SEMIANNUAL REPORT 

TO THE NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 

NASA CONTRACT NAG5-459 

“Plate Motions and Deformations from Geologic and Geodetic Data” 

for the period 

1 July 1988 - 31 December 1988 

Principal Investigator: Professor Thomas H. Jordan 

Department of Earth, Atmospheric, 

and Planetary Sciences 

Massachusetts Institute of Technology 

Cambridge, MA 02139 

DEFORIYATIONS (NASA-CR-184987) FROB GEOLOGIC PLATE HOTIONS AND GEODETIC AND DATA N 8 9- 247 57 

Semiannual Report, 1 Jul. - 31 Dec. 

(nassachusetts Inst. of Tech.) 222 p Unclas 

1988 

CSCL 98G G3/46 0210330 
TABLE OF CONTENTS 

1. SIGNIFICANT ACCOMPLISHMENTS 

2. PROBLEMS AND RECOMMENDATIONS 

3. DATAUTILITY 

4. FUNDSEXPENDED 

5. APPENDIX 1: Geodetic Measurement of 

Deformation in California 
3 

SIGNIFICANT ACCOMPLISHMENTS 

This Semiannual Report covers research conducted under NASA Contract NAG5-459 for the 

period 1 July through 31 December 1988. 

The research effort sponsored by our NASA contract during this half-year period has been 

directed at understanding the distribution of deformation between pairs of CDP observing sites in 

the western United States. An article on this subject for Scientific American by T. H. Jordan and 

J. B. Minster appeared in the August issue. Reprinted copies are included with this report. 

Several other papers are being prepared for publication, one by J. Sauber and T.H. Jordan on the 

implications of the VBLI measurements for deformation west of the Basin and Range, and 

another by K. Feigl, T.H. Jordan and R. King that focuses on deformation in the Santa Maria 

Basin. A copy of Dr. Sauber's PhD thesis, which was partially supported by this contract, is 

included as an appendix. 

PROBLEMS AND RECOMMENDATIONS 

None 

DATA UTILITY 

Not applicable 

FUNDS EXPENDED 

As of 31 December 1988 a total of $293,710 had been spent, out of the current fund limitation of 

$293,710. 
GEODETIC MEASUREMENT OF DEFORMATION IN CALIFORNIA 

by 

Jeanne Marie Sauber 

B.S., University of Michigan 

(1976) 

M.S., University of South Carolina 

(1979) 

SUBMllTED TO THE DEPARTMENT OF 

EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES 

IN PARTIAL FULFILLMENT 

OFTHE REQUIREMENTS 

FOR THE DEGREE OF 

DOCTOR OF PHILOSOPHY 

at the 

MASSACHUSE'ITS INSTITUTE OF TECHNOLOGY 

November 1988 

0 Massachusetts Institute of Technology 

Signaturc of Author 

Certifkd by W Sean C. Solomon n 

Thesis Co-Supervisor 

Thomas H. Jordan 

Thesis Co-Supervisor 

Thomas H. Jordan Accepted by 

Chairman, Departmental Graduate Committee 
2 

GEODETIC MEASUREMENT OF DEFORMATION IK CALIFORNIA 

Jeanne M.Sauber 

Submitted to the Department of Earth, Atmospheric, and Planetary Sciences on 

November 22,1988, in partial fulfillment of the requirements for the 

Degree of Doctor of Philosophy in Geophysics 

Abstract 

The very long baseline interferometry (VLBI) measurements made in the western 

U.S. since 1979 as part of the National Aeronautics and Space Administration Crustal 

Dynamics Project provide discrete samples of the temporal and spatial deformation field. 

The interpretation of the VLBI-derived rates of deformation requires an examination of 

geologic information and more densely sampled ground-based geodetic data. In the first 

two of three related studies embodying this thesis I process mangulation and trilateration 

data measured on two regional networks, one in the central Mojave Desert and one in the 

Coast Ranges east of the San Andreas fault. At the spatial scales spanned by these local 

geodetic networks, auxilliary geologic and geophysical data have been utilized to examine 

the relation between measured incremental strain and the accommodation of strain seen in 

local geological structures, strain release in earthquakes, and principal stress directions 

inferred from in situ measurements. In the third study I process VLBI data from stations 

dismbuted across the Pacific - North American plate boundary zone in the western United 

States. The VLBI data have been used to constrain the integrated rate of deformation 

across portions of the continental plate boundary in California and to provide a tectonic 

framework to interpret regional geodetic and geologic studies. 

Shear strain rates in the cennal Mojave Desert of California have been calculated with 

data from triangulation and mlateration surveys made during 1934-1982. For the region 

between the Helendale and Camp Rock faults the shear strain rate was determined to be 

0.16 f 0.03 pradyr, with maximum right-lateral shear straining occurring on a plane 

oriented N41'W k 5'. If we assume that this deformation is due to right-lateral motion 

across the northwest trending local faults, the average shear straining corresponds to a 

relative displacement of 6.7 f 1.3 mdyr across this portion of the network. From the 

Camp Rock fault eastward across the network then is a transition from significant to very 

low strain rates. Examination of nine focal mechanisms and their relation to the local 

geology and the strain data suggests that most of the long-term displacement occurs on the 

major northwest trending faults oriented nearly along the direction of relation motion 

between the North American and Pacific plates. Secondary faulting, controlled by a 

CoulombAnderson failure mechanism or by slip on preexisting faults, can account for the 

occurnnce of earthquakes on faults of other orientations. 

Triangulation and trilateration data from two geodetic networks located between the 

San Andreas fault and the Great Valley have been used to calculate the shear strain rates in 

the Diablo Range and to estimate the slip fate alopg the Calaveras and Paicines faults in 

central California. The shear strain rates, y1 and y, , have been estimated independently 

from angle changes using Prescott's method and from the simultaneous reduction for 

station position and strain parameters using the DYNAP method with corrections to reduce 

the triangulation and mlateration data to a common reference surface. On the basis of 

Prescott's method, the average shear strain rate across the Diablo Range for the time period 

between 1962 and 1982 is 0.15 f 0.08 pradyr, with the orientation of the most , compressive strain (p) at N16'E f 14'. With corrections for the deflection of the vertical 
3 

and the geoid - reference ellipsoid separation computed on the basis of local gravity 

observations, the average shear strain estimFted using the DYNAP method is 0.19 f 0.09 

prad/yr, and p = N16'E f 13'. Although y is not significantly greater than zero at the 

95% confidence level, the onentation p is similar to the direction of maximum compressive 

strain indicated by the orientation of major fold structures in the region (N25'E). We infer 

that the measured strain is due to compression across the folds of this area; the average shear straining corresponds to a relative shortening rate of 5.7 f 2.7 dyr. In contrast to 

the situation throughout most of the Coast Ranges, where fold axes have orientations 

approximately parallel to the San Andreas fault, within the Diablo Range between Hollister 

and Coalinga the trends of the fold axes arc different and are thought to be controlled by 

reactivation of older smctures. From trilateration measurements made between 1972 and 

1987 on lines that arc within 10 km of the San Andreas fault, a slip rate of 10-12 mm/yr 

has been calculated for the Calaveras-Paicines fault south of Hollister. The slip rate on the 

Paicines fault decreases to 4 mm/yr near Bitter. 

To distinguish between different models that describe the distribution of strike-slip 

and compressive displacements within the southern Coast Ranges we compared the 

findings of regional geologic and geodetic studies with predictions from kinematic plate 

models. Such comparisons support the view that the fault-parallel component of the San 

Andreas "discrepancy vector" may be accommodated by strike-slip motion on the 

Rinconada as well as the San Gregorio fault. Geological and seismicity data, as well as our 

geodetic results, suggest that northeast-southwest compression in the Coast Ranges of 

central California may be localized to two regions, the 30-km-wide zone spanned by the 

triangulation and mlateration network of this study and a second zone to the west of the 

Rinconada fault. The inferred shortening to the east of the San Andrcas fault may represent 

a significant component of the fault-normal compression predicted by the discrepancy 

vector. 

The geocenmc position vectors from a set of 77 VLBI experiments beginning in 

October 1982 have been used to estimate the tangential rate of change of station positions in 

the western U.S. in a North-America-fixed reference frame. These data have been 

processed with a procedure that removes from apparent tectonic motion the contamination 

due to errors in Earth-orientation parameters and non-uniform station geometry; this 

procedure accounts fully for the position covariance between stations. For three regions, 

across southern California just north of the Imperial fault, in the "big-bend" region, and in 

central California, the rates of deformation derived from VLBI and ground-based geodetic data have been compared, and the relationship between the rates of deformation determined 

from geological data and those estimated from the geodetic data have been examined. 

Deformation across southernmost California is fairly well described by simple rightlateral shear on the San Andreas, San Jacinto, Elsinore, and possibly the offshore faults of 

the California borderlands. An estimate of the integrated rate of deformation across the 

southern region of the Basin and Range province given by the station Yuma (3.4 f 2.7 

mm/yr at N84'W f 16') is consistent with the low rate of deformation inferred from 

geologic data. A large earthquake has not occurred on the southern segment of the San 

Andreas fault within the last -400 years, and strain accumulation is observed over a broad 

region. If the vector veIocity given by the Monument Peak - Yuma difference vector (37.6 

f 3.4 dyr at NWW f 8') is approximately equal to the accumulated rate of long-term 

slip across the San Andreas, San Jacinto, and Elsinore faults, additional deformation is 

predicted to occur on faults offshore in the California borderlands. The velocity difference 

vector between Vandenberg and Monument Peak (5.9 f 2.9 dyr at N23'W f 4') further 

supports the hypothesis that additional deformation occurs on such offshore faults. 
4 

In the big-bend region of the San Andmas fault recent deformation has been measured 

across the right-lateral strike-slip faults of the central Mojave, along the San Andrcas fault, 

and as northeast-southwest compression across the western Transverse Ranges and the 

offshore faults in the Channel Islands. The result for the VLBI station Mojave (7.1 f 0.9 

mdyr at NSWW f lo), along with ground-based geodetic and geologic data from the 

Mojave Desert, the Garlock fault, and the Basin and Range, suggest that the estimated rate 

of deformation on the northwest-striking faults of the central Mojave may be kinematically 

related to deformation north of the Garlock. The station Mojave as well as the western 

Garlock fault are then within a deforming region connecting slip in the central Mojave to 

deformation north of the Garlock. The alternative hypothesis that the Mojave VLBI and 

central Mojave trilateration-triangulation results arc due to elastic strain accumulation which 

will be relieved in the next large earthquake on the San Andrcas fault is rejected on the basis 

of several arguments, the most convincing of which is that rccent slip has been documented 

along the faults of the central Mojave. Over the broad region between Mojave and PL the 

rate of deformation given by the differenced velocity vector is 26.9 f 2.6 mm/yr at N43'W 

f 5' and suggests that the long term rate of slip on this segment of the San Andreas fault 

may be -25 mm/yr. The velocity difference vector for Vandenberg - Santa Paula suggest 

15.2 f 6.7 mm/yr of northeast-southwest compression (N15'E f 7') between the two 

sites. 

In central California slip along the San Andreas fault is thought to occur primarily 

through surface creep. As noted above, recent deformation has also been measured on 

tectonic elements east and west of the San Andreas and include extension across the Basin 

and Range, right-lateral strike-slip motion on the Rinconada and San Gregorio faults and 

northeast-southwest compression within the Coast Ranges. "he vector rate of change of 

the station position for OVRO (Owens Valley Radio Observatory), 10.3 f 2.7 dyr at 

N37'W f 43, is closer to the local orientation of the Owens Valley fault than the assumed 

direction of extension in the Basin and Range (NWW). The difference velocity vector 

between Fort Ord and OVRO, 37.1 f 2.8 dyr at N37'W f 5', is similar to the integrated 

rate of deformation estimated from ground-based geodetic networks and from geological 

data. 

Thesis Supervisors: Sean C. Solomon, Professor of Geophysics 

Thomas H. Jordan, Professor of Geophysics 

, 
5 

Acknowledgements 

Along the yellow brick road of my graduate career I have encountered numerous 

people that have taken the time and effort to transmit their expertise, to assist me with my 

work, and to befriend me by providing personal support and encouragement. Since the 

hour is late and my memory is short I briefly acknowledge only some of these people. 

It has been both a priviledge and constant intellectual challenge to work with my two 

advisors Sean Solomon and Tom Jordan. The scientific and personal integrity Sean brings 

to his work are inspirational and the amount of red ink that has gone into his critical input 

of my work is monumental. Throughout the years Sean's optimistic anticipation of my 

future accomplishments have always helped me to get there. The energy and enthusiasm 

emanating from Tom is impressive and the extent of his intellect comprehensive. Tom and 

Robin's generosity is displayed regularly as a notice near the elevator reading: "Party at the 

Jordan's ...'I. I thank both Tom and Sean for encouraging me to extend my scientific reach 

farther than I would of done on my own. 

Five years ago, after deciding to conduct research on problems related to crustal 

deformation, Paul Okubo made the wise suggestion that I try to work with scientists at the 

U.S. Geological Survey in Menlo Park. Thanks to Wayne Thatcher I was given a Student 

Internship which enabled me to spend portions of four summers at the USGS. Wayne's 

thoughtful guidance and constructive reviews of my papers are greatly appreciated. As pan 

of the San Benito study I had the opportunity to work with Michael Lisowski. I thank 

Michael for patiently answering my geodesy questions. While at the USGS I benefited 

from conversations with Will Rescott and Jim Savage, as well as many others. 

For the last two and half years of graduate school I was awarded a NASA Graduate 

Student Fellowship. This fellowship enabled me to travel to Goddard Space Flight Center 

to work with the VLBI group headed by Tom Clark. Tom's insatiable curiosity and ability 

to learn a new field are really admirable. David Gordon, Ed Himwich, Jim Ryan, and 
6 

Chop Ma introduced me to the processing of VLBI data and fielded my many questions. 

During the last year I have had the joy of working with Lynda Bell. 

Other teachers that have aided my academic progress include Clark Burchfiel, Bob 

King, Yehuda Bock, Bernard Minster, Tom Herring, Renata Dmowska, Jim Rice, Nafi 

Toksoz, Ted Madden, Victor Li, John NabeIek and Jay Pulli. 

The quality of my everyday life as a graduate student working on the fifth floor was 

enhanced and my research progress made easier thanks to my officemates Lind, Anne, 

John, and Steve, Dave's generous assistance in the computer room, Jan and Katherine's 

administrative wizardry, and due to the help of Mark, Lind, Kurt, Bob, Justin, and others. 

Without Greg Beroza's contribution to the VLBI work given in this thesis I would of spent 

a much longer time on the fifth floor of the Green Building. 

In the middle of my sprint to the PhD finish line I suffered a serious back injury and I 

learned an Egyptian proverb that I will not forget: "Good health is a halo over the heads of 

the healthy that only the ill can see." I would like to express my deepest appreciation to 

Lind Gee whose generosity and kindness made my stay in the infirmary more bearable, 

Don Vasco for making me laugh, Mark Murray for his determination in fulfulling an errand 

for me and Greg Bema for commiserating with me. I thank Anne Sheehan, John Goff, 

Dave Krowitz, Dan Rothman, the rest of my MIT colleagues, and friends from all over the 

country for the flowers, cards, phone calls and visits. I also thank Tom Clark and Dave 

Smith for extending my graduate fellowship and Lynda Bell and my other NASA 

colleagues far their thoughtfulness. 

I would like to thank Itzhak Reichman, my roommate and dear friend Kaye Shedlock, 

and Paul Okubo for their support and encouragement during my first three years at MIT, 

Lucianna Astiz for her kindness, my domunates at Green Hall - Christine, Rick, Effat, and 

many others - for giving me such a "warm" home to return to at night, and Elana Doering 

and Jonathan Sigler for their unfailing friendship. Finally, I would like to thank my 

parents William and Shirley Sauber and the rest of my family for their love and devotion. 
For the first time in six years I will be going home for Christmas. There is no place like 

home. 

This research was supported by the National Aeronautics and Space Administration 

through a Graduate Student Research Fellowship (NGT-50103) and through the Crustal 

Dynamics Project under grant NAG 5-814 and NAG 5-459. Support for part of this 

research was provided by the U.S. Geological Survey while I worked in Menlo Park. 
8 

Table of Contents 

Page 

Abstract ......................................................................................... 2 

Acknowledgements ............................................................................ 5 

Table of Contents .............................................................................. 8 

CHAPTER 1 . INTRODUCTION .......................................................... 11 

Figure Captions ................................................................................ 15 

Figures .......................................................................................... 16 

CHAPTER 2 . GEODETIC MEASUREMENT OF DEFORMATION IN THE 

CENTRAL MOJAVE DESERT. CALIFORNIA ......................................... 17 

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

General Setting of the Mojave Desert Block ............................................... 

Geodetic Strain Rates ......................................................................... 

Method ................................................................................... 

Results ................................................................................... 

Other Geodetic Studies in the Mojave Block ........................................ 

Earthquake Focal Mechanisms .............................................................. 

Method and Results .................................................................... 

Comparison of Principal Stress Directions Estimated from Earthquake Focal 

Mechanisms With Geodetic Strain Directions ....................................... 

Comparison of Results to Models of a Region under Simple Shear .............. 

Contribution of Earthquakes to Measured Strain .......................................... 

Tectonic Implications of Deformation in the Mojave Desert ............................. 

18 

19 

21 

21 

23 

25 

26 

27 

28 

30 

31 

32 

Summary ....................................................................................... 35 

.......................................................................................... 37 Tables 
9 

Figure Captions ............................................................................... 

Figures ......................................................................................... 

CHAPTER 3 . GEODETIC MEASUREMENT OF DEFORMATION EAST OF 

THE SAN ANDREAS FAULT IN CENTRAL CALIFORNIA ........................ 

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

Tectonic Setting ............................................................................... 

Geodetic Strain Rates ......................................................................... 

San Benito Network ................................................................... 

Coalinga Trilateration Network ....................................................... 

Comparison with Other Geodetic and Geologic Observations ........................... 

Principal Directions of Strain and Stress .................................................... 

Relation of Deformation East of the San Andreas Fault to the Accommodation 

of Plate Motion ................................................................................ 

Summary ....................................................................................... 

Appendix ....................................................................................... 

Assumptions Made in the Estimiition of Horizontal Shear Parameters ........... 

Accuracy of Triangulation and Trilateration Measurements ....................... 

Presco tt's Method ...................................................................... 

DYNAP Method ........................................................................ 

Corrections to Reduce Observations to a Common Reference System .......... 

Tables ........................................................................................... 

Figure Captions ................................................................................ 

Figures .......................................................................................... 

CHAPTER 4 RATES OF DEFORMATION IN SOUTHERN AND CENTRAL 

CALIFORNIA FROM VLBI. GROUND-BASED GEODETIC. AND GEOLOGIC 

DATA ........................................................................................... 

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

40 

42 

50 

51 

52 

55 

56 

60 

63 

65 

69 

73 

75 

75 

76 

77 

78 

79 

82 

88 

91 

97 

98 
10 

Determination of Rates of Deformation Utilizing VLBI .................................. 103 

Single-Epoch Processing .............................................................. 103 

Multi-Epoch Processing for Determination of the Vector Motion of VLBI sites 107 

Data Analysis ............................................................................ 115 

Results ................................................................................... 117 

Path Integral Formulation .................................................................... 120 

Comparison of Geodetic and Geologic Rates of Deformation in Southern 

and Central California ......................................................................... 122 

Path Integrals Utilizing Geodetic Data ................................................ 124 

Path Integral Utilizing Geological Data ............................................... 127 

Discussion ...................................................................................... 129 

The Rate of Deformation Across the Basin and Range Province .................. 129 

Geologic Strain versus Incremental Strain ........................................... 131 

Slip on Offshore Faults ................................................................ 135 

Summary ....................................................................................... 137 

Tables ........................................................................................... 140 

Figure Captions ................................................................................ 151 

Figures .......................................................................................... 156 

CHAPTER 5 . CONCLUSIONS ............................................................ 193 

REFERENCES ................................................................................ 200 
11 

Chapter 1. Introduction 

Historically geodetic measurements, although imprecise by today's standards, have 

been utilized to address fundamental scientific questions. The founder of scientific 

geodesy, Eratosthenes, deduced the radius of the Earth on the basis of the measurement of 

the baseline between Alexandria and Aswan made with a camel whose walking speed was 

well-calibrated. The value he obtained departs from the radius of a mean spherical Earth 

(6371 km) by -2% [Torge, 19801. Early in this century two scientists, H.F. Reid and A. 

Wegener, proposed models central to modern crustal deformation studies. Geodetic 

surveys made before and after the 1906 earthquake have provided considerable information 

on the crustal deformation that accompanied the great San Francisco earthquake. These 

data led Reid [ 19101 to postulate that swain accumulated elastically by continuous slow 

motions at great distances from the San Andreas fault and that such strain is released by 

sudden slip on the fault surface at the time of an earthquake. Wegener [ 19291 tested his 

hypothesis of continental drift by the direct measurement of drift rates through repeated 

observations of astronomical positions. In his words " ... only recently this method 

furnished the fmt real proof of the present-day displacement of Greenland predicted by 

drift theory ... .I' Unfortunately, Wegener had to rely on inaccurate data, and the 

calculated rates of separation between North America and Europe were two orders of 

magnitude larger than current estimates. 

High-precision space geodetic data from very long baseline interfemmctry (VLBI), 

satellite laser ranging (SLR) and the U.S. global positioning system (GPS), along with 

trilateration and spirit leveling measurements, are providing present-day rates of 

deformation at intercontinental, regional, and local spatial scales. In some situations where 

an extended measurement period yields an improved estimate of rates of strain, historical 

mangulation and leveling data can also be utilized in concert with the more prccise modern 

8 
12 

measurements. The recent influx of high-resolution data has the potential to influence 

significantly the way we formulate studies of tectonic deformation. 

In the western U.S., VLBI measurements have been made since 1979 as part of the 

National Aeronautics and Space Administration (NASA) Crustal Dynamics Project. These 

measurements provide discrete sampling of the temporal and spatial deformation field. The 

proper interpretation of the VLBI-derived rates of deformation requires an examination of 

geologic and more densely sampled ground-based geodetic data. At the spatial scales 

spanned by a local geodetic network, auxilliary geologic and geophysical data can be 

utilized to examine the relation between measured incremental strain and the 

accommodation of strain seen in local geological stucturcs, strain release in earthquakes, 

and principal stress directions inferred from in situ measurements. Integration of the 

results from local areas to the regional spatial scale provides a framework for developing 

kinematic models testable by VLBI measurements. 

In this thesis I examine the rates of deformation across the Pacific - North American 

plate boundary zone in California. In the fmt two studies I process triangulation and 

ailateration data measured on two regional networks, one in the central Mojave Desert and 

one in the Coast Ranges east of the San Andreas fault (Figure 1). In the third study I 

process VLBI data from stations distributed across the Pacific - North American plate 

boundary zone in the western United States. Several common themes are pursued in each 

study: (1) the relation of the measured incremental strain to long-term deformation (2) the 

integration of diverse data that provide estimates of the rate and orientation of deformation, 

and (3) spatial scales of deformation and the relation of deformation in subregions to the 

overall accommodation of deformation across the plate boundary. 

The Mojave Desert block is a major structural element in southern California which 

lies to the northeast of the 'big-bend region and contains active right-lateral strike-slip 

faults oriented nearly parallel to the direction of Pacific - North American relative motion. 

This portion of the plate boundary represents a transition from primarily simple right-lateral * 
13 

slip on the faults in southernmost California to extension in the Great Basin and 

transcurrent motion on the San Andreas fault in cenaal California. In Chapter 2 I estimate 

the present-day rate of deformation across the northwest striking faults of the central 

Mojave Desert. To relate the measured incremental strain to long-term deformation, focal 

mechanisms are determined for recent earthquakes and the relative contribution of 

earthquakes to the measured strain is evaluated The tectonic implications of these geodetic 

and seismological results, together with other regional geodetic and geologic data, are then 

explored. 

The May 1983 Coalinga earthquake (ML = 6.7 ), which involved slip on a thrust or 

reverse fault beneath a young fold, has focused attention on the importance of 

understanding the mode and rate of deformation east of the $an Andreas fault in central 

California. In Chapter 3, I determine rates of crustal strain in the Diablo Range north of 

Coalinga from a triangulation and trilateration network and from line-length changes 

determined by means of trilateration measurements within 10 km of the San Andreas fault. 

To distinguish between models relating the formation of fold structures in the southern 

Coast Ranges to motion along the San Andreas fault, the principal directions determined 

geodetically for the rate of strain within the Diablo Range are compared with the 

orientations of the maximum principal stress (q) estimated from wellbore breakouts, the 

azimuths of P axes determined from earthquake focal mechanisms, and the ands of major 

fold structures. The distribution of strike-slip and compressive displacements within the 

Coast Ranges is constrained by a comparison of the predictions from plate kinematic 

models and from the findings of ngional geologic and geodetic studies. 

VLBI measurements of changes in vector baselines that both span and are distributed 

within the Pacific - North American plate boundary zone over the last six years provide a 

unique geodetic data set . In Chapter 4 I process VLBI data to obtain estimates of the rate 

of change of tangential station position in a North-America-fixed reference frame. These 

data are used as constraints on the integrated rate of deformation across portions of the 
14 

continental plate boundary in California and provide a framework to interpret regional 

geodetic and geologic studies. On the basis of geologic data the rates of deformation have 

been estimated in southern and central California over time scales of approximately 102 - 

106 years, while with mangulation, mlateration, and VLBI data the rates of deformation 

over the last 100 - 1@ years may be determined. For three regions, across southern 

California just north of the Imperial fault, in the 'big-bend' region, and in central 

California, I compare the rates of deformation derived from VLBI and ground-based 

geodetic data, and I examine the relationship between the rates of deformation determined 

from geological data and those estimated from geodetic data. 

In Chapter 5, I summarize the principal conclusions of this thesis and suggest several 

topics for future research. 
15 

Figure Captions 

Figure 1. Locations of VLBI sites (mangles with station codes) and geodetic networks 

utilized in this thesis. CMN = Central Mojave Network and SBN = San Benito Network. 

Quaternary fault traces are from Jennings [ 19751. Mercator projection of California, 

Nevada, and western Arizona. 
16 
17 

Chapter 2. Geodetic Measurement of Deformation in the Central 

Mojave Desert, California 
18 

Introduction 

The boundary between the Pacific and North American plates in California is 

characterized by active deformation over a broad region (Figure 1). Quaternary fault slip 

rates [Sieh and Jahns, 1984; Weldon and Sieh, 19851, as well as geodetic estimates of slip 

rate from trilateration data [Prescorr er al., 19851 and very long baseline interferometry 

(VLBI) [Lyzenga et al., 19861, indicate that in central and southern California the San 

Andreas fault system has accommodated approximately 68% of the relative plate motion of 

SOmm/yr predicted from the NUVEL-1 global plate velocity model [DeMets er ai., 19871. 

Where the remaining fraction of the relative plate motion is accommodated is uncertain; 

high angle strike-slip faults subparallel to the San Andreas system may take up a significant 

proportion of this “missing” plate motion. 

The strike of the San Andreas fault system is approximately parallel to the slip 

direction of relative plate motion, N35’W, along most parts of the plate boundary. 

However, in the ‘big-bend section the San Andreas fault locally changes its trend by 20’- 

30’ along a 190-km-long segment between San Gorgonio Pass and Tejon Pass. An 

essential structural element at this portion of the plate boundary is the Mojave Desert block, 

which lies to the northeast of the bigbend region and contains active right-lateral strike-slip 

faults oriented nearly parallel to the direction of Pacific-North American relative motion. 

The rate and mode of deformation in this block is thus important to an understanding of the 

character and distribution of deformation at the plate boundary and to earthquake risk 

assessment in southern California. 

In this chapter, data from triangulation and ailateration surveys conducted between 

1934 and 1982 arc used to determine rates of shear strain in the central Mojave Desert 

(Figure 2). On the assumption that these strain rates represent a long-term average rate, 

they permit an improvement to the estimates of slip rate obtained from geological 

observations. In addition, focal mechanisms determined for six recent earthquakes, in 

combination with three previously detennined focal mechanisms [KuMmori and Fuis, 
19 

19761, are used to examine the relationships among seismicity, strain data, and local 

geology. Finally, the data from this study, along with other geologic and geodetic data, are 

used as a basis for exploring the tectonic implications for southern California. 

General Setting of the Mojave Desert Block 

The dominant active structural elements of the Mojave Desert block are right-lateral, 

strike-slip faults trending approximately N35'W - N42'W. The surface traces of these 

faults are 8-80 km long and are spaced approximately 8-30 km apart (Figure 2). Dokka 

[ 19831 has documented cumulative right-lateral displacement on the major northweststriking faults of 27-38 km in the last 20 m.y. The time of initiation of fault slip is poorly 

constrained, however, because of the lack of mappable offsets of rock units along the 

faults. From field observations, Dokka [ 19831 has suggested that strike-slip faulting may 

have started as late as Pliocene or Quaternary. According to this view, the northweststriking faults of the central Mojave may be in an early stage of development. If most of 

the strike-slip motion began -5 m.y. ago, when major spreading initiated in the Gulf of 

California and acceleration of slip occurred on the San Andreas fault [Moore and Curray, 

1982; Page and Engebretson, 1984; Winkcr and Kidwell, 19851, the average rate of slip 

along the northwest-trending faults may be as much as -7 mdyr. If slip instead initiated 

20 m.y. ago, the slip rate could be as low as 1 mdyr. All the faults from Helendale to 

Ludlow show some Quaternary displacement [Dokko, 19831, with no one fault appearing 

to dominate. This is further corroborated by field observations (B.C. Burchfiel and J.D. 

