. 

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1906, report of the State Earthquake Investigation Commission: 

Carnegie Institution of Washington Publication 87, 2 v. 

Lindh, A.G., Moths, B.L., Ellsworth, W.L., and Olson, J.A., 1982, Historic seismicity of the San Juan Bautista, California region, in 

Hill, D.P., and Nishimura, Keiji, chairmen, Proceedings of the 

Second Joint Meeting of the U.S.-Japan Conference on Natural 

Resources (UJNR) Panel on Earthquake Prediction Technology, 

July 13-17, 1981: U.S. Geological Survey Open-File Report 82- 

180, p. 45-50. 

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

1990, Geodetic estimate of coseismic slip during the 1989 Lorna 

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

no. 9, p. 1437-1440. 

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. 8360-8389. 

Nishenko, S.P., and Williams, P.L., 1985, Seismic hazard estimate for the 

San Jose-San Juan segment of the San Andreas fault; 1985-2005, in 

Shearer, C.F., ed., Minutes of. the National Earthquake Prediction 

Evaluation Council, July 26-27, 1985, Menlo Park, California: U.S. 

Geological Survey Open-File Report 85-754, p. 351-366. 

Niemi, T.M., and Hall, N.T., 1992, Late Holocene slip rate and recurrence of great earthquakes on the San Andreas fault in northern California: Geology, v. 20, no. 3, p. 195-198. 

Sarna-Wojcicki, A.M., Pampeyan, E.H., and Hall, N.T., 1975, Recent active breaks along the San Andreas fault between the central Santa 

Cruz Mountains and the southern Gabilan Range, California: U.S. 

Geological Survey Miscellaneous Field Studies Map MF-650, scale 

1 :24,000. 

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 Michael Lisowski, 1990, Surface displacements in the 

1906 San Francisco and 1989 Loma Prieta earthquakes: Science, 

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

Slemmons, D.B., 1977, State-of-the-art for assessing earthquake hazards 

in the United States; faults and earthquake magnitude: U.S. Army 

Corps of Engineers, Waterways Experiment Miscellaneous Paper S3-73-1, Report 6, 166 p. 

Sylvester, A.G., Burford, R.O., and Schulz. S.S., 1990, Almost no surface 

displacement occurred at San Juan Bautista as a result of the Loma 

Prieta earthquake [abs]: Eos (American Geophysical Union Transactions), v. 71, no. 8, p. 290. 

Thatcher, Wayne, and Lisowski, Michael, 1987, Long-term seismic potential of the San Andreas fault southeast of San Francisco: Journal 

of Geophysical Research, v. 92, no. B6, p. 4771-4784. 

Tuttle, M.P., and Sykes, L.R., 1992, Re-evaluation of several large historic earthquakes in the vicinity of the Loma Prieta and peninsular 

segments of the San Andreas fault, California: Seismological Society of America Bulletin, v. 82, no. 4, 1802-1 820. 

U.S. Geological Survey staff, 1990, The Loma Prieta, California, earthquake; an anticipated event: Science, v. 247, no. 4940, p. 286-293. 

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THE LOMA PRIETA, CALIFORNIA, EARTHQUAKE OF OCTOBER 17,1989: 

EARTHQUAKE OCCURRENCE 

TECTONIC PROCESSES AND MODELS 

THREE-DIMENSIONAL LITHOSPHERIC KINEMATICS 

IN THE LOMA PRIETA REGION, CALIFORNIA: 

IMPLICATIONS FOR THE EARTHQUAKE CYCLE 

CONTENTS 

By Kevin P. Furlong and David Verdonck, 

Pennsylvania State University 

ABSTRACT 

The earthquake has served as powerful motivation to improve our understanding of the kinematic and dynamic behavior of the boundary between the North American and 

Pacific plates in the San Francisco Bay region. We combine 

investigations of the plate-boundary evolution, the kinematics of crustal and lithospheric components of the system, and 

three-dimensional finite-element modeling of the deformational behavior of the region to evaluate the causality of the 

earthquake. Our modeling tests the implications of a proposed plate-boundary structure that includes a viscously deforming, horizontal shear zone in the lower crust connecting 

the Santa Cruz Mountains and peninsular sections of the San 

Andreas fault with east-bay (Hayward, Calaveras) faults and 

the plate-bounding shear zone within the lithospheric mantle. 

Inclusion of this plate-boundary structure is motivated by 

the results of studies of plate-boundary evolution, geodetic 

observations of crustal deformation, and modeling of faultsegment geometries. The results of our study indicate that 

the 1989 Loma Prieta earthquake may represent decoupling 

of the Santa Cruz crustal block from its underlying mantle 

in response to stress accumulation after such events as the 

1906 San Francisco earthquake. Inclusion of a middle- to 

lower-crustal detachment surface in the modeling significantly changes the crustal-stress regime in comparison with purely 

elastic crustal models, allows more efficient transfer of stress 

among the fault segments in the Loma Prieta region, and 

provides a mechanism to increase stress on the peninsular 

section of the San Andreas fault consistent with the occurrence 

of major earthquakes on that section. Observations of transient stress and crustal deformation resulting from the 1989 

earthquake during coseismic and 10- to 20-year postseismic 

periods can distinguish among various proposed plate-boundary models of the region. Combination of these observations 

with modeling studies provides a strong discriminant of the 

geometry and rheology of the plate boundary in the Santa 

Cruz Mountains and San Francisco Bay region. 

INTRODUCTION 

The earthquake drew immediate attention to the power and 

effects of plate-tectonic processes. It clearly demonstrated 

the inherent complexity in tectonic processes along a boundary of lithospheric plates and reminded us of the need to 

expand our understanding of these complexities if we hope 

to improve our abilities to assess future hazards from earthquakes along the San Andreas fault system. In particular, it 

is becoming clear, as a result of both the faulting characteristics of the earthquake and other studies, that the threedimensional geometry of the Pacific-North American plate 

boundary is not nearly as simple as that typically shown for 

transform plate boundaries. The three-dimensional complexity of the plate boundary in the Loma Prieta region is the 

expected result of the thermal-mechanical evolution of this 

plate boundary (Furlong and others, 1989; Furlong, 1993). 

One key ingredient in our understanding of the causality of 

the earthquake is knowledge of the plate-boundary structure, 

its evolution, the consequences of this structure for crustal 
F104 TECTONIC PROCESSES AND MODELS 

and lithospheric kinematics, and the connections between 

plate kinematics and the earthquake cycle. 

Most studies of the dynamics of the San Andreas fault 

system either have used predictions of regional relative 

plate motions, given in part by global models (for example, 

Minster and Jordan, 1978; DeMets and others, 1990), or 

have focused on the kinematic information contained in 

regional seismicity. Global models provide information on 

the large-scale components of relative plate motions but do 

not attempt to be directly applicable to investigations of the 

length scale appropriate for the Loma Prieta region. Kinematic studies provide detailed information on deformationa1 behavior in the upper seismogenic crust but little 

information on the coupling between upper-crustal deformation and large-scale plate-tectonic processes. In this 

study, we focus on this link between seismogenic processes 

in the upper crust and the broader deformation associated 

with plate tectonics. 

The 1989 Loma Prieta earthquake is more than a simple 

manifestation of plate-tectonic processes; it is also a tool 

that has sampled the properties of the regional lithosphere 

in various ways. Most direct is the information that the 

earthquake provided on crustal structure (both lithologic 

and seismic velocity). Less obvious but no less important is 

the sampling of the rheologic properties of the lithosphere. 

Some of this rheologic sampling occurred with the earthquake itself and has helped map the depth of transition 

from brittle to ductile modes of deformation (Furlong and 

Langston, 1990), the spatial extent of aseismic fault rupture, and the coseismic deformational response of the crust 

(for example, Marshall and others, 1991). Potentially more 

important in addressing questions of future earthquake hazards in the San Francisco Bay region is the information that 

the earthquake will allow us to gather on the transient response of the plate-boundary system to seismic events. 

With this information, we can better constrain the role of 

lithospheric rheology in the earthquake cycle. Many of 

these data will be gathered during the next 10 to 20 years, 

allowing postseismic transients driven by the seismic loading of the earthquake to constrain models of lithospheric 

rheology and plate-boundary structure. Although such data 

were not immediately available after the earthquake, such 

modeling studies as ours and the others described in this 

chapter help to identify observational strategies that can test 

the possible implications for the earthquake cycle. 

The applicability of earthquake-hazard evaluations to the 

San Francisco Bay region will depend on the completeness 

of the earthquake-cycle models used. The degree to which 

seismic activity along one segment of the San Andreas fault 

system in the region affects the earthquake cycle on other 

segments is at present unclear. Historical patterns of large 

earthquakes in the region hint at earthquake pairing between the San Andreas and east-bay faults (Ellsworth, 

1990). Although the historical record is far too short to be 

rigorously tested, modeling studies of the role plate-boundary structures may play in producing particular patterns of 

earthquake occurrence can provide needed constraints on 

estimating the possible consequences of the 1989 earthquake for other fault segments in the region. 

