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Inception of the eastern California shear zone and evolutionof the Pacific‐North American plate boundary: From kinematicsto geodynamics

Mian Liu,1 Hui Wang,1,2 and Qingsong Li3

Received 15 October 2009; revised 2 March 2010; accepted 5 March 2010; published 7 July 2010.

[1] The San Andreas Fault (SAF) is the transform boundary between the Pacific and theNorth American plates, yet up to 25% of the relative plate motion is now accommodatedby the eastern California shear zone (ECSZ). Here we investigate the inception of theECSZ and its geodynamic interactions with the SAF using a 3‐D viscoelastoplastic finiteelement model. For a given fault configuration of the plate boundary zone, the modelsimulates long‐term slip on the faults and plastic strain outside the faults. Our results showthat the formation of the Big Bend of the SAF around 5–12 Ma impeded fault slipand localized strain along the ECSZ, causing its inception. Development of the ECSZwas further enhanced by the activation of the Garlock Fault (GF) and lithosphericweakening caused by the encroachment of the Basin and Range extension. Similarly,the San Jacinto Fault (SJF) in southern California developed along a belt of localizedstrain, which resulted from the formation of the restraining bend along the San BernardinoMountains segment of the SAF ∼2 Myr ago. Once activated, the SJF reduced slip onboth the southern SAF and the ECSZ across the Mojave Desert. These results indicatecausative relationship between the SAF and the ECSZ. The inception of the ECSZ andother young faults is the consequence of the evolving SAF plate boundary zone thatcontinuously adjusts itself to accommodate the relative plate motion.

Citation: Liu, M., H. Wang, and Q. Li (2010), Inception of the eastern California shear zone and evolution of the Pacific‐NorthAmerican plate boundary: From kinematics to geodynamics, J. Geophys. Res., 115, B07401, doi:10.1029/2009JB007055.

1. Introduction

[2] As the transform boundary between the Pacific and theNorth American plates (Figure 1), the San Andreas Fault(SAF) proper accommodates 20%–75% of the relative platemotion along its various segments [Becker et al., 2005; Meadeand Hager, 2005; Powell and Weldon, 1992; CGS, Proba-blistic Seismic Hazards Assessment, 2002, http://www.consrv.ca.gov/CGS/rghm/psha/index.htm]. The rest of the relativeplate motion is taken up by a system of fault strands sub-parallel to the SAF proper, collectively referred to as the SanAndreas Fault system [Wallace, 1990]. Furthermore, up to25% of the present‐day relative plate motion is accommo-dated by the eastern California shear zone (ECSZ) [Dixonet al., 2003; Dokka and Travis, 1990; Gan et al., 2000;McClusky et al., 2001;Miller et al., 2001; Peltzer et al., 2001;Reheis and Dixon, 1996; Sauber et al., 1994; Savage et al.,2001], which include a set of NW‐trending dextral faultscutting across the Mojave Desert [Dokka and Travis, 1990]

and the Walker Lane belt along the western edge of theBasin and Range province [Cashman and Fontaine, 2000;Hearn and Humphreys, 1998; Wesnousky, 2005] (Figure 1).[3] The inception and development of the ECSZ and other

young faults in the SAF system is part of the history of theevolving San Andreas Fault system that started ∼29 Myrago, when subduction of the Farallon plate brought theencounter of the Pacific plate with North America [Atwater,1970; Atwater and Stock, 1998] (Figure 2). The San AndreasFault formed as the transform boundary between the Pacificand the North American plates and lengthened as the Far-allon plate continued its subduction. The Pacific spreadingcenter migrated eastward into the subduction zone in mid‐Miocene, leading to fragmentation of the borderland of theNorth American plate and ∼90° clockwise rotation of theTransverse Ranges. Around 5–12 Ma, the SAF jumpedinland as the result of the opening of the Gulf of California,in the process producing the “Big Bend” of the SAF[Atwater and Stock, 1998; Oskin and Stock, 2003] (Figure 2).[4] The ECSZ initiated around the same time as the

opening of the Gulf of California and the formation of theBig Bend [Holt et al., 2000; Oskin and Stock, 2003; Stockand Hodges, 1989] (Figure 2); development of the ECSZmay also be associated with a kinematic change around∼8 Ma when the Sierra Nevada‐Great Valley block switchedfrom moving westerly, driven by the Basin and Range

1Department of Geological Sciences, University of Missouri, Columbia,Missouri, USA.

2Institute of Earthquake Science, China Earthquakes Administration,Beijing, China.

3Lunar and Planetary Institute, Houston, Texas, USA.

Copyright 2010 by the American Geophysical Union.0148‐0227/10/2009JB007055

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extension, to its modern NW‐directed motion [Wernicke andSnow, 1998]. Such kinematic changes are witnessed by achange in stress direction in the Walker Lane belt about 7–10 Ma [Bellier and Zoback, 1995; Zoback et al., 1981].[5] How these kinematic changes led to the inception of the

ECSZ, however, is unclear. Furthermore, lithospheric het-erogeneity could also have contributed to the developmentof the ECSZ. The Walker Lane belt straddles the boundary

between the rigid Sierra Nevada‐Great Valley block and theweak and extending Basin and Range province and ismarked by high gradients of heat flow [Lachenbruch andSass, 1978] and other geophysical properties, such as GPSsite velocities [Dixon et al., 2000].[6] In this study we investigate the geodynamic impacts

of the changing configuration of the SAF. This work is builton our previous studies of the geometrical impact of theSAF proper on fault slip rates and seismicity in California[Li and Liu, 2006] and the long‐term mechanical interactionbetween the San Jacinto Fault and southern SAF [Li andLiu, 2007], using a 3‐D viscoelasoplastic finite elementmodel. We have further developed this model for simulatingstrain partitioning and crustal deformation around restrain-ing bends on strike‐slip faults [Li et al., 2009]. Here we applythis model to simulate the long‐term geodynamic interac-tion between the SAF, the ECSZ, and other major faults insouthern California by sequentially incorporating thesefaults in the model and exploring the consequent changes ofstresses and strain partitioning in the SAF plate boundaryzone. We show that the inception of the ECSZ is the con-sequence of the evolving SAF plate boundary zone, whichcontinuously adjusts its configuration to best accommodatethe relative plate motion.