Walker, personal communication, 1985) indicating that any long-term deformation 

occurring on the northwest-striking faults is probably not confined to a single active fault. 

Geologic field observations [Dokko and Glazner, 1982; B.C. Burchfiel and I.D. Walker, 

personal communication, 19851 further suggest that compressional and extensional features 

are small and erratic in the central Mojave and are due to local irregularities in fault 

gwmtry* 
20 

Left-lateral faults of approximately east-west strike arc also common, especially in the 

northeast corner of the Mojave block( Figure 2). The Garlock and Pinto Mountain faults 

that bound the Mojave block show this type of motion. The surface expressions of 

northwest-trending strike-slip faults of the central Mojave terminate, to the south, at the 

Pinto Mountain fault; at the northern boundary of the Mojave block such faults do not cross 

the Garlock fault. Left-lateral displacements of at least 48 to 65 km have been documented 

on the central and western portions of the Garlock fault [Davis and Burchfief, 19731. An 

average displacement rate of about 11 mrdyr on the central part of the Garlock fault has 

been estimated from a match of displaced Pleistocene alluvial fan gravels by Carter 

[ 19801. A lower rate of 7 Wyr during the Holocene period has been suggested by Astiz 

and Allen (19833 from a compilation of alignment may data and offset of primarily 

Holocene strata. 

The Mojave block is bounded on the west by the big-bend portion of the San Andreas 

fault. The long term slip rate on this portion of the fault is estimated to be 35 mm/yr 

[Weldon and Sieh, 19851. The average strike is N65'W. The maximum shear strain rate 

measured between 1973 and 1983 across the San Andreas fault on the Palmdale network is 

0.37 f 0.02 pstrain/yr oriented N65'W [King and Savage, 19841. Between the San 

Andreas fault and the most western fault of the central Mojave, the Helendale fault, there 

are a few small reverse faults. Focal mechanisms in this transition region an mostly thrusttype events [Sauber er af. , 19831. On the southwestern boundary, north-south crustal 

shortening of the San Bemardino block occurs at a step in the San Andreas fault [Meisling, 

19841. 

Historically, the Mojave block has been characterized by small to moderate-size 

earthquakes. In the area of the central Mojave examined in this study (Figure 3), five 

earthquakes with local magnitude ML 2 5.0 have occurred since 1932 (Figure 4). Nonh of 

the study area a M~4.2 earthquake occurred in 1947 on the Manix fault near Barstow. No 

additional earthquakes of ML~ 6.0 have OCCUHC~ in the Mojave block since 1860 [Moths 
21 

and Ellsworth, 1980; B.M. Sheffels, personal communication, 1985). Just south of the 

study area the Homestead Valley sequence (ML= 4.9, 5.2, 4.5, 4.8) occurred in 1979 

[Stein and Lisowski, 19831. Active seismicity terminates eastward along a line given 

approximately by an extension southward of the Death Valley fault [Hilemcut et al., 19731. 

Geodetic Strain Rates 

Method 

Triangulation surveys were conducted by the National Geodetic Survey (N.G.S.) 

throughout much of the Mojave Desert between 1934 and 1940 and again in 1965. To 

examine deformation in the central Mojave, the United States Geological Survey 

(U.S.G.S.) performed a mlateration survey in 1982 of the area shown in Figure 3. This 

geodetic network extends -1 10 km east-west and spans the ana from west of the Helendale 

fault to east of the Ludlow fault. The stations are distributed such that most angle 

observations cross one of the major faults. For comparison with the earlier surveys the 

distances measured using mlateration were reduced to angles between different geodetic 

stations. The standard deviation for angles derived from triangulation is approximately 

0.8" and for the angles derived ftom mlateration measurements is approximately 0.1" 

[Federal Geodetic Control Committee, 19841. 

An equation is formed relating the observation of the k th angle at the i th station 

during the j th survey at a given time tii to the engineering shear strain rate components f, 

and *2 and the initial angle @~ Ofor each angle observation [ FrMk, 1966, Prescott, 19761: 

when 
22 

are coefficients which depend on the azimuths and 02& of sides 1 and 2 of the k th 

angle at the i th station. The quantities Y1= 61 1 - E22 and Y2 = E12 - e21, where &ij are 

elements of the strain tensor, are the shear components in a geographic coordinate system 

in which the l-axis pints to the east and the 2-axis points north; y, measures right-lateral 

shear across a vertical plane striking N45'W (or left-lateral shear across a vertical plane 

striking N45'E); y2 measures right-lateral shear across a vertical plane striking eastward (or 

left-lateral shear across a vertical plane striking northward). The total engineering shear 

strain rate +and the azimuth of maximum right-lateral shear Y are related to +l and t2 by: 

To estimate strain rates, angle changes between successive surveys wen fit to a strain 

rate field assumed to be spatially and temporally uniform. By using both the older 

triangulation data and the recent ailateration data, the shear strain rate could be determined 

over a 48 year period. The two shear strain rate components +1 and +2 were derived by 

weighted least squares. Since the angles determined using trilateration are more accurate it 

is desirable to include a weighting matrix in the least squares inversion. The inverse of the 

data variance-covariance matrix was therefore used for the weight matrix [Prescott, 19761; 

thus angle changes determined from triangulation measurements alone (1934/4O - 1965) 

wen downweighted relative to angle changes obtained from trilateration and triangulation 

together (1934/40 - 1982,1965 - 1982). 

The full three dimensional strain tensor includes dilatation, horizontal and vertical 

shear components, and vector rotation [Rumsay, 19671. By examining only angle changes 

between successive surveys we can estimate only the horizontal distortion of the region. 

Even in two dimensions rotation about a vertical axis, 0 (E1 2 - E2 1)/& cannot be derived ' 
23 

without a reliable external, or a conventionally adopted internal, reference direction. 

Likewise surface dilatation, A = @I I + &2i)/2, cannot be derived from angle measurements 

without an accurate reference length [Frank, 19661. Dilatation and rotation affect the 

determination of shear strain only if such modes of deformation occur within the network 

in a non-uniform manner. 

Results 

Strain fields were determined for a number of different spatial subnets using a 

moving window approach. In addition, we searched for strong spatial strain gradients by 

examining and comparing the observed angle changes with thosc predicted by least squares 

analysis assuming a uniform strain field. The predicted angle changes wm obtained from 

the estimates of and i2 determined from the entire data set. Standard deviations reflect 

both misfit and data uncertainities due to measurement imprecision. 

The most western subnet included stations that crossed the Helendale and Ltnwood 

faults (Figure 3). For this subnet we found = 0.17 f 0.05 prad/yr and V = N41'W f 

11'. Moving eastward across the network, in a subnet that spans the Lenwood fault, 

Johnson Valley fault, and part of the Camp Rock fault (Figure 3). we found = 0.15 f 

0.04 pradyr and \Y = N38'W f 7'. In the next subnetwork, which spans only the 

Johnson Valley and Camp Rock faults, we found = 0.15 f 0.05 prad/yr and Y = 

NWW f 8'. Thus, for the region between the Helendale and Camp Rock faults, in the 

western half of the network, the strain rate was nearly constant. Because thm are not 

enough stations located between potentially active faults, it is uncertain whether there is 

strain accumulation associated with the Helendale and Camp Rock faults or if all the 

observed strain is associated with the Lenwood and Johnson Valley faults. The average 

strain rate parameters for this western region are given in Table 1. Significant strain is 

indicated for the component in this @on. Since the geologic data indicate large rightlateral displacements along northwest-trending faults, $ is most simply interpreted as ' 
24 

representing right-lateral shear strain accumulation across a vemcal plane striking N45'W. 

The maximum rate of right-lateral shear strain occurs on a plane oriented N41'W f 50 and 

is equal to 0.16 f 0.03 Angle changes at individual station combinations are well 

predicted by this strain field. If we assume that the measured deformation is due to rightlateral motions across the local faults, this rate of average shear strain corresponds to a net 

displacement rate of 6.7 f 1.3 mdyr across this portion of the survey area. This region of 

active deformation is measured on the central Mojave network at a distance of 40 to 90 km 

from the big-bend segment of the San Andreas fault. The orientation of the maximum 

right-lateral shear strain is N41'W f 5'- significantly different from the orientation of 

maximum shear strain, N65'W, near the San Andreas fault [King and Savage, 19841. 

From Camp Rock fault eastward across the net there is a transition from significant 

strain rates to very low sfrain rates; i.e., rates that arc less than the errors in the shear strain 

components and +2 (eastern region, Table 1). In the castan portion of the network the 

density of throughgoing northwest-oriented faults decreases (Figure 3) and one of the few 

major faults, the Ludlow fault, shows little Quaternary displacement [Doh, 19831. 

The spatial pattern and orientation of the observed strain field suggest a relation to the 

northwest-trending faults of the cend Mojave and argue against an influence from the 

more distant San Andrcas fault. First, the direction of maximum right-lateral shear strain is 

parallel to the trends of local faults and differs significantly from the San Andreas strike and 

the orientation of contemporary shear straining across it. Furthermore, the active 

deformation measured on the central Mojave network is located 40 to 90 km from the 

nearest adjacent portions of the San Andreas. While some observations [Thatcher, 1979bJ 

and deformation models [Thatcher, 1983) suggest that interseismic straining may be 

broadly distributed across the southern San Andreas, neither the shear strain orientation nor 

the sharp decline in its magnitude across the Mojave network support the existence of a San 

Andreas strain field sufficiently widespread to account for the deformation reported here. 
25 

The average rate estimate of -7 dyr for the western region is similar to the geologic 

slip rate determined from the cumulative fault offset across all the northwest faults, 

assuming slip initiated on the major faults about 5 m.y. ago. Since Dokku [ 19831 and 

previous workers such as Galfunkel [ 19741 report Quaternary fault movement on all the 

faults from Helendale fault east to the Ludlow fault, the results of this study may suggest a 

change in the distribution of faults which accommodate motion. This change may represent 

an evolution within the Quaternary or it may reflect a fluctuation which occurs on the 

shorter time scales of a plate boundary seismic cycle. 

In an effort to search for temporal variations in the strain data, we examined the angle 

residuals (predicted angle changes minus observed angle changes) when the entire data set 

(1934/40 - 1965, 1934/40 - 1982, 1965 - 1982) was used to determine the strain 

parameters, and we calculated separately the strain parameters for the time periods 1934140 

- 1965 and 1965 - 1982. Since strain accumulation is insignificant in the eastern portion of 

the network, only the results from the western region are discussed. No systematic 

temporal trends were found in the angle residuals. Unfortunately not as many stations 

were used in the 1965 survey, so the number of angles for the two time periods 1934/40 - 

1965 and 1965 - 1982 arc quite small. Additionally, for the two early surveys only the less 

accurate mangulation method was used. Thus, the strain rate and orientation for the early 

time period is poorly resolved. For 1934/40 - 1965, = 0 .09 f 0.07 prad/yr and Y = 

N58'E f 28', not a statististically meaningful result. For 1965 - 1982, = 0.20 5 0.08 

pad& and Y=N28'W f 14'. The two values for ?are not significantly different. 

Other Geodetic Studies in the Mojave Block 

Two other recent geodetic studies in the Mojave block show strain rates similar to 

those documented here. The orientation of the plane of maximum shear strain, however, 

differs among the studies. Timmerman et ul. [ 19851 estimated horizontal strain within a 

large area adjacent to and including the big-bend portion of the San Andreas fault; their area 
26 

includes the northern two thirds of the Mojave block. They used mostly triangulation data, 

but they also considered astronomic azimuth and mlateration data. The triangulation data 

used for our study (1934/40, 1965) arc a subset of the triangulation data used by 

Timmerman et al. [ 19851. None of the U.S.G.S. mlateration data obtained after 1979, 

however, was used in their work. For a zone which includes our region of active 

deformation (Table 1, western region) and extends from the central Mojave northward to 

the Garlock fault (their District VI), Timmermun et uf. [ 19851 found = 0.13 ,+ .04 prad/yr 

and Y = N75'W 5 8'. This orientation is closer to the trend of the San Andreas fault than 

to the strike of the local faults in the Mojave block 

' 

King [ 19851 examined mlateration measurements taken between 1979 and 1983 from 

a network that spans the Calico and Camp Rock faults near Barstow (Figure 2). The 

maximum shear strain rate from the Barstow network data was found to be 0.08 f 0.05 

prad/yr with Y = N21'W f 17'. This network spans only two of the northwest-striking 

faults and falls within the transition region between active deformation to the west and low 

strain rates to the east observed on the central Mojave network (Table 1). The strain rate 

for data from a subnet of our central Mojave network extending from the Calico fault to just 

west of the Camp Rock fault (Figure 3) was determined to be 0.03 f 0.05 cuad/yr, a result 

not significantly different from that of King [1985]. 

Earthquake Focal Mechanisms 

It is of interest to compare the derived strain field with the directions of principal 

stresses infd fn>m fault plane solutions of earthquakes within the Mojave block (Figure 

4). We have determined the focal mechanisms for six earthquakes that occurred in the 

central Mojave Desert between May 1976 and February 1984. These mechanisms 

supplement the focal mechanisms of the June 1, 1975, Galway Lake and the NovemberDecember 1975 Goat Mountain earthquakes previously determined by Kruuunori und Fuis 

[ 19761 and G. Fuis (personal communication, 1985). 
27 

Method and Results 

Earthquakes for which we have determined fault plane solutions are listed in Table 3. 

The arrival time and first motion data are from the Southern California Seismic Network 

and were obtained with the assistance of U.S.G.S. and Caltech staff. A version of 

HYPO71 [tee and Lahr, 19751 was used to locate these events. The adopted crustal 

smcm is taken from the refraction study of Fuis 119803 and is given in Table 2. Station 

polarities were checked against a list with polarity data from teleseisms, local quarry blasts, 

and Nevada Test Site blasts (courtesy of T. Webb). The P-wave first motion data and focal 

mechanisms for these events are given in Figure 5. 

As shown in map view in Figure 6, the focal mechanisms of earthquakes in the 

region of the Mojave network arc primarily strike-slip. Some normal faulting events also 

occur. Since two completely different mechanisms are consistent with the data for event 4, 

both solutions are considered in the analysis; the strike-slip solution is refed to as event 

4*. A preferred nodal plane for each event, based on surface rupture, aftershock patterns 

and local geology [Kamri and Fuis, 1976 ; Hill and Beeby, 19771, is also indicated in 

Table 3. 

The strikes of the fault planes for some of these events (4*, 8 and 9, Table 3) are 

similar to the orientation of the major faults in the area and to the dircction of relative slip 

between the North American and Pacific plates. For a second group the preferred fault 

planes have strikes that arc more northerly by 5-20' (1.3.5 and 7, Table 3). Events 2 and 4 

are normal faulting earthquakes that accommodate east-west extension. The preferred 

nodal plane for event 6 is consistent with the more northerly orientation of some of the 

surface faults observed nearer to the San Bernardino mountains and the Pinto Mountain 

fault (Figure 2). There does not seem to be a correlation between mechanism type and 

focal depth (Table 3). There is an apparent discrepancy between the orientation of rupture 

for recent large events (Goat Mountain, Galway Lake, and Homestead Valley earthquakes) 
28 

and the orientation of the major faults in the area. Understanding this discrepancy is 

important for the determination of the state of stress in the region. For example, in their 

estimate of the principal stress orientation in the Mojave Desert, aback and Zoback 

[ 19801 relied on first motion data, the distribution of aftershocks, and ground breakage data 

from the 1975 Galway Lake earthquake. They estimated the least principal horizontal 

stress to be oriented N75'W, with a maximum horizontal stress thus directed at N15'E. A 

more northerly direction for the maximum stress would have been estimated if the 

orientation of the main faults in the area had instead been used. As the field data suggest 

that the strike-slip faulting may be in an early stage of development [Dokka and Gluzner, 

1982; Dokka, 19831, we compare below the focal mechanism results to experimental 

simulations of simple shear. From the relation between the focal mechanism results, the 

strain data, and the local geology, we then make tentative conclusions on the long-term slip 

behavior of this region. 

.Comparison of Principal Stress Directions Estiwdfrom Eurthq& Focal Mechanisms 

with Geodetic Strain Directions 

We first compare principal stress directions inferred from the fault plane solutions in 

Table 3 with the direction of the most compressive strain determined geodetically. 

Following the suggestion of Celerier and Brace [1984] and B. Celerier (personal 

communication, 1985), the orientation of principal stresses may be estimated by testing the 

alternative assumptions that (1) slip occurred on the plane of maximum resolved shear 

stress, (2) the fault planes are detennined by a CoulombAnderson failure criterion, and (3) 

slip occd on a preexisting plane of weakness. 

The most common method for relating focal mechanisms to the stress field is to 

equate the P, B, and T axes to the directions of the principal sasses bl, 62 and b3, 

respectively. The nodal planes in this case are assumed to coincide with the planes of 

maximum shear stress. The P and T axes for the nine events of Table 3 are given in Figure ' 
29 

7a. The inferred orientation of a,(taken to equal the P axis) is approximately northnortheast and that of a3 (T axis) is east-southeast for most events. The P axis for many of 

the events is more easterly than the direction of maximum shortening (nearly north-south) 

determined from the strain data. For a homogeneous, isotropic medium the principal stress 

and strain directions should be the same. The difference Seen in Figure 7a may be due to 

(1) a heterogeneous stress field or heterogeneous medium properties, (2) an orientation of 

measured incremental strain that differs from the orientation of the absolute strain field, or 

(3) slip occurring at an orientation other than that corresponding to the maximum shear 

stress. The assumption that the axes of measured incremental strain and regional stress 

commonly coincide is supported by the result of Prescort et al. [ 19791 that the direction of 

maximum shear strain agrees very well with the surface strike of nearby faults in several 

regions of California. Therefore, we examine the effect of assuming that slip occurs on 

faults with an orientation other than that of the plane of maximum shear stress. 

If slip on the fault planes is controlled by a Coulomb-Anderson criterion instead of 

the maximum-shear-stress criterion, the angle a between the fault nOnnal and a1 will be: 

et=+/2+lr/4 

whm + is the angle of internal friction. When faults have no strength + becomes zero and 

slip will occur on the maximum shear plane, as assumed above. Since a preferred fault 

plane has been chosen for each earthquake (see Table 3), a is measurcd from the auxiliary 

plane. We denote the resulting estimate of the direction of al by PF For a fault strength 

approximately equal to the average strength of crustal material, that is $ = 30' (coefficient 

- 

of internal friction p = 0.6 ), PI is as given in Figure 7b. For events 1,3,5 and 7 Pf is 

nearly aligned with the orientation of the most compressive principal strain given by the 

geodetic data. The occurrence of normal faulting events (2,4) and event 6 are still 

unexplained. 
30 

For a region where pre-existing zones of weakness occur, slip may occur on such 

planes before the formation of CoulombAnderson failure planes. In this case a fault plane 

may bear no simple geometric relation to the stress directions. McKenzie [ 19691 has 

shown that the maximum compressive stress may have an Orientation anywhere within the 

dilatational quadrant. For a variety of focal mechanisms from a region of uniform stress, 

the maximum principal stress direction may be approximated by the dilatational region 

common to all events [Sbur, 19821. This region of acceptable orientations for 01 includes 

the orientation of the axes of the most compressive strain (Figurc 7b). 

Comparison of Results to Models of a Region under Simple Shear 

Experimental simulatations of simple shear indicate an evolution in the formation of a 

shear zone [Tchalenko, 1970; Freund, 1974; and Wilcox et al., 1973) that may be 

compared with existing structures in the field [Tchalenko and Ambraseys, 1970; Freund, 

1974; and Aydin and Page, 19841. In the initial stages of shear the net displacement is 

accommodated on faults with orientations that differ from that of the maximum shear stress 

by $/2 and W-@, where Q is the angle of internal friction. Failure at these orientations is 

consistent with a Coulomb-Anderson failure condition. In the central Mojave, events 1,3,5 

and 7 occur on faults oriented approximately $0 from the maximum shear direction. In 

later stages of development in the shear experiments, additional shears at other orientations 

form; finally, continuous horizontal shears develop ('D shears'). The D shears are at an 

orientation parallel to the direction of applied shear and are the major smctures that 

accommodate motion. Events 4*, 8, and 9 have fault planes similar to the major faults of 

the Mojave region and axe probably displacement controlled. 

In summary, the smke of the major faults of the region are at the orientation of 

maximum strain accumulation and thus, are the faults along which long term displacement 

will preferentially occur. Secondary faulting controlled by a Coulomb-Anderson type 
31 

failure mechanism or by slip on pre-existing faults can account for slip on faults of other 

orientations. 

Contribution of Earthquakes to Measured Strain 

The measured strain could be due to one or more of several different mechanisms: 

(1) earthquakes, (2) fault creep, or (3) elastic and anelastic strain accumulation. An 

estimate of the strain due to earthquakes from January 1932 - June 1984 was determined 

using the method of Mofnur [ 19831. All earthquakes with ML 2 3.0 that occurred within 

the region between 34.33 and 34.92" and between 115.60 and 117.33.W wen included 

in the calculation (Figure 4). The maximum depths of well located events fall between 10- 

15 km [Corbetr and Heurn, 19831. Most events, however, occur at depths of less than 6 

km. Assuming a thickness of 10 km for the seismic zone gives a volume V of the region of 

8.2 x 1019 cm3. The empirical relation between ML and seismic moment M,, derived for 

southem California earthquakes by Thatcher and Hunks [ 19731 was used to estimate the 

moment for individual events. Without detailed information on the mechanism of these 

earthquakes we calculate a moment sum assuming the same mode of release for all 

earthquakes, that is, right-lateral strike-slip on a vertical plane oriented N4lOW. A moment 

sum (E M,) of 6.8 x 10 24 dyn-cm was determined. Given a shear modulus appropriate 

for granite (3.0 x 1011 dyn/cm2), a seismic strain release value of y = 0.6 psuain over a 

time period of 52.5 years was determined. This is equivalent to less than four years of 

strain accumulation in the western region of the Mojave sutvey area. 

. 

While this simple calculation is, of course, only a rough estimate because of 

uncertainitics in the completeness of the catalog and because of the exclusion of events with 

ML< 3.0, it is safe to conclude that slip due to earthquakes accounts for only an 

insignificant portion of the deformation measured in the region between Helendale and 

Camp Rock faults. All five of the ML 1 5.0 events in fact occur east of the Camp Rock 

fault. Some combination of fault creep and elastic or anelastic deformation of the ' 
32 

lithosphere must therefore be responsible for the measured strain. Seven millimeters per 

year of creep along some combination of the northwest-striking faults from Helendale to 

Camp Rock could account for the rate and orientation of the measured strain. Possible 

creep on the Lenwood/Lockhart fault is reported near Barstow [Jennings, 19751. 

Alternatively, if most of the deformation is stored as elastic strain energy, larger 

earthquakes would be expected to occur in the future in the Mojave region. 

Tectonic Implications of Deformation in the Mojave Desert 

Previous models of the kinematic behavior of the Mojave block [Garfunkel, 1974; 

Bird and Rosenstock, 1984; Weldon and Humphreys, 19861 differ significantly. This is at 

least in part due to uncertainties in the slip rate across the northwest-sttiking faults of the 

central Mojave. Provided that the strain rates over the 50-year time period of this study 

represent the long-term average rate across the northwest-trending faults, the rate of -7 

mm/yr represents an important additional constraint on kinematic models for the region. 

This constraint on the slip rate, along with other geologic and geodetic data, serve as a 

basis for exploring the tectonic implications and examining previous kinematic models of 

deformation far the Mojave block. 

In the geometric model of Garfunkel [ 19741 the Mojave block is crossed diagonally 

by many right-lateral faults. The San Andreas and Garlock faults are the southwestern and 

northern boundaries of the model. Assuming that the northern boundary of the Mojave 

block remained adjacent to the southern part of the rigid Sierra Nevada block, the 

cumulative right-lateral slip estimated by Dokka [1983] would require approximately 10- 

12’ of counterclockwise rotation in such a model. The internal deformation of the Mojave 

block would be accompanied by an inmase in the magnitude of the bend of the San 

Andrcas fault. Such counterclockwise rotation of the Mojave block might eventually act to 

rotate the northwest-striking faults out of an orientation favorable to accommodate relative 

plate motion [Garfunkel and Ron, 19851. . 
33 

In contrast, in the kinematic model of Bird and Rosenstock [ 19841, the northwestmnding right-lateral shear zone of the Mojave Desert is represented as a single fault with an 

overall slip rate of 6.8 Wyr. Bird and Rosenstock predict that as a result of the -7 mm/y 

of relative motion across the central Mojave, either crustal shortening occurs on the western 

portion of the Garlack fault or crustal extension takes place on the eastern portion of this 

fault. Thrusting in the Tehachapi Mountains (Figure 2) is their preferred interpretation. 

Alternatively, the dismbuted deformation on the northwest-striking faults of the Mojave 

may instead be kinematically related to saike-slip motion on the right-lateral faults north of 

the Garlock fault (Figure 2) that bound the region of extensional tectonics in the Great 

Basin. Walker [ 19851 combined the offsets documented by Dokka [1983] and the 

predicted counterclockwise rotation of 10- 12' to construct a model connecting these 

displacements to movements on the Furnace Creek fault. 

One of the geologic constraints on kinematic models of the Mojave block is the slip 

rate on the Garlock fault. The observed left-lateral displacement on the Garlock fault has 

generally been considered to be due to the westward displacement of the Sierra Nevada 

block relative to stable North America [Davis and Burchfiel, 1973; Wefdon and 

Hwnphreys, 19851. Thus, the Garlock fault would accommodate the difference in motion 

between east-west extension in the Great Basin and a more stable Mojave block. In 

contrast, if the Mojave block mves northeast relative to North America, less extension is 

required in the Great Basin to acccount for Garlock motions [Bird and Rosenstock, 19841. 

Such a motion would result in significant compression across the Avawatz Mountains 

(Figure 2). Minster and Jordan [ 19851 have estimated the rate of spreading in the direction 

eN71.W in the Basin and Range to be 7.1 f 1.5 dyr on the basis of VLBI observations 

constrained by orientation information. Thus, assuming that the slip rate of about 1 ldy 

given by Caner [ 1980) for the Garlock fault is representative, the Mojave block is required 

to move to the northeast relative to North America. However, for the lower slip rate of 7 
34 

mdyr on the Garlock fault given by Asriz and Allen [ 19831 this additional northeastern 

motion of the Mojave Block may not be necessary. 

Within the Mojave block there are actually two domains of transcurrent faults that 

show Quaternary movement, right-lateral faults of the central Mojave and left-lateral faults 

in the northeast comer of the block (Figure 2). Paleomagnetic data could provide some 

constraint on the amount of rotation in the two domains of the Mojave block. However, 

paleomagnetic directions derived from rocks of Miocene or younger age give contrasting 

results. Miocene volcanic rocks collected near Bantow suggest counterclockwise rotations 

of up to 30' [Burke et al., 19821, and MacFudden er al. [ 19871 indicate that the 13-18 Ma 

Barstow Formation was rotated about 15' counterclockwise. Paleomagnetic results from 

the western Mojave Desert suggest that the region may have been rotated 35' - 45' 

clockwise between 20 and 16 Ma and then subsequently rotated 10' - 20' counterclockwise 

[Golombek and Brown, 19881. Weldon er al. [ 19841 found paleomagnetic evidence 

indicating that the southwestern Mojave has rotated less than 4' since mid-Miocene time. 

Adjacent to the domain of left-lateral faults, the eastern portion of the Garlock fault is bent 

(Figure 2). This geometry is suggestive of clockwise rotation [Luyendyk et al., 19801. 

Horizontal strain accumulation across the eastern 150 km of the Garjock fault estimated 

from trilateration measurements between 1972 and 1984 indicate a maximum shear strain 

rate of 0.18 f 0.01 cuad/yr across a vertical plane oriented N59'E f 2' for left-lateral shear 

or N31'W for right-lateral shear [King and Lisowski, 1985; M. Lisowski, personal 

communication, 19851. The Iocal strike of the eastern section of the Garlock fault is, 

however, approximately east-west. The clockwise rotation of this domain may thus be 

rotating the Garlock out of its original orientation. 

The relation of slip on the northwest-trending faults of the central Mojave to the 

tectonics of surrounding region will require additional data to resolve the outstanding 

questions. Regardless, the deformation measured across the western portion of the central 

Mojave network accounts for 14% of the predicted 50 mm/v of relative motion between . 
35 

the North American and Pacific plates or appoximately one-third of the 'missing' plate 

motion not accommodated by the San Andreas system. With significant deformation 

occurring east of the San Andreas fault in the central Mojave Desert less deformation is 

needed west of the San Andreas to account for the total predicted plate motion [e.g., 

Weldon and Humphreys, 19861. 

Summary 

We have examined mangulation/nilateration data from a geodetic network that spans 

the northwest-striking faults of the central Mojave Desert of California. For the region 

between the Helendale and Camp Rock faults the shear strain rate was determined to be 

0.16 f 0.03 prad/v, with maximum right-lateral shear strain occuning on a plane oriented 

N41'W f 5'. If we assume that this deformation is due to right-lateral displacement across 

the local faults, the average shear straining corresponds to a relative displacement of 6.7 f 

1.3 Wyr across this portion of the network. This slip estimate is similar to the geologic 

slip rates given by Dokka [ 19831, on the assumption that slip began -5 m.y. ago when 

major spreading initiated in the Gulf of California and acceleration of slip occurred on the 

San Andreas fault. From the Camp Rock fault eastward across the network there is a 

transition from significant to very low strain rates. 

From an examination of nine focal mechanisms and their relation to the local geology 

and the strain data, our results suggest that most of the long term displacement (or at least 

the strain accumulation) occurs parallel to the orientation of the local northwest-trending 

faults. This orientation is nearly along the direction of relative motion between the North 

American and Pacific plates. Secondary faulting controlled by a CoulombAnderson failure 

mechanism or by slip on prccxisting faults can account for earthquakes on faults of other 

orientations. 