In this study, we address each of the issues described 

above. First, we describe the plate-tectonic evolution of the 

Loma Prieta region and the implications of this evolution 

for details of the three-dimensional plate-boundary structure in the region and the rheology of the plate boundary 

itself. Next, we investigate the kinematics of the crust-mantie system in the region and the role Loma Prieta-type 

events play in this kinematic regime. Finally, using the 

framework provided by analyses of the plate-tectonic evolution and crust-mantle kinematics, we investigate, using 

finite-element modeling, the time-varying three-dimensional stress and strain regimes during simulated earthquake 

cycles in the region. This last issue provides important constraints on the nature of stress transfer in the region and 

points up characteristics of the strain field that are diagnostic of details of the proposed plate-boundary structure. 

LITHOSPHERIC EVOLUTION 

Most studies of the evolution and behavior of the San 

Andreas fault system have focused on the stress and deformation regime in the middle to upper crust, a reasonable 

region to investigate because it encompasses the seismogenic component of the plate boundary. We take a somewhat-different approach, focusing instead on the behavior 

of the lithosphere below the seismogenic layer (representation of earthquakes in our models is quite simple). The 

stress and deformation regime within the nonseismogenic 

lithosphere plays an important role in the earthquake cycle 

along the San Andreas fault system, and we believe that 

our study, in conjunction with those by Bodin and Bilham 

(this chapter) and Simpson and Reasenberg (this chapter), 

complements studies of the seismogenic layer in unraveling the processes which drive the earthquake cycle along 

the San Andreas fault system. 

The present characteristics of the San Andreas fault system, in contrast to intraplate fault zones, can be directly 

linked to a series of plate-tectonic events and associated 

processes of lithospheric evolution. Additionally, the deformational behavior of the San Andreas fault system differs from that of intraplate fault zones because this fault 

system is part of a plate boundary. Because it forms only a 

small part of the boundary between the North American 

and Pacific plates, however, its rheologic characteristics 

play little role in the overall dynamics of either plate-that 

is, the San Andreas fault system does little to drive or retard plate motions but, instead, has developed in response 

to externally applied boundary conditions of plate motions. With the applied conditions of relative plate velocities, the evolution of the lithosphere and plate-boundary 
THREE-DIMENSIONAL LITHOSPHERIC KINEMATICS IN THE LOMA PRIETA REGION F105 

structure can be investigated in the light of the fault system's thermal and rheologic characteristics, both of which 

play important parts in the linkage between the relative 

plate velocity and the resulting stress and strain fields in 

the plate-boundary region. 

PLATE TECTONICS OF 

THE LOMA PRIETA REGION 

As described by various investigators (for example, Atwater, 1970; Dickinson and Snyder, 1979; Zandt and Furlong, 1982), the formation of the San Andreas fault system 

resulted from the northward migration of the Mendocino 

triple junction. The formation of a transform boundary in 

place of a convergent boundary is fundamental to the rest 

of the fault system's evolutionary history. A three-dimensional schematic view of the plate-tectonic cause of this 

lithospheric evolution is shown in figure 1. 

This three-dimensional view of lithospheric structure in 

the vicinity of the Mendocino triple junction shows a typical subduction configuration north of the triple junction, 

where the Gorda plate is being subducted beneath the 

North American plate. The specific characteristics of the 

relative plate motions at this fault-fault-trench triple junction require that the Gorda plate have a component of motion relative to North America comparable to the motion 

between the Pacific and North American plates. This requirement leads not only to the cessation of subduction 

with the passage of the triple junction but also to the concurrent removal of the subducted Gorda slab. These events 

produce a region of thin North American lithosphere, the 

North 

plate 

American 

Mendocino 

structure ' 

Figure 1.-Block diagram of three-dimensional lithospheric structure in 

vicinity of the Mendocino triple junction. Plate-boundary structure develops in region of emplaced asthenospheric mantle. Arrows indicate directions of relative plate motion. View northwestward. 

base of which is exposed to relatively hot mantle (Lachenbruch and Sass, 1980; Zandt and Furlong, 1982; Furlong, 

1984; Benz and others, 1992). This region of the upper 

mantle beneath the west edge of the North American plate 

has been variously called the slabless or asthenospheric 

window. The emplaced asthenospheric mantle cools over 

time, becoming either Pacific or North American lithosphere, and the Pacific-North American plate boundary develops within this slabless window at the center of 

deformation in this region of accreted lithosphere (Furlong 

and others, 1989; Furlong, 1993). 

Schematic cross-sectional views of this lithospheric evolution are shown in figure 2, which illustrates several details of the plate-boundary structure that play important 

roles in the plate kinematics of the Loma Prieta region. The 

Pacific-North American plate boundary develops where deformation is concentrated. Because this is a plate-boundary 

structure, the overall relative Pacific-North American plate 

velocities (excluding effects of internal deformation within 

the North American plate, such as in the Basin and Range) 

must be accommodated within the plate-boundary region. 

Although the Pacific-North American plate boundary within the seismogenic crust is a broad deformation zone comprising several active faults, consideration of upper-mantle 

thermal structure and rheology indicates a fairly simple 

plate-boundary structure within the lithospheric mantle 

(Furlong and others, 1989; Furlong, 1993). The specific 

location of the center of deformation and the width of the 

high-strain region depend primarily on the temperature 

structure of the slabless window. The thermal regime controls the initial location of the plate boundary (~urlon~ and

others, 1989), but rnineralogic conditions (most likely 

San Andreas & fault 

Â¥ Asthenosphere 

B San Andreas Hayward - Rodgers Creek 

fault fault 

I surface 1 Lithospheric 

boundary 

Figure 2.-Simplified cross-sectional views of proposed plate-boundary structure (A) immediately south 

of the Mendocino triple junction (lat 40' N.) and (B) 

in the San Francisco Bay region (lat 37'-38' N.). 

Modified from Furlong and others (1989). 
F106 TECTONIC PROCESSES AND MODELS 

regions of strain-induced reduced grain size) may serve to 

further localize and maintain the position of the plate 

boundary within the mantle lithosphere (fig. 2). 

Deformation within the lithospheric mantle occurs dominantly by temperature-dependent creep processes. The nonlinear relation between strain rate and temperature for the 

appropriate deformation mechanisms (dislocation-creep or 

diffusion-creep) leads to a localization of strain to the sites 

of highest temperature (at any given depth). As a result, strain 

will localize, and the associated plate boundary will form, 

within the slabless window, as shown in figure 2. The exact 

position of this boundary depends on both the cross-sectional 

geometry of the slabless window and details of the kinematics 

of the underlying mantle. Geodetic data (for example, 

Lisowski and others, 1991), particularly in regions where 

upper-crustal faults are locked, can also be used to estimate 

the position of the plate boundary within the lithospheric 

mantle-specifically, the center of deformation of the plateboundary deformation zone. Both thermal-mechanical modeling (Furlong and others, 1989) and geodetic data (Lisowski 

and others, 1991) point to a plate boundary forming within 

the slabless window substantially east of the west edge of 

the thinned North American lithosphere, in a position that 

approximately corresponds (on the surface) to the Hayward 

fault in the San Francisco Bay region. 

The proposed offset between the surface trace of the San 

Andreas fault in northern California, which during recent 

geologic time has served as the primary crustal component 

of the plate boundary, and the deeper plate-boundary structure lies at the heart of our model for plate-boundary evolution in the Loma Prieta region. Within this model, one 

necessary component is a connection between the base of 

the San Andreas fault and the plate boundary forming within the slabless window. Rheologic considerations and the 

rupture behavior of the 1989 earthquake (Furlong and 

Langston, 1990; Langston and others, 1990) lead us tentatively to place this structure within the lower crust at approximately 18-km depth. Although we cannot tightly 

constrain the depth of this connecting structure, it should be 

contained within the lower crust, and so its maximum extent would be from approximately 18-krn depth to the local 

Moho. We would expect strain-localization processes (as 

described below) to further limit this structure to less than 

5 km in thickness-in our preferred model, a 2- to 3-kmthick detachment surface. 