2. The Geodynamic Model

[7] This study builds on the 3‐D viscoelastoplastic finiteelement model for simulating steady‐state fault slip andlithospheric dynamics [Li et al., 2009]. Here we modifiedthis model to systematically and explicitly incorporate theSAF, the ECSZ, the Garlock Fault (GF), and the San JacintoFault (SJF) in southern California with their first‐ordergeometric features (Figure 3). The faults are represented by400 m wide vertical plastic layers; the ECSZ is treated as abroad rheological weak zone.[8] The model consists of a 20 km thick upper crust with

an elastoplastic rheolegy and an underlying 40‐km thick

Figure 1. Topographic relief, active faults, and seismicityin the San Andreas Fault plate boundary zone. Numbersshow geological slip rates on segments of the SAF (datafrom Calif. Geol. Survey, 2002 http://www.consrv.ca.gov/CGS/rghm/psha/index.htm). Thick lines are the faults incor-porated into the model.

Figure 2. Simplified kinematic history of the San Andreas Fault (SAF) plate boundary zone, redrawnafter Atwater (http://emvc.geol.ucsb.edu/download/conejovolcanics.php). Thick lines are the active plateboundaries at the time. SB, Santa Barbara block (western Transverse Ranges); GL, Garlock Fault; SJF,San Jacinto Fault.

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viscoelastic layer representing the ductile lower crust andmantle. The model simulates plastic deformation both withinthe fault zones (plastic sliding) and outside fault zones whenstress reaches the respective yield criteria (nonassociatedDrucker‐Prager model). For the viscoelastic layer, we usedviscosities in the range of 1019–1021 Pa s, based on theinferred values for the lower crust and upper mantle inCalifornia [Flesch et al., 2000; Hager, 1991; Kenner andSegall, 2000; Pollitz et al., 2001]. The plastic yield criteriafor the upper crust, outside the faults, are characterized bythe values of cohesion (50 MPa) and internal frictionalcoefficient (0.4). For the fault zones, the cohesion is takento be 10 MPa [Lachenbruch and Sass, 1980], and theinternal frictional coefficient is set to zero, reflecting weakfault zones suggested by previous studies [Bird and Kong,1994]. In some cases we also tested the effects of variablefault strength by changing the cohesion. The elastic con-stants for the entire model domain are conventional valuesfor the lithosphere: 8.75 × 1010 Pa for the Young’s modulusand 0.25 for the Poisson’s ratio [Turcotte and Schubert,2002]. Using different values of these parameters does notsignificantly change the model results.[9] The eastern side of the model, set in the stable North

American plate, is fixed. The western side is loaded by ashear velocity of 49 mm/y, reflecting the relative motionbetween the Pacific and the North American plates [DeMetset al., 1994]. Other tectonic forces are not considered, andtheir potential impacts are discussed later. To minimizeartificial boundary effect, we added a 300 km wide extramodel domain with straight fault zones to the northern andsouthern ends, which are free to move in the direction ofrelative plate motion and restricted in other directions.[10] To simulate the long‐time evolution of the faults, we

run the model for more than 100,000 years with 5 year timesteps until the system reaches a quasi steady state. By then,the impact of initial stresses, which are arbitrarily chosen tobe zero, is negligible, and the stress state of the model iscontrolled by the rheological structure, the geometry andproperties of the faults, and the tectonic loading. We thenexplore how the changing fault configuration influencesthe long‐term regional stress and strain fields. Because weare interested in the steady‐state results, addition of eachfault zone is run as a new model; the transient processes are

not simulated. In doing so, we also avoid the need to remeshthe finite element model.

3. Model Results

[11] On the basis of the geological reconstructions, weconducted a series of forward models to explore the geody-namic impact of the changing fault configuration (Figure 2),on crustal deformation within the SAF plate boundary zone.Specifically, in the model, we sequentially incorporated theBig Bend of the SAF, the Garlock Fault, the eastern Cali-fornia shear zone, and the San Jacinto Fault in their chro-nological orders of formation and explored the geodynamicimpact of each fault.

3.1. Impact of the Fragmentation of the CaliforniaBorderland

[12] Before the fragmentation of the rim of the Californiaborderland, the San Andreas Fault was probably relativelystraight, parallel to the direction of the relative Pacific‐North American plate motion [Atwater and Stock, 1998](Figure 2a). We use such a SAF configuration as a startingmodel both to test our numerical model and to show theimpact of changing configuration of the SAF on crustaldynamics.[13] In this starting model, the only fault is a straight SAF

parallel to the relative plate motion. Figure 4 shows thepredicted velocity of the crustal motion and the maximumshear stress (capped by the plastic yield strength of the crustoutside the fault). The results are what we would expect foran ideal plate model: the relative plate motion is accom-modated entirely by