The documented active deformation on the northwest-trending faults of the central 

Mojave accounts for -14% of the 50 mm/yr of relative motion between the North Amencan 
36 

and Pacific plates. With some of the relative plate motion occurring to the east of the San 

Andrtas fault, less slip is needed west of the San Andreas fault to account for the total 

predicted plate motion. 
37 

TABLE 1. Rate and Orientation of Maximum Right-Lateral Shear Strain, 

Mojave Network, 1934-1982 

~~ 

Western Region Eastern Region 

No.of 

Angles 

w 

64 59 

0 .16 & 0.03 

-0.02 f 0.03 

0.16 f 0.03 

0.02 f 0.04 

0 .04 f 0.03 

0.05 f 0.03 

N41'W f 5' unresolvable 
38 

TABLE 2. Crustal Model for the Central Mojave Desert 

Depth, P-wave velocity, 

lun WSeC 

0-5 

5- 10 

10-25 

25-30 

>30 

5.3 

6.1 

6.3 

6.7 

7.8 

[Puis, 19801 
39 

TABLE 3. Source Parameters of Earthquakes in the Central Mojave Desert 

Time. Latitude, Longitude, Depth (flu), 

Event Rue UT" W km Mr, Strike Dip Azimuth Plunge 

1 

2 

3 

4 

4' 

5 

6 

7 

8 

8 

June 1,1973 0138 

Nov. 16, 1973 0743 

Dec. 14.1975t 1816 

May 10, 1976 1024 

June 10,1978 2258 

Apnl9, 1979 1732 

Jan. 16, 1983 2007 

Jan. 18, 1984 0825 

Jan. 18, 1984 0835 

34.52 

34.29 

34.29 

34.47 

34.54 

34.42 

34.42 

34.53 

34.53 

116.49 

116.33 

116.32 

116.88 

116.82 

116.46 

116.01 

116.82 

116.82 

2.0 k 1.0 5.2 

5.5 f 0.6 3.0 

2.1 k 1.0 4.7 

1.8 f 6.0 3.6 

5.6 f 1.5 2.7 

3.9 f 0.8 3.5 

6.7 f 0.9 3.0 

1.8 f 0.8 2.5 

1.5 f 0.8 2.7 

M20'W 

NWW 

NWW 

N18'E 

N44% 

N19'W 

N-S 

N14'W 

N38'W 

NWW 

70'sw 

WW 

90' 

54'W 

90' 

90' 

WW 

90' 

80% 

WE 

NWW 

N38'W 

NWW 

NWW 

N44'W 

N19'W 

N14'W 

S42'E 

S38'E 

N-S 

0' 

32' 

0' 

50' 

0' 

0' 

8' 

0' 

20' 

20' 

Strike-slip solution. 

f Ko~mori and Fuis [1976] and G. Fuis (personal communication, 1985). 

.- 

e 
40 

Figure Captions 

Figure 1. Major Quaternary faults in California and Nevada shown on an oblique Mercator 

projection about the Minsrer and Jordan [ 19781 RM2 rotation pole for the Pacific and North 

American plates (modified from Minsrer and Jordan [ 19841). G, Garlock fault; M, Mojave 

Desert block; SA, San Andreas fault; WT, western Transverse Ranges. 

Figure 2. Quaternary faults of southern California (modified from Lienkaemper [1985]). 

AM, Avawatz Mountain; DV, Death Valley fault; ETR, eastern Transverse Ranges; FC, 

Fumace Creek fault; G, Garlock fault; PM, Pinto Mountain fault; PV, Panamint Valley fault; 

SA, San Andreas fault; SN, Sierra Nevada fault zone; TM, Tehachapi Mountains. The 

Barstow trilateration network [King, 19851 and the outline of the central Mojave network are 

shown for reference. 

Figure 3. Triangulation/rrilateration network in the central Mojave Desert. Quaternary faults 

for the central Mojave Desert are from Bishop [ 19631 and Rodgers [ 19671. The location of 

the city of Barstow is indicated by the "*B." 

Figure 4. Earthquakes in the study region with ML 2 3.0 between January 1932 and June 

1984. The outline of the central Mojave geodetic network and Quaternary faults from Figure 

3 art shown for reference. 

Figure 5. Focal mechanism solutions and P wave first motions for earthquakes 4-9 in Table 

3. Solid circles indicate compressional first motions, and open circles dilatations, on equalarea projections of the lower focal hemisphere. The dashed nodal planes for events 4,5, and 

7 represent alternate solutions. Since the two mechanisms depicted for event 4 are . 
41 

completely different, both solutions are considered in the analysis; the strike-slip solution is 

refemd to as event 4* in Table 3. 

Figure 6. 

Compressional quadrants are shaded. Faults are from Figure 3. 

Earthquake focal mechanisms (Table 3) in the Mojave Desert region. 

Figure 7a. P and T axes for the events given in Table 3. The P axes are given by solid 

circles and the T axes by open circles. The orientation of the most compressive principal 

strain direction (N4'E f 5') indicated by the geodetic measurements is given for reference. 

Figure 7b. Pfaxes (see text) and the region common to the dilatational quadrants for all 

events. The dashed line is the upper boundary of the region if the normal faulting mechanism 

instead of the strike-slip solution is adopted for event 4. 
42 

e’ NORTH AMERICAN PLATE 

’\ 

-- 

--e / 

/ 

/ 

PACIFIC PLATE 

FIGURE 1 
43 

/ 

0 

(0 

M 

0 tn 

M 

0 

d 

rr) 
44 
45 

I 

7 i e 

. .. ..... .’ 

e 

/ 

I 

01 

0 

rr) * 

rr) 

0 

d 
46 

d 

a 
I_;;;;( 

'0 

n * 

n + 
FIGURE 7a 

48 
FIGURE 7b 

49 
50 

Chapter 3. Geodetic Measurement of Deformation 

East of the San Andreas Fault in Central California 
51 

Introduction 

Although most of the relative motion between the Pacific and North Amcrican plates 

in central California is accommodated by slip along the San Andreas fault, distributed 

compressive and right-lateral strike-slip motion also occurs on faults with surface traces 

subparallel to the San Andreas fault located between the continental escarpment and the 

Great Valley [Gawthrop, 1977; Page, 1981; Crouch et al., 1984; Eaton, 1984; Minster and 

Jordan, 1984, 1987; Namson and Davis, 19881. The axis of greatest compression across 

this region, the southern Coast Ranges subprovince [Page, 19811, is thought to be oriented 

nearly perpendicular to the trend of the San Andreas fault, a result atmbuted to a 

combination of slightly convergent relative motion between the Pacific and North American 

plates and low shear strength along the fault zone [Mount and Suppe, 1987; Zoback et al., 

19871. While most recent earthquakes in central California are located on the San Andreas 

fault (Figure 1). scattered diffuse activity also occurs between the San Andreas fault and the 

Great ValIey. The May 1983 Coalinga earthquake (M~=6.7), which involved slip on a 

thrust or reverse fault beneath a young surface fold [Stein and King, 1984; Stein, 19851, 

has focused attention on the importance of understanding the state of stress and the rates of 

deformation to the east of the San Andreas fault in this region and their relation to the 

overall deformation in the Coast Ranges. In this chapter I determine rates of crustal strain 

in the Diablo Range north of Coalinga from a triangulation and trilateration network and 

from line-length changes detcxmined by means of trilateration measurements within 10 km 

of the San Andreas fault. These geodetic results are then compared with other geological 

and geophysical data to characterize the nature of deformation across the southern Coast 

Ranges. 
52 

Tectonic Setting 

The principal strike-slip faults in central California have been well characterized by 

geologic and geodetic studies. The branched system of subparallel faults near Hollister 

coalesces southward into a single shear zone, the San Andreas fault, south of Hepsedam 

(Figure 2). The Calaveras fault is the primary active fault to the northeast of the San 

Andreas fault near Hollister, while to the southeast of Hollister several faults comprise the 

southern end of the Calaveras fault zone, among which the Paicines fault is most 

prominent. Horizontal deformation across the San Andreas and Calaveras-Paicines faults 

in central California has been measured with near-fault alinement arrays, creepmeters, and 

mlateration at short and intermediate distances [Savage and Bu#ord, 1973; Thatcher, 

1979a; Burford and Harsh, 1980; Lisowski and Prescott, 1981 1. Between Hollister and 

Hepsedam (Figure 2), the rate of steady surface slip (creep) across the San Andreas fault 

increases from - 13 to 32 dyr and surface slip on the Calaveras-Paicines fault decreases 

from -17 to 0 mm/yr. Between Hepsedam and the latitude of Coalinga (Figure 2) nearfault and intermediate-scale geodetic measurements of right-lateral slip are in good 

agreement and indicate creep at a rate of approximately 32 mm/yr. The rate of slip on this 

segment of the San Andrcas fault estimated from Holocene geological data is 34 f 3 Wyr 

[Sieh and Johns, 19841 at an azimuth of N41'W f 2' [Minster and Jordan, 1984; Mount 

and Suppe, 19871. Southward of the latitude of Coalinga shallow slip on the San Andreas 

fault decreases and the width of the zone of deformation increases over the transition to a 

locked segment of the San Andreas fault in the Carrim Plain (the southern aseismic portion 

of the San Andreas in Figure 1). 

The major struchual features in the region of this study arc shown in Figures 2 and 3. 

Within 5-10 km to the east of the San Andreas fault the primary geologic structures are 

related to dextral shear on the San Andreas and Calavems-Paicines faults (Figure 2). The 

Diablo Range to the east of this region is a broad antiform which trends approximately 
53 

N65'W [Page, 19851 and encompasses subsidiary fold structures such as the Vallecitos 

syncline (Figure 3). North of Coalinga the range is pierced by the New Idria diapir (Figure 

3) of serpentine and Franciscan rocks. Along the northeast boundary of the study area is 

the Ortigalita fault (Figure 2), a high-angle fault along or near the contact of Franciscan 

rocks and the Great Valley sequence to the east [Raymond, 19731. Trenching of the 

Ortigalita fault zone shows exposed offsets of late Pleistocene and Holocene soils, with 

possibly as much as 5 km of Quaternary right-slip displacement [Hart et uf., 19861. 

Multiple phases of deformation in the Diablo Range have been documented by 

structural analysis [Numson and Davis, 19881. Harding [ 19761 pointed out that there are 

folds of middle to late Miocene age which are synchronous with the initiation of 

displacement on the San Andnas fault. The most recent uplift of the Diablo Range began 

in Pliocene time and most likely accelerated in the Pleistocene [Page, 198 1 ; Page and 

Engebretson, 19841. The Quaternary (c 2.2 Ma) folding is more widely distributed and of 

much greater structural relief than the Miocene folds [Namson und Dovis, 1988). 

Focal mechanisms of earthquakes in the Diablo Range [Euton, 19851 show a mixture of 

thrust, reverse, and strike-slip faulting. The locations of three of the larger earthquakes 

with well-determined focal mechanisms, the October 1982 Idria event (M~=5.5), the May 

1983 Coalinga event (M~=6.7), and the August 1985 North Kettleman Hills event 

(M~=5.5), are given in Figure 1. The focal mechanism determined for the Idria earthquake 

indicates thrust faulting on a plane oriented N72'E or reverse slip on a plane oriented 

N64'W [Eaton, 19851. The Coalinga and Kettleman Hills events have similar focal 

mechanisms with slip occurring on fault planes oriented at about N53'W as either thrusting 

on a plane dipping shallowly to the southwest or reverse slip on a plane steeply dipping to 

the northeast [Eaton, 1985; J.P. Eaton, personal communication, 19871. A preliminary 

focal mechanism determined for an earthquake which occd on the Ortigalita fault on 

January 6, 1988 (M~=3.7), indicates right-lateral slip on a fault plane oriented -N25'W or 
53 

left-lateral slip on a plane oriented N65'E (P.A. Reasenberg, personal communication, 

1988). The earthquake focal mechanisms and geological structures in the ana suggest two 

primary modes of deformation to the northeast of the San Andreas fault: compression 

normal to the major fold structures of the region and right-lateral strike-slip motion on 

faults such as the Calaveras-Paicines and the Ortigalita. 

By way of comparison, in the Coast Ranges to the west of the San Andreas fault focal 

mechanisms [Gawrhrop, 1977; Eaton, 1984; Dehlinger and Bolt, 1987) and extensive 

geological mapping [summarized in Crouch et al., 1984; Slemmons, 19871 suggest 

variable modes of deformation. Between the San Andreas and the Rinconada faults (Figure 

1) is the seismically quiescent Salinian block. The upper crust is composed of highstrength granite which is only weakly folded and sparsely faulted [Dehlinger and Bolt, 

1987; Slemmons, 1987). Focal mechanisms from the Rinconada fault show a mixture of 

right-lateral smke-slip faulting on northwest smking planes, oblique slip, and reverse 

faulting [Gawthrop, 1977; Dehlinger and Bolt, 1987). From field mapping of recent 

offsets, D.B. Slemmons (personal communication, 1987) and E.W. Hart (personal 

communication, 1988) suggest that right-lateral smke-slip faulting dominates the 

displacement along the Rinconada fabIt. Between the Rinconada and the San GregorioHosg~i faults (Figure 1) the upper crust consists of the very heterogeneous Franciscan 

complex. Focal mechanisms from this region indicate dominantly oblique reverse faulting 

along northwest-trending, northeast dipping planes, with P axes oriented N20'-50'E or 

S20'-50'W [Detrlinger and Bolt, 19871. Significant latc-Quaternary right-lateral strike-slip 

offsets have been measured on the San Gregorio fault [Clark et af., 19843. South of 

Monterey Bay this fault branches into several splays, with some branches showing 

primarily right-lateral strike-slip displacement and others showing east-up reverse faulting 

[Hamilton, 19871. Focal mechanisms from the San Gngorio-Hosgti fault also indicate 
55 

right-lateral strike-slip faulting and oblique reverse faulting with a right-lateral component 

on a northeast dipping plane [Gawthrop, 1977; Eaton, 1984; Dehlinger and Bolt, 19871. 

Geodetic Strain Rates 

We make use of two geodetic networks to estimate current rates of deformation to the 

east of the San Andreas fault in central California. The San Benito triangulation and 

trilateration network spans the Paicines fault zone just east of the San Andreas fault, 

extends eastward to the western margin of the Great Valley, and is 50 km in extent in the 

southeast-northwest direction across the Diablo Range (Figure 3). To examine more 

localized deformation within the zone 10 lan to the east of the San Andreas fault, short and 

intermediate range lines from the U.S. Geological Survey (USGS) Coalinga trilateration 

network were utilized. The geodetic results derived from the Coalinga mlateration data 

provide an update to the slip rates estimated for the Calaveras and Paicines faults by 

Lisowski and Prescott [ 19811. 

To distinguish between engineering and tensor shear strain, we denote the former by 

yand give in units of pad, whereas the latter is denoted by E and is given in units of 

pstrain [Savage, 19831. Uncertainties, where not otherwise stated, are one standard 

deviation (a). 

San Benito Network 

A triangulation survey of the San Benito network was conducted in 1962 by the 

National Geodetic Survey, and in 1982 a mlateration survey of the San Benito network 

was performed by the USGS. For interstation visibility, triangulation and mlateration 

stations are situated on the highest points in a region; thus, many of the stations in the San 

Benito network are located near anticlinal peaks (Figure 2). To determine the rates of 

deformation from the San Benito data the observations were processed utilizing two 
56 

independent proceduns: an extended version of Frank's method [Prescorr, 1976) and the 

DYNAP method [Snuy, 1986; Drew and Snay, 19881. In the Appendix we discuss the 

accuracy of the mangulation and trilateration measurements utilized in this study, the 

assumptions made in our estimation of the horizontal shear parameters, the considerations 

involved in combining triangulation and trilateration data to determine the rate of shear 

strain utilizing the Prescott and DYNAP methods, the corrections applied to reduce the 

mangulation and trilateration observations to a common reference system, and the methods 

used to estimate the deflection of the vertical and the geoid - reference ellipsoid separation 

needed to make the reduction corrections. 

Utilizing both methods we calculate the horizontal shear strain rate components t, 

and 4;. In terms of elements of the strain tensor Eij, yl= ell- €22 and y, = e12 + ~2~ , 

where the strain tensor is referred to a geographic coordinate system in which the 1-axis is 

dincted east and the the 2-axis is directed north. The strain component y, is qual to the 

decrease induced by strain in the right angle between northward- and eastward-directed 

lines, whereas yl is equal to the increase in the angle between lines directed northwest and 

northeast. Results are generally given in terms of the maximum shear strain rate i.( where 

i.2 = f12 + f22, and the orientation w of the vertical plane with maximum rate of rightlateral shear [Frank, 1966; Prescorr, 1976). For comparison with the trends of fold 

structures of the Diablo Range, the orientation p of the maximum rate of compressive saain 

is sometimes given instead of the orientation of maximum rate of right-lateral shear. 

Results wirh Prescorr's rnerhod. The observations used to estimate +l and i2 in the 

extended version of Franks method [Prescotr, 19761 arc changes in angles. In this study 

we determined angle changes from two different data types, reflecting the different types of 

surveys made in 1962 and 1982. Further, we compared angles measured on the Earth's 

surface to angles determined from a network adjustment on a reference ellipsoid. In using 
data derived from different measurement techniques it is preferable to reduce the data to a 

common reference surface. The required reduction corrections are discussed in the 

Appendix. In employing Rescott's procedure to determine the strain parameters we did 

not make these corrections. In our use of the alternative DYNAP method these corrections 

are performed, and we compare the results from the two techniques to illustrate in part the 

utility of making these corrections. 

The angle changes associated with the stations Bitter, Hepsedam, and Panoche were 

significantly larger than angle changes from other portions of the network and were, 

therefore, examined separately. Bitter and Hepsedam are located near the Paicines fault 

zone. Using only the 11 angle measurements that include one of the stations Bitter or 

Hepsedam gives i. = 0.56 f 0.16 prad/yr and Y = N28'W f 11' The shear strain rate 

across the approximately 10- km-wide zone to the northeast of stations Bitter and 

Hepsedam, assuming right-lateral motion on the Paicines fault, implies a rate of slip of 5 f 

2 dyr. Additional geodetic data from the Coalinga trilateration network relating to 

deformation across the San Andreas and Calaveras-Paicines faults is discussed in the next 

section. 

The relatively large angle chang5s around station Panoche arc not_ so easily explained. 

Using only the seven angle changes that include Panoche gives i. = 0.76 f 0.27 prad/yr 

and w = N58'W f 9', or = N13'W f 9'. These results arc not consistent with either 

shear strain across the Ortigalita fault zone or contraction across the major fold smctures of 

the region. 

The strain rate parameters estimated on the basis of 25 angle changes in the central 

portion of the San Benito network, excluding angles to Bitter, Hepsedam, or Panoche, 

were = 0.15 f 0.08 prad/yr and p = N16'E f 14', or w = N29'W f 14'. The standard 

deviations reflect both misfit and data uncertainities due to measurement imprecision. 
58 

To search for significant strain inhomogeneity, the shear strain parameters were 

estimated from spatial subsets of these data, again excluding the Bitter, Hepsedam, and 

Panoche stations (Table 1). There is a trade-off between improving the precision of the 

strain estimate by using a larger number of angles and averaging spatial variations as the 

size of the sampled region is increased. The data were first broken into two distinct 

groups, one set closer to the Great Valley ("east") and one set closer to the San Andreas 

fault ("west"). If the measured rates of shear strain were due to strain accumulation on the 

adjacent San Andreas fault, the rate of shear strain would be higher in the western subnet. 

Alternatively, if the rate of compressive strain was higher across the folds near the Great 

Valley, the eastern subnet might show a higher shear strain rate. There is no suggestion of 

a significant rate difference, however, between the strain rates determined from the eastern 

and western data subgroups. The set of 25 angles wm also divided into "north" and 

"south" sets to look for any change which might be associated With along-strike variations 

on the San Andreas and Calaveras-Paicines faults. Although the strain rate results differ in 

the subnets, particularly in the orientation of maximum rate of compression, the magnitudes 

and orientations of strain rate in the various subregions are not significantly different from 

the average values determined from the complete set of 25 angles. 

Results with the DYNAP method. In a second approach, the directions observed in 

1962 and the distances measured in 1982 were employed to solve simultaneously for 

crustal mtion parameters and the horizontal positional coordinates of the geodetic stations 

using the DYNAP method [Snay, 1986; Drew and Snay, 19881. With DYNAP we are able 

to make single epoch adjustments to search for any observational errors during the 

individual surveys, and we arc able to evaluate the effect of making reduction corrections to 

the distance and direction observations. 
59 

We first performed separate network adjustments for 1962 and 1982. A particular 

solution was determined by holding the minimum number of free parameters fixed. For the 

two-dimensional adjustment of 1962 mangulation data, these free parameters are two 

components of translation, a network rotation, and scale. For the two-dimensional 

adjustment of the 1982 trilateration data, scale is not a free parameter. Examination of the 

largest standardized residuals (given by the difference between observed and calculated 

values divided by the standard deviation of the observation) indicates that the 1962 

direction observations to the station Panoche have large residuals. This may account for 

the anomalously large angle changes associated with Panoche discussed earlier. Large 

residuals are not systematically associated with any one station in the 1982 adjustment. 

. 

From the analysis utilizing the Prescott method we obtained the result that the angle 

changes associated with the stations Bitter and Hepsedam were consistent with right-lateral 

slip at the approximate orientation of the Paicines fault. To test this result we solved for 

strain parameters and horizontal coordinates for a small subnetwork consisting of Bitter, 

Hepsedam, Smoker, and Ley (Figure 2) using DYNAP. The rate of shear strain was 

estimated to be 0.53 f 0.35 pdyr with y/ = NWW f 19', similar to the orientation of the 

San Andreas and Paicines faults. 

The shear strain rate parameters i, and t2 were estimated by the DYNAP method 

using data from the central pomon of the network (excluding measurements to Panoche, 

Bitter and Hepsedam). Without taking into account corrections the rate of shear strain = 

0.15 f 0.09 and p = N17OE f 16O, similar to the result obtained utilizing Prescott's 

method. The rate of shear strain determined using the corrected data is = 0.19 f 0.09 

pradyr, with p = N16'E f 13' (Figure 4). 

As shown in Figure 4, at the 95% confidence level +is not significantly greater than 

zero and p is not significantly different from the orientation predicted for shear strain 

associated with slip on the San Andreas fault (N4'E). The orientation p, however, is 
60 

similar to the direction of maximum compressive strain indicated by the orientiation of 

major fold structures in this region. If we assume that the strain represents uniform 

horizontal contraction across a 30-km-wide region in the direction N16'E and that there is 

no extension in the orthogonal direction, this average strain rate corresponds to 5.7 f 2.7 

mm/v of shortening. 

The error in the estimate of shear strain rate determined in this study is dominated by 

the less accurate triangulation survey (see Appendix). It is instructive to estimate the 

accuracy that could be achieved with an additional mlateration or GPS survey of this 

network. An additional mlateration survey of all the stations in the San Benito network in 

1992, for instance, would provide -0.02 pstrain/yr accuracy in the principal strains, and all 

of the horizontal components of the tensor rate of strain (hj) could be estimated. At this 

level of accuracy we could better consuain the rate of crustal deformation across the Diablo 

Range as well as discern spatial variations in the deformation field. 

Coalinga Trilateration Network 

We have employed short and intermediate-length lines from the Coalinga trilateration 

network (Figure 2) to update previous estimates [Lisowski and Prescott, 1981 J of the slip 

rates on the Calaveras and Paicines faults. Since 1972 trilateration measurements have 

been made periodically by the USGS in central California on a regional scale spanning a 

20-km-wide zone centered on the San Andreas fault and including several distinct faults, as 

well as on smaller (1-2 km) aperture networks that span a single fault (Pionne, Dry Lake 

and Tully nets). The estimated accuracy in the line lengths determined from the short-range 

measurements is 4 mm [Lisowski and Prescott, 19811. The estimates of line-length change 

made by Lisowski und P rescott [ 1981 J also included earlier data collected by the California 

Division of Mines and Geology, but we have utilized only the more homogeneous set of 

USGS data. 
61 

For the region within 10 km to the east of the San Andreas fault we assume that the 

predominant mode of crustal defoxmation is right-lateral fault slip on the Calaveras-Paicines 

fault system. This is equivalent to the assumption that the measured deformation in this 

region is due neither to elastic strain accumulation that will be released episodically in 

earthquakes on the adjacent San Andreas fault nor to crustal shortening normal to the San 

Andreas fault. Several lines of reasoning support this assumption. As discussed above, 

on the segment of the San Andreas fault adjacent to the San Benito network, fault slip 

occurs primarily by steady creep, and we expect little right-lateral shear strain accumulation 

associated with the San Andreas fault to be measured on off-fault geodetic lines. In 

addition, elastic strain accumulation associated with the San Andreas fault would be 

measurable geodetically on both sides of the fault, yet to the west of the San Andreas fault 

the maximum right-lateral shear strain within the Salinian block, estimated from 

triangulation data measured during the time interval 1944-1963, is poorly resolved and is 

not oriented parallel to the San Andreas fault [Thatcher, 1979a). An alternative mode of 

deformation adjacent to the San Andreas is compression across structures such as the 

Paicines syncline (Figure 3). Strike-slip motion across this region would shorten northsouth lines and extend east-west lines, whereas contraction would shorten northeastsouthwest lines. Line length changes in the Pionne short-range network and the lines from 

Bitter to Hepsedam and Browns to Cross arc consistent with the hypothesis of right-lateral 

slip on the Calaveras-Paicines fault system. As discussed above, results from the San 

Benito geodetic subnetwork that includes measurements to Bitter and Hepsedam are most 

consistent with right-lateral shear at the orientation of the San Andreas and Paicines fault. 

If the deformation in this region occurs as rigid block motion along the CalaverasPaicines fault system, the observed length changes can be converted into a fault-parallel 

displacement rate from the slope of the least-squares linear fit to the interstation length data 

[Prescort and Lisowski, 19831. The slip rates determined from lines crossing the fault at a 

. 
62 

low angle arc given in Table 2 for the Calaveras-Paicines region just south of Hollister and 

for the Paicines fault zone between Bitter and Coalinga. The sum of the slip rate 

determined from the station pairs that cross only the San Andreas fault (Cross-Chalone and 

Chalone-Bitter lines) and the slip rate from pairs that are completely cast of the San Andreas 

fault (Browns-Cross and Bitter-Hepsedam) are approximately equal to the slip rate from 

station pairs that span both fault zones (Browns-Chalone and Chalone-Hepsedam lines). 

The line length changes across the Calaveras-Paicines fault zone are consistent with -10 

mm/p of right-lateral slip. The rate of slip estimated for the Paicines fault south of the city 

of San Benito is 4 f 1 Wp. 

The Bitter to Hepsedam line showed a significant change in slope beginning in mid1978. This change cornsponded to an increase in the rate of slip on the Calavcras-Paicines 

system and a decrease in slip rate on the San Andreas fault. A similar change after 1979 in 

the slip rates for the Calaveras and San Andreas faults has been inferred from geodetic 

measurements of the USGS Hollister trilateration network [G. Gu and J. C. Savage, 

personal communication, 1986; Mutsu'uru et ul., 19861. The inmase in slip on the 

Calaveras Paicines fault approximately coincided with the occurrence of the 1979 Coyote 

Lake earthquake (M~=5.7) on the northern Calaveras fault. The rate of line length change, 

i, between Bitter and Hepsedamfor the 1973-1978 time period was 1 f 1 mm/yr 

[Lisowski and Prescott , 19811. The higher rate of slip given in Table 2 thus is largely due 

to the haeased rate during 1978-1984. 

The average fault slip indicated by the three short-range networks (Figure 2), again 

assuming simple block motion, is given in Table 3. The rate of slip on the Pionne net, 12 

f 2 mm/yr* is similar to the rate estimated from the line between Cross and Browns which 

crosses the Calaveras-Paicines fault zone (10 f 1 e). Between the Dry Lake and Tully 

networks the rate of creep on the San Andreas fault increases from 27 f 2 to 32 f 1 dyr. 

South of the Tully network the rate of slip determined from near-fault data on the San 

# 
63 

Andreas fault is the same as the rate estimated from the Chalone to Hepsedam line [Prescon 

and Lisowski, 19811. 

The short and intermediate-range mlateration measurements document a transfer of 

slip associated with the Calaveras-Paicines fault zone to the San Andreas fault. The 

narrowing of the region that accommodates the -32 dyr slip rate also corresponds to a 

transition from a complex multi-stranded portion of the fault system with locked segments 

that break in periodic moderate-to-large earthquakes to a geometrically simpler segment that 

accommodates slip through creep. 

Comparison with Other Geodetic and Geologic Observations 

As noted above, the strain rate parameters estimated on the basis of angle changes in 

the central portion of the San Benito network arc = 0.19 & 0.09 crrad/yr and p = N16'E f 

13', or w = N29'W f 13'. Interpreted in terms of uniform horizontal contraction in the 

direction given by the angle p, the rate of shortening is 5.7 f 2.7 mm/. Although there is 

no significant strain at the 95% confidence limit, the orientation of the principal strain 

directions are consistent with the geological structures of the region (Figure 3). The 

azimuth of the least compressive strain (N74'W f 13') is close to the trend of the major 

fold st~ctuns of the region (N65'W). The direction of maximum rate of right-lateral shear 

is also close to the and of the major strike-slip faults of the region. 