Additional aspects of plate-boundary evolution, which 

are important components of the kinematic and deformational model presented below, are the width and deformation regime of the plate boundary within the mantle. Within 

regions of significant strain, the equilibrium grain sizes of 

deforming minerals will be controlled by the stress regime 

and stress history (Karato and others, 1986; Rutter and Brodie, 1988). In addition, the mode of temperature-dependent 

creep that will dominate plate-boundary deformation depends strongly on the characteristic grain size within the 

deformation zone. We have combined laboratory-derived 

parameters for the stresslgrain-size relations and deformation mechanism (dislocation or grain-size-dependent diffusion-creep) with the evolving thermal model of Furlong and 

others (1989) to investigate localization processes within 

the plate boundary. The results for the San Francisco Bay 

region are plotted in figure 3 (K.P. Furlong, unpub. data, 

1992). The localized strain as a result of substantial lateral 

temperature variations, in combination with general cooling 

of the region of the original slabless window, creates a 

relatively narrow region (approx 10-20 km wide) of significantly reduced grain sizes and associated concentrated 

strain. The localization of this mineralogically preferred 

site for deformation, coupled with continuing lateral temperature variations, results in additional localization of 

strain (within a region <lo km wide). Characteristic grain 

sizes in this region of high strain are small, and so strain is 

accomplished primarily by grain-size-dependent diffusioncreep, allowing deformation at relatively low stresses. A 

similar process is envisioned to produce the proposed horizontal detachment surface within the lower crust. 

The combination of plate-tectonic events with the thermal 

and rheologic evolution of the lithosphere proposed above 

results in a plate-boundary configuration in the Loma Prieta 

region similar to that shown in figure 4. In this model, the 

plate boundary within the crust includes both the San Andreas and east-bay (Hayward, Calaveras) faults, which connect by way of a lower-crustal structure to the plate 

boundary within the mantle that lies approximately below 

the east-bay faults. This complex, three-dimensional plateboundary structure is ephemeral, and the faults that sit 

above the deeper extent of the plate boundary (for example, 

east-bay faults) eventually become the dominant components of the plate boundary within the crust. Such a developmental step has already occurred in central California, 

where the plate-boundary structure within the crust (San 

Andreas fault) lies above the plate boundary within the lithospheric mantle, and faults to the west of the San Andreas 

fault have become progressively less active. The 1989 

earthquake occurred along a section of the San Andreas 

fault that links these two types of crustal-plate boundary 

and thus forms the region in which the lower-crustal detachment surface begins to play a critical part in the overall 

stress and strain regime. This characteristic alone makes 

understanding the deformational processes in the Loma Prieta region important to any analysis of earthquake hazards 

in the San Francisco Bay region. 

KINEMATICS OF THE LITHOSPHERE 

Our evolutionary model of the San Andreas fault system 

significantly complicates the kinematics of what is commonly considered a simple strike-slip plate boundary. The 

position and orientation of the plate boundary within the 
THREE-DIMENSIONAL LITHOSPHEFUC KINEMATICS IN THE LOMA PFUETA REGION F107 

lithospheric mantle reflect both the process of boundary 

formation (cooling of mantle material within the slabless 

50 100 

DISTANCE,IN KILOMETERS 

Figure 3.-Thermal-rheologic structure of plate boundary in the San 

Francisco Bay region. A, Temperature (in degrees Celsius; from Furlong 

and others, 1989). B, Grain size (from Furlong, 1990). C, Strain rate 

(from Furlong, 1990). Figures 3B and 3C localize plate boundary as a 

result of grain-size reduction and change in deformation mechanism to 

diffusion-creep. Region of highest strain rate (-10-l3 s-I) corresponds to 

position of plate boundary within mantle. This high-strain-rate region 

(40 km wide) results from combination of lateral temperature gradients 

and localized regions of grain-size reduction. Trapezoidal region outlines 

area of slabless window after triple-junction passage. 

window) and the directions of relative motion between the 

North American and Pacific plates. Geodetic observations 

and our previous modeling studies (Furlong and others, 

1989) indicate that this boundary is located approximately 

as shown in figure 5. Plate motion at the boundary consists almost entirely of right-lateral shear, which, on the 

basis of rheologic modeling, we believe to be occurring in 

a relatively narrow deformation zone (~10-20 km wide) 

within the lithospheric mantle. Relative to a North American reference frame, the subcrustal Pacific lithosphere extends to this boundary. The kinematics of the crustal 

components of the plate boundary differs from this configuration and plays an important part in the earthquake cycle 

in the Loma Prieta region. The position of the plate 

boundary can also be inferred from results of recent seismic-tomography studies of the mantle beneath northern 

California (Benz and others, 1992). In those models, the 

east limit of the pacific plate corresponds to the region of 

transition from fast to slow velocities in the depth range 

30-100 km. These results indicate a similar position to 

that shown in figure 5 for the east edge of the Pacific plate 

and provide the information to link the plate boundary 

with the Mendocino triple junction. 

Crustal kinematics leads us to consider the crust along 

the San Andreas fault in the Loma Prieta region in terms 

of the four blocks shown in figure 6. East of the lithospheric-plate boundary (east of the Hayward-Calaveras 

fault systems), North American crust overlies and is coupled to North American lithosphere. Similarly, offshore to 

the west, Pacific crust is well coupled to Pacific lithosphere. The kinematics of these crustal blocks mimics that 

of the underlying mantle. Between these regions of strong 

crust-mantle coupling lie two crustal blocks of less certain 

San Andreas 

plate boundary 

Figure 4.-Block diagram of plate-boundary structure in the San Francisco Bay region. Vertical cut is approximately at latitude of Lorna Prieta. 

Shading indicates plate affinity of various crustal and mantle components 

of plate boundary. Proposed detachment surface is shown connecting 

base of the San Andreas fault with east-bay faults and lithospheric-plate 

boundary. The Pacific plate therefore extends to east-bay faults beneath 

this surface. 
F108 TECTONIC PROCESSES AND MODELS 

affinity. First, between the San Andreas and east-bay faults 

lies what we term the "Bay Area block" (similar to the 

Sebastopol block of Fox, 1983). In the Loma Prieta region, this block is largely uncoupled from the underlying 

mantle (which in our model is Pacific lithosphere; see figs. 

2, 4; Furlong and Langston, 1990). The kinematics of this 

block is complex because the block is partly linked to 

North American crust to the east (when the east-bay faults 

are locked) and to the northeast (where the bounding 

faults are less well developed), and drag along its base 

from the motion,of the underlying mantle may affect internal deformation and motion. 

Second, west of the San Andreas fault lies what we term 

the "Santa Cruz block.'' The kinematics of this crustal 

block is similar to that of the Pacific plate, in that no obvious active fault boundary separates the block on the west 

from adjacent oceanic crust. However, seismicity within 

the block (associated with the San Gregorio fault?) and 

possible faulting observed in multichannel seismic profiles 

in the Santa Cruz region (Stephen Lewis, oral commun., 

1992) indicate that the Santa Cruz block is undergoing internal deformation and possible westward displacement, 

particu1arly at the approximate latitude of Loma Prieta. 

The eastern margin of the block is well defined (San Andreas fault), and so its motions are prescribed by the ge- 

-0 100 KILOMETERS I I 

Figure 5.-San Francisco Bay region, showing location and kinematics 

of Pacific-North American plate boundary within lithospheric mantle. 

Double arrows indicate directions of fault movement; large arrows indicate direction of Pacific-plate motion. Plate boundary is constrained to lie 

approximately below east-bay fault system by analysis of regional geodetic results (Lisowski and others7 1991), thermal-rheologic modeling 

(Furlong and others, 1989), and seismic tomography (Benz and others7 

1992). 

ometry of the San Andreas fault. The kinematics of the 

Santa Cruz block is illustrated in figure 6. The discrepancies between the kinematics of this crustal block and the 

underlying mantle lead to partial coupling, possibly substantial internal strain, and likely westward partial obduction of the block over Pacific crust (structures observed in 

seismic data show evidence of significant east-west shortening; Stephen Lewis, oral commun., 1992). 

The differences between the kinematics of the crustal and 

mantle components of the Pacific-North American plate 

boundary in the vicinity of the San Andreas fault played an 

important part in the generation of the 1989 earthquake. 

Loma Prieta is situated where the motions of the Santa Cruz 

block differ most from those of the Pacific plate, and in this 

region the proposed decoupling of the block from the underlying mantle must occur (Furlong and Langston, 1990). Thus, 

the generation of the earthquake reflects two types of processes: (1) decoupling of the Santa Cruz block from the 

underlying mantle and (2) interactions between the largely 

uncoupled Bay Area block and the Santa Cruz block. Both 

of these processes are ultimately driven by Pacific-North 

American plate motions, but because of the complexity of 

the Loma Prieta region, we must consider both crustal and 

mantle kinematics in our investigation of the earthquake. 

A schematic cross section (fig. 7) of the plate interactions 

near Loma Prieta (along the strike of relative Pacific-North 

American plate motions) indicates the correlation of the 

Figure 6.-San Francisco Bay region, showing location and kinematics of 

crustal blocks in plate-boundary region. Dashed lines7 inferred boundaries 

of crustal blocks, with sawteeth on upper plate. Double arrows indicate 

directions of fault movement (queried where uncertain). Bay Area block is 

proposed to be effectively decoupled (along detachment surface shown in 

fig. 4) from underlying mantle, whereas Santa Cruz Block (which includes 

both Salinian and San Simeon [Franciscan] terranes) appears to be partly 

coupled to underlying mantle but undergoes some internal deformation. 
THEE-DIMENSIONAL LJTHOSP~RIC KINEMATICS IN THE LOMA PRETA EGION F109 

San Andreas 

fault 

cn 

i3 Bay Area block Santa Cruz block lo (Pacific plate ?) (North America 

- plate ?) @ 

36 37 38 

LATITUDE NORTH, IN DEGREES 

Figure 7.-Schematic cross section of Loma Prieta region, Calif., illustrating kinematics of crustal and mantle components of plate-boundary 

system (modified from Furlong and Langston, 1990). Arrows indicate directions of relative plate motion given by lithospheric system: bull's-eye, 

toward viewer; crosshairs, away from viewer. Rectangle, focus of 1989 

Loma Prieta earthquake. 

Loma Prieta rupture with the location of initial decoupling 

of the Santa Cruz block from the underlying mantle. We 

recall that the crustal kinematics of the region includes significant motioddeformation out of the plane of the cross 

section as the Santa Cruz block is translated westward. 

The conceptual aspects of deformation processes shown 

schematically in figure 7 are supported by the results of fully 

three dimensional modeling of the dynamics of the plate 

boundary. The details of this modeling are presented in the 

next section, and three cross sections applicable to the Loma 

Prieta region in figure 8. This series of cross sections parallel 

the relative Pacific-North American plate motion and show 

the velocity in the plane of the cross section for the 10-year 

period before the earthquake: Figure 8A is located entirely 

within the Pacific plate west of the plate-boundary-deformation zone; figure 8B, which is equivalent to the schematic 

cross section in figure 7, slices through the plate-boundarydeformation zone; and figure 8C is east of the plate boundary 

entirely, within the North American plate. Figures 8A and 

8C show the displacement fields expected for a well-coupled 

60-----------G 

100 150 200 250 

DISTANCE, IN KILOMETERS 

Figure 8.-Velocity field in plane parallel to relative Pacific-North American plate motion. A, Cross section 

entirely within Pacific plate (west of the San Andreas fault), with well-coupled Pacific crust. B, Cross section 

through Santa Cruz and Bay Area blocks, showing partial coupling of Santa Cruz block to underlying mantle. 

Uncoupling of Bay Area block (shaded area) is shown by velocity differences and large gradient across 

crustal detachment surface (dashed horizontal line). 1989 Lorna Prieta earthquake occurred at transition from 

Santa Cruz block (unshaded area) to Bay Area block (shaded area). Cross section approximately corresponds 

to cross section in figure 7. C, Cross section entirely within North American plate (east of the San Andreas 

and east-bay faults), with well-coupled North American crust. 
Fllo TECTONIC PROCESSES AND MODELS 

crust-mantle system away from the plate boundary, and figure 

8B indicates the complex pattern of displacement within the 

plate-boundary-deformation zone, the transitional behavior 

of the Bay Area block relative to both Pacific and North 

American plate displacements, and the abrupt change in 

crustal motions near Loma Prieta. 

The kinematics of the Bay Area and Santa Cruz blocks 

relative to the larger scale motions of the North American 

and Pacific plates leads to significant spatial variation in 

the lithospheric stress regime. In particular, the crust-mantle decoupling (Santa Cruz block from underlying mantle) 

and the internal strain in the Santa Cruz block near Loma 

Prieta produced by displacements along the San Andreas 

fault (for example, in the 1906 San Francisco earthquake) 

lead to a stress increase in the source region of the 1989 

Loma Prieta earthquake. The details of the assumptions 

and constraints of this modeling are discussed in the next 

section, and the cross sections in figure 9 show the large 

spatial variation in shear stress (acting in the horizontal 

plane-the decoupling shear stress) and the evolution of 

shear stress in our model from before the 1906 earthquake 

until just before the 1989 earthquake. The stress that increases with the 1906 earthquake is relaxed in areas where 

the horizontal detachment surface exists but persists southwest of the San Andreas fault in the Loma Prieta region. 

The kinematics of the two crustal blocks and the associated crust-mantle decoupling play crucial roles in the generation of the 1989 earthquake, a seismic event that thus 

reflects both the local effects of plate-boundary geometry 

and the regional effects of plate motions. 

The kinematic model described above provides a framework within which to evaluate, through finite-element 

modeling, the events that led up to the 1989 Loma Prieta 

earthquake and the postearthquake effects on the crustal 

and lithospheric stress regime throughout the San Francisco Bay region. The response of the regional stress field to 

the earthquake is not static but varies in time and space. In 

the finite-element model described below, we investigate 

the first-order effects of the earthquake on patterns of deformation and stress in the San Francisco Bay region. Our 

results provide additional insight into the possible effects 

of the earthquake on the seismic potential of other faults 

in the San Andreas system, as well as a means to relate 

observations of crustal deformation to the underlying 

plate-tectonic framework of the region. 

MODELING 

PLATE-BOUNDARY DEF'OMATION 

DURING THE EARTHQUAKE CYCLE 

We tested several models of plate-boundary structure 

and rheology in evaluating the plate-boundary deformation 

leading up to the earthquake and the subsequent effects on 

the stress regime along adjacent segments of the San Andreas fault system. In each model, we placed the primary 

plate boundary through the mantle lithosphere, as shown 

in figure 5, and focused on the effects of different types of 

coupling between the crust and underlying mantle. Although the models described here are fully three dimensional, it is easiest to visualize the differences among our 

three types of models by considering schematic cross sections of each model. The three model geometries (fig. 10) 

include our preferred (detachment) model, in which a midcrustal shear zone connects the base of the San Andreas 

fault through its Santa Cruz Mountains and peninsular sections to east-bay faults and the plate boundary in the lower 

crust and upper mantle (lithospheric shear zone). This first 

model contrasts with the second, elastic-crust model, in 

which all stress transfer between the San Andreas and 

east-bay faults is simply through the elastic crust (see 

Simpson and Reasenberg, this chapter, for a similar elastic-crust model under different boundary conditions). Although we do not believe that this model is compatible 

with the observations of large displacements on the San 

Andreas fault and the post- 1906 transient-deformation pattern, the elastic-crust model is appropriate for the crustaldeformation regime in the San Francisco Bay region. Our 

third model, here termed the weak-crust model, incorporates a weak (low viscosity) lower crust throughout, where 

the crust-mantle coupling is reduced but similar everywhere in the region. In the detachment model, we assume 

that because of strain localization, the shear zones in both 

the lower crust (horizontal) and lithospheric mantle (vertical) deform by diffusion-creep. In the weak-crust model, 

the lithospheric shear zone deforms by diffusion-creep, 

whereas the lower crust (with distributed deformation) undergoes dislocation-creep. In the elastic model, only the 

lithospheric shear zone deforms by ductile mechanisms 

(diffusion-creep). Specific parameters for these models are 

listed in table 1. The values chosen for effective viscosity 

(and, equivalently, relaxation time) in all the models are 

appropriate for the inferred thermal conditions and assumed deformation mechanism in the lower crust and 

upper mantle (for example, Rutter and Brodie, 1988). No 

data were available for difision-creep in lower-crustal 

rocks, and so we use the same viscosity in the lower-crustal detachment surface as in our mantle shear zone. We believe that this estimate is reasonable for the properties of 

such a lower-crustal shear zone because the expected increase in viscosity with the lower temperatures at shallower depths will be offset by a decrease in viscosity with the 

change in composition from mantle to crustal rocks. 

FINITE-ELEmNT MODEL 

The finite-element program TECTON (Melosh and Raefsky, 1980, 1981) was used in our modeling. This program 
THREE-DIMENSIONAL LITHOSPHERIC KINEMATICS IN THE LOMA PRIETA REGION Fill 

allows the use of various rheologies (for example, elastic, seismogenic crust ye represented by the split-node technique 

viscous, viscwlastic, and so on) and the inclusion of faults of Melosh and Raefhky (1981) in the finite-element formuof finite dimension that are held locked except during "earth- lation, allowing us to specify displacements of arbitrary 

quakes." Earthquakes are simulated in a simple manner: orientation (relative to the orientation of the initial element 

Specified displacements (in three-dimensional space) are ap- boundary) during earthquakes. Thus, we can incorporate the 

plied to the faults (which are unlocked over a specified depth) strike, dip, and rake for each earthquake simulated. This 

during the time step of an earthquake. The faults within the approach is essentially equivalent to that used by both Bodin 

DISTANCE, IN KILOMETERS 

EXPLANATION 

Stress (MPa) 

Figure 9.-Horizontal shear stress in detachment model (A) kfore 1906 San Francisco earthquake, (B) 10 yr 

after 1% earthquake, (C) 20 yr after 1% earthquake, and (D) before 1989 Loma Prieta earthquake. Cross 

sections correspond to those in figures 7 and 8B. Shaded area, extent of Bay Area block. Large stresses 

produced by 1% earthquake decay rapidly within and below Bay Area block but do not decrease significantly within Santa Cruz block. Accumulation of this shear stress through occurrence of several 1906-type events 

may lead to less frequent but periodic Lorna Prieta-type events. 
F112 \ TECTONIC PROCESSES AND MODELS 

and Bilham (this chapter) and Simpson and Reasenberg (this 

chapter). 