From a geological reconstruction of the structures between the Great Valley and the 

San Andreas fault at the approximate latitude of Coalinga, Numson and Davis [ 19881 

inferred that 11 krn of late Cenozoic shortening has occurred perpendicular to the San 

Andreas fault. If active folding commenced 5 m.y. ago, the average rate of shoxtening has 

been 2.2 mm/yr. If folding began as recently as 2 m.y. ago an average rate of shortening 

of 5.5 Wyr is implied. These figures arc comparable to the geodetically infd rate. 
64 

The rate of slip obtained in this study for the Calaveras-Paicines fault zone south of 

Hollister is 10 f 1 mm/yr (Browns to Cross, Table 2) and 12 f 2 mm/yr (Pionne net, Table 

3). These slip rates may be compared to other estimates of slip rate derived from geotogical 

and geodetic observations. Ham et af. [ 19871 inferred a late Quaternary slip rate on the 

Paicines fault of 3.5 - 13 mm/yr from an offset terrace riser and an offset hill -10 km south 

of Hollister. Between 1973 and 1986 the average rate of slip obtained from offset of the 

USGS Thomas Road alinement array, which spans the Paicines fault near its intersection 

with the Browns-Cross line, is approximately 6 mdyr [Harsh and Puvoni, 1978; S. 

Burford, personal communication, 19881. From mlateration measurements made between 

the stations Browns and Cross during an interval earlier than but overlapping that of our 

study (69.8-78.4), Prescott and Lisowski [1981] determined a slip rate of 8 f 1 Wyr. 

Prescott and Lisowski [1981] also calculated the rate of the slip from short-range 

mlateration measurements of the Pionne net to be 10 f 3 mdyr for approximately the same 

period. These estimates are not significantly different from the results reported here. 

Utilizing data from the (USGS) Hollister mlateration network, located north of our study 

region, Matsu'ura et al. [ 19861 inverted for fault displacement rate versus depth on the San 

Andreas, Calaveras, and Sargent fauns. They estimated the rate of sup on the CalaverasPaicines fault between 1971 and 1983 and between latitudes 36.70' and 36.87" to be 18 

k 4 dyr, with no significant surface crcep. Their result is higher than the rate of surface 

slip documented from the Thomas Road alinement array as well as with that obtained in 

this study. The inconsistency of the Matsu'ura et uf. [ 19861 rate with other results from the 

region may be due to the fact that the Hollister network does not span the southern portion 

of the Calaveras fault; in particular, the 18 Wyr value may reflect an average rate over a 

region where slip on the Calaveras fault is decreasing to the southeast. 

The rate of slip obtained in this study for the Paicines fault south of the city of San 

Benito is 4 f 1 mm/p (Bitter to Hepsedam, Table 2). While geological mapping indicates 
65 

that recent right-lateral slip has occurcd on the Paicines fault as far south as the city of San 

Benito, no active fault trace has been mapped further south (J. Perkins, personal 

communication, 1988). Sedimentation rates are high in this region, however, so a low rate 

of slip on the fault may be masked by alluvium. From a study of earthquake focal 

mechanisms and seismicity of this region, Effsworth [ 19751 suggested that slip on the San 

Andreas fault is transferred to the faults northeast of the San Andreas between Bitter and 

Cross (Figure 2). The rate of slip estimated from the change in the Bitter-teHepsedam line 

length, 3-4 dyr, however, suggests that some slip may be occurring on an extension of 

the Paicines fault south of San Benito. As discussed above, the slip rate inferred for this 

line is higher than the rate of slip of 1 f 1 dyr estimated by Lisowski and Prescott 

[ 19811 for an earlier period and may indicate a temporal variation in the rate of deformation 

in this region. 

Principal Directions of Strain and Stress 

The principal directions determined geodetically for rate of strain within the San 

Benito network may be compared with the orientation of the maximum principal stress (q) 

estimated from wellbore breakouts and the azimuths of P axes determined from earthquake 

focal mechanisms for the region east of the San Andreas fault. As noted earlier, the 

orientations of principal stress directions determined from breakout orientations, earthquake 

fault plane solutions, and the azimuths of major fold structures in central California have 

been used to distinguish between models relating the formation of fold structures in the 

southern Coast Ranges to motion along the San Andreas fault and to infer the state of stress 

on and near the San Andreas fault [aback er al., 1987; Mount and Suppe, 1987; Namson 

andDavis, 19881 

Due to extensive drilling for oil to the east of the San Andreas fault, a large number of 

wells have been available for measurement of stress-induced wellbore breakout 
66 

orientations. Borehole breakouts are caused by unequal stress concentrations around a 

borehole wall and create elongations of the hole in directions perpendicular to the 

orientation of the maximum horizontal stress [Springer, 19871. Breakouts are generally 

oriented northwest-southeast, indicating a northeast-southwest orientation for the greatest 

compressive stress, a direction perpendicular to the axes of major folds near the Great 

Valley and at a 70'40' angle to the San Andreas fault [Springer, 1987; &back et al., 1987; 

Mount and Suppe, 1987). To the east of the San Andreas fault the majority of breakout 

measurements have been made in wells near the western edge of the Great Valley (Figure 

5); comparatively few wellbore breakout orientations have been obtained closer to the San 

Andreas fault within the arca of the geodetic measurements reported in this paper. 

' 

The orientation of maximum principal stress may also be inferred from welldetermined fault plane mechanisms, notably from the 1982 Idria, the 1983 Coalinga, and 

the 1985 North Kettleman Hills earthquakes (Figure 5). For the Coalinga and the North 

Kettleman Hills events the P-axis orientation is wN37.E [Eaton, 1985; J.P. Eaton, person& 

communication, 19871, similar to the directions of 01 infed from breakout orientations 

in the same region. The azimuth of the P axis for the Idxia event is N12'E [Eaton, 19851. 

As may be seen in Figure 5, the breakout orientations and the P-axis directions are 

very similar to the orientation of maximum compressive strain implied by the trend of local 

fold structures and by the inferred direction of horizontal shortening amss the San Benito 

network. Along the western edge of the Great Valley and near Coalinga, the kaon of 

o1 inferred from the breakout orientations and two earthquake focal mechanisms and the 

orientation of maximum compressive strain inferred from the fold trends is N30-5O'E. To 

the northwest of Coalinga, including the region spanned by the San Benito network, the 

direction of maximum compressive strain predicted from the azimuth of the local fold 

structures, the 01 direction infed from one wellbore breakout orientation, and the P-axis 

orientation of the Idria earthquake arc N12-35'E. While Mount and Sqpe [ 19871 have 
67 

suggested that the folds in this area have been inactive since the Miocene, the rate of 

deformation determined for the region spanned by the San Benito network suggests that 

ongoing compressive strain is being accommodated across these folds. The recency of 

folding in this region is further supported by the geological observation that the folds 

deform Quaternary deposits [Namron and Davis, 19881. 

As summarized by Mount and Suppe [ 19871 and Namson and Davis [ 19881 the 

occurrence of folding in the Coast Ranges has been variously attributed to distributed rightlateral shear associated with the San Andreas fault or to oblique displacement across the 

region. On the basis of experimental simulations of simple shear and field studies of 

wrench faulting, en echelon fold structures are predicted to occur adjacent to a strike-slip 

fault due to distributed shear [Wilcox er 01.. 19731. Fold axes are expected to be oriented 

perpendicular to o1 in the early stages of wrench faulting; the folds may subsequently rotate 

into parallelism with the strike-slip fault through distributed shear [Mounr and Suppe, 

19871. In central California, the axes of early-forming en echelon folds would be at an 

angle of 30' f 15' to the trend of the San Andreas fault (mN41.W) in a counterclockwise 

direction, or N71'W f 15' (p = N19'E f 15'). 

In an alternative model deformation is due to oblique displacement, sometimes termed 

"transpression"[HatZand, 197 11, across the southern Coast Ranges. This deformation is 

thought to be decoupled into a low-shear-stress, strike-slip component and a highdeviatoric-stress, thrust component [Mounr and Suppe, 1987; Zobclck er al., 19871. In this 

model the strike-slip component is accommodated within a nmw (< 3-10 km wide) zone 

and the compressive component is accommodated over a wider zone (10-100 km). The 

compression is held to be at least partly the result of a small (- 6') difference between the 

orientation of the San Andreas fault in central California and the local direction of PacificNorth American relative plate motion [DeMers et al., 19871. The precise orientation of 61 

adjacent to the San Andreas fault, according to this model, depends on the relative strength 

. 
68 

of the fault zone and the surrounding lithosphere [Mounr and Suppe, 1987; aback et af., 

19871; for a substantially weaker fault zone 01 may be nearly normal to the fault me ( p - 

N49.E). 

The direction of maximum compressive strain indicated by orientations of the local 

fold structures in the $an Benito region is N25'E, close to the orientation of maximum 

incremental compressive strain estimated from the geodetic data (p = N16'E f 13.). These 

orientations are in apparent agreement with the wench faulting model. The significant 

difference between the trend of the fold axes in the San Benito region and in the San 

Emigdo Mountains [Davis, 19861 and the strike of the San Andreas fault is in contrast, 

however, to the situation throughout most of the Coast Ranges in central California, where 

fold axes have orientations approximately parallel to the San Andreas [Mount and Suppe, 

19871. In these two regions the fold orientations are thought to be controlled by 

reactivation of older structures (T.L. Davis, personal communication, 1988); in the San 

Benito area these older structures may be related to a late Miocene deformation event 

[Namson and Davis, 19881. Given such structural control, the geodetic data reported here 

are also consistent with the oblique displacement, or transpression, model for deformation 

of the Coast Ranges. 

As discussed earlier there an two observations which argue against models in which 

right-lateral shear strain is distributed across a zone significantly greater than 10 km in 

width. Because slip on the adjacent San Andreas fault occurs primarily by steady creep, 

little of the right-lateral shear strain accumulation associated with fault should be 

measurable on off-fault geodetic lines. Additionally, distributed shear strain associated 

with the San Andreas fault would be observable on both sides of the fault, yet there is no 

geodetic or geologic evidence of deformation within the Salinian block [Thatcher, 1979al. 

There are several factors which may complicate the interpretation of measurements 

used to distinguish between models relating the formation of fold structures in the Coast 
69 

Ranges to motion along the San Andreas fault. First, there may be processes that act on 

different length scales which might explain the change in the ol direction and the trend of 

fold structures at different distances from the San Andreas fault. Within a narrow zone 

centered on the San Andreas fault, local geological structures and focal mechanisms may be 

the result of geometrical complexities in the fault trace [Segaff and Pollard, 19801 or the 

rheological structure of the fault zone [Horns et al., 19851. Between the San Andreas fault 

and the Paicines fault, for example, the focal mechanisms determined by Effsworth [ 19751 

may be due to interaction between the two faults. As seen in the San Benito region, fold 

orientations may also vary due to reactivation of older structures or material heterogeneity. 

Finally, as will be discussed in the next section, there is the additional complexity that 

deformation in the southern Coast Ranges is related, in a kinematic sense, to the overall 

deformation across the Pacific-North American plate boundary. 

. 

Relation of Deformation East of the San Andreas Fault to the 

Accommodation of Plate Motion 

The results of the geodetic measurements presented in this chapter are relevant to 

deformation in other subregions of the Coast Ranges and to the question of how PacificNorth American plate motion is accommodated across California. 

Global plate motion models, which yield the relative motion between the North 

American and Pacific plates, have been used as kinematic boundary conditions on the 

integrated deformation across the plate boundary zone in the western United States [Minster 

and Jordan, 1984, 1987; Bird and Rosenstock, 1984; Weldon and Humphreys, 19861. If 

the San Andreas fault functioned as a simple boundary that accommodated the full motion 

between two rigid plates, the rate of slip in central California predicted by the NUVEL-1 

global plate motion model would be about 49 mm/v at N35'W [DeMefs et af., 19871. 

Deformation across the Pacific-North American boundary is instead thought to be 
70 

distributed across a broad zone between the continental escarpment and the eastern front of 

the Basin and Range province. As summarized above, the rate of slip on the San Andreas 

fault in central California oriented at N41'W f 2' is constrained from Holocene geological 

data and ground-based geodetic measurements to be 34 f 3 mdyr. The vector difference 

between the plate motion and the San Andreas rate is about 16 mdyr in the direction 

N21'W. The integrated rate of extensional deformation to the east of the San Andreas fault 

across the Basin and Range has been estimated from geological observations averaged over 

the Holocene and from very long baseline interferometry (VLBI) to be 9.7 f 2.1 mm/yr at 

N56'W f 10' [Minster and Jordan, 19871. The vector difference derived using the above 

rates of motion for the San Andreas fault and Basin and Range, referred to as the 

discrepancy vector by Minster and Jordan [ 19871, is about 10 dyr in the direction 

N14.E, or 5 dyr of slip parallel to the San Andrtas fault and 8 mm/y of convergence 

normal to the fault. On the basis of the estimates of Minster and Jordan [ 19871, the 

uncertainities in the discrepancy vector an approximatelly f 5 mm/p far the rate of slip and 

f 15' for the direction. Although some minor internal deformation within the Sierra 

Nevada block [Lockwood and Moore, 19791 or across the Great Valley syncline may 

occur, most of the deformation represented by the discrepancy vector is thought to occur 

within the Coast Ranges. Weldon and Humphreys [ 19871 and Saucier and Humphreys 

[ 19881 have constructed a self-consistent description of deformation in southern and central 

California from geodetic data and Quaternary geologic slip rates. From their model they 

predict that the Pacific-North American relative plate motion vector is 9' mon westerly than 

that given by NUVEL-1. They estimate - 5 mdyr of convergence normal to the San 

Andreas fault in central California 

A compilatation of estimated and measured rates of deformation in the Coast Ranges, 

separated into right-lateral strike-slip motion on specific faults and distributed compression, 

is given in Table 4. In general the geological data are most useful for indicating long- term 
71 

modes of deformation and for placing upper and lower bounds on rates. The large range in 

most geologically determined rates is due to uncertainities in dating rock units and in the 

timing of geological reconstructions. 

A comparison of incremental strain rates determined over a geologically short interval 

to long-term slip rates is meaningful only if the deformation process accumulates strain in a 

temporally uniform manner. On short-time scales (100 - 102 yrs) there are a number of 

mechanisms associated with temporal variations in strain rate. An increase in the rate of 

shear strain has been documented to occur after large earthquakes in a region adjacent to the 

rupture zone [Thatcher, 19861. There is no evidence, however, for a change in the rate of 

slip on the San Andreas fault in central California for the time interval that spans the 

Occurrence of the pat 1906 earthquake on the northern locked segment of the San Andreas 

fault [Thatcher, 1979al. As discussed above, then is a suggestion that the rate of slip on 

the Paicines and Calaveras faults changed at about the time of the 1979 Coyote Lake 

earthquake. 

Within a fold and thrust belt such as the southern Coast Ranges the short-term 

temporal variations in the rate of deformation arc poorly constrained. The pattern of 

moderate size earthquakes (ML > 5.0) between 1932-1982 in the southern Coast Ranges 

[Engdahf and Rinehurt, 19881 is similar to the seismicity pattern given in Figure 1; there is 

some additional seismicity in the region between the Rinconada fault (Figure 1) and the 

continental escarpment. This result suggests that over the past -50 years the pattern of 

release of strcss and strain by earthquakes has been approximately time-stationary. 

Comparison with geological data is further complicated by the observation that the plate 

boundary zone undergoes evolution on geological times scales. Field geological evidence 

from the Coalinga region indicates that the most recent episode of uplift began only 2-3 

m.y. ago, well after slip commenced on the San Andreas fault [Namson and Davis, 19881. 

A fold and thrust belt typically undergoes an evolution such that the locus of deformation 

* 
72 

changes. In the initial stages of deformation the locus of activity is controlled by such 

factors as the nature and position of the driving and resisting forces, pre-existing zones of 

weakness, and rock properties such as the elastic moduli, effective viscosity, and 

stratification of the deforming medium [Biut, 1961; Hariand, 19711. At some point beyond 

this initial stage less work may be required to break new faults or build new folds, and the 

folding and faulting may commence elsewhere. 

To explore the implications of the constraints provided by the San Andreas 

discrepancy vector we compare the predicted rate of -5 mm/yr of fault-parallel and -8 

mm/yr of fault-normal deformation to the values given in Table 4. The rates of right-lateral 

slip on the Rinconada and San Grcgorio faults estimated from geological observations are 

0-2 and 6-9 mdyr, respectively [Clark et al., 19841. These values compare with 

geodetically measured rates of 2 f 1 dyr (Table 4) and 0 f 8 mnJyr [Prescutt ond Yu, 

19861, respectively. These results for the rate of slip on the San Gregorio fault are 

significantly smaller than some earlier estimates [Minster and Jordan, 1984; Weldon and 

Humphreys, 19861 but are more consistent with recent kinematic models [e.g, Model D, 

Minster und Jordan, 19871. 

Geological and seismicity data suggest that northeast-southwest compression across 

the southern Coast Ranges may be localized to two regions, the 30-Ian-wide zone spanned 

by the San Benito network and a second zone to the west of the Rinconada fault [Eoton, 

1984; Dehlinger and Bolt, 19871. If shortening across the Coast Ranges is divided equally 

between these two regions, approximately 4 mm/yr of shortening should be occumng 

within the Diablo Range. If, in contrast, the predicted 8 mm/Yr [Minster ad Jordan, 19871 

is distributed uniformly across the 170-km-wide zone between the continental escarpment 

and the Great Valley, the shortening across the region spanned by the San Benito network 

would be approximately 1.4 mm/yr. The rate of deformation estimated from the San 
73 

Benito study is most consistent with the frst hypothesis, but the uncertainities in our 

calculated values do not allow the latter possibility to be ruled out, 

Results from ongoing geodetic studies with stations in central California should 

provide additional constraints on the rate and distribution of slip within the Coast Ranges. 

The rate of slip estimated from VLBI measurements made at Vandenberg, Fort Ord, 

Presidio, and Point Reyes (Figure 6) could potentially be used to constrain the rate of 

deformation across the Coast Ranges. To distinguish between different models will require 

that uncertainities in the rate of slip, relative to a fixed reference, be 2-3 dyr or less. Our 

preliminary analysis of VLBI data, based on measurements between October 1982 and 

March 1987, indicate that only the rate of slip at the station Vandenberg meets this 

requirement [Sauber et al., 1987; see also Clark et al., 19871. Additional measurements at 

all of the VLBI stations in central California have been made within the last year, and an 

analysis of these measurements will be the subject of the next chapter. The rate of 

deformation estimated from measurements to the Farallon Islands (Figure 6) will be 

updated following a mlateration survey of the network by the USGS in 1988; such 

information should provide a better constraint on the rate of slip on the San Gregorio fault. 

Summary 

Triangulation and ailateration data from two geodetic networks located between the 

San Andrcas fault and the Great Valley have been used to calculate shear strain rates in the 

Diablo Range and to estimate the slip rate along the Calaveras and Paicines faults in central 

California. The shear strain rates,*yl and $, were estimated independently from angle 

changes using Prescott's method and from the simultaneous reduction for station position 

and strain parameters using the DYNAP method. On the basis of Prescott method, the 

average shear strain rate for the time period between 1962 and 1982 is 0.15 f 0.08 pad&, 

with the orientation of the most compressive strain (p) at N16'E f 14'. Utilizing the 
DYNAP method with corrections for the deflection of the vertical and the geoid - reference 

ellipsoid separation computed on the basis of local gravity observations, = 0.19 f 0.09 

pradyr and p = N16'E f 13'. At the 95% confidence level is not significantly greater 

than zero. The orientation p, however, is similar to the direction of maximum compressive 

strain indicated by the orientations of major fold structures in the region (N25'E). We 

infer that the measured strain is due to compression across the folds of this area; the 

average shear straining corresponds to a relative shortening rate of 5.7 f 2.7 Wyr. 

The orientations of maximum principal stress inferred from wellbore breakouts and 

the azimuths of P axes determined from earthquake focal mechanisms within the Diablo 

Range and near the western edge of the Great Valley are similar to the orientation of 

maximum compressive strain implied by the trend of local fold structures. In contrast to 

the situation throughout most of the Coast Ranges in central California where fold axes 

have orientations approximately parallel to the San Andrcas fault, within the Diablo Ranges 

between Hollister and Coalinga the and of the fold axes are different and are thought to be 

controlled by reactivation of older structures. Given such structural control, the gdetic 

data repored here are consistent with transpression across the Coast Ranges. 

For a zone within 10 km of the $an Andreas fault, nilateration measurements on offfault lines east of the San Andreas fault as well as lines that cross the San Andreas fault 

have been used to estimate the rate of slip along the Calaveras-Paicines fault and to 

document the gradual southward transition in the width of the zone accommodating rightlateral fault slip. South of Hollistcr the inferred rate of slip on the Calaveras-Paicines fault 

was found to be 10-12 mm/yr. The rate of slip on the Paicines fault near Bitter is -4 

mm/yr. Further to the south all of the right-lateral slip (at least across the 20-km-wide zone 

of measurements) occurs on the San Andreas fault. 

To distinguish between different models that describe the distribution of strike-slip 

and compressive displacements within the Coast Ranges we examined data from rtgional 
75 

geologic and geodetic studies and global plate models. Geological and seismicity data 

[Eaton, 1984; Dehlinger and Bolt, 19871, as well as our geodetic results, suggest that 

northeast-southwest compression across the southern Coast Ranges may be localized to 

two regions, although uniform compression across the 170-km-wide zone between the 

continental escarpment and the Great Valley cannot be ruled out. 

Appendix. Details of Data Reduction for the San Benito Network 

Accuracy of the Triangulation and Trilateration Measurements 

Triangulation is a measurement system consisting of joined or overlapping mangles 

of angular observations. During a single session observations of direction arc made from a 

particular mark to several other marks that arc located within a few tens of kilometers from 

the mark occupied. An angle observation is determined by differencing two direction 

measurements. Seventy of the 72 directions utilized in this study were second-order 

observations, with a priori uncertahity estimated to be bd = 3.4 pad [Federal Geodetic 

Control Committee, 19841, and two were third-order observations (bd =5.8 prad). The 

expected uncertahity in a second-order angle measurement (ad is fi ad, or about 4.8 

Hrad. The order of the triangulation denotes the measurement precision, which is 

determined by survey procedures and is reflected in the degree to which internal checks of 

the data are satisfied [Thazcher, 1979bl. The principal internal check is the triangle closure 

requirement that the angles within each mangle sum to 180" plus the known excess due to 

the Earth's sphericity. Triangle closures for these data indicate that the standard deviation 

of a single angle is approximately 5.3 pad, very close to the expected value. 

As practiced by the USGS, mlateration consists of distance measurements among a 

network of stations. The distances between geodetic monuments were measured in this 

study with a Geodolite, a precise electro-optical distance-measuring instrument. Regional 
mlateration measurements made by the USGS on line lengths of 10-40 km have a precision 

of approximately 0.2-0.3 ppm [Savage and Prescott, 1973). After corrections for 

refractivity and instrument and reflector height, a line length corresponds to the distance 

between two geodetic monuments. 

Assumptions Made in the Estimation of Horizontal Shear Parameters 

The full three-dimensional strain tensor includes horizontal and vertical shear 

components, dilatation, and vector rotation. Since height changes were not directly 

measured in either the 1962 or 1982 survey, we can estimate only the horizontal 

components of the strain tensor. Here we assume that vertical changes in station height are 

negligible. Since no large earthquakes occurred within the region spanned by the San 

Benito network between 1932-1982 [Engdahf and Rinehurt, 19881, the estimated rate of 

uplift on the folds of the Diablo Range is only 1-3 mm/yr [Zepedo et 01.. 19871, or 2-6 cm 

over the 20-year time period of this study. A 6-cm change in the height of Tum (Figure 2) 

between 1962 and 1982, for example, will cause a 0.1 ppm change in the 20-km-length 

line between Tum and Bonito (calculated from equation 1.72 of Bornford [1980]). 

Because of ground-water-induced subsidence, larger vertical changes may have occumd at 

the stations Stubble, located in the Great Valley, and Panoche, located in Panoche Valley. 

Further, astronomic azimuth measurements arc made only at Hepsedam. Without a reliable 

external or conventionally adopted internal reference ktion, we cannot estimate rotation 

of the network about a vertical axis. Additionally, since length measurements were made 

only in the 1982 survey, surface dilatation can not be estimated. We are thus able to 

estimate only the rate of change of horizontal shear components <i; and +*). If the fold 

structures of the region arc deforming as the result of simple uniaxial compression, bloc6 

rotation is not expected and dilatation is assumed to be uniform. 

76 
77 

The two modes of deformation suggested from the geological st~ctures of the region 

(see text) can be used to interpret the 'u, and f2 values. Right-lateral strike-slip motion at 

the orientation of the San Andreas fault (N41.W) would be seen primarily as tl > 0. 

North-south compression is also consistent with > 0. If the orientation of 

compressional strain is northeast-southwest, as is predicted from the orientation of the 

folds within the southern Coast Ranges, then +2 c 0. 

Prescort's Method 

Angle changes are the observations used to estimate and t2 in the extended version 

of Frank's method [Prescorr, 19761. The fundamental equation of the technique, 

when 

1 . = [(sine i2 - sine 1> ~1112 

- 

- 

relates an observed angular change A% for the time interval ti - b to the parameters and 

t2. Here Oil and 8i2 represent the azimuths (clockwise from north) of the initial and 

terminal sides of the angle. To derive angles the 1982 data were used to adjust for station 

position. Rather than making an adjustment on a three-dimensional surface, the distances 

were projected onto the Clark 1866 reference ellipsoid (NAD27 geodetic system, Defeme 

Mopping Agency [1987]), and an adjustment was made employing a variation of 

coordinates method [Anderson, 19691. Azimuths for each station-testation pair were then 

determined for comparison to the 1962 observations. In this approach we are comparing 

angles measured on the Earth's surface to angles determined from a network adjustment on 
the reference ellipsoid. The classical solution to the adjustment of geodetic data derived 

from different measurement techniques has involved making corrections to the direction 

and distance observations such that the measurements arc then given on a common 

reference ellipsoid [Bornford, 1980; Vunicek and Krukiwsky, 19861. In employing the 

DYNAP method an alternative approach is used. 

DYNAP Method 

In the DYNAP (DYNamic Adjustment Program) technique the directions measured in 

1962 and the distances measured in 1982 are used simultaneously to solve for both crustal 

motion parameters and positional coordinates of the geodetic marks for a specified 

reference time via weighted least squares [Snuy, 1986; Drew and Snay, 19881. A twodimensional adjustment was carried out by holding the station elevations fixed. In this 

approach the direction observations arc corrected for the deflection of the vertical, and the 

separation of the geoid and a reference ellipsoid are used to correct the distance 

observations. This technique is based on the assumption that the velocity field is linear in 

space and constant over the time interval of interest. The time dependent station positions 

can be written as 

where x(ti) are the two dimensional station coordinates at time ti and b is the reference 

time. The four components of the 2 x 2 tensor L parameterize the velocity field v by its 

gradient [Muhrern, 19691: 

78 
79 

In equation (A.2) the origin is arbitrary. In practice one station is chosen as an origin and 

is held fixed for all epochs. L can be decomposed into a sum of a symmemc tensor D, 

called the rate of deformation tensor, and a skew-symmemc tensor W, called the spin 

tensor [Malvern, 19691 

L=D+W (A.4) 

For the case where all of the components of rate of deformation are zero, the instantaneous 

motion is then a rigid-body rotation. When displacements and displacement gradients are 

small D is approximately equal to kij. 

Corrections to Reduce the Observations to a Common Reference System 

When a direction measurement is made the theodolite is leveled; thus the measurement 

is made normal to the geoid, not normal to a reference surface. A correction for the 

deflection of the vertical is therefore required [Bomford, 1980; Vunicek and Krakiwsky, 

19861. The deflection of the vertical is the spatial angle between the vector normal to the 

geoid and the vector normal to an ellipsoidal surface. The correction Aqj to a direction of 

azimuth qj and elevation angle Vij [Bornford, 1980, P. 1061 is 

where si and Ti are the meridian and prime vertical components of the deflection of the 

vertical at the observing, or i th, station. Deflections of the vertical are usually estimated 

from astronomical azimuth observations or from computed values based on local gravity 

observations [Coleman and Lumbeck, 19831. Alternatively, the deflections can be 

computed from the long-wavelength part of the geopotential together with necessary 

transformation parameters between the geoid and the ellipsoid reference system. 
80 

In this study the initial latitude and longitude of the station are positions given in the 

NAD83 reference system [Defense Mapping Agency, 19871. The initial heights are 

orthometric heights, the height above the geoid estimated primarily from spirit leveling. 

For the station coordinates to be in a common reference frame, the heights need to be 

converted to heights above the GRS 80 reference ellipsoid [Defense Mapping Agency, 

19871. To make this calculation the separation of the geoid and the reference ellipsoid 

needs to be estimated. Since astronomical azimuths arc not available, the deflection of the 

vertical and the geoid -ellipsoid separation are initially estimated from the long-wavelength 

part of the geopotential. 

The global gravity field representation given by the WGS 84 Earth Gravitational 

Model (EGM) [Defense Mapping Agency, 19871 was used to calculate the deflection of the 

vertical and geoid height at each station using the Defense Mapping Agency program 

CLENQUENT [Gleam, 19851. The form of the WGS 84 EGM is a spherical harmonic 

expansion of the gravitational potential; we used an expansion to degree and order 360. 

The gravitational coefficients are from Rupp and Cruz [ 19861 and R. Rapp (personal 

communication, 1988). The reference ellipsoid used to calculate the deflections of the 

vemcal and the geoid - ellipsoid height separation was GRS 80 [Defense Mapping Agency, 

19871, which is used in both the WGS 84 and NAD83 reference systems. The deflections 

of the vertical vary in the network from 1.14"s to 0.14"N for 5 and from 1.40"E to 3.60"E 

for q. Utilizing the geoid - reference ellipsoid height separation and deflections of the 

vertical calculated from the long-wavelength part of the geopotential, the strain rate 

parametas were estimated using the DYNAP method, yielding += 0.12 f 0.09 psnain/yr 

and p = N17'E f 21' and an increase in the variance of unit weight by 2%. The strain rate 

results arc similar to those obtained without mmtions ( += 0.15 f 0.09 pmd& and p = 

N17'E f le.) The surface topography as well as the density distribution within the crust 
81 

of the San Benito region is irregular, so the geoid representation used represents poorly the 

higher order features of the gravity field. 