The 1906 San Francisco earthquake was simulated by 

4 m of slip on the entire model length of the San Andreas 

fault, similar to estimates of average slip over the simulated region (Thatcher, 1975). In this earthquake, fault nodes 

were unlocked from the surface to a depth of 18 lun. This 

coseismic displacement represents both brittle deformation 

(0-12-km depth) and rapid postseismic relaxation in the 

middle crust (for example, Thatcher, 1975). The 1989 

Loma Prieta earthquake was simulated by 2.25 m of strike 

slip and 2 m of dip slip (strike, N. 150' E.; dip, 60'; rake, 

A San Andreas fault East-bay faults 

B San Andreas fault East-bay faults 

C San Andreas fault East-bay faults 

Crust 

Mantle 

Figure 10.-Schematic cross sections (at approximately latitude of San 

Francisco) showing three models of plate-boundary structure investigated 

with finite-element method: (A) detachment model, (B) elastic-crust 

model, and (Q weak-crust model. Rheologic characteristics of components of each model are listed in table 1. In each figure, location of principal plate-bounding shear zone is beneath east-bay (Hayward, Calaveras) 

faults. Models in figures 105 and 10C test rheologies similar to those used 

by Simpson and Reasenberg (this chapter), although boundary conditions 

differ somewhat. 

138'; total displacement, 3 m), compatible with the range 

determined by geodetic and seismic studies (Marshall and 

others, 1991) on a 60-km-long section of the Santa Cruz 

Mountains section of the San Andreas fault. The slip at 

Loma Prieta extended to a depth of 18 km but did not 

include the surface node in the finite-element model, to be 

consistent with observations of little or no rupture at shallow levels (for example, Langston and others, 1990; Wald 

and others, 1991). Although the finite-element model 

shown in figure 11 has a vertical boundary along the 

Loma Prieta rupture, the split nodes allow us to account to 

first order for the strike, dip, and rake of the rupture. The 

result is a representation of the rupture (essentially composed of two "shingled" fault segments) that does not exactly simulate the near-field effects but for all practical 

purposes adequately simulates the overall displacement 

patterns observed after the earthquake-both the reverse 

dip slip on the fault and the vertical and horizontal deformation in the Loma Prieta region. This simple simulation 

of earthquakes is intended not to provide information on 

the instantaneous response of the stress regime during and 

in the immediate vicinity of the earthquake but to evaluate 

the deformational behavior on the time scale of crust and 

mantle relaxation. 

The three-dimensional finite-element mesh is composed 

of 3,080 nodes and 3,192 elements. The global-stiffness 

matrix contains 8,734,797 terms, with a mean bandwidth 

of 1,070. A plan view of the mesh is shown in figure 11, 

with this same horizontal mesh throughout the vertical extent of the model. The shaded area shows the model domain on which we focus our analysis. This region is 

sufficiently removed from side boundaries to be relatively 

insensitive to artifacts produced by assumed conditions 

along the boundaries. 

A vertical view of the finite-element mesh and the implementation of the three types of models is shown in figure 

12. We have modeled the entire depth of the lithosphere 

(assumed thickness of the mechanical lithosphere, -60 km), 

allowing us to apply what we consider the most realistic 

boundary conditions for the plate velocities along the sides 

and bottom of the model. A relative Pacific-North American plate velocity of 40 mmlyr (NUVEL-1 velocity of 

DeMets and others, 1990, modified by Sierra Nevada-North 

American motions of Argus and Gordon, 1991) was used 

for this boundary condition. We believe that the principal 

deformation associated with the San Andreas fault is driven 

by far-field plate motions. Such an assumption is easily 

converted to appropriate side and end boundary conditions. 

It is less clear, however, how to implement this condition 

along the base of the model. If basal drag serves to help or 

hinder plate motion in the Loma Prieta region, the appropriate condition is a specified displacement rate along the base 

of the model. If basal drag is insignificant near the plate 

boundary, however, then a free-slip boundary condition 

should be applied to the base. In our modeling, we tried 
THREE-DIMENSIONAL LITHOSPHERIC KINEMATICS IN THE LOMA PRIETA REGION 

Table 1 .-Rhologic parameters for finite-element model 

[E, Young's modulus; %, approximate effective viscosity for a strain rate of lo3 st. Do., ditto] 

Material E Deformation Region of model rle Relaxation 

(GPa) mechanism (Pa-s) time (yr) 

0 100 200 300 

DISTANCE. IN KILOMETERS 

Figure 11 .-Plan view of finite-element mesh used in modeling. Shaded area, region of interest in this study. 

Heavy lines, locations of faults (split nodes) in model, sections of which are displaced during simulated 

earthquakes; faults extend to depth of 18 km. Diamonds, locations of stresses plotted in figure 14, corresponding approximately to geographic locations of San Francisco (SF), Oakland (OAK), Loma Prieta (LP), Morgan 

Hill (MH), and Pinnacles National Monument (PNM). Dot-dashed line, location of vertical cross sections 

shown in figure 12. 
F114 TECTONIC PROCESSES AND MODELS 

various conditions and found that the results for the region 

of interest (crust and uppermost mantle) are relatively insensitive to the width of the zone at the base of the model 

under free-slip conditions. In the results shown here, basal 

conditions of free slip were applied over the distance range 

100-200 km in the model coordinates of figures 11 and 12; 

elsewhere, plate velocities of k20 mrntyr were applied. 

The results of our modeling are shown here in several 

forms. In these three-dimensional time-dependent models, 

complete descriptions of both the stress and strain fields 

are available at all points for all time steps. Interpreting 

such results is a daunting task, and so we have tried to 

distill these results into a suite of figures that contain the 

fundamental aspects and implications of our modeling. 

The results are shown in two forms, stress and velocity, 

for each of the three models in figures 13 through 19. The 

stress field is presented in two ways. Along the faults, the 

fault-parallel shear stress is shown at specific times 

throughout the earthquake cycle (pre- 1906 to post- l989), 

providing some insight into the interaction of the stress 

field among fault segments and the spatial variation of the 

stress regime. We emphasize that the faults are not necessarily the sites of maximum shear stress but are reasonable 

places to consider in each model because they represent 

regions that have failed repeatedly in earthquakes (see 

Linker and Rice, in press; Bodin and Bilham, this chapter; 

Simpson and Reasenberg, this chapter). In addition, the 

stress histories at the sites indicated in figure 11 are shown 

throughout the model history. Such stress histories provide 

a means to investigate both the relaxation phase of crustal 

deformation and the coseismic and postseismic interaction 

of the various fault segments. 

The results for the deformation field are shown in terms 

of velocities throughout the earthquake cycle. In most of 

DISTANCE, IN KILOMETERS 

Figure 12.Ã‘Cross-sectiona views of finite-element mesh (fig. 1 I), showing implementation of three models 

shown in figure 10: (A) detachment model, (B) elastic-crust model, and (0 weak-crust model. Heavy lines, 

faults; dark-shaded area, shear zones; medium-shaded area (fig. 120, lower crust; light-shaded area, viscoelastic mantle. Rheologic parameters assigned to various elements are listed in table 1. 
THREE-DIMENSIONAL LITHOSPHERIC KINEMATICS IN THE LOMA PRIETA REGION F115 

the figures, the difference between the upper-crustal and 

lithospheric-mantle velocity fields is shown. We followed 

this approach because the velocity difference highlights locations where crustal displacement/deformation differs 

from that of the underlying mantle: Regions of the crust 

well coupled to the underlying mantle appear as regions of 

minimum velocity difference, and regions with large velocity-difference vectors are sites of significant stress accumulation in the lowerlmiddle crust and (or) decoupling 

between the crust and underlying mantle. To allow for the 

application of these results to observations of crustal displacement/deformation, we also show some results for surface velocity. This presentation helps delineate target areas 

where the deformation response allows discrimination 

among the assumptions of the various models. 

STRESS HISTORY 

The results shown here encompass the effects of both 

the 1906 San Francisco and 1989 Loma Prieta earthquakes. Results are shown in each model for the time period beginning about 10 yr before the 1906 earthquake until 

about 20 yr after the 1989 earthquake. Note that the model 

"runs" for approximately 500 yr before the 1906 earthquake in an attempt to prestress the regime, so that the 

coseismic and postseismic strain relaxation occur in conjunction with a simulation of the inherited stress field, as 

is necessary for consideration of viscous relaxation because strain rates are proportional to stress levels. Our prestress conditions should be seen simply as an attempt to 

incorporate first-order effects. We have omitted all events 

during the 1800's, partly because of the large uncertainties 

in their location, rupture characteristics, and extent. As 

shown in the figures, the effects of the 1906 earthquake 

are still significant at the time of the 1989 earthquake; 

however, any effects of smaller events before 1906 were 

probably overwhelmed by 1906 displacements. Because 

the continuously deforming lithospheric shear zone is located beneath the east-bay faults, that region accumulates 

the largest stresses which are not significantly relieved by 

1906 displacements. During the prestress period, all the 

faults are locked, and stress accumulates everywhere in 

conjunction with strain on the lithospheric shear-zone 

plate boundary (and on the lower-crustal detachment surface and (or) weak lower crust, where present). In the simplified geometry of our models, surface faults generally 

parallel the plate boundary, except for the Santa Cruz 

Mountains section of the San Andreas fault. As a result, 

we monitor shear stress in the plane oriented along the 

fault, although the shear stress on any plane can be calculated from our results (full stress tensor computed). Thus, 

the effects of such situations as fault-normal compression 

can be evaluated, if desired, by resolving the stress tensor 

onto the appropriate planes. 

The results for fault-parallel shear stress at both the 

base of the seismogenic layer (that is, base of the locked 

fault) and in the lower crust (that is, above the crust-mantie boundary) in the three models are illustrated in figure 

13, and the corresponding stress histories at the sites 

identified in figure 11 are plotted in figure 14. With the 

inclusion of a detachment surface within the lowerlmiddle 

crust connecting the peninsular and east-bay fault segments, the stress on the peninsular section of the San Andreas fault in the detachment model is increased relative 

to that in both the elastic- and weak-crust models. In all 

the models, shear stresses on the peninsular section of the 

San Andreas fault are lower than on the east-bay faults. A 

first-order result of this and previous modeling (Verdonck 

and Furlong, 1992) is that the apparent role played by the 

peninsular section of the San Andreas fault as the major 

plate-bounding fault in the San Francisco Bay region implies that this fault section must somehow be weaker than 

the east-bay faults because it appears to fail at lower 

fault-parallel shear stresses. 

Comparing the results shown in figures 13 and 14, we see 

that the detachment model produces a stress field which 

differs from those in the other two models in several important ways. Firs t, as mentioned above, the detachment model 

produces the highest stresses on the base of the locked Santa 

Cruz Mountains and peninsular sections of the San Andreas 

fault. Second, the detachment model allows the stress (on 

the peninsula section) that is transferred to the lower crust 

during the 1906 earthquake to be relaxed postseismically, 

whereas such stress cannot be relaxed in the elastic- or weakcrust model. Clearly, the elastic-crust model contains no 

deformation mechanism to relax the stress. 

The minimal stress relaxation in the weak-crust model 

results from the characteristics of the crust in the Loma 

Prieta region, which, though weak relative to the upper 

crust and underlying upper mantle, still has a characteristic 

viscous-relaxation time of thousands of years (consistent 

with lower-crustal temperatures in the range 300-400OC 

and a dislocation-creep deformation mechanism). Although a lower viscosity for the entire lower crust would 

allow stress relaxation over interseismic time intervals, 

such a low viscosity would imply unreasonable temperatures in the lower crust. We cannot solve this problem by 

assuming that diffusion-creep acts throughout the entire 

lower crust as a "weaker" deformation mechanism. Diffusion-creep, which is grain-size dependent, requires regions 

of highly reduced grain size (such as localized shear 

zones) to operate. We do not believe that such wholesale 

lower-crustal grain-size reduction is likely for the crust in 

the San Francisco Bay region. The existence of a weak 

shear zone within the lower crust in the plate-boundary 

region (deforming by diffusion-creep), however, does 

allow plate motions without substantial stress accumulation and is consistent with the temperature regime and deformation history. 
F116 TECTONIC PROCESSES AND MODELS 

The stress histories during the earthquake cycle shown greatest along the fault segments that ruptured in 1906 but 

in figure 14 provide insight into the effects of the 1906 is also evident at the east-bay sites (MH, OAK, fig. 11). In 

San Francisco earthquake on the other fault segments and the elastic- and weak-crust models, the stress drop associthe possible stress loading caused by the 1989 Loma Prie- ated with the 1906 earthquake places the peninsular secta earthquake. In all three models, the 1906 earthquake tion of the San Andreas fault into a left-lateral stress 

causes a decrease in shear stress (acting in the vertical regime (that is, the stress drop is larger than the preevent 

plane along the fault strike) at all sites. This stress drop is stress). This result appears to be incompatible with continFigure 13.-Stress regimes at specific times in earthquake cycle in (A) km deep) but above detachment surface (left half) and in lower crust 

detachment model, (B) elastic-crust model, and (C) weak-crust model, above crust-mantle boundary (right half). Shaded rectangles, segments 

showing fault-parallel (horizontal) shear stress along segments of major with right-lateral stress; unshaded rectangles, segments with left-lateral 

faults in the San Francisco Bay region at base of seismogenic layer (18 stress. All distances in kilometers from arbitrary origin. 
THREE-DIMENSIONAL LITHOSPHERIC KINEMATICS IN THE LOMA PRIETA REGION F117 

ued right-lateral postseismic stress relaxation (Thatcher, 

1975) but may reflect an underestimation of the pre-1906 

stress regime. Such a result is not obtained in the detachment model, because pre-1906 stresses (boosted over the 

stresses in both the elastic- and weak-crust models by 

strain transfer across the detachment surface) are comparable to the 1906 stress drop along the peninsular section of 

the San Andreas fault. In both the elastic- and weak-crust 

models, the stress increase in the Loma Prieta region after 

the 1906 earthquake is minimal, and relative stresses at the 

time of the 1989 earthquake are quite low. The detachment 

model shows a somewhat greater stress increase and 

higher stresses in the Loma Prieta region (see fig. 9 for 

depthltime patterns of stress in the horizontal plane in the 

Loma Prieta region), reinforcing the concept that the 1989 

earthquake is more likely representative of a release of 

horizontal decoupling stresses rather than a typical San 

Andreas- type strike-slip event. 

The 1989 Loma Prieta earthquake was significantly 

smaller than the 1906 San Francisco earthquake, and so 

Figure 13.Ã‘Continued 
F118 TECTONIC PROCESSES AND MODELS 

the effects of the 1989 earthquake on the regional stress 

field are reduced over those in 1906. However, as a result 

of the more complex rupture geometry (dipping fault, no 

surface rupture), the pattern of stress response in 1989 is 

more complex than in 1906. The 1989 earthquake produces a stress drop at Morgan Hill (MH, fig. 11) but no effect 

or a stress increase at the other sites. The effect on the 

peninsular section of the San Andreas fault is relatively 

minor but shows a slight increase in the detachment 

model. The stress changes from the 1989 earthquake are 

small (51 MPa), and so it is hard to imagine that they 

alone can trigger paired earthquakes. What may be more 

important than the actual decrease or increase in stress associated with the 1989 earthquake (because the changes 

are small) is the change in stress patterns. Although this 

change is quite small and must be validated by more complete modeling studies, the 1989 earthquake changed the 

relative stress levels along both the east-bay faults and the 

Figure 13.Ã‘Continued 
THREE-DIMENSIONAL LITHOSPHERIC KINEMATICS IN THE LOMA PRIETA REGION F119 

Santa Cmz Mountains and peninsular sections of the San 

Andreas fault. Just before the earthquake, Oakland (OAK, 

fig. 11) shows a minimum stress, and Morgan Hill (MH) 

and Pinnacles National Monument (PNM) slightly higher 

stresses. After the 1989 earthquake, however, Morgan Hill 

shows a minimum stress, Oakland effectively no change, 

and Pinnacles National Monument a higher stress. How 

this result may relate to future earthquakes is not entirely 

clear, because earthquakes are not simply a consequence 

of cmstal stresses, although it is tempting to speculate that 

changes in stress patterns may play an important part in 

the earthquake cycle along the San Andreas fault in the 

San Francisco Bay region. 

As briefly discussed earlier, the initiation of the Lorna 

Prieta rupture and the style of faulting may be largely controlled by decoupling of the Santa Cmz block from the 

underlying mantle (which continues to move in the direction of relative plate motion). The shear stress in the horizontal plane along a profile parallel to plate motion 

through the Santa Cmz Mountains (approximately the 

Figure 13.Ã‘Continued 
F120 TECTONIC PROCESSES AND MODELS 

stress component that would produce an initial decoupling component, generating less frequent (but still quasi-periodevent) is shown in figure 9. This stress is largest in the ic) Loma Prieta-type events. 

vicinity of the focus (or slightly south) of the 1989 earthquake, and so it may reflect the stress regime that initiated 

the Lorna Prieta rupture. In the sequence shown in figure VELOCITY FIELD 

9, this stress results from the displacements associated 

with the 1906 earthquake, but is not substantially relaxed The various models produce different results for the evduring the interseismic period. A series of 1906-type olution of the stress regime. Although the results may be 

events can thus lead to a significant increase in this stress most directly applicable to understanding the earthquake 

Figure 13.Ã‘Continued 
THREE-DIMENSIONAL LITHOSPHERIC KINEMATICS IN THE LOMA PRIETA REGION F121 

process in the San Francisco Bay region, stress observations (particularly magnitude) are difficult, and so these results cannot easily be compared directly with observations. 