Because we expect significant short wavelength variations in the geoid, we have 

obtained from the Defense Mapping Agency geoid - reference ellipsoid separations and 

deflections of the vertical computed for network station positions from local gravity 

observations. The deflections of the vertical vary in the network from 6.00"s to 7.38"N 

for 6 and from 12.47"E to 6.38"W for q. The strain rate parameters utilizing these 

corrections are += 0.19 f 0.09 psnain/yr and p = N16'E f 13'. The variance of unit 

weight decreases by 8%. This decrease is due to a lower misfit for the direction 

observations; the corrections do not change the m misfit for distance observations. These 

results suggest that while it is desirable to correct for deflection of the vertical and for the 

separation between the geoid and the reference ellipsoid, these carnctions an valuable only 

when based on local observations. 

8 
82 

TABLE 1. Strain Rate Parameters for Spatial Subsets of the San Benito Network 

East 14 0.18 f 0.1 1 0.01 f 0.12 0.18 f 0.10 N 1'W f 20' N46.W t 20' 

West 9 0.07 f 0.14 -0.18 f 0.13 0.19 f 0.13 N34'E f 22' Nll'W 2 22' 

North 13 0.04 f 0.10 -0.12 f 0.10 0.16 f 0.11 N37'E f 20' N 8'W 2 20' 

south 7 0.22 f 0.16 -0.13 f 0.22 0.25 f 0.20 Nl0'E f 20' N35'W f 20' 

All stations 

except BIT, 

HEP,andPAN 25 0.13 f 0.08 -0.08 f 0.08 0.15 f 0.08* N16'E f 14'* N29'W k 14'* 

* These strain parameters have been scaled by the u posteriori variance factor [Vanicek 

and Krakiwsky, 19861. 
83 

TABLE 2. Fault-Slip Rates Inferred from Length Changes on Fault-Crossing Lines 

Calaveras - Paicines Fault Zone 

Station Station No. Period i, Azimuth, Slip Rate, 

1 2 of Obs. &F deg &F 

BRN CRS 7 72.7-83.9 -8.7 f 0.8 168 9.9 f 0.9 

CRS CHL 9 72.1-83.9 -18.5 k 0.4 181 24.9 f 0.5 

BRN CHL 8 72.1-83.9 27.4 f 0.4 175 33.8 f 0.5 

Paicines Fault Adjacent to the Central Creeping Portion of the San Andrem Fault 

Station Station No. Period L Azimuth, Slip Rate, 

1 2 of Obs. dyr deg R1III/yT 

BIT HEP 6 73.1-83.9 3.7 f 0.5 129 3.8 f 0.5 

CHL BK 8 72.1-83.9 19.8 f 0.7 280 25.8 f 0.9 

CHL HEP 7 72.7-83.9 27.4 f 0.6 113 30.7 f 0.6 

The quantity i is the rate of change of line length determined by least-squares, shown 

together with one standard deviation. Azimuth is measured clockwise from north. The 

slip rate is that appropriate to the strike-slip fault crossed by the indicated line. The time 

intervals of observations are given in decimal fractions of years. 

. 
84 

TABLE 3, Fault Slip Rates Indicated by Short-Range Trilateraaon Networks 

Network No. of Period Slip Rate, 

Observations mm/yr 

~~ ~ 

75.2-87.3 12f2 

79.0-87.3 27 f 2 

74.9-87.3 32f 1 

See Table 2 for explanation of notation. 
85 

TABLE 4. Summary of Deformation Rates within the central Coast Ranges 

Fault Orientation Geological Slip Rate, Geodetic Slip Rate, 

WYr 

Righr-lateral snike-slip faults 

oreigalita N35'W 0.20 

Rinconada N35'W @2d 

san Andreas N41'W 3 1 -37b 

San Simeon N34'W 6-9 f 

San Grcgorio ~209~ 7-1 18 

32f3C 

2f le 

Of 8h 

Compresswn in the Coast Ranges 

East of San Andreas 2.2- 5.5i 5.7 f 2.7 i 

West of San Andreas 4.4- 1 li 6.1 f 1.7kJ 
Notes For Table 4 

a 

b 

C 

and Prescott [ 198 11; this study. 

d 

personal communication, 1988. 

e The line between Brush and Mulligan of the USGS Pajaro mlateration network has 

been measured five times between May 1978 and April 1983. If it is assumed that the 

average line length change is due to right-lateral slip on the King City fault, a northern 

extension of the Rinconada fault, then a slip rate of 2 f 1 dyr is indicated. 

f 

shoreline; a preferred slip rate of 6 mm/yr is given by Clurk et al. [ 19841. 

8 

preferred slip rate of 7 mdyr is given by Clurk et d., [ 19841. 

h 

late 1985 [Prescort and Yu, 19861. 

i Namson and Davis [ 19881 estimated that 11 km of late Cenozoic shortening has 

occurred between the San Andreas fault and the Great Valley. The 22 km of shortening to 

the west of the San Andreas fault was computed by Namun and Davis [ 19881 from a 

solution that satisfies the observed structural relief. The range in rate estimates were 

obtained by assuming that shortening commenced between 5 and 2 m.y. ago. 

l' This study. The direction of maximum contraction is N16'E f 13'. 

k Segall and Harris [ 19861; Harris and Segall[ 19871. Average rates of change of line 

length from the San Luis trilateration network were used to invert for slip rate at depth on 

the San Andreas fault. In order to fit the mlateration measurements from this network, it 

Hart et af. [ 19861. 

Sieh and Jahns [ 19841. 

Savage and Buqord [ 19731; Thatcher [ 1979aj; Bwford and Harsh [ 19801; Lisowski 

Hurt et al. [ 19861; D. B. Slemmons, personal communication, 1987; E. W. Hart, 

Rate of right-vertical oblique slip inferred from the offset of an ancient marine 

Rate of right-lateral slip inferred from the offset of an ancient marine shoreline: a 

From trilateration measurements made to the Farallon Islands between mid-1979 and 

86 
87 

was necessary to include a component of contraction normal to the trend of the San 

Andreas fault. The inversion results suggest a spatially uniform normal strain of -0.06 

pstrain/yr. The net Shortening rate across the network is 6.1 f 1.7 mrdyr. This estimated 

compression, however, may be due to a systematic bias in the older trilateration data [J.C. 

Savage, personal communication, 19871 . 

1 Two additional geodetic studies using historical triangulation data have been made 

west of the San Andreas fault. Burford [ 19671 analyzed triangulation data measured 

between 1930 and 1951 from two networks. One extends from Monterey Bay to the 

region where the San Andreas and Calaveras faults diverge (Figure 1), and one extends 

from Kettleman Hills near Parkfield west to San Luis Obisbo. Outside a zone close to the 

San Andreas fault, the direction of maximum shortening was estimated to be approximately 

N35'E. As part of a general study of the deformation in central California, Thatcher 

[1979a] examined triangulation data measured during the time interval 1944-1963 from the 

Salinias Valley network. Most of this network lies within the Salinian block located 

between the San Andreas and Rinconada faults. Examination of subregions suggest that 

the strains an poorly resolved, with the orientation of the infemd strain field not correlated 

with any known faults or tectonic txtnds. Because of the uncertainities in the results, 

neither of these studies were used for rate detexminations. 

. 
88 

Figure Captions 

Figure 1. Epicenters of earthquakes (ML 2 4.0) in the Coast Ranges during 1962 - 1982 

[Engduhl and Rimhurt, 19881. The locations of three earthquakes with welldetermined 

focal mechanisms, the 1982 Idria, the 1983 Coalinga, and the 1985 North Kettleman Hills 

events, are indicated by stars. Fault traces are simplified from Jennings [ 19753: HF = 

Hosgri fault, RF = Rinconada fault, SAF = San Andreas fault, SGF = San Gregorio fault, 

WTR =Western Transverse Ranges. An outline of the San Benito triangulation/uilatcration 

network is given for reference. MB = Monterey Bay. 

Figure 2. Location of stations in the San Benito mangulation/mlateration network (solid 

circles), the Coalinga mlateration network (open circles), and small aperture ailateration 

networks (triangles). Half-filled circles denote stations that were part of both the San 

Benito and Coalinga networks. Surface traces of Quaternary faults are indicated by solid 

lines where well located and by dashed lines where approximately located or inferred 

[Jennings, 19751: CFZ= Calaveras fault zone, OF% Ortigalita fault zone, PF=Paicines 

fault, RF=Rinconada fault, SAF=San Andreas fault. Stations discussed in the text include 

BIT = Bitter, BON = Bonito, BRN = Browns, CHL = Chalone, CRS = Cross, HEP = 

Hepsedarn, LEY = Ley, PAN = Panoche, SMO = Smoker and TUM = Tum. Also shown 

are the locations of Coalinga (C), Hollister (H), and San Benito (SB). 

Figure 3. Major structural features of the Diablo Range between Hollister (H) and 

Coalinga (C), modified from Dibblee [ 19791. The locations of stations in the San Benito 

triangulation/trilateration network are shown as circles for reference. Structures shown 

include: CA = Coalinga anticline, CFZ = Calaveras fault zone, NI = New Idria diapir, OFZ 

= Ortigalita fault zone, PF = Paicines fault, PS = Paicines syncline, and VS = Vallecitos 
89 

syncline. Inward pointing double arrows indicate a syncline, outward pointing double 

arrows an anticline. Single arrows indicate the direction of plunge of a fold axis. 

Figure 4. Strain rate inferred for the San Benito network by use of the DYNAP method, 

including corrections for deflection of the vertical and separation of the geoid and reference 

spheroid. (a) The orientation p of the axis of maximum compressive strain. The 

uncertainty in azimuth, at 95% confidence, is shown by an arc. (b) The shear strain rate 

parameters il and q2, together with a 95% confidence ellipse. 

Figure 5. Fold structures and measured stress orientations in the region east of the San 

Andreas fault in central California [modified from Mount and Suppe, 19871. Synclines are 

indicated by dashed lines, anticlines by dotted lines. Single arrows indicate the direction of 

plunge of a fold axis. Wellbore breakout measurements are given by a solid line with 

inward pointing arrows perpendicular to the direction of ol. The direction of o1 inferred 

from the azimuth of the P axes for three earthquakes are labeled by number: 1 = 1982 New 

Idria earthquake, 2 = 1983 Coalinga earthquake, and 3 = 1985 North Kettleman Hills 

earthquake. The axis of maximum compressive strain (p) determined from triangulation 

and mlateration data from the San Benito network is given along with its standard 

deviation. 

Figure 6. Reference figure for the geodetic and geological studies cited in Table 4. Brush 

(B) and Mulligan (M) arc two stations in the USGS Pajaro mlateration network. At sites f 

and g, rates of fault slip were estimated geologically [Clark et 01.. 19841 for the San 

Gregorio and Hosgri faults. The line A-A' is that for which Namson and Davis [ 19881 

constructed their geological cross section (see Table 4). Fault traces are as given in Figure 

1. Geodetic networks include FIN = Farallon Islands network, SBN = San Benito 
90 

network, and SLN = San Luis network. VLBI stations include FORT = Fort ord, PRES = 

Presidio, FT. R = Point Reyes, and VNDN = Vandenberg. 
91 

Great Valley 

0 

0 

I 

to 

0 

Net 

0 

o 4.0 

0 5.0 

30' 

36' 

-!22O -120O 

FIGURE 1 
92 

E 

x ! 

8 
93 
94 

-0.6 

rd 

4 

k 

0 

z 

I 

I (b) 

*-I I I I I I I 

I 

0.6 

n 0.4 

k 

\ 0.2 

Td 

cd k 0.0 

-0.2 w 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I (a) 

East 

c cu '* -0.4 

0 I 

---- 

-0.4 0.0 0.4 

FIGURE 4 
I 

I 

I 

I 

I 

I 

I 

+ 

/q' 

,II-t- I 

I I 

I /+; I 

I 

vi 

.' 

.. 

.. 

v... i 

i+ 

:+ 

.. 

.. 

.. 

.. 

.. 1 

1 .. I 

\ \ I \ 

\ 

\ 

\ 

\ 

\ 

'I 

II 

\ 

\ 

\ 

\ 

\' 

\ 
96 

I I I 

- 122" - 120° 

38'. 

36" 

FIGURE 6 
97 

Chapter 4. Rates of Deformation in Southern and Central 

California from VLBI, Ground-based Geodetic, and Geologic 

Data 
98 

Introduction 

Although rigid-plate models have been successfully used to describe global plate 

motions, the complexity in the spatial and temporal pattern of deformation at plate margins, 

particularly continental margins, are inadequately described by such simple interactions. 

The Pacific - North American plate boundary zone in the western U.S. has thus been a 

major focus of research on active tectonics. Although the San Andreas fault is usually 

identified as the major kinematic element at the plate boundary, significant deformation both 

east and west of the San Andreas has long been recognized by geologists [Carey, 1958; 

Hamilton and Myers, 1966; Arwater, 19701. The distribution of deformation across 

different portions of this boundary document the transition from crustal spreading in the 

Gulf of California to right-lateral transcmnt motion along the San Andreas and extension 

in the Basin and Range province. How deformation is accommodated between different 

kinematic elements and the relation of this deformation to the overall accommodation of 

motion across the plate boundary on geodetic and geologic time scales is currently being 

examined. To address these questions previous workers have used the relative motion of 

the Pacific and North American plates determined from global plate motions and the rate of 

spreading in the Gulf of California, the rate and orientation of fault slip estimated from 

geological data, strain release patterns as seen in earthquakes, and the present-day rates of 

deformation estimated from data obtained from local and regional geodetic networks. 

Throughout much of the United States space-geodetic measurements are currently being 

made at intercontinental and regional spatial scales. In the last five years baselines that both 

span and arc distributed within the Pacific - North American plate boundary zone have been 

measured with very long baseline interferometry (VLBI). In this study I use VLBI data to 

obtain estimates of the rate of change of tangential station position in a North-America-fixed 

reference frame. These data are used to constrain the integrated rate of deformation across 

portions of the continental plate boundary in California and to provide a tectonic framework 
99 

to interpret regional geodetic and geologic studies. For three regions, across southern 

California just north of the Imperial fault, in the 'big-bend region, and in central 

California, I compare the rates of deformation derived from VLBI and ground-based 

geodetic data, and I examine the relationship between the rates of deformation determined 

from geological data and those estimated from geodetic data. 

The rate of relative motion between the Pacific and North American plates obtained 

from global plate models such RM2 [Minster and Jordan, 19781 and NUVEL-1 [DeMers et 

al., 19871 are based on magnetic anomalies averaged over the last several million years. 

Utilizing recently available marine magnetic data, the spreading rate in the southern Gulf of 

California has been estimated to be -48 dyr [DeMets et al., 19871. To determine the 

present-day spreading rate across the Gulf of California satellite laser ranging (SLR) and 

global positioning system (GPS) measurements are currently being made [Traffi et al., 

19871. The relative motion between the North American and Pacific plates determined 

from global plate models have been used as boundary conditions on kinematic models that 

describe the rate and dismbution of deformation across the plate boundary in the western 

U. S. [Minster and Jordan, 1984, 1987; Bird and Rosenstock, 1984; Weldon and 

Humphreys, 19861. 

In central California, the rate-of-slip vector of the San Andreas estimated from 

Holocene geological data [Sieh and Jahns, 19841 and ground-based geodesy [Savage and 

Burford, 1973; Thatcher, 1979a; Lisowski and Prescort, 1981; Sauber et al., 19881 is 34 k 

3 dyr at N41'W f 2' [Minster and Jordan, 1984; Mount and Suppe, 19871. If the San 

Andreas fault functioned as a simple boundary that accommodated the full motion between 

two rigid plates, the rate of slip in central California predicted by global plates models 

would be 56 k 3 mm/y-r at N35'W i2' [W, Minster and Jordan, 19781 or approximately 

49 mm/y at N35'W [NUVEL-1, DeMets et al., 19871. The discrepancy between the San 

Andreas fault and the global plate rate is represented by the integratd rate of deformation to 
100 

the east of the San Andrcas in the Basin and Range province and across the Coast Ranges. 

The integrated rate of extensional deformation across the Basin and Range has been 

estimated from geological observations and from VLBI baselines that cross the region to be 

9.7 f 2.1 mdyr at N56'W f 10' [Minster and Jordan, 1984, 19871. The vector 

difference derived using the above rate of motion for the San Andreas fault and Basin and 

Range, referred to as the discrepancy vector, is about 10 Wyr in the direction N14.E. or 

5 Wyr of slip parallel to the San Andreas fault and 8 mm/yr of convergence normal to the 

fault [Model D, Minster and Jordan, 19871. On the basis of estimate made by Minster and 

Jordan [ 19871 the uncertainities in the discrepancy vector are approximately f 5 dyr for 

the rate of slip and f 15' for the direction. Although some minor internal deformation 

within the Sierra Nevada block [Lockwood and Moore, 19791 or across the Great Valley 

syncline may occur, most of the deformation represented by the discrepancy vector is 

thought to occur within the Coast Ranges. To distinguish between different models that 

describe the distribution of strike-slip and compressive displacements within the southern 

Coast Ranges in Chapter 3 we compared the findings of regional geologic and geodetic 

studies to the predictions represented by the discrepancy vector. These results support the 

view that the fault-parallel component of the discrepancy vector may be accommodated by 

strike-slip motion on the Rinconada as well as the San Gregorio fault. Geological and 

seismicity data, as well as our geodetic results, suggest that northeast-southwest 

compnssion in the Coast Ranges of cennai California may be localized to two regions, the 

30-km-wide zone spanned by the San Benito triangulation and mlateration network 

[Chapter 31 and a second zone to the west of the Rinconada fault. The inferred shortening 

to the east of the San Andrcas fault may represent a significant component of the faultnormal compression prtdicted by the discrepancy vector. 

Utilizing geologic slip rates Bird and Rosenstock [ 19841 constructed a block model 

for the present horizontal velocity of the crust in southern California consistent with the 
101 

constraints of the RM2 Pacific - North American plate vector. On the basis of Quaternary 

slip rates derived from geological data Weldon and Humphreys [ 19861 proposed an 

alternative kinematic model for southern California which made very different predictions 

regarding the distribution of deformation. In southernmost California, Bird and 

Rosenstock estimated that approximately 57 mrn/y-r of right-lateral slip is distributed across 

the San Andreas, San Jacinto and Elsinore faults. In contrast, Weldon and Humphreys 

estimated only 37 mdyr across the same faults, and they predicted that additional 

deformation occurs on the offshore faults in the California borderlands. Another major 

difference is seen in the rate of slip estimated for the northwest striking faults of the central 

Mojave Desert. Weldon and Humphreys assumed that the Mojave block is part of stable 

North America, whereas Bird and Rosenstock estimated 6.8 dyr of right-lateral strikeslip motion across the local faults. Both groups used a geological estimate of the 

cumulative displacement across the northwest trending faults [Doh, 19831 to calculate the 

rate of slip for these faults. Unfortunately the time of initiation of fault slip is poorly 

constrained, and very different rates were thus assumed in the two models. Sauber et al. 

[ 19861, given in Chapter 2, used data from triangulation and trilateration surveys made 

during 1934 - 1982 to calculate shear strain rates in the central Mojave. If we assume that 

the rate of deformation measured across the network was due to right-lateral displacement 

across the local faults, the average shear straining corresponds to a relative displacement of 

6.7 f 1.3 dyr. Bird and Rosenstock predict that as a result of the - 7 mm/yr of relative 

motion across the central Mojave, either crustal shortening occurs on the western portion of 

the Garlock fault or crustal extension takes place on the eastern portion of this fault. We 

proposed that the distributed deformation on the northwest saiking faults of the Mojave 

may instead be kinematically related to strike-slip motion on the right-lateral faults north of 

the Garlock fault that bound the region of extensional tectonics in the Gnat Basin. 

. 
102 

In general the geological data are most useful for indicating long-term modes of 

deformation and for placing upper and lower bounds on rates. The differences in the 

kinematic models of southern California are due primarily to the uncertainities in the 

geologically determined rates associated with dating rock units and in the timing of 

geological reconstructions. The present-day rate of deformation can be estimated from 

geodetic measurements. Of course, the use of these rates of deformation, determined over 

a geologically short interval, to infer long-term deformation patterns is meaningful only if 

strain accumulates in a temporally uniform manner [Chapter 31. 

Ground-based geodetic measurements from as early as 1880 have been used in 

crustal deformation studies in California. Historical surveys sample a long portion of the 

seismic cyle and have recorded coseismic and postseismic movements during and 

following earthquakes like the 1906 San Francisco and 1940 Imperial Valley earthquake 

[Thatcher, 1979b; Thatcher, 19861. Combining historical triangulation and astronomic 

azimuth data with mlateration measurements, Snay et al. [ 19871 estimated the average rate 

of shear strain across most regions of California. From precise trilateration measurements 

made over the last 20 years on local and regional networks, the rates of horizontal 

deformation have been obtained for seismically active regions in the western U.S. [Savage, 

19831. Surface strain associated with an individual strike-slip fault occurs on distance 

scales that make it easy to measure with ground-based geodetic methods. In extensional 

and compressional regimes deformation, in contrast, may be distributed over a broad 

region, and it has therefore been difficult to obtain accurate estimates of the rate of such 

deformation. The northwest - southeast extension of the Basin and Range province could, 

in principle, be determined by repeated measurement of a network spanning the entire 

province. This would be a tedious and expensive operation, however, requiring the survey 

of many intermediate reference marks. Moreover, due to the propagation of errors across 

the network the estimated rate of extension would not be accurate enough for tectonic , 
103 

modeling [Minster and Jordan, 19881. Longer baselines can alternatively be measured 

using space-geodetic techniques. In this chapter, we utilize such data obtained from VLBI 

measurements made in the western U.S. 

Determination of Rates of Deformation Utilizing VLBI 

VLBI experiments have been conducted in the western US. since 1979 as part of the 

National Aeronautics and Space Administration (NASA) Crustal Dynamics Project. To 

supplement data available from large fixed radio antennae, mobile radio telescopes have 

been deployed at stations throughout the western U.S. The location of all the VLBI 

stations used in this study are shown in Figure 1. In Figure 2 the VLBI sites in California 

are shown along with Quaternary fault traces simplified from Jennings [1975]. The 

observational history of the 5 stations used in this study with permanent antennae, referred 

to as base stations, and the 17 sites which are periodically occupied by mobile VLBI units 

are given in Table 1. The station acronyms, full station names, approximate locations, and 

the geodetic Iatitudes and longitudes are given in Clark er al. [ 19871. The antenna size of 

the base stations range from 9 to 40 m [Clark et al., 19871. The two mobile systems, MV 

2 and MV 3, that are used for temporary occupation of sites in the western U.S. and Alaska 

have smaller antennae (3.7 m and 5.0 m, Davidson and Trask, 1985; Clark et al., 1987). 

Data from frequent measurements to the base stations are available over an approximately 

five year time period (Table 1). Of the mobile sites in the western U.S., MON and JPL 

have been observed most frequently; DEAD, FLAG, MAMM, OCOT, and PVER have 

been observed less than 4 times. 

Sing le- Epoch Processing 

A VLBI experiment consists of two or more widely separated radio telescopes which 

simultaneously observe and record noise signals from extragalactic radio sources; these 
104 

recorded signals are later cross-correlated in pairs to determine the delay, with respect to 

local station clocks, between their arrival at the two antennae and the rate of change of this 

delay [Shapiro, 1983; Cfark et af., 1985al. All the data utilized in this study have been 

acquired in a dual-band MARK I11 system VLBI geodesy experiment. In a Mark I11 

experiment, observations are made at X-band (center frequency -8.4 GHz) and S-band 

(center frequency -2.2 GHz). During a typical 24-hour experiment, 10-15 sources are 

observed 5- 15 times each. 

After the cross-correlation process the delays and rates arc used to estimate geodetic 

and nongeodetic parameters such as the station positions, the orientation of the Earth in 

inertial space, and the coordinates of the radio sources. From a priori site and source 

coordinates, theoretical delays and delay rates were computed by Goddard Space Flight 

Center (GSFC) using a VLBI model which includes the effects of precession, nutation, 

polar motion, sidereal rotation, UT1 , Earth tides, and special and general relativity [Clark et 

af., 19871. Corrections for the ionosphere's dispersive effects were calculated from the 

differences in delay at the two frequencies. Tropospheric refraction corrections were 

estimated using meteorological data. The observations, their theoretical values, and the 

comtions mentioned above were combined to compute observation residuals which were 

used in a weighted least squares adjustment of the site locations and other parameters. 

These other parameters include low-ordcr polynomial coefficients to describe relative clock 

and atmosphere behavior at each station and carrcctions to the a priori nutation model. 

The principal sources of emr in the determination of VLBI station positions are the 

troposphere and the Earth's orientation [Shapiro, 1983; Davis et af., 1985; Clark et al., 

19871. To minimize tropospheric errors the Saastamoinen zenith model, which utilizes 

surface measurements of pressure, temperature, and humidity, along with the CfA-2.2 

mapping function [Davis et af., 1985; C. Ma, personal communication, 19881 was utilized. 

To supplement this model one or more corrections to the tropospheric zenith path deIay at 
105 

each site was made in a least squares estimation process. Variations in the rate of rotation 

of the Earth (UT1) and in the position of the axis of figure with respect to axis of rotation 

(polar motion) affect the directions of baseline vectors. To minimize orientation errors the 

GSFC group utilized an Earth orientation series based on primarily VLBI experiments 

[Malfm and Ryan, 19881. Utilizing IRIS (International Radio Interferometric Surveying) 

experiments an Earth orientation series containing values of pole position and UT1 at 5-day 

intervals were compiled. The four station IRIS network, Westford, Fort Davis (lT.D), 

Richmond, and Wettzell in the Federal Republic of Germany became fully operational in 

January 1984. The predecessor to IRIS, the polar motion analysis by radio interferomemc 

surveying (POLARIS) project, was a two-station network and could not simultaneously 

measure all components of Earth orientation. To supplement the POLARIS infoxmation, an 

Earth orientation series derived from SLR data was also used for the earlier time period. 

The standard deviation in the values derived utilizing IRIS experiments arc appoximately 

0.002 arcsec for pole position and O.OOO1 s for UT1. 

Through the least squans adjustment process briefly described above (see also Clark 

et af., 1987) a priori geocenmc position vectors, denoted as rio where i represents the 

station, were adjusted to obtain geocentric position vectors of Nk-1 stations which were 

free to move in the kth experiment, denoted by Xi,lk, relative to the position vector of the 

one station that is held fixed. For experiments in the western U.S. the number of stations 

Nk in an individual experiment k ranged from 3 to 7. For each experiment k the 

geocenmc position vectors for the free stations, Xi.1’. are given with the corresponding 

covariance matrix Vd. 

The difference between the position vector at one site Xlk and the position vector at a 

second site X2k is referred to as the baseline vector and is given by B = X2k - X lk. The 

orthogonal vectors L, transverse T, and vertical V are defined in terms of the a priori 

station position vectors rio a~ 
106 

L = r20 - r10 

T = L x r20 

V=TxL 

The length L, transverse T, and vertical V components of the measured baseline are defined 

as the projections of B on L, T, and V, respectively. The length component L of this 

vector is the magnitude of the baseline vector. The transverse component is positive when 

the azimuth of the baseline is rotated in the clockwise direction. The vertical component V 

is the adjustment from the u priori baseline perpendicular to the length and transverse 

components and is directed toward the local zenith at the midpoint of the baseline. The 

length L, transverse T, and vertical components V of the baseline vectors have been used in 

previous studies, and they provide a useful reference frame for the discussion of the effect 

of different observation erors. 

The precision of baseline measurements in the western United States was estimated 

by Cfurk et uf. [ 19871 from an examination - of the weighted rms of the post-fit residuals of 

the least squares linear fits to each baseline component. The scatter in length L averages - 1 

cm for a 500-km baseline and incrcases to 2 crn at 5000 km. For measurements made after 

1984, the scatter in the transverse component T averages -1 cm for a 500-km baseline and 

increases to -2 cm at 5000 km. The scatter in the vertical component V was found to be 

much larger (-5 cm) and does not scale with baseline length. 

The length component L of the baseline vector provides information similar to that 

obtained using mlateration. For trilateration measurements the basic observable is the 

round-trip travel time of a laser signal between two sites. From this obsewation the scalar 

length L between the sites can be calculated. Trilateration observations an made between 

stations in the area of interest and are not tied to an external reference frame. Since sites are 
1 07 

not simultaneously observed with mlateration the baseline length estimates from a network 

of stations are generally assumed to be uncorrelated. The stations in an individual VLBI 

experiment are, however, observed simultaneously and therefore the baselines are 

correlated. 

With VLBI the delay or delay rate between the radio signal arrival at two stations is 

the basic observable. The theoretical delay or delay rates are calculated in the solar system 

barycenmc coordinate system. Since geodesists are interested in motions in a terrestrial 

reference frame, e.g., geocentric coordinates, it is necessary to apply a series of 

transformations to change coordinate systems. Small errors in the determination of these 

transformations can map into rigid body motions of the geodetic network. These errors 

affect the T and V component; L is insensitive to rotations and translations of the entire 

network. 