We can, however, directly observe the displacement field. 

Excellent data describing the behavior of the cmst in the 

San Francisco Bay region have been collected since 1900 

(see Lisowski and others, 1991 for a recent synthesis) and 

can provide constraints on and, possibly, distinguish 

among the various models. Time-dependent finite-element 

modeling provides results on the displacement history of 

all nodes in the mesh. To focus on the component of cmstal displacement that differs from the overall plate-boundary behavior (as given by the displacement history of the 

lithospheric mantle), we present our results in the form of 

the velocity difference between the upper crust and the 

mantle. We use velocity rather than strain simply for ease 

in relating the results to plate-boundary processes. The velocity fields in the various models for the interval from 

just before the 1906 earthquake until approximately 20 

years after the 1989 earthquake are plotted in figure 15. 

Figure 13.Ã‘Continued 
F122 TECTONIC PROCESSES AND MODELS 

The behavior of the velocity field changes drastically tween the Bay Area and Santa Cruz blocks during interthroughout the earthquake cycles studied here. Under the seismic periods (after loading by the 1906 earthquake). 

assumptions of the detachment model, the velocity of the The detachment model also produces a Bay Area block 

Bay Area block (see fig. 6) differs substantially from that that undergoes relatively little internal deformation (that is, 

of the underlying mantle. Thus, a substantial gradient in velocity-difference gradients across the block are small) 

velocity difference exists across the San Andreas fault be- relative to the other models. This result is consistent with 

- - - * - - - Oakland 

-5 1 I I I I 1 I I 1 I I 1 I 1 

450 500 550 600 

TIME, IN YEARS 

-5 I 8 I I I I I I , I I I I I I 

450 500 550 600 

TIME, IN YEARS 

Figure 14.2Stress histories at base of seismogenic layer in (A) detachment model, (B) elastic-crust model, 

and (0 weak-crust model. Curves correspond to sites identified in figure 11. Shaded bars, intervals of "earthquake" slip. Time scale begins 500 yr before 1906 San Francisco earthquake; time step, 5 yr. 
THREE-DIMENSIONAL LITHOSPHERIC KINEMATICS IN THE LOMA PRIETA REGION F123 

the observation by Fox (1983) of the absence of deformation of his Sebastopol block relative to the adjacent North 

American crust in the region north of San Francisco Bay. 

In general, as might be expected, the detachment model 

produces a deformation field in which the Bay Area block 

behaves differently from the adjacent Santa Cruz block or 

the North American plate, whereas the other models show 

the Bay Area block behaving similarly (except during coseismic periods) to the adjacent Santa Cmz block. 

Of particular interest in these results are the differences in 

the models for the coseismic and postseismic responses to 

the 1989 earthquake. The first 5- to 10-yr period after the 

1989 earthquake will provide the opportunity to differentiate among the possible plate-boundary scenarios. To clarify 

these effects, surface velocity (rather than velocity difference) for the Loma Prieta region during the post-1989 period is plotted in figure 16. Velocity profiles (perpendicular to 

the plate boundary) of the south bay and Loma Prieta region for the pre- 1906, pre- 1989, and post- 1989 periods are 

plotted in figures 17, 18, and 19, respectively. Such results 

can be used in conjunction with geodetic observations to 

constrain the model parameters and assumptions. Both the 

elastic- and weak-crust models rapidly return to interseismic deformation patterns (see figs. 15B, 150, whereas 

with the inclusion of a detachment surface, deformation in 

the south bay and Loma Prieta region is significantly altered by the 1906 earthquake, and the post- 1906 transients 

in conjunction with the Loma Prieta stress relaxation produce strain patterns quite different from those in the elasticand weak-crust models. 

The critical period for distinguishing the effects of the 

1989 earthquake is the first 5 to 10 yr after the event. In 

the elastic- and weak-crust models, the deformation pattern is essentially equivalent for all three periods shown 

(figs. 17-19). The detachment model, however, shows 

three quite distinct deformation patterns. For the pre-1906 

period (equivalent to very late in the earthquake cycle), 

the effect's of a detachment surface are minimal, and the 

patterns are nearly identical to those in the other two models (fig. 17). The effects of the 1906 earthquake are substantial in the detachment model and continue to affect the 

deformation pattern up to the time of the 1989 earthquake 

(fig. 18). A signal of the 1989 earthquake included in the 

overall response that is visible in the 5-yr post-1989 model 

(figs. 16, 19) can distinguish it both from the deformation 

patterns in the other models and from the post-1906 effects. Variations in the displacement rate of about 2 to 3 

rnmlyr that are also visible, primarily near Loma Prieta 

(southern part of the Bay Area block and vicinity of eastbay faults), will require detailed observations in that area 

over the critical period. Although the results plotted in figure 19 indicate patterns for a single profile, the spatial variation in the displacement field visible in figure 16 should 

help to delineate the earthquake response. 

DISCUSSION 

Combining our understanding of the three-dimensional 

plate-boundary structure and kinematics with numerical 

450 

Figure 14.Ã‘Continued 

500 550 

TIME, IN YEARS 
TECTONIC PROCESSES AND MODELS 

Coseismic 1906 

DISTANCE, IN KILOMETERS 

+ 

200 mmlyr 

+ 

20 mmlyr 

+ 

20 mmlyr 

Pre- 1 989 Post-1 989 (20 yr) 

100 120 140 160 180 200 100 120 140 160 180 200 100 120 140 160 180 200 

DISTANCE, IN KILOMETERS 

+ 

20 mmlyr 

- 

200 mmlyr 

-+ 

20 mmlyr 

Figure 15.-Velocity-difference fields during earthquake cycle in (A) detachment model, (B) elastic-crust model, and (Q weak-crust model. Shaded 

area. Bay Area block. Velocity vectors are plotted as difference between upper-crustal and upper-mantle velocities (Vrnist-Vmanrie). Vectors shown for 

coseismic periods are scaled by a factor of 10 to those shown for interseismic periods. 
THREE-DIMENSIONAL LITHOSPHERIC KINEMATICS IN THE LOMA PRIETA REGION F125 

DISTANCE, IN KILOMETERS 

-+ + 

200 mmlyr . 20 mmlyr 

Coseismic 1989 

,111 1000 

100 120 140 160 180 200 100 120 140 160 180 200 100 120 140 160 180 200 

DISTANCE, IN KILOMETERS 

+ 

200 mmlyr 

+ 

20 mmlyr 

Figure 15.Ã‘Continued 
TECTONIC PROCESSES AND MODELS 

Coseismic 1906 

DISTANCE, IN KILOMETERS 

+ 

20 mmlyr 

Pre- 1 989 

+ 

200 mmlyr 

+ 

20 mmlyr 

Coseismic 1989 

100 120 140 160 180 200 100 120 140 160 180 200 100 120 140 160 180 200 

DISTANCE, IN KILOMETERS 

+ 

200 mmlyr 

+ 

20 mmlyr 

Figure 15.Ã‘Continued 
THREE-DIMENSIONAL LITHOSPHERIC KINEMATICS IN THE LOMA PRIETA REGION F127 

modeling of the stress and deformational response of the 

lithosphere to earthquakes along the San Andreas fault 

system provides insight into the causality of the 1989 

Loma Prieta earthquake. First, viewed from the perspective of our model of three-dimensional plate kinematics 

and stress loading after the 1906 San Francisco earthquake, the occurrence of the 1989 earthquake can be considered to be associated with decoupling of the Santa Cruz 

block from the underlying mantle, rather than simply as a 

smaller version of the 1906 earthquake. Such events as the 

1906 earthquake lead to stress accumulation within the 

crust in the Santa Cruz Mountains section of the San Andreas fault. These stresses produce crustal deformation 

(growth of the Santa Cruz Mountains) and in the detachment model are largely relieved by postseismic creep at 

the base of the Bay Area block (for the region north and 

east of the San Andreas fault), resulting in a large stress 

accumulation in the middle crust south and west of the 

San Andreas fault and a substantial stress gradient across 

the San Andreas fault in the Santa Cruz Mountains. Second, particularly when incorporating the transient response 

to an earthquake, it is important to evaluate the deformational effects of the 1989 earthquake in concert with the 

deformation associated with the 1906 earthquake and with 

larger scale plate motions, as seen in lithospheric deformation. Models of viscous deformation after an isolated 

Loma Prieta-type event (without a strain history) will not 

include the effects of continuing post-1906 relaxation. 