Multi-Epoch Processing for Determination of the Vecror Motion of VU/ stations 

Repeated geodetic observations can be used to infer information about movement of 

the crust of the Earth. The interesting - parameters to be obtained from the data are the rate 

of change of the tangential station position, denoted by vi, in a well defined reference 

frame. The description of tangential velocity fields is natural for geological and 

geophysical studies across the Pacific - North American plate boundary zone. The rate of 

change of the local vertical component denoted by 6 zi in a region undergoing uplift such as 

the Coast Ranges is expected to be only 1-3 mdyr. As noted earlier, the local vertical 

component of site position is less well constrained than the horizontal components of 

position and it would be difficult to discern such small vertical changes over the five year 

interval of measurements. 

A number of different approaches have been used to process repeated VLBI 

observations for crustal deformation studies. The rate of change of the length component, 
108 

denoted i, can be estimated from the slope of the least-squares linear fit to the interstation 

length data. In the initial VLBI studies the rate of change of the length component i was 

utilized [Clark et al., 1985k Kroger et al., 1985; Herring et al., 1986; Minster andJordan, 

19871. This is partially due to the fact that the Earth orientation series was less accurate 

prior to 1984 when IRIS experiments commenced. i from individual baselines have been 

compared to rates of deformation determined from geological data. b from individual 

baselines in a network have been used to solve for the tangential rate of change in station 

position Vi relative to some reference frame. If only b data are used, the problems 

encountered are similar to those with trilateration data; Le., the station velocities derived 

from observations are ambiguous; the addition of an arbitrary translation or rotation will 

have no effect on the residuals to the observations resulting from the adjustment [Prescurr, 

19811. This datum defect can be removed in a number of different ways; for example, the 

rotational and translational ambiguity can be removed by fixing the position of one station 

and the azimuth to a second station. The velocities obtained depend on the azimuth of the 

fixed line and on the choice of the stations. In an alternative approach the indeterminate 

components of the displacement field are overcome by minimizing the difference between 

the computed displacements and those predicted by a geophysical model [Prescotr, 1981; 

Beroza et al., 1985; Murray et al., 1985; Segall and Matthews, 19881. Prescott [ 198 1 ] has 

pointed out that in some tectonic environments, there is a reasonable expection that 

displacements in one direction are more likely than in the orthogonal direction. In the 

vicinity of a strike-slip fault, for example, displacements parallel to the fault strike are 

expected to be larger than fault-normal displacements. An outer coordinate solution is 

defined as a solution that minimizes the displacement components in a particular direction. 

Cfark et al. [ 19871 utilized the average rates of change of length i and transverse ? 

components to estimate the tangential station velocities Vi for stations distributed 

throughout the western U.S. Due to the large uncenainities in the earth orientation series 
109 

before IRIS experiments commenced, data from the transverse component was included 

only after 1984. The station velocities were estimated in two different reference tiames, 

one in which MOJA and Westford, Massachusetts were held fixed and one in which ELY, 

FLAG, PLAT, FI'.D, Westford and Fairbanks, Alaska were held fixed. In a reference 

frame in which the eastern stations were held fixed the horizontal velocity of MOJA was 

estimated to be 6.9 f 0.8 mmlyr, N29'W [Clark et ai. 1987; Gordon and Sauber, 1988). 

This result accounts for the observation that in the reference frame in which MOJA was 

held fixed the stations ELY, FLAG, PLAT, and FT.D were all shown to have similar 

velocities to the south or southeast. In their solution the effects of possible correlations 

between baseline rates of change were neglected. 

The data used in our study arc the geocentric position vectors Xi" of VLBI sites in the 

western U.S. In each experiment k the geocentric position vector for Nk-1 stations were 

determined relative to the station position MOJA. The station position data are used to 

estimate the rate of change of tangential station position vi utilizing an algorithm developed 

by Beroza et ai., [ 19861 (see also G.Beroza, unpublished manuscript, 1986). Murray er af. 

[1986] have applied the same techniques with slightly different model parameterimions to 

LAGEOS SLR data. 

A problem common to most geodetic networks is that the distribution of sites 

surveyed varies considerably between epochs. In the VLBI data set utilized in this study, 

the number of stations participating in any one experiment ranged from three to seven; thus 

a given site is not included in all epochs. Such variable network geometry can introduce 

biases in the estimation of station positions. Additionally, analysis of a large geodetic 

network requires a more general procedure than analysis of small local networks. The 

outer coordinate solution or a homogeneous strain appoximation arc not appropriate for the 

large inter-station distances between VLBI sites, and a more flexible and general kinematic 

framework to relate the vector rate of change of station position to other tectonic 
110 

information is essential [Beroza et al., 1986; G. Beroza, unpublished manuscript, 19861. 

In the method utilized in this study we minimize the tangential displacement field with 

respect to an u priori geophysical model of deformation. We parameterize this model in 

terms of a tangential velocity of a station denoted by Vi0 in a North-America-fixed reference 

frame. 

In the analysis of the VLBI position data we must discriminate between tectonic 

motions and apparent motions due to emrs in Earth orientation parameters and mors in the 

vertical component due to the unmodeled tropospheric effects. It is desirable therefore to 

minimize the conmbution that these parameters make to our estimate of the rate of change 

of tangential station position vi. Rigid body rotations of the network are given by RR, 

when R is an antisymmetric matix of geocentric coordinates of the position vector r which 

optrate on the angular rotation vector R: 

RQ =Rxr 

Rigid-body rotations of the network RQ and changes in the local vertical component 52, 

are considered to be what T.H. Jordan and coworkers have called "nuisance parameters". 

Correlations between errors in site positions in each epoch should be fully accounted 

for when analyzing the data. In addition to the comlations for the data within a single 

epoch it would be desirable to account for the correlation between station positions made in 

different epochs. Enors in the data between epochs are, however, probably only weakly 

correlated through the assumed source positions and local site conditions (G. Beroza, 

unpublished manuscript, 1985). In this study we have assumed that errors in 

measurements made in different epochs are uncomlated. 

We assume that the parameters that map a station position from its initial position rjo 

to its position in the k * experiment Xik arc given by the relationship 
111 

where 6 vi is the tangential perturbation to the a priori reference velocity vio, A t k is the 

time interval between the first epoch measurement and the k * experiment, and ei k is the 

error in the geocentric station position Xikof an individual station i. The estimate of the 

rate of change of tangential station position vi is then given by: 

During an interseismic time period the rate of deformation may reasonably be assumed to 

be steady in time. There may, however, be changes at more local spatial scales that are 

non-tectonic in origin. Without other information we assume that vi is constant. 

In equation (1) the a priori reference velocity vi0 and the a priori station position r,O 

are then known quantities that can be subtracted from both sides of equation (1). The 

change in local vertical 6 zi and Ri Rk are nuisance parameters. As we are interested in 

determining the tangential rate of change of station position we tranform the geocentric 

position vectors to local position vectors, and the local vertical component q is removed. 

Rearranging terms, (1) is given by 

The model equation for multiple epochs can be written in the general form: 

Am+ Bn = d (4) 

8 
112 

The first term in (4) represents the model vector m of station positons Xk which is 

operated on by the differencing matrix A to produce displacements due to 6 vi A t k. The 

second term in (4) is the B operator which is composed of antisymmetric submamces R of 

geocenmc coordinates of the positon vector r, which operate on the vector n, of angular 

rotation vectors Q to produce the rigid-body motions of the network between epochs. In 

equation (4) the effects of the model and nuisance parameters are equated with the left hand 

side of the equation given in (3). 

In the first step the nuisance parameters n are determined using the data from nonfixed stations, referred to as free stations and denoted by the subscript f. For the free 

stations the error ei k is assumed to have zero mean and a variance given by Vd. The 

correlations in site positions are accounted for by weighting the model equation with the 

inverse square root of the data covariance matrix denoted by Vd-112. The nuisance 

parameters n are later used to determine the motion of the fixed station, referred to as 

stationary and denoted by the subscript s. The model equation for the free stations for 

multiple epochs can be written in the general form 

We seek to minimize the weighted 4 norm [Menke, 19841 of the error vector. 

This can be re-written in the simpler form 

im - Pn) (7) 
where we have made the substitutions: 

113 

The weighted normal equations to be solved for m and n are 

Solving the second normal equation for the estimate of the nuisance vector n we obtain 

(10) Y 

n = (a~i)-1 6~(a - Xm) 

Backsubstituting (10) into the nOnnal equation for m (9a): 

(&TA)m=;iTii - ~~k(b~ii)-1 iP(a - Am) 

Re-arranging and simplifying to get the model parameters on the left hand side: 

i~( I - piit) Am = ;i~< I -Bit) d^ 
114 

where the dagger denotes the least-squares, minimum-norm generalized inverse. Solving 

for m we have 

where Qg is the symmetric, indempotent projection operator that annihilates B n, the effect 

of the nuisance parameters: 

Equation (13) is equivalent to: 

Substituting in the relationships given in (8) into equation (15) : 

In the next step we seek to estimate the model parameters for the fixed station denoted m,. 

The estimate of n is then used in the equation form, 

A,m + B,n = d, 

where 

. 
m = m, -m,o 

115 

(17) 

to obtain 

A,m = d, - B,n. (18) 

We assume the covariance for the right-hand side, the denuisanced data, is just the 

covariance propagated through the nuisance parameters n. That is, we assume that Vh = 

BsT V, B,. Weighting and solving for m we obtain: 

4 A A h 

m, = A,?( d, - B,n). 

or substituting back in (17) 

Thus, this algorithm provides an estimate of all the model parameters. 

DaraAnalysis 

A total of 81 experiments was used to estimate the rate of change of station position. 

Without rescaling the variance, the error in the rate of change of station position reflects 

only the uncertainity in the station position for a single epoch. An Q posteriori variance was 

calculated from the condition that the x* per degree of freedom of the postfit residuals be 

unity. The rescaling factor, denoted by a,2, was estimated to be 4.2 for the set of 81 

experiments. To look for data outliers the error residual was examined for each station. 

The error associated with one station was large for three of the experiments, and for one of 
116 

the experiments, April 12, 1984, the residuals were large at more than one station. T. 

Herring (personal communication, 1988) found a similar result and is currently examining 

problems with the phase calibrations made in the April 12, 1984, experiment. These four 

experiments were removed from the data set. In the remaining 77 experiments a,* was 

estimated to be 2.1. 

As discussed above, a reference coordinate system can be obtained by minimizing the 

displacement field relative to an u priori geophysical model. Ideally, the rate of change of 

station positions within a network relative to one another will remain the same regardless of 

the u priori geophysical model used. However, because of biases due to the 

inhomogeneous distribution of stations in each experiment the results may be sensitive to 

the u priori model. A set of 50 experiments were analyzed with three different a priori 

models: (1) a model based on ground-based geodetic and geologic data (Table 2), (2) a 

model given by a uniformly dismbuted right-lateral shear strain over a 400-km-wide zone 

centered on the San Andreas fault, and (3) Model 2 with the addition of Basin and Range 

extension. The estimated station velocities for the three models do not differ by more than 

f 4 mm/yr and are at orientations similar to within f 5'. Using a larger set of data 

obtained from 77 experiments we tried using model 1 and model 2 and found results 

similar to that obtained for the set of 50 experiments. In the model given by dismbuted 

right-lateral shear distributed over a broad region centered on the San Andreas fault the rate 

of change of station positions for the sites YUMA, ELY, and FLAG all had southeast 

velocities, similar to result obtained by Cfurk et uf. [1987] with MOJA held fixed. The 

results obtained using Model 1 represent our best estimate of the deformation field on the 

basis of ground-based geodetic and geologic data, and the results utilizing this u priori 

model are discussed below. 

- 
117 

Results 

In Table 2 are the calculated vector velocities with standard deviations, given as rates 

and orientations for all 23 stations. Uncenainities, where not otherwise stated, are one 

standard deviation (a). Since OCOT, DEAD, MAMM, FLAG and PVER have been 

observed less than four times the vector velocities for these stations are not discussed in 

detail. In Figures 3 to 21 I show the estimated rates of change of station position for sites 

which have been measured at least four times and for a minimum of two years. The 95% 

confidence error ellipses given on each plot reflect the marginal uncertainity associated with 

the individual station velocities. 

FT.D and PLAT are thought to be on cratonic North America, and ELY and FLAG 

are located within the Basin and Range province. The station velocities at FI'.D (Figure 4), 

PLAT (Figure 5), and ELY (Figure 6) do not show a systematic trend, and the rate of 

change of station position is not significant at the 95% confidence level. 

The station YUMA is located along the western boundary of the southern Basin and 

Range province. Although the station YUMA shows a rate of change of station position 

suggestive of Basin and Range extension (3.4 f 2.7 mmlyr, N84'W f 16', Table 2) the 

value is not significant at the 95% confidence level (Figure 7). 

BLKB and PINF are located near the southern segment of the San Andreas fault. 

The vector velocities of BLKB (Figure 8) and PINF (Figure 9) are 11.1 f 3.3 mdyt at 

N65'W f 17' and 25.5 f 3.7 mm/yr at N49'W f 13' respectively. For comparison the 

azimuth of the San Andreas fault in this region is -N45'W [Jennings, 19751. 

The station MON is located approximately 15 km west of the Elsinore fault (Figure 

2). Of the mobile VLBI sites MON was observed most frequently (21 times) and the 

vector velocity 40.1 f 2.5 mdyr at N44'W f 6' (Figure 10) has a uncenainity comparable 

to the error for the vector velocity of the base station VNDN (45.7 f 2.9 mdyr at N3 1 W 

f 6.). 
118 

The VLBI station MOJA is located just west of the domain of left-lateral faults in the 

northeast comer of the Mojave block (Figure 2, Chapter 2). The vector veocity of MOJA is 

7.1 f 0.9 dyr at N50'W f 1'. The rate of change of station position of MOJA in a 

reference frame in which PLAT, ELY, FT.D, FLAG, Fairbanks and Westford are held 

fixed is 6.9 f 0.8 mm/yr at N29'W [Clark et al., 19871. This result is similar to that 

obtained in a separate analysis by T. Hemng [Herring and Sauber, 19881. The rate of 

baseline length change i between MOJA and OVRO has shown no significant variation 

over the -5 years that it has been measured [Clark et al., 19871. 

PBLO and JPL are located near the segment of the San Andreas fault referred to as 

the 'big-bend' region in which the azimuth of the San Andreas is -N65'W [Jennings, 

19751. PBLO is located less than 5 km to the northeast of the San Andreas fault. Although 

these two stations are located on opposite sides of the San Andreas fault the vector velocity 

of JPL ( 34.0 f 2.6 mdyr at N44'W k 6'. Figure 13) is not much higher than the vector 

velocity at PBLO (25.5 k 2.7 mm/yr at N48'W f 7', Figure 12). 

The station SAW is located in the Ventura Basin. Compression across this basin is 

thought to be oriented approximately north - south [Years, 1983; Donnellan et al., 19881. 

The vector velocity of SAW is 39.4 f 4.5 mdyr at NWW f 31'. This station has been 

measured only four times over a three and half year time period. 

Of all VLBI sites in California VNDN is located at the greatest distance west of the 

San Andreas fault. The vector velocity of this station is 45.7 f: 2.9 mdyr at N4 1 'W C 6'. 

Between the San Andreas fault and the VNDN site northeast - southwest compression is 

thought to occur across the Santa Maria Basin [Feigl et d., 19881. 

OVRO is located at the northern end of the Owens Valley graben between the Sierra 

Nevada Range to the west (Figure 2) and the Inyo Range and White Mountains to the east. 

Holocene offset on the Owens Valley fault is primarily right-lateral strike-slip with the 

azimuth of major segments of the fault zone varying from N5'W to N35'W [Beanlund md 
119 

Clark, 1987). The vector rate of change of the station OVRO is 10.3 f 2.7 mm/yr at 

N37'W f 4.5 (Figure 16). The orientation of the maximum right-lateral shear strain (i) 

estimated from the Owens Valley mlateration network [Savage and Lisowski, 19801 is 

N20'W. 

FORT is located just west of the Rinconada fault in central California. This station 

has been observed 7 times over a 4-year time period. The vector velocity of this station is 

47.4 f 2.8 dyr at N37'W +_ 5' (Figure 17). 

The HATC and QUIN sites are located west of the northern Basin and Range within a 

transition region between the Sierra Nevada and the Cascade Ranges (G. Beroza. 

unpublished manuscript, 1985). Both of these sites show significant motion, QUIN, 12.0 

f 3.1 dyr at N52'W f 9' and HATC, 9.4 f 2.6 dyr at N62'W f 8'(Table 2, Figures 

3, 18, and 19). 

PRES and PT.R are located near the northern segment of the San Andreas fault which 

broke in the 1906 San Francisco earthquake. Although PRES is located east of the San 

Andreas fault the velocity of this station is quite high, 28f 7 mdyr at N43'W f 8' (Figure 

20). 

For the most western stations MON (Figure lo), SAW (Figure 14), VNDN (Figure 

15), FORT (Figure 17) and PT.R (Figure 21) the NUVEL-1 Pacific - North American 

relative plate motion vector [DeMets et al, 19871 is shown for comparative purposes. 

To examine the integrated rate of deformation between two VLBI sites it is desirable 

to calculate a differenced velocity vector for pairs of stations in regions of interest (Figures 

22 through 29). The 95% confidence ellipse represents the scaled variance of the two 

stations as well as the station covariance. 

Five difference vectors were determined for station pairs that arc located on either side 

of the San Andreas fault (Table 3). MON - YUMA (Figure 22), MON - BLKB (Figure 

23), JPL - MOJA (Figure 25), JPL - PBLO (Figure 26). and FORT - OVRO (Figure 28). 
120 

The difference vector for MON - YUMA is 37.6 f 3.4 mdyr at NWW f 8' and for MON 

- BLKB is 30.0 f 4.5 mdyr at N35'W k 12', consistent with right-lateral shear strain 

associated with the San Andreas, San Jacinito and Elsinore faults. The distance between 

the stations is -110 km. For JPL - PBLO the difference vector is only 8.7 k 3.7 at 

N34'W f 6'; these two stations are located -40 km apart. For JPL - MOJA the difference 

vector is 26.9 f 2.6 mdyr at N43'W k 5'. The difference vector for OVRO and FORT is 

37.1 f 2.8 mdyr at N37'W k 5'; the distance normal to the San Andreas fault between 

these two stations is -300 km. 

The difference vector was also calculated between VNDN and three coastal stations, 

MON, SANP, and FORT. These results provide a constraint on the integrated rate of 

deformation along the coastal and offshore faults. Between VNDN and MON the 

difference vector is 5.6 k 2.9 mdyr, N23'W k4'; consistent with primarily right-lateral 

strike-slip motion on northwest striking faults. The difference vector for VNDN - SANP 

indicate 15.2 k 6.7 mdyr of northeast-southwest compression (N15'E f7') between the 

'two sites. The difference vector for VNDN - FORT is 3.8 f 3.1 mdyr at S25'W f 4'. 

Path Integral Formulation 

The VLBI data provide discrete sampling of the temporal and spatial deformation field 

across a complex continental plate boundary. Individual stations are located within 

different tectonic domains. To interpret the VLBI-derived rates of deformation in terms of 

a regional tectonic framework requires integration with more densely sampled data. As is 

evident from Figure 30 and Figure 5 in Chapter 3 the VLBI, ground-based geodetic and 

geologic data are scattered throughout central and southern California. To provide a 

framework for discussion we construct three path integrals [Minister and Jordan, 1984; 

Bird and Rosenstock; 1984; Weldon and Humphreys, 19861. For each path I consider two 

. 
121 

different integrals, one in which geodetic data are used and one in which geological data are 

Utilized 

For any given path connecting two points Q and b the velocity of 6 relative to a, v(b), 

is given by 

rb 

v(b ) = v(a + J, its) V, v(r(s))dS 

where t is the unit tangent vector to the path dr/ds, Vs is the surface gradient operator on 

S, v(r) is the tangential velocity field, and Vsv(r) is the spatial gradient of velocity. Over 

the small distances (e100 km) between points we assume planar geometry; Le., curvature 

of the Earth's surface is neglected. 

On the assumption that a rate of change of station position determined from VLBI 

data represents the integrated rate of deformation between the VLBI site and stable North 

America this datum can be used as a fidicual point for the more densely sampled groundbased geodetic data. For example, when the VLBI stations are collocated with stations 

'within the ground-based network v(a) can be taken as the velocity of the point on the 

southeastern edge of a network and v(b) the velocity on the northwestern edge of the 

network. For most regions of California VLBI stations are not collocated with groundbased networks and it is necessary to integrate the rate of deformation between sites. 

For the sum of p independent determinations of the geological rate of slip on discrete 

faults equation (21) reduces to a simple sum of the relative slip across each fault between a 

and b: 

~(b ) = V(U) + VI + ~2 + ... vp 

We assume the bounds on geological estimates of slip rate scale with the standard 

deviations so that if the estimates are independent their squares are additive and the standard 

deviation of v(a) is 
122 

222 2 

a,+ a1 + Oz+ ... ap 

[Bornford, 1985; p. 6951. Implicit in this formulation is that geological deformation occurs 

on discrete faults; these faults are assumed to be separated by rigid blocks. This 

approximation is most appropriate in a strike-slip environment where fault displacements 

can be measured most directly. In either extensional or compressional regimes deformarion 

may be distributed over a broad region where slip on individual faults may be difficult to 

measure. 

Comparison of Geodetic and Geologic Rates of Deformation in Southern 

and Central California 

The rate of recent deformation estimated from geologic data in southern and central 

California is appropriate to time scales of approximately 1@ - 106 yrs. The rate of 

deformation obtained with mangulation, mlateration, and VLBI data correspond to the last 

100 - l@ yrs. In Tables 4 and 5 rates of deformation on the San Andreas system in 

southern California and east of the San Andreas fault are given for both types of estimates. 

Rates of defoxmation in central California estimated from geologic and geodetic data were 

presented in Chapter 3, Table 4. In this section I briefly consider how these rates of 

deformation are derived, and I present the results of the construction of path integrals based 

on these data. 

The locations of the three path integrals are given in Figure 31. Along each path I 

plot the velocity of each appropriate station resolved into fault-normal and fault-parallel 

velocity components as a function of the distance from the San Andreas fault (Figures 32 

through 37 ). I choose to plot these profiles perpendicular to the local orientation of the 

San Andreas fault for two reasons. As discussed in Chapter 3 if the shear stnss parallel to 

the San Andreas fault is relieved through surface creep, as in central California, or during 
123 

periodic earthquakes, the maximum principal stress direction immediately adjacent to the 

San Andreas fault should be reoriented perpendicular to the San Andreas fault. 

Additionally, mlateration data from the Salton Sea and Eastern Transverse Ranges were 

processed employing the outer coordinate solution in which the fault-normal velocity 

component is minimized and the data are resolved into a fault-parallel and and fault-normal 

components. 

Path 1 is located at the latitude of southernmost California (Figure 31). Deformation 

along this path includes possible extension in the southern Basin and Range and rightlateral slip along the the San Andreas, San Jacinto, Elsinore and possibly offshore faults 

(Table 4 and 5). The integrated rate of extension across the southern Basin and Range is 

given by the rate and orientation of slip at the station YUMA. For the region between the 

San Andreas and Elsinore faults we assume simple right-lateral slip at the orientation given 

by the fault-parallel component of velocity (N39'W). Due to the paucity of available 

geologic and geodetic data on the rate of offshore slip the path integral does not continue 

west of MON. 

The second path crosses the 'big-bend portion of the San Andreas fault. In this 

section the San Andreas fault locally changes its trend by 20'-30' along a 190-km-long 

segment between San Gorgonio Pass and Tejon Pass. Recent deformation is thought to 

occur as extension in the Basin and Range east of the Mojave Desert, right-lateral smke-slip 

motion on the faults of the central Mojave, right-lateral strike-slip on the San Andreas fault, 

and north-south to northeast-southwest compression across the western Transverse Ranges 

and the offshore faults in the Channel islands (Table 4 and 5; see also compilation given in 

Bird and Rosenszock, [ 19841 andweldon and Hwnphreys, [ 19861). N62'W is used as the 

fault-parallel orientation with N28'E for the fault normal component. 

Although slip along the San Andreas fault is thought to occur primarily through 

surface creep within a narrow zone in central California, path 3 crosses numerous distinct 
124 

tectonic elements east and west of the San Andreas fault (Chapter 3; see also Minsrer and 

Jordan, [1984]). Relative to stable North America the first region where active deformation 

= is thought to occur is across the Basin and Range through a combination of right-lateral 

strike-slip motion and extension on pull-apart basins. As discussed in Chapter 3 little 

deformation is thought to occur within the Sierra Nevada batholith or across the Great 

Valley. To the west of the Great Valley deformation across the Coast Ranges is separated 

into right-lateral slip on the San Andreas, Rinconada, and San Gregorio faults and 

dismbuted northeast-southwest compression across the Coast Ranges (Chapter 3). The 

geological and seismicity data suggest that northeast-southwest compression may be 

localized to two regions, one zone within the 30-km-wide zone spanned by the San Benito 

network (Chapter 3) and a second zone west of the Rinconada fault (Chapter 3). The faultparallel orientation is taken as N41'W with a fault-normal component of N49'E. 

Path Integrals Utilizing Geodetic Data 

The rate of change of angles or baseline length are the basic observable used to 

estimate the rate of deformation with either triangulation or mlateration data. From these 

data either the rate of strain (i or i) or the rate of change of individual station positions are 

determined. In the central Mojave Desert (Chapter 2) and in the Diablo Range (Chapter 3) 

the rate of slip was estimated from the average rate of shear strain (t) determined from 

triangulation and trilateration data. In Chapter 3 we utilized the average rate of line length 

change on individual mlateration lines to estimate the rate of right-lateral slip on the San 

Andreas, Paicines, and Rinconada faults in central California. To estimate the displacement 

rate across the Salton Sea and Eastern Transverse Range networks repeated mlateration 

measurements have been utilized to calculate the average rate of change of tangential station 

positions [Prescott et al., 1987). Since all observations were made between stations in the 

area of interest rigid body translation and rotation of the network can not be estimated; the 
125 

ambiguity expresses itself as a rank defect of 3 in the coefficient mamx of the normal 

equations [P rescott, 19811. This ambiguity is overcome by selecting the rigid-body 

translation such that the centroid of the network remains fixed and the rms velocity 

component normal to a preselected direction is a minimum. The preselected direction is 

taken as the strike of the vertical plane of maximum right-lateral shear as determined from a 

uniform-strain-rate approximation to the observed values of line length change. This 

direction was N39'W for the Salton Sea network and N58'W for the Eastern Transverse 

Range network (J. Savage and M. Lisowski, personal communication, 1988). The 

requirement that the centroid of the network be fixed only specifies the point relative to 

which all velocities were detexmined; it does not affect the pattern of velocities. 

Path 1. In Figures 32 and 33 the fault parallel (N39'W) and fault normal component 

(N51'E) of the rate of change of position of geodetic stations along path 1 are given in a 

North America (NOAM) fixed reference frame. Although the station YUh4A shows a rate 

of change of station position suggestive of Basin and Range extension (3.4 f 2.7 mdyr at 

N84'W f 16'. Table 2) the value is not significant at the 95% confidence level (Figure 7). 

The Salton Sea network, located northwest of YUMA, spans the San Andreas, San Jacinto 

and Elsinore faults. In Figures 32 and 33 the velocity profile for the northwestern portion 

of this subnetwork is given. The station BLKB is located just east of the network. PINF to 

the north, and MON is collocated with the USGS mlateration station Monument Peak 

within the network. Since the rate of change of station position is well determined for 

MON the velocity of the USGS station is set equal to the vector rate of change of station 

position of the VLBI station MON (40.1 mm/yr at N44'W). 

The fault parallel component of the velocity of PINF and BLKB and the ailateration 

data are in close agreement (Figure 32). Although the fault-normal component of velocity 

of the VLBI stations have larger values than the corresponding uilateration data these 

velocities are not significantly different than the mlatcration results. . 
126 

Path 2. In Figures 34 and 35 the fault parallel (N62.W) and fault normal component 

(N28'E) of the rate of change of position of geodetic stations along path 2 are given in a 

North America-fwed-reference frame. Since there are few ground-based geodetic networks 

across the broad region given by the Basin and Range province to the east of the Mojave 

Desert block, we are unable to estimate the geodetic rate of deformation from geodetic data. 

The station MOJA is, however, is located north of the region traversed by our path and is 

included on the path 2 velocity profile. As discussed in Chapter 2, a geodetic estimate of 

6.7 f 1.3 dyr at N41'W of right-lateral slip has been estimated for the region between 

the Helendale and Camp Rock faults (Table 4, K) in the central Mojave Desert. The 

Eastern Transverse Ranges network (ETR) spans the San Andreas near Palmdale. There 

are two VLBI stations within the network, JPL in the south and PBLO in the northeast. 

Since more observations have been made to JPL the vector velocity of this station (34.0 

mm/yr at NWW) was used to fix the corresponding site velocity in the ETR network. One 

VLBI station, SANP, located northwest of JPL is also included in the profile. 

The rate and orientation of slip on the central Mojave faults determined from 

triangulation and trilateration data are-similar to those of the vector velocity estimated for 

MOJA (the MOJA velocity vector is more westerly by lo'). After fixing the velocity of one 

station in the ailateration network the velocity of the other VLBI station, PBLO, is similar 

to the mlateration data results from the ETR network. The N28'E or fault-noma1 

component (Figure 35) appears to be erratic in both the mlateration and VLBI data. 

Path 3. In Figures 36 and 37 the fault parallel (N41'W) and fault normal component 

(N49'E) of the rate of change of position of geodetic stations along path 3 are given in a 

North America fad reference frame. The station OVRO is used as a starting point for the 

path integral utilizing geodetic data. Between OVRO and the next most western station 

along this path, FORT, there are several geodetic networks. These include the San Benito 

network that spans the Diablo Range east of the San Andreas fault, the Coalinga 
127 

trilateration network that spans the Paicines and San Andreas fault, and one line from the 

Pajaro network which spans the Rinconada fault. The FORT - OVRO difference vector is 

37.1 k 2.8 dyr at N37'W f 5'. The integrated rate of deformation estimated from the 

ground-based geodetic networks is 36.5 mdyr at N34'W. 

Path Integral Utilizing Geological Data 

Geologic estimates of the rate of deformation depend on two key elements: the age 

and amount of deformation of a given stratigraphic unit. The current techniques that are 

available for estimating the age of late Cenozoic deposits can be grouped into three 

categories: numerical methods such as the radiomemc I4C technique, correlation methods 

which tie the deformed sequence with the age of a Stratigraphic unit that can be dated, and 

relative dating methods such as soil development [Pierce, 19861. The radiometric 

techniques yield accurate ages, but suitable samples for dating are often difficuIt to find and 

the less precise correlation and relative dating methods are instead used. Some of the 

methods employed to estimate the amount of deformation in southern and central California 

are offset of distinctive stratigraphic units [Dokku, 19831 and land forms such as alluvial 

fans, stream channels [Sieh and Jahns, 19841, and marine temaces[CZark et al., 19841, 

degradation of fault-scarp morphology, and palinspastic reconstructions [Narnson and 

Davis, 19881. As discussed in Chapter 3, the geological data are most useful for indicating 

the long-term modes of deformation and for placing upper and lower bounds on rates of 

deformation. Thus in Tables 4 and 5 the geological estimate of slip rate is given as an 

upper and lower bound; a best estimate of the long-term average fault slip rate is also 

indicated. 

- 

Path 1. Little recent deformation is thought to occur within the southern Basin and 

Range; the rate of deformation is, however, poorly constrained by geological data (Table 5. 

M). Along Path I, geologic slip is documented on the San Andreas, San Jacinito and 
128 

possibly the Elsinore fault. In Figures 32 and 33 the integrated rate of deformation 

estimated from the geological data , resolved into a fault-norma1 and a fault-parallel 

component, is given for path 1. Since we assume simple right-lateral slip at the orientation 

given by the fault-parallel component of velocity (N39.W) for the region between the San 

Andreas and Elsinore faults, no geological data are included on the fault-normal plot. The 

geologic data as well as the the station velocities estimated from VLBI and ground-based 

geodetic data suggest a broad zone of right-lateral deformation (at least 150 km wide). The 

best estimates of right-lateral slip across the San Andreas (Table 4, B), San Jacinto (Table 

4, H), and Elsinore (Table 4, I) faults is higher than the corresponding velocity determined 

from geodetic data. 

Path 2. The integrated rate of deformation estimated fn>m the geological data is given 

for path 2 in Figures 34 and 35. Within the Quaternary little or no deformation is thought 

to have occurred between the Colorado Plateau and eastern Mojave Desert block (Table 4, 

M). Although Quaternary slip has been documented across all the faults of the central 

Mojave, the rate of slip on the faults of central Mojave is poorly constrained from 

geological data. The geological estimates of the long-term rate of slip on the San Andreas 

fault range from 16 to 60 mdyr (Table 3, E), with the best estimate 30 f 5 mdyr [USGS, 

19881. As with the result noted on the Path 1 profile, the best estimate of the iV58'E 

component of velocity from geological data are higher than the velocities predicted from the 

strain data. 

Path 3 . The integrated rate of deformation estimated from the geological d;tu IS 

given for path 3 in Figures 36 and 37. From the geological data the best estimate of the rare 

and orientation of extension in the Basin and Range are 9 xnm/yr and NWW (Table 1. LV). 

In contrast, the estimated vector velocity of OVRO is 10.3 f 2.7 mm/yr at N37.W t 1'. 

With the exception of these discrepant directions, the geologic and geodetic data for the 
129 

Diablo Range, San Andreas fault, and the Rinconada fault are in good agreement (Chapter 

3, Table 4) for both the fault-noma1 and fault-parallel components (Figures 36 and 37). 

Discussion 

The VLBI, ground-based geodetic, and geologic data provide a basis to to discuss the 

relation between deformation in the southern Basin and Range province, the Mojave Desen 

block, and the northern Basin and Range province, the relation between geologic and 

geodetic rates of deformation in central and southern California, and constraints on the rate 

of deformation west of the San Andreas fault. 

The Rate of Deformation Across the Basin and Range Province 

The Basin and Range province is a region of active crustal spreading characterized by 

high regional elevation, thin crust, and high heat flow [Zobwk and Zoback, 19801. On the 

basis of the uniformity of the stress field inferred from in situ stress measurements, 

seismicity and stress sensitive geological features Zoback and Zoback [ 19801 delineated the 

Basin and Range - Rio Grande rift stress province. This province extends from the Sierra 

Nevada eastward to the Colorado Plateau physiographic province and around the southern 

margin of the Colorado Plateau and northward into the Rio Grande rift in New Mexico. 

Although the northern and southern Basin and Range have similar stress field orientations 

little recent deformation is thought to occur in the southern Basin and Range. The rate of 

change of station position at the VLBI station YUMA is not greater than the 95% 

uncertainity in the determination (Table 2 and Figure 7). This station has been observed 

approximately the same number of times over a similar interval as the station QUIN located 

along the western edge of northern Basin and Range. The results for QUIN (Figure 18), 

however, show significant slip at a rate and orientation consistent with other estimates of 
130 

Basin and Range extension (Table 5, W). This result supports a lower rate of deformation 

across the southern Basin and Range. 

Within the Basin and Range extension occurs in approximately the N60'W k 20' 

direction (Table 5, W). To the north of the Garlock fault in the Basin and Range extension 

occurs as right-lateral strike-slip motion on northwest trending faults separated by pullapart basins [Zobuck and Zoback, 1980; Burchfel er al., 19871. The vector rate of change 

of the station OVRO, 10.3 k 2.7mdyr at N37'W f 43, is closer to the local orientation 

of the Owens Valley fault than the assumed direction of extension in the Basin and Range. 

Within the northern Basin and Range purely dip-slip motion is observed on north-northeast 

striking faults. The vector velocities for HATC are 9.4 f 2.6 mdyr at N62'W f 8', and 

for QUIN, 12.0 f 3.1 mm/yr at N52'W k 9'. Within the uncenainities in estimated vector 

velocities, the stations north of the Garlock are consistent with the rate and orientation of 

deformation derived from local geodetic and geological data. 

The VLBI station MOJA is located in the northeast comer of the Mojave Desert block. 

. The vector velocity of MOJA is 7.1 f 0.9 mdyr at N50'W f 1'. similar the rate of change 

of station position determined for OVRO (Table 2). The velocity of the Mojave Desert site 

is puzzling because the rate of extension in the southern region of the Basin and Range 

province is not thought to be greater than 1 - 3 mdyr [Herring and Suuber, 19881. As 

discussed in Chapter 2, the left-lateral slip observed on the Garlock fault has been 

hypothesized to occur due to the difference in motion between extension in the Basin and 

Range and a more stable Mojave block. Within the Mojave block there are two domains of 

transcurrent faults that show Quaternary movement, right-lateral faults in the central Mojave 

Desert and left-lateral faults in the northeast comer of the block (Figure 2, Chapter 2). In 

Chapter 2 we proposed the hypothesis that the deformation on the northwest striking faults 

of the central Mojave may be kinematically related to strike-slip motion on the right-lateral 

faults that bound the region of extensional tectonics in the Great Basin. By this view, the 
131 

MOJA station as well as the Garlock fault are within a deforming region connecting slip in 

the central Mojave to deformation north of the Garlock fault. 

The maximum shear rate on the eastern segment of the Garlock fault was determined 

to be 0.18 f 0.01 pradyr, oriented N59'E f 2' if left-lateral or N31'W f 2' if right-lateral 

(Table 5, P). The strain data along the Garlock fault arc thus consistent with the rate and 

orientation of strain estimated from the central Mojave region and north of the Garlock 

fault. The accommodation of this strain along faults of the region is geometrically 

complex. The orientation of the surface trace of the Garlock fault is approximately eastwest, significantly different from the orientation of the rate of maximum shear strain. The 

geomeay of the Garlock fault is suggestive of clockwise rotation. This interpretation is 

further supported by the presence of left-lateral faults in the northeast corner of the Mojave 

block. 

An alternative hypothesis is that the slip in the central Mojave Desert, including the 

rate of change of the station MOJA, is due to elastic shear strain accumulation associated 

with the 'big-bend' portion of the San Andreas fault. The last large earthquake along this 

segment occurred in 1857 [USGS, 19881. In Chapter 2 we argued against the hypothesis 

that strain in the central Mojave was associated with elastic strain which would be released 

in a large San Andreas earthquake on the basis of the orientation of the measured shear 

strain (N41'W versus -N65'W for the San Andreas fault) and the 40-90 km distance of the 

central Mojave deformation from the San Andreas fault. MOJA is located approximately 

125 km from the San Andreas fault. The relation of deformation in tectonic domains 

adjacent to the San Andreas to slip on the San Andreas fault is discussed further below. 

Geologic Strain versus Incremental Strain 

Although we have parameterized the strain results in terms of a velocity vector relative 

to North America, the rate of change of an individual station may be due to elastic strain 
132 

accumulation which may be relieved in a large earthquake. Extensive modeling of geodetic 

data has been used to examine the parameters thought to influence the rate and pattern of 

surface deformation throughout the seismic cycle [Reid, 1910 Savage and Buqord, 1973; 

Yang and Toksoz, 1981; Thatcher, 1983; Cohen and Kramer, 1984; Li and Rice, 19871. 

Reid [ 19101 assumed that a major earthquake would not recur until all strain released by the 

preceding even had reaccumulated. Implicit in this assumption is that all crustal 

deformation is elastic and recoverable [Thatcher, 19861. The contribution viscous 

relaxation makes to the rate and pattern of deformation following a large earthquake just 

south of profile 1 in the Imperial Valley (the 1940 El Centro earthquake, Ms = 7.1) was 

examined for several rheological models [Sauber et af., 1984; J. Sauber unpublished 

manuscript, 19843. The effect of post-seismic relaxation on both horizontal and vertical 

displacements was estimated utilizing a three dimensional finite element method with a 

viscoelastic earth model [Yang and Toksoz, 19811. Externally applied displacements 

conesponding to coseismic slip associated with the 1940 earthquake were prescribed, and 

the time-dependent displacements were calculated. Similar to the results reponed by Yang 

and Toksoz [ 19811 and Cohen and Kramer [ 19831 the temporal and spatial patterns of 

surface deformation were found to be most sensitive to the geometry and rheological 

properties of the material that lies below the slip plane in a volume whose extent is a few 

times the seismogenic fault depth. Although horizontal displacements are much larger than 

vertical displacements for a strike-slip earthquake, the time dependent behavior of vertical 

displacements were found to be particularly sensitive to lateral changes in viscosity 

dismbution. Post-seismic vertical movements were most closely matched with an Earth 

model with an elevated low viscosity zone near the fault; viscous relaxation accounted for 

approximately 25% of the post-seismic deformation measured adjacent to the Imperial fJult 

between 1941 and 1954. 
133 

A large earthquake has not occurred on the southern segment of the San Andreas fault 

within the last -400 years [Sieh, 19861, and the last large earthquake to occur in the 'bigbend region was in 1857 [USGS, 19881. In central California slip along the San Andreas 

fault is thought to occur primarily through surface creep. For the interseismic period, a 

simple model that approximates the postulated behavior of strain along a strike-slip 

boundary is a screw dislocation in an elastic half-space [Savage and Bulford, 19731. The 

rate of slip in the elastic half-space is assumed to be zero down to a depth given by D but 

equal to b below that depth. The strike-slip velocity, denoted by Q on the Free surface is 

then given by 

where x is the distance perpendicular to the fault. In California, the depth of the 

seismogenic zone along the San Andreas fault is approximately 10 km; it is assumed that in 

the upper 10 km most slip is accommodated by stick-slip at the time of infrequent large 

earthquakes [Sibson, 19821. The velocity b controls the overall range of I)* and D specifies 

the breadth of the zone of deformation. In such a model 50% of the relative slip is 

accommodated in the interval -D < x c D; to include 90% of the relative slip one must span 

-6.3 D < x < 6.3 D [Savage and Lisowski, 19881. This simple relationship is used to 

approximate the width over which elastic strain which may be relieved in a large earthquake 

on the San Andreas fault in southern California or the 'big-bend' region of the California. 

The velocities estimated from geodetic data represent the average of the rate of 

deformation over only a small portion of a plate boundary seismic cycle. The geological 

estimates of rates of deformation, as indicated by the upper and lower bounds on the 

profiles, are subject to large uncertainities. Given these limitations we discuss the results 

obtained by comparing geologic and geodetic data. 
134 

The best estimate of the geologically derived value for the integrated rate of slip 

across the southern Basin and Range and the San Andreas, San Jacinto, and Elsinore 

faults, if correct, is close to the relative plate motion vector predicted by NUVEL- 1 (46.5 

mdyr at N39'W); little deformation is then predicted to occur offshore. The geological 

estimate of 30 mm@ (Table 4, B) for the southern San Andreas fault is higher than other 

estimates of the slip rate on this segment [Weldon and Humphreys, 1986) and is higher 

than the rate of slip on the San Andreas fault in Cajon Pass [Table 4, D]. If the long term 

slip rate on the San Andreas is instead 25 mdyr, the geologically derived values for the 

integrated rate of slip are in Figure 32 is shifted down 5 mdyr and the geological and 

geodetic estimates of velocity are similar near the San Jacinito and Elsinore faults. If strain 

along this segment of the San Andreas were being relieved through surface creep, as in 

central California, we wou!d expect the velocity profile to have an abrupt step across the 

fault. Between BLKB, located -25 km east of the San Andreas fault, and MON located 

-85 km southwest of the San Andreas fault, the differenced velocity vector is 30.0 k 4.5 

mm/yr at N35'W k 2'. Between YUMA, located -105 km east of the San Andreas fault, 

and MON the differenced velocity vector is 37.6 f 3.4 mm/yr at NWW f 8'. If the MON 

- YUMA differenced velocity vector represents the rate of slip that will be accommodated 

by geological slip on the San Andreas, San Jacinto, and Elsinore faults, then additional 

deformation, as suggested by Weldon and Humphreys [ 19861, is predicted on the offshore 

faults in the California borderlands. 

Along Path 2, the geologically estimated velocities is also higher than the rate of slip 

given by the geodetic data. If the rate of slip on the San Andreas fault is as low as 25 

mm/yr as suggested by the Cajon result, the geologic and geodetic results are closer. The 

rate of deformation between the station pairs JPL - PBLO and JPL - MOJA can be used to 

look at deformation associated with the 'big-bend' portion of the San Andreas fault. 

Between PBLO, located -5 km northeast of the San Andreas fault, and JPL located - 40 
135 

km southwest of the San Andreas fault, the differenced velocity vector is 8.7 k 3.7 mm/yr 

at N34'W f 6'. Between MOJA, located -125 km east of the San Andreas fault, and JPL 

the differenced velocity vector is 26.9 k 2.6 mdyr at N43'W f 5'. Over the broad region 

between MOJ and JPL the rate of deformation given by differenced velocity vector is quite 

low. This result suggests that the long term rate of slip on this segment may be only 25 

mdyr. 

Slip on Offshore Faults 

Within the central and southern Gulf of California the plate boundary may be traced 

along a series of well-defined en echelon transform fault zones, each trending 

approximately along the mean direction of plate motion [Goff et af., 19871. In the northern 

Gulf of California, plate motion appears to be taken up over a wider zone of deformation 

that includes faults in northern Baja California, such as the Agua Blanca and San Miguel 

faults, as well as the principal continental transform fault, the Cierro Prieto fault. Both the 

Agua Blanca and San Miguel faults are currently active on the basis of recent seismicity, 

large historic earthquakes and Quaternary stream offsets [Allen et al., 1960; Lomnitz et af., 

1970 1. Slip on the Agua Blanca and San Miguel faults arc thought to transfer motion onto 

the offshore faults of the southern California borderland [Weldon and Humphyreys, 1986; 

Goff et af. 19871. Schug et al. [ 19871 report a lower mid-Pleistocene to present rate of -4 

mdyr along the western reach of the Agua Blanca fault and a slip rate of 2 to 5 mdyr for 

the Agua Blanca 50 km inland from the Pacific Ocean. 

The relative motion between the North American and Pacific plates in southern 

California is predicted to be 46.5 mm/yr at N39'W (NUVEL-1, DeMers et al., 1987). 

West of MON an additional -6 mdyr of primarily right-lateral northwest slip is predicted 

to occur on the basis of the VLBI results. This rate is consistent with the recent estimates 

slip along the Agua Blanca and San Miguel faults. Further north, the rate of slip at the 
136 

station VNDN suggest that most the Pacific - North American relative plate motion is 

accommodated east of this site (Figures 3 and 15 ). The velocity of VNDN relative to 

MON, SANP, and FORT could ideally be used to constrain the amount of deformation 

occurring between the site pairs in southern California, the western Transverse Ranges, 

and in central California. Between VNDN and MON the difference vector is 5.6 f 2.9 

mdyr at N23'W f4'. consistent with primarily right-lateral strike-slip motion on 

northwest striking faults. The difference vector for VNDN - SANP indicates that 15.2 k 

6.7 mm/yr of northeast-southwest compression (N15'E f 7') between the two sites may be 

occumng. The difference vector for VNDN - FORT, 3.8 f 3.1 at S25'W f 4'. is not 

consistent with other geologic and geodetic from the region (Chapter 3). 
I37 

Summary 

The geocentric position vectors from a set of 77 experiments beginning in October 

1982 have been used to estimate the tangential rate of change of station position of VLBI 

sites in the western U.S. These data were processed utilizing a procedure developed to 

remove from apparent tectonic motion the contamination due to errors in Earth-orientation 

parameters and non-uniform station geometry; this procedure accounts fully for the position 

covariance between stations. In this method the tangential displacement field is minimized 

with respect to an a priori geophysical model of deformation. This model is parameterized 

in terms of a tangential velocity of a station in a North-America-fixed-reference frame. The 

vector velocities estimated for the stations in the western U.S. provide discrete sampling of 

the temporal and spatial deformation field. 

To interpret the VLBI derived rates of deformation an examination of geologic and 

more densely sampled ground-based geodetic data. For three regions I compared the rates 

of deformation derived from VLBI and ground-based geodetic data, and I examined the 

relationship between the rates of deformation determined from geological data and those 

estimated from the geodetic data. - 

Deformation across southernmost California is fairly well de&bed by simple rightlateral shear on the San Andreas, San Jacinto, Elsinore, and possibly the offshore faults of 

the California borderlands. An estimate of the integrated rate of deformation across the 

southern region of the Basin and Range province is given by the station YUMA (3.4 2 2.7 

mm/yr at N84'W f lv). A large earthquake has not occurred on the southern segment of 

the San Andreas fault within the last -400 years [Sieh, 19861, and strain accumulation is 

observed over a broad region. Within the Salton Sea region there are three VLBI sites, 

BLKB, PINF, and MON, and with denser spatial coverage the Salton Sea trilateration 

network. MON is collocated with a mlateration station, and the velocity of the mlateration 

station is set equal to the MON vector velocity. The fault-parallel components of velocity 
138 

of PINF and BLKB are in close agreement with the velocity profile given by the 

mlateration data. If the vector velocity given by the MON - YUMA difference vector (37.6 

k 3.4 Wyr at N40'W 2 8') is approximately equal to the accumulated rate of long-term 

slip across the San Andreas, San Jacinto, and Elsinore faults, additional deformation is 

predicted to occur offshore in the California borderlands. This rate of deformation is 

similar to that given by Weldon and Hrimphreys [ 19861. The velocity difference vector 

between VNDN and MON is 5.9 +, 2.9 mm/yr at N23'W f 4'. 

In the 'big-bend' region of the San Andreas fault recent deformation has been 

measured across the right-lateral strike-slip faults of the central Mojave, along the San 

Andreas fault , and as northeast-southwest compression across the western Transverse 

Ranges and the offshore faults in the Channel Islands. The vector velocity of MOJA is 7.1 

f 0.9 mdyr at NSVW k 1'. MOJ is located in the northeast comer of the the Mojave 

Desert block. This result, along with ground-based geodetic and geologic data From the 

Mojave Desert, the Garlock fault, and the Great Basin suggest that the estimated rate of 

deformation on the northwest smking faults of the central Mojave (6.7 k 1.3 mdyr at 

N41'W f 2', Chapter 2) may be kinematically related to deformation north of the Garlock. 

The station MOJA as well as the western Garlock fault arc then within a deforming region 

connecting slip in the central Mojave to deformation north of the Garlock. The alternative 

hypothesis that the MOJA and central Mojave strain results are due to elastic strain 

accumulation which will be relieved in the next large earthquake on the San Andreas fault is 

rejected on the basis of several arguments; the most convincing argument is that recent slip 

has been documented along the faults of the central Mojave [Dokka , 1983; E. Hart, 

personal communication, 19871 . 

Two VLBI stations, JPL and PBLO, are located within the Eastern Transverse 

Ranges trilateration network. After fixing the site velocity of JPL to be the same in both 

networks the fault-parallel component of PBLO closely resembles the velocity profile given 
139 

by the mlateration results. Over the broad region between MOJA and JPL the rate of 

deformation given by the differenced velocity vector is quite low (26.9 f 2.6 mdyr at 

N43'W f 5') and suggests that the long term rate of slip on this segment may be -25 

mdyr. The velocity difference vector for VNDN - SANP suggest 15.2 f 6.7 mdyr of 

northeast-southwest compression (N15'E f 7') between the two sites. The SANP station, 

which is located in the Ventura Basin, however, has been measured only 4 times. 

In central California slip along the San Andreas fault is thought to occur primarily 

through surface creep. Recent deformation has also been measured on tectonic elements 

east and west of the San Andreas. These include extension across the Basin and Range, 

right-lateral strike-slip motion on the Rinconada and San Gregorio faults and northeastsouthwest compression within the Coast Ranges. The vector rate of change of the station 

positon for OVRO, 10.3 f 2.7 mdyr at N37'W f 4.5'. is closer to the local orientation of 

the Owens Valley fault than the assumed direction of extension in the Basin and Range 

(N60'W). The integrated rate of extensional deformation across the Basin and Range 

estimated from geological observations and VLBI baseline that cross the region is given by 

Minster and Jordan [ 1984, 19871 to be 9.7 f 2.1 mdyr at N56'W f lo'. The difference 

velocity vector between FORT and OVRO, 37.1 f 2.8 mm/yr at N37'W f 5', is similar to 

the integrated rate of deformation estimated from ground-based geodetic networks (36.5 

mm/yr at N34'W) and from geological data (35.2 mdyr at N34'W). The rate of 

shortening to the east of the San Andreas [Chapter 31 estimated from ground-based 

geodetic data may represent a significant component of the fault-normal compression. 
140 

TABLE 1. VLBI Station Observation History 

Station No. of Experiments Period 

CDP Bare Stations 

FT.D 

HATC 

MOJA 

OVRO 

VNDN 

Mobile VLBI Sites 

BLKB 

DEAD 

ELY 

FLAG 

FORT 

JPL 

MAMM 

MON 

m 

PBLO 

PINF 

PLAT 

PRES 

PTR 

PER 

QUN 

SANP 

YUMA 

38 

30 

75 

43 

63 

10 

3 

4 

3 

7 

15 

2 

21 

3 

8 

15 

7 

9 

6 

3 

6 

4 

16 

82.79 - 87.82 

83.48 - 87.81 

83.48 - 87.82 

82.79 - 87.82 

83.64 - 87.82 

83.85 - 87.81 

84.16 - 87.24 

84.31 - 87.36 

84.29 - 86.23 

83.64 - 87.79 

82.79 - 87.79 

84.81 - 86.81 

82.79 - 87.82 

84.17 - 85.17 

83.14 - 87.79 

83.84 - 87.23 

84.29 - 86.25 

83.65 - 87.81 

84.16 - 87.81 

83.86 - 87.23 

83.49 - 87.82 

83.66 - 87.24 

83.84 - 87.81 

The time interval of observations are given in decimal fractions of years. 
141 

TABLE 2. VLBI Station Velocities 

Station A Priori A Posteriori 

Velocity, Orientation Velocity, Orientation 

mmlyr dyr 

BLKB 

DEAD 

ELY 

FLAG 

FORT 

FT.D 

HATC 

JPL 

MAMM 

MON 

OCOT 

OVRO 

PBLO 

PINF 

PLAT 

PRES 

PTR 

PVER 

QUW 

SANP 

VNDN 

YUMA 

McxlA 

21.0 

7.0 

1 .o 

0.5 

40.0 

0.0 

7 .O 

35.0 

0.0 

40.0 

28.7 

9.0 

25.0 

30.0 

0.0 

30.0 

35.0 

35.9 

9.0 

35.0 

48.0 

2.0 

7.0 

N39'W 

N41'W 

N58'W 

N58'W 

N41"W 

N50"W 

N65"W 

N45'W 

N40'W 

N60'W 

N65'W 

N45'W 

N41'W 

N41'W 

N38'W 

N60'W 

N65'W 

N36'W 

NWW 

N41'W 

11.1 f 3.3 

14.8 f 6.7 

3.9 f 4.0 

6.1 f 7.2 

47.4 f 2.8 

5.7 f 3.9 

9.4 f 2.6 

34.0 f 2.6 

11.5 f 9.4 

40.1 f 2.5 

18.9 f 28.5 

10.3 f 2.7 

25.5 f 2.7 

25.5 f 3.7 

3.8 f 4.5 

28.7 f 3.3 

38.8 f 3.8 

42.4 f 5.4 

12.0 f 3.1 

39.4 f 4.5 

45.7 f 2.9 

3.4 f 2.7 

7.1 f 0.9 

N65'W f 17' 

N72'W f 7' 

S72'W f 28' 

S51'W f 46' 

N37'W f 5' 

N12'W f 4' 

N62'W f 8' 

N44'W f 6' 

N65'W f > 90' 

NWW f 6' 

SWWf>W 

N37'W f 4' 

N48'W f 7' 

N49'W f 13' 

N77'W f 37' 

N43'W f 8' 

N36'W f 8' 

N39'W f 17' 

N52'W f 9' 

NWW f 31' 

N41'W f 6' 

N84'W f 16' 

N50'W f 1' 

. 
142 

TABLE 3. Difference Vectors 

Stations Rate, 

WYr 

Orientation 

Southern California 

MON-YUMA 

MON - BLKB 

VNDN - MON 

'Big-Bend' Region 

JPL - MOJA 

JPL - PBLO 

VNDN - SAW 

Central Cal~ornia 

FORT - OVRO 

VNDN - FORT 

37.6 k 3.4 

30.0 k 4.5 

5.9 k 2.9 

NWW It 8' 

N35'W f 12' 

N23'W k 4' 

26.9 k 2.6 

8.7 f 3.7 

15.2 k 6.7 

N43'W f 5' 

N34'W f 6' 

N15'E f 7' 

37.1 k 2.8 

3.8 k 3.1 

N37'W f 5' 

S25'W +, 4' 
143 

TABLE 4. Summary of Deformation Rates along the San Andreas system in southern 

California 

Fault 

Segment 

Orientation Geological Slip Rate Geodetic Slip Rate, 

myr mY-r 

Imperial fault N38'W 35 f 5* 

San Andrcas fault 

Coachella Valley N45'W 2043 34.5 k 1.3c 

Cajon Pass N45 - 66'W 2 1 -29D 

Mojave N65'W 25-35E 18.3 k 1.2F 

C holame-carri zo N40'W 3 1 -37G 

San Jacinto fault N45'W 8- 14H 34.5 k 1.3c 

Elsinore fault N45'W 1-71 1.4 k 0.6' 

All fauIt orientations are approximate azimuths determined from fault map of Jennings 

[ 19751. Lettered notes follow on the next page. 
133 

Notes for Table 4 

A. Triangulation and trilateration surveys have been performed by the National Geodetic 

Survey to monitor horizontal crustal movement in the Imperial Valley since 1934. Six 

surveys were carried out between 1934 and 1980. These geodetic observations include coseismic deformation from the 1940 El Centro (M, = 7.1) and 1979 Imperial Valley (M, = 

6.8) earthquakes. The rate of slip determined from the triangulation and trilateration data 

for the interseismic interval, 1941-1978, was 35 f 5 mm/y-r; however, due to the uncertain 

effect of the 1940 earthquake a value of 30 f 5 mm/yr has been estimated for the long term 

slip rate [USGS, 19881. Slip on the Imperial fault is thought to be transferred to the San 

Andreas and San Jacinto faults to the north. 

B. Excavations at one site along the southern 200 km of the San Andreas fault (B, Figure 

30) provide evidence of at least four large slip events and a slip rate of over 30 mm/yr 

during the time period 1000-1700 [Sieh, 19861. The rate of slip on this segment of the San 

Andreas fault is poorly constrained by geologic data [USGS, 19881; a slip rate of 30 mrdyr 

is used as the best estimate. 

C. From trilateration measurements made on the USGS Salton Sea Network between 1972 

and 1981 the total differential velocity across the network was estimated to be 34.5 f 1.3 

mm/yr [Prescotr et af., 19871. 

D. From four independent determinations of the slip rate at Cajon Creek (D, Figure 30) on 

the San Andreas fault spanning different intervals of time from 5900 to 14,400 yr Weldon 

and Sieh (19851 estimated an average slip rate of 24.5 k 3.5 dyr. 

E. The estimated slip rate ranges from 16 to 60 mdyr. Salyards et al. [ 19871 used dated 

offsets for the last three slip events at Pallet Creek (E, Figure 30) to obtain an averaged slip 

rate, corrected for non-brittle warping across the fault, of 22 dyr over the past -500 yr. 