Third, during the first 5- to 10-yr period after the 1989 

earthquake, observations of crustal deformation can provide important constraints on the details of the three-dimensional structure and rheology of the plate boundary in 

the San Francisco Bay region. In particular, the behavior 

of the Bay Area block relative to both the North American 

plate and the Santa Cruz block during this period differs 

considerably in each of the models tested here. Detailed 

observation can help to test and calibrate the assumptions 

in the various models, allowing the results to be more confidently applied to tectonic models of the earthquake cycle 

in the Loma Prieta region. 

The occurrence of the 1989 Loma Prieta earthquake 

along a segment of the San Andreas fault system that also 

+ 

10 mrnlyr 

+ 

10 mrnlyr 

+ 

10 mrnlyr 

Figure 16.-Surface-velocity fields for 5-yr period after 1989 Loma ted in figure 16A (particularly in vicinity of Bay Area block) indicate 

Prieta earthquake in (A) detachment model and (B) elastic-crust potential to discriminate detachment model from other two models by 

model, and for 20-yr period after 1989 earthquake in weak-crust using post-1989 geodetic observations. Results plotted in figure 16C 

model (C). Shaded area, Bay Area block. Far-field velocities are at do not differ significantly from those for shorter periods after earth- 

&% rate of relative Pacific-North American plate motion. Results plot- quake. 
F128 TECTONIC PROCESSES AND MODELS 

ruptured in 1906 makes it natural to relate processes associated with the 1989 earthquake to those associated with 

the 1906 earthquake. The initiation of rupture on the Santa 

Cruz Mountains section of the San Andreas fault at the 

base of the seismogenic layer is compatible, we believe, 

with considering the 1989 earthquake to be associated 

with decoupling of the crust from the underlying mantle 

(which continues along the path shown in fig. 5). The increase in stress (shear stress in the horizontal plane) in the 

vicinity of the Loma Prieta rupture during the interval 

1906-89 (fig. 9) provides the mechanism for such a style 

of rupture. This horizontal shear stress (and one-sided relaxation) increases with each 1906-type event and thus can 

lead to less frequent (but quasi-periodic) Loma Prieta-type 

events. The longer recurrence interval for Loma Prietatype events (events with a significant vertical component) 

relative to 1906-type events (Anderson, 1990; Valensise 

and Ward, 1991) may reflect the need for several strikeslip events to increase this decoupling stress to the point 

of generating an earthquake. The existence of an easily deforming detachment surface on the "North American" side 

of the fault through the Santa Cruz Mountains and San 

Francisco Bay allows the dissipation of any similar horizontal stresses in that region (fig. 9). 

'Consideration of the series of events that led to the 1989 

Loma Prieta earthquake is important in evaluating the effects of this earthquake. Although much of the postseismic 

relaxation after the 1906 San Francisco earthquake had already occurred, the stress regime in the San Francisco Bay 

region before the 1989 earthquake evolved in response to 

both the 1906 relaxation and post-1906 plate motions. 

This preloading of the system plays an important part in 

post-1989 events. Although much of the coseisrnic deformation and even some of the long-term deformation field 

can be adequately simulated by elastic-dislocation models, 

we believe that explicit incorporation of viscous rheologies more closely represents the deformational behavior of 

the crust, lithospheric mantle, and plate-boundary zone 

DISTANCE, IN KILOMETERS 

Figure 17.-Pre-1906 surface velocity (A, B) and lithospheric-mantle velocity (C, D) in profiles (perpendicular to plate boundary) in south-bay region (A, 

C; at -220 km, fig. 16) and Loma Prieta region (B, Q at -170 km, fig. 16) in detachment model (solid curve), elastic-crust model (dotted curve), and 

weak-crust model (dashed curve). Before 1906 San Francisco earthquake (that is, late in earthquake cycle), all models produce similar displacements. 
THREE-DIMENSIONAL LITHOSPHERIC KINEMATICS IN THE LOMA PRIETA REGION F129 

than do simple elastic models. The evaluation of crustal 

deformation on the time scale of the earthquake cycle in 

the San Francisco Bay region, which for large events is 

about 100 to 200 yr, requires the incorporation of viscous 

theologies and the inclusion of the series of events (at 

least the largest) that precede the earthquake of interest. 

Although the 1989 Loma Prieta earthquake does not 

rank with the great earthquakes that have occurred along 

the San Andreas fault system in northern California, it 

does provide an important tool for improving our understanding of lithospheric behavior. Throughout our modeling, we have tested several scenarios for lithospheric 

structure and plate-boundary rheology. Our preferred 

model, which incorporates deformable structures in the 

lower crust, produces deformational behavior that can be 

tested by observations during the first 5- to 10-yr period 

after the earthquake. The preearthquake deformation regime, though well documented in the San Francisco Bay 

region, cannot conclusively distinguish among the various 

models, which have quite different implications for the 

overall stress regime in the bay region, and so the resulting seismic potential of the various fault segments differs 

from model to model. The early stages of postearthquake 

lower-crustal and plate-boundary relaxation may provide 

the key to unlocking intermodel differences. 

We emphasize that three-dimensional modeling of the 

deformation field associated with a complex plate boundary is still in its infancy. Our models serve as important 

extensions of other models of the coseismic response of 

the San Francisco Bay region and regional deformation. 

We have found that combining this modeling with improved kinematic models of plate-boundary behavior allows us to focus on those details of plate-boundary 

deformation which are important in the earthquake cycle. 

DISTANCE, IN KILOMETERS 

Figure 18.-Pre-1989 surface velocity (A, B) and lithospheric-mantle ve- eta earthquake, both elastic- and weak-crust models produce similar 

l&ity (C, D) in profiles (perpendicular to plate bound&) in south-bay displacements, essentially no different from pre-1906 patterns, whereas 

region (A, C; at -220 km, fig. 16) and Loma Prieta region (B, D; at -170 detachment model still shows effects of 1906 San Francisco earthkm, fig. 16) in detachment model (solid curve), elastic-crust model (dot- quake-that is, velocity curve is shifted toward the San Andreas fault 

ted curve), and weak-crust model (dashed curve). Before 1989 Loma Pri- and away from deep plate boundary. 
F130 TECTONIC PROCESSES AND MODELS 

However, use of these results to directly answer questions 

of earthquake potential on specific fault segments is still 

premature. Although it is tempting to cite the results 

shown in figure 14A as providing the information needed 

to evaluate the concept of paired earthquakes, we do not 

believe that our results, at present, argue conclusively for 

or against such a concept. We do, however, believe that 

the style of modeling we have undertaken can improve our 

understanding of the spatial and temporal variations in 

stress and deformation associated with the earthquake 

cycle. This improved understanding of the underlying dynamics of plate-boundary deformation in the San Francisco Bay region is a key to an improved assessment of 

earthquake risk and potential in the region. The 1989 

earthquake has focused attention on these processes and 

has served as an important tool that will allow improved 

observations of the postseismic response of the plate 

boundary. 

ACKNOWLEDGMENTS 

This research was supported by U.S. National Science 

Foundation grants EAR-88 16966 and EAR-9 104 1 85 and 

U.S. Geological Survey grant NEHRP 1434-92-G-22 1 3. 

We thank Jay Melosh for the use of his finite-element program TECTON. Discussions with numerous individuals 

throughout this research have been invaluable to us in 

crystallizing our thoughts; in particular, we thank George 

Zandt, Charles Langston, Charles Arnmon, Harley Benz, 

Thorne Lay, and Michael Lisowski. Computations were 

performed in part on a Cray YMP-2E computer, courtesy 

DISTANCE, IN KILOMETERS 

Figure 19.-Surface velocity (A, B) and lithospheric-mantle velocity (C, pre-1906 or pre-1989 pattern, whereas detachment model still shows efD) during 5-yr period after 1989 Loma Prieta earthquake in profiles (per- fects of 1906 San Francisco earthquake, although these effects are overpendicular to plate boundary) in south bay (A, C; at -220 km, fig. 16) printed by transient effects of 1989 earthquake. That is, velocity curve 

and Loma Prieta region (B, D; at -170 km, fig. 16) in detachment model for detachment model is shifted even closer to San Andreas fault, away 

(solid curve), elastic-crust model (dotted curve), and weak-crust model from deep plate boundary, and region of concentrated deformation is nar- 

(dashed curve). Shortly after 1989 earthquake, both elastic- and weak- rower. If 1989 earthquake had ruptured to surface, its effects would be 

crust models produce similar displacements, essentially no different from more noticeable in these plots. 
THREE-DIMENSIONAL LITHOSPHERIC KINEMATICS IN THE LOMA PRIETA REGION F131 

of the Earth System Science Center at the Pennsylvania 

State University, and on equipment graciously donated by 

the Hewlett-Packard Co. Reviews of the manuscript by 

Gene Humphreys, Joseph Andrews, and Robert Simpson 

are greatly appreciated. 

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