Eight kilometers northwest of Pallet Creek Schwarrz and Weldon [1987] estimated a 
minimum slip rate of 16 to 19 mdyr and a maximum rate of 38 mm/yr from the offset of a 

swam channel. From an examination of displacements across a 10-km wide zone along a 

26 km-long portion of the San Andreas Rust [ 19861 found that the total fault-zone slip rate 

was 46-60 Wyr. The best estimate of the geological slip rate is 30 k 5 mm/yr [USGS, 

19881. 

F. From trilateration measurements made between 1972 and 1981 the total differential 

velocity across a profile perpendicular to the San Andreas fault (N58.W) near Palmdale is 

18.3 f 1.2 mdyr [Prescotr et af., 19871. 

G. The offset history of Wallace Creek (G, Figure 30) requires that the average rate of slip 

along the San Andreas fault has been 33.9 f 2.9 mdyr for the past 3,700 yr [Sieh and 

Jahns, 19841. This slip rate is similar to the rate determined for the central creeping portion 

of the San Andreas fault [Chapter 3, Tables 2,4, and 51. 

H. The estimated slip rate on the Clark fault, a strand of the San Jacinto fault near Anza, is 

12-17 mm/yr for the last 30,000 yr [Merifield et al., 19871. An earlier estimate by Sharp 

[ 19811 gave a long-term minimum rate of 8 to 12 mdyr for the past 730,000 yr. Further 

to the northwest, Wesnousky et af. [ 19871 and Prentice et af. [ 19881 suggest a minimum 

slip rate of 5.4 f 1 mdyr for the past 2000 years. Because of structural complexities of 

this part of the fault zone and the proximity of the San Andreas fault, it is unclear how slip 

is partitioned on the different structural elements; additionally the rate of slip could be 

decreasing toward the northern end of the fault. The best estimate of the geological slip rate 

is 11 f 3 dyr [USCS, 19881. 

I. Rockwell et af. [1985], Glen Ivy north stand. The rate of slip on the Elsinore fault is 

poorly constrained by geologic data; a rate of 2 mdyr is used as a best estimate [ Weldon 

and Humphreys, 19861. 

J. The USGS Ana Trilateration network, which spans the Elsinore and San Jacinto faults 

near Palm Springs, has been surveyed seven times between late 1973 and December 198 1. 
136 

On a subnetwork (-20 km in width) which spans only the Elsinore fault the rate of faultparallel shear is -0.07 _+ 0.03 prad/yr [King and Savage, 1983, Figure 21. If we assume 

that the measured deformation is due to right-lateral slip across the Elsinore, this average 

shear strain corresponds to net displacement rate of 1.4 f 0.6 WF. 
147 

TABLE 5. Summary of Deformation Rates East of the San Andreas fault 

Fault or region Orientation Geological Slip Rate Geodetic Slip Rate, 

mm/yr mm/yr 

Central Mojave (RL) 

Basin and Range east of 

Mojave Desert (E) 

E. Garlock fault (LL) 

W. Garlock fault (LL) 

Owens Valley (RL) 

Hunter Mountain fault (RL) 

N. Basin and Range (E) 

N41'W 2- 13K 6.7fl.3L 

N60'W 0-3M < 1N 

(Rio Grande Rift only) 

E- W 0.7- 1.10 7.9 f l.lP 

N63'W 5->20Q 

1-3' 

5-8s 

N25'W 0.7-2.2T 

N55'W 2 .O-3.2" 

N60'W 1-12w 

3.2 k 1.2" 

RL = right-lateral slip, LL = left-lateral slip, E = extension. Lettered notes follow on the next 

page. 
138 

Notes for Table 5 

K, Dokka [ 19831 has estimated that 27-38 km of cumulative slip has occurred across the 

northwest trending faults from detailed mapping and the location of a distinctive Miocene 

detachment terrain. Dokka [ 19831 has suggested that strike slip faulting may have started 

as late as Pliocene or Quaternary. If slip initiated 2 m.y ago the average rate of slip wou!d 

correspond to 13-19 mdyr. If slip initiated 20 m.y ago the slip rate could be as low as 1-2 

mm/y-r. A best estimate of the slip rate of 6.5 mdyr is determined by assuming slip 

initiated 5 m.y. ago. 

L. From triangulation and trilateration surveys made during 1934-1982 an average shear 

strain rate of 0.16 k 0.03 pradyr at N41°W k 5' was determined for the region between 

the Helendale and Camp Rock faults [Chapter 2, Figure 3, Sauber et al., 19861. If we 

assume that this deformation is due to right-lateral motion across the northwest tending 

local fauits the average shear straining corresponds to a relative displacement rate of 6.7 f 

1.3 mdy-r. The Barstow mlateration network has been surveyed four times between 1979 

and 1984 [King, 19851. The maximum shear strain rate (9) was determined to be 0.08 +, 

0.05 prad/yr, with 9 = N21'W f 17'. This network spans only two of the northwest 

striking faults of the central Mojave and falls within the transition region between active 

deformation to the west and low snain rates to the east observed on the central Mojave 

network [Sauber et al., 19861. 

M. Within the Quaternary, little or no deformation is thought to occur between the eastern 

Mojave Desert block and the Colorado Plateau. This assessment is based on mapping of 

young fault scarps [Howard er af., 19781, geologic field mapping [I. Lucchitta, personal 

communication, 1988; J. Knapp, personal communication, 19881 and recent seismicity 

[Engdahl and Rineharr, 19881. The estimated range in the rate of extension across the 

southern Basin and Range is 0-3 mdyr [R. Weldon, personal communication 1987); the 

midpoint value of 1.5 mdyr is used as a best estimate. , 
149 

N. Savage et uf. [ 19801. The Socorro tnlateration network spans the Rio Grande rift at the 

eastern end of the southern Basin and Range province. The mlateration measurements 

place an upper bound of about 1 mdyr on the average east-west spreading across the 60- 

km-wide rift during the time interval 1972-1979. 

0. Cfurk er of. [ 19841. 

P. The Garlock mlateration network has been surveyed nine times between 1972 and 1984 

[King and Lisowski 1985; N. King and M. Lisowski, unpublished data, 19881. In 

addition to spanning the eastern 150 km of the Garlock fault, the network spans the 

Panamint Valley fault (right-lateral slip at N55'W) and the Owl Lake fault (left-lateral slip at 

N57'E). The maximum shear strain rate (i.> is 0.18 f 0.01 pdyr, oriented N59'E f 2' if 

left-lateral or N31'W k 2' if right-lateral. The rate of slip was estimated from dislocation 

modeling; the locking depth was taken from the depths of earthquakes, with 7.5 km being 

the typical depth and 15 km the lower limit. The slip rate on the eastern east-west trending 

fault segment was found to be insignificant at any depth. The slip rate on the central 

pomon of the western fault striking N63'E scales with depth. The best fitting slip rate for 

a locking depth of 7.5 km was estimated to be 7.3 f 1.1 mdyr. 

Q. Cfurk et uf. [ 19841. Slip estimate from Goler Gulch. 

R. Cfurk er al. [ 19841. Slip estimate from Oak Creek. 

S. Cfurk et uf. [1984]. Slip estimate from Koehn Lake. 

T. The azimuth of major segments of the fault zone vary from 325' to 355' [Beanland and 

Clark, 19871. The slip rate of 0.7-2.2 mm/yr on the Owens Valley fault was estimated 

from combining the average horizontal slip rates on the Owens Valley fault and the Lone 

Pine fault, a secondary fault [Zoback and Beanfund, 1986; Beanfund und Clark, 19871. 

Holocene offset on the Owens Valley fault is primarily right-lateral strike-slip slip, with an 

estimated ratio of lateral to vertical offset for the 1872 (1M, -7.6) event averaging 6: 1 and 
possibly as great as 1O:l. Late Pleistocene slip on the subparallel Sierra frontal fault, 

located 5 to 20 km west of the Owens Valley fault, is primarily vertical. 

U. Trilateration surveys in 1974 and 1979 of a network spanning Owens Valley indicate 

that right-lateral tensor shear (i) is accumulating on the Owens Valley fault at a rate of 

about 0.08 f 0.03 pstrain/yr at N20'W [Savage and Lisowski, 19801. Neither the 

measured extension (0.01 k 0.03 psnain/yr) perpendicular to the Owens Valley fault nor 

the conaaction (0.01 f 0.03 pstrain/yr) parallel to it is significant. The rate of shear strain 

estimated from two triangulation surveys in 1934 and 1956 plus the 1974 trilateration is 

consistent with the 1974-1979 rate. If we assume that the measured deformation is due to 

right-lateral motion across the Owens Valley fault and that 6 represents an average strain 

across a 20-km-wide zone, the average shear rate comesponds to a net displacement rate of 

3.2 f 1.2 dyr. 

V. The formation of the northern Panamint Valley and Saline Valley has been attributed to 

the development of a late Pliocene to recent extensional system that consists of paired pullapart basins connected by the Hunter Mountain transfer fault [Burchfiel er al., 1987; 

Srernlof, 19881. Assuming 3.0 Ma for the age of inception of the Hunter Mountain fault 

zone, a minimum average slip rate on the fault is 2-3.2 mdyr. Palinspastic reconstructions 

of the Saline Range faults yield 4.5 f 0.6 km of extension since 1.4 Ma, giving an average 

displacement rate of 2.8 to 3.6 mdyr. 

W. The orientation of Basin and Range extension of N60'W is the median azimuthal value 

from the Zoback and Zoback [ 19801 data set, and the f 20' range corresponds to the 

standard deviation of a single observation [Minster and Jordan, 1984, 19871. The rate of 

extension within the Basin and Range of 1 - 12 mdyr was estimated by Minsrer and Jordan 

[ 19841 from geologic strain, heat flow, paleoseismicity and recent seismicity. Eddington er 

al. [ 19871 estimated a rate of 8- 10 mdyr from a detailed analysis of historical earthquakes. 

A value of 9 dyr is used for 3 best estimate of the geologic slip rate. 
151 

Figure Captions 

Figure 1. Location of the VLBI sites, given by solid circles, utilized in this study. An 

orthomemc projection of the western United States and Mexico about the pole 30"N, 

130'W is given. The nominal Pacific-North American plate boundary is indicated in central 

California by the San Andreas fault (SA). The eastern extent of the Basin and Range 

province is delineated by the Wasatch front (WF). G of C = Gulf of California. 

Figure 2. VLBI sites (triangles) in California, Nevada, and western Arizona in mercator 

projection. Quaternary faults traces are simplified from Jennings [ 19751: E=Elsinore fult, 

IF = Imperial fault, G = Gariock fault, OV = Owens Valley fault, R = Rinconada fault, SA 

= San Andreas fault, SF = Sierra Frontal fault, SJ = San Jacinito fault. 

Figure 3. The vector rate of change of station positions relative to fixed North America 

. given on an oblique mercator projection of the western United States about the NUVEL- 1 

Pacific - North American pole of rotation [DeMets et ai., 19873. The stations velwitiss are 

given for sites in California with at least four observations spanning at least 2 years. The 

95% confidence error ellipses reflect the marginal uncenainity associated with the 

individual station velocities. In this projection, station velocities parallel to the bottom of 

the page are at the orientation predicted by NUVEL-1; the PCFC-NOAM relative motion 

vector is given at the bottom center for reference. 

Figure 4. Vector rate of change of position of station R.D. 

Figurt 5. Vector rate of change of position of station PLAT. 
152 

Figure 6. Vector rate of change of position of station ELY. 

Figure 7. Vector rate of change of position of station YUMA. 

Figure 8. Vector rate of change of position of station BLKB. 

Figure 9. Vector rate of change of position of station PINF. 

Figure 10. Vector rate of change of position of station MON. The Pacific-North American 

plation motion vector predicted by NUVEL-1 is given by the dashed line. 

Figure 11. Vector rate of change of position of station MOJA. 

Figure 12. Vector rate of change of position of station PBLO. 

Figure 13. Vector rate of change of position of station JPL. 

Figure 14. Vector rate of change of position of station SANP. The Pacific-North 

American plation motion vector predicted by NUVEL-1 is given by the dashed line. 

Figure 15. Vector rate of change of position of station VNDN. The Pacific-North 

American plation motion vector predicted by NUVEL-1 is given by the dashed line. 

Figure 16. Vector rate of change of position of station OVRO. 
153 

Figure 17. Vector rate of change of position of station FORT. The Pacific-North 

American plation motion vector predicted by "EL-1 is given by the dashed line. 

Figure 18. Vector rate of change of position of station QUIN. 

Figure 19. Vector rate of change of position of station HATC. 

Figure 20. Vector rate of change of position of station PRES. 

Figure 21. Vector rate of change of position of station PT.R. The Pacific-North American 

plation motion vector predicted by NUVEL- 1 is given by the dashed line. 

Figure! 22. The velocity of MON relative to YUMA. 

Figure 23. The velocity of MON relative to BLKB. 

Figure 24. The velocity of VNDN relative to MON. 

Figure 25. The velocity of JPL relative to MOJA. 

Figure 26. The velocity of JPL relative to PBLO. 

Figure 27. The velocity of VNDN relative to SANP. 

Figurc 28. The velocity of FORT relative to OVRO. 

. 
154 

Figure 29. The velocity of VNDN relative to FORT. 

Figure 30. Reference figure for the studies cited in Tables 4 and 5. At sites B, D, E, and 

G geologically estimated rates of fault slip were estimated geologically for the San Andreas 

fault; at sites 0, Q, S and R for the Garlock fault; and at V for the Hunter Mountain fault. 

USGS ground-based geodetic networks include SSN = Salton Sea Network, ETR = 

Eastern Transverse Ranges Network, CMN = Central Mojave Network, BN = Barstow 

Network, OVN = Owens Valley Network. Also shown are the locations of the cities Anza 

and Palmdale (PL). 

Figure 31. Reference figure for three path integrals. See Figure 30 for symbols and 

Fig= 2 for fault names. 

Figure 32. Fault-parallel component of velocity relative to North America (NOAM) along 

path 1 in southern California. The * indicates the best .estimate of the geologically 

determined slip rate; the error bar indicates lower and upper bounds on these geological 

estimates. Solid circles indicate USGS mlateration data. Vertical error bars indicate the 

standard deviation relative to the network centroid (J. Savage and M. Lisowski, personal 

communication, 1988). Open triangles denote VLBI data with associated standard 

deviations shown by error bars. 

Figure 33. Fault-normal component of velocity relative to North America along path 1 in 

southern California. Symbols are as in Figure 32. 
155 

Figure 34. Fault-parallel component of velocity relative to North America along path 2 in 

the 'big bend' region. The horizontal error bars indicate the region over which the 

measurement was made. Other symbols as given in Figure 32. 

Figure 35. Fault-normal component of velocity relative to North America along path 2 in 

the 'big bend region. Symbols as in Figures 32 and 34. 

Figure 36. Fault-parallel component of velocity relative to North America along path 3 in 

central California. Symbols as in Figures 32 and Figure 34. 

Figure 37. Fault-normal component of velocity relative to North America along path 3 in 

central California. Symbols as given in Figures 32 and Figure 34. 

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Chapter 5. Conclusions 

In this thesis I estimated the rates of deformation across Pacific - North American 

plate boundary zone in California utilizing geodetic data. The rates of deformation in the 

central Mojave Desert and east of the central creeping portion of the San Andreas fault were 

estimated from triangulation and trilateration data. In these two studies the measured 

incremental strain was compared with the accommodation of strain seen in local geological 

structures, strain release in earthquakes, and principal stress directions infemd from in situ 

measurements. To address the question of the relation of deformation measured on local 

scales to the overall accommodation of deformation across the Pacific - Nonh American 

plate boundary zone I utlized VLBI data. These data constrain the integrated rate of 

deformation across portions of the continental plate boundary in California and provide a 

tectonic framework to interpret regional geodetic and geologic studies. 

The dominant active structural elements of the Mojave Desert block are right-lateral 

strike-slip faults trending approximately N35'W-N42'W. Data from triangulation and 

trilateration surveys made during 1932 - 1982 were used to calculate shear strain rates in 

the central Mojave Desert. The geodetic network extends -1 10 km east - west and spans 

the area from west of the Helendale fault to east of the Ludlow fault. For the region 

between the Helendale and Camp Rock faults the shear strain rate was determined to be 

0.16 f: 0.03 Wyr, with maximum right-lateral shear strain occurring on a plane oriented 

N41'W f 5'. To search for strong spatial gradients in the strain field the rates of shear 

strain werc determined for a number of different spatial subnets and the observed angle 

changes were compared with those predicted by least squares analysis assuming a uniform 

strain field. Because there are not enough stations located between potentially active faults, 

it is uncertain whether there is strain accumulation associated with the Helendale and Camp 

Rock faults or if all the observed strain is associated with the Lenwood and Johnson Valley 

faults. If we assume that the deformation measured between Helendale and Camp Rock . 
194 

faults is due to right-lateral motion across the local faults, the average shear straining 

corresponds to a relative displacement of 6.7 f 1.3 mm/yr across this portion of the 

network. From the Camp Rock fault eastward across the network there is a transition from 

significant to very low strain rates. 

The spatial pattern and orientation of the observed strain field suggest a relation to the 

northwest trending faults of the central Mojave and argue against the observed strain being 

due to elastic strain accumulation that will be released in a large earthquake on the 'bigbend portion of the San Andreas fault. The region of active deformation is measured on 

the central Mojave network at a distance of 40-90 km from the San Andreas. While the 

observations given by the trilateration and the VLBI data given in Chapter 4 and 

deformation models [Thatcher, 1983 1 suggest that interseismic elastic straining may be 

broadly distributed, neither the shear strain orientation nor the sharp decline in its 

magnitude across the Mojave network support the hypothesis that the observed strain will 

be released on the San Andreas during a large earthquake instead of on the local faults 

through fault creep or local earthquakes. The geological observation of Quaternary slip on 

the central Mojave faults [Dokka, 19831 further supports the view that the measured strain 

is associated with the Iocal faults. 

The measured strain could be due to one or more of severaI different mechanisms: (1) 

earthquakes, (2) fault creep, or (3) elastic and anelastic strain accumulation. On the basis 

of a calculation of strain due to earthquakes of ML2 3.0 we concluded that slip due to 

earthquakes accounts for only an insignificant portion of the deformation measured in the 

region between Helendale and Camp Rock faults. Some combination of fault creep and 

elastic or anelastic deformation of the lithosphere must therefore be responsible for the 

measured strain. 

The fault plane solutions for six earthquakes that occurred in the central Mojave Desen 

along with those of three events determined by others were used to compare the derived 

strain field with the directions of principal stress inferred from these focal mechanisms. 
195 

The strikes of the fault planes for some of these events were found to be similar to the 

orientation of the major faults in the area, a second group have preferred fault planes with 

strikes that are more northerly by 5' - 20', and two events are normal faulting earthquakes 

that are thought to accommodate esst-west extension. We concluded that the major faults 

of the region strike at the orientation of maximum strain accumulation and thus are the 

faults along which long term displacement will preferentially occur. Secondary faulting 

controlled by a Coulomb-Anderson type failure mechanism or by slip on preexisting faults 

can account for slip on faults of other orientations. Recent paleomagnetic evidence from 

the western Mojave suggest that the region may have rotated lo' - 20' counterclockwise 

since - 16 Ma [McFadden et al., 1987; Golombek and Brown, 19881. Such 

counterclockwise rotation of the Mojave block might eventually act to rotate the northwest 

striking faults out of an orientation favorable to accommodate relative plate motion. 

Triangulation and trilateration data from two geodetic networks located between the San 

Andreas fault and the Great Valley have been used to calculate shear strain rates in the 

Diablo Range between Hollister and Coalinga and to estimate the slip rate along the 

Calaveras and Paicines faults in central California. The earthquake focal mechanisms and 

geological structures in the area suggest two primary modes of deformation to the northeast 

of the San Andreas fault: compression nod to the major fold structures of the region and 

right-lateral strike-slip motion on faults such as the Calaveras and the Paicines. 

The Diablo Range in this region is a broad antiform which trends approximately 

N65'W and encompasses subsidiary fold structures such as the Vallecitos syncline. The 

shear strain rates, 9, and i2, were estimated independently from angle changes using 

Prescott's method and from the simultaneous reduction for station position and strain 

parameters using the DYNAP method with corrections to reduce the mangulation and 

trilateration data to a common reference surface. On the basis of Prescott's method, the 

average shear strain rate across the Diablo Range for the time period between 1962 and . 
196 

1982 is 0.15 f 0.08 prad/yr, with the orientation of the most compressive strain (p) at 

N16'E f 14'. Utilizing corrections for the deflection of the vertical and the geoid - 

reference ellipsoid separation computed on the basis of local gravity observations, = 0.19 

k 0.09 prad/yr and p = N16'E 2 13'. Although ?is not significantly greater than zero at 

the 95% confidence level, the orientation of p is similar to the direction of maximum 

compressive strain indicated by the orientation of major fold structures in the region 

(N25'E). We infer that the measured strain is due to compression across the folds of this 

area; the average shear straining corresponds to a relative shortening of 5.7 f 2.7 mdyr. 

In contrast to the situation throughout most of the Coast Ranges, where fold axes have 

orientations approximately parallel to the San Andreas fault, within the Diablo Range 

between Hollister and Coalinga the trend of the fold axes are different and are thought to be 

controlled by reactivation of older structures. Given such structural control, the geodetic 

data nported hen are also consistent with an oblique displacement, or transpression, model 

for deformation of the Coast Ranges. There are two observations which argue against 

models in which right-lateral shear strain is dismbuted across a zone significantly greater 

than 10 km in width. Because slip on the adjacent San Andreas fault occurs primarily by 

steady creep, little of the right-lateral shear strain accumulation associated with the fault 

should be measurable on off-fault geodetic lines. Additionally, distributed shear strain 

associated with the San Andreas fault should be observable on both sides of the fault, yet 

there is no geodetic or geologic evidence of deformation to the west of the San Andreas 

fault within the Salinian block in this region. 

Within 5 - 10 km to the east of the San Andreas fault the primary geologic structures are 

related to dextral shear on the San Andreas and Calaveras - Paicines faults. Since 1972 

trilateration measurements have been made by the USGS in central California on a regional 

scale spanning a 20-km-wide zone centered on the San Andreas fault and including several 

distinct faults, as well as on smaller (1 -2 km) aperture networks that span a single fault. A . 
197 

slip rate of 10 - 12 mdyr was calculated for the Calaveras - Paicines fault south of 

Hollister. The slip rate on the Paicines fault decreases to 4 mm/yr near Bitter. 

The geocentric position vectors from a set of 77 VLBI experiments beginning in 

October 1982 were used to estimate the tangential rate of change of station positions in the 

western U.S. These data were processed utilizing a procedure developed to remove from 

apparent tectonic motion the contamination due to errors in earth-orientation parameters and 

non-uniform station geometry; this procedure accounts fully for the position covariance 

between stations. In this method the tangential displacement field is minimized with respect 

to an a priori geophysical model of deformation. This model is parameterized in terms of 

the tangential velocity of a station in a North-America-fixed reference frame. 

The vector velocities estimated for the stations in the western U.S. provided discrete 

samples of the temporal and spatial deformation field. To interpret the VLBI-derived rates 

of deformation for three regions, across southern California just north of the Imperial fault, 

in the "big-bend' region, and in central California, I compared the rates of deformation 

derived from VLBI and ground-based geodetic data, and I examined the relationship 

between the rates of deformation determined from geological data and those estimated from 

the geodetic data. 

Deformation across southernmost California is fairly well described by simple rightlateral shear on the San Andreas, San Jacinto, Elsinore, and possibly the offshore faults of 

the California borderlands. An estimate of the integrated rate of deformation across the 

southern region of the Basin and Range province is given by the station YUMA (3.4 f 2.7 

mdyr at N84'W f 16') and is consistent with the low rate of deformation inferred from 

geologic data. Within the Salton Sea region there are three VLBI sites, BLKB, PINF, and 

MON, and with denser spatial coverage the Salton Sea trilateration network. MON is 

colocated with a mlateration station, and the velocity of the mlateration station is set equal 

to the MON vector velocity. The fault-parallel components of velocity of PINF and BLKB 

are in close agreement with the velocity profile given by the mlateration data. A large 
198 

earthquake has not occurred on the southern segment of the San Andreas fault within the 

last -400 years [Sieh, 19861, and strain accumulation is observed over a broad region. If 

the vector velocity given by the MON - YUMA difference vector (37.6 f 3.4 mm/yr at 

N40'W f 8') is approximately equal to the accumulated rate of long-term slip across the 

San Andreas, San Jacinto, and Elsinore faults, additional deformation is predicted to occur 

offshore in the California borderlands. This rate of deformation is similar to that given by 

Weldon and Humphreys [ 19861. The velocity difference vector between VNDN and MON 

is 5.9 f 2.9 mdyr at N23'W f 4' and further supports the hypothesis that additional 

deformation occurs on the offshore faults of the California borderlands. 

In the big-bend region of the San Andreas fault recent deformation has been measured 

across the right-lateral smke-slip faults of the central Mojave, along the San Andreas fault, 

and as northeast-southwest compression across the western Transverse Ranges and the 

offshore faults in the Channel Islands. The VLBI station MOJA is located in the northeast 

comer of the the Mojave Desert block. The vector velocity of MOJA is 7.1 f 0.9 mm/yr at 

N50'W f 1'. This result, along with ground-based geodetic and geologic data from the 

Mojave Desert, the Garlock fault, and the Great Basin suggest that the estimated rate of 

deformation on the northwest striking faults of the central Mojave (6.7 & 1.3 mdyr at 

N41'W f 2', Chapter 2) may be kinematically related to deformation north of the Garlock. 

The station MOJA as well as the western Garlock fault are then within a deforming region 

connecting slip in the central Mojave to deformation north of the Garlock. The alternative 

hypothesis that the MOJA and the central Mojave strain results are due to elastic strain 

accumulation which will be relieved in the next large earthquake on the San Andreas fault is 

rejected on the basis of several arguments; the most convincing argument is that recent slip 

has been documented along the faults of the central Mojave [Dokka , 1983; E. Han, 

personal communication, 19871 . 

Two VLBI stations, JPL and PBLO, are located within the Eastern Transverse 

Ranges (ETR) trilateration network. The ETR network spans the big-bend segment of the ' 
199 

San Andreas near Palmdale. After fixing the site velocity of JPL to be the same in both 

networks the fault-parallel component of PBLO is similar to the velocity given by the 

mlateration data. Over the broad region between MOJA and JPL the rate of deformation 

given by the differenced velocity vector is quite low (26.9 k 2.6 mm/yr at N43'W f 5') 

and suggests that the long term rate of slip on the big-bend segment of the San Andreas 

may be -25 dyr. The velocity difference vector for VNDN - SAW suggest 15.2 f 6.7 

mdyr of northeast-southwest compression (N15'E It 7') between the two sites. The 

SAW station, which is located in the Ventura Basin, however has been measured only 4 

times. Extensive GPS measurements being made in the western Transverse Ranges and to 

the offshore Channel Islands will provide additional constraints on the rate of deformation 

in this @on. 

In central California slip along the San Andreas fault is thought to occur primarily 

through surface creep. Recent deformation has also been measured on tectonic elements 

east and west of the San Andreas; these include extension across the Basin and Range, 

right-lateral strike-slip motion on the Rinconada and San Gregorio faults and northeastsouthwest compression within the Coast Ranges. The integrated rate of deformation given 

by the vector rate of change of thestation positon for OVRO is 10.3 f 2.7 mdyr at 

N37'W f 4.5'; the azimuth is closer to the local orientation of the Owens Valley fault than 

the assumed direction of extension in the Great Basin (NWW). The integrated rate of 

extensional deformation across the Basin and Range estimated from geological 

observations and VLBI baselines that cross the region is given by Minster and Jordan 

[ 1987) to be 9.7 f 2.1 mm/yr at N56'W f 10'. The difference velocity vector between 

FORT and OVRO, 37.1 f 2.8 mdyr at N37'W f 5', is similar to the integrated rate of 

deformation estimated from ground-based geodetic networks (36.5 mdyr at N34'W) and 

from geological data (35.2 mdyr at N34'W). The VLBI results thus are consistent with 

the conclusions obtained from an examination of regional geologic and geodetic studies 

from the Coast Ranges and global plate models; specifically, that the fault-parallel 
component of the San Andreas discrepancy vector may be accommodated by strike-slip 

motion on the Rinconada as well as the San Gregorio fault and that the inferred shortening 

to the east of the San Andreas fault may represent a significant component of the faultnormal compression predicted by the discrepancy vector. 

For the three regions where ground-based geodetic and VLBI results could be directly 

compared the results are similar and suggest that at least the differenced velocity vectors 

from VLBI may be used to estimate the integrated rate of deformation between sites. 

Although there is some uncertainity in interpreting the VLBI station velocities in terms of an 

absolute velocity in a North-America-fixed coordinate system, the VLBI data provide a 

framework to interpret the local and regional geodetic results. 

The comparison of geodetic results to the long-term accommodation of deformation 

as seen in the local geological structures has been used to examine tectonic models of 

deformation. Additionally, the geodetic results may provide an improved estimate of the 

rate of deformation that can be used for comparison to geologic rates of slip. The geodetic 

results given in this thesis were determined by assuming steady-state deformation. The 

major challenge to using the measured incremental strain to infer the long-term rate of 

deformation is to understand temporal varations in the rate of strain accumulation. Five 

years ago I attempted to estimate the conmbution viscous relaxation makes to the rate and 

pattern of deformation following a large earthquake in the Imperial Valley (Chapter 4); with 

the geodetic data available at that time I was unable to determine a unique model of postseismic deformation. In the future I hope to use the findings of this thesis to tie the 

kinematic results to such dynamic models of deformation. 
20 1 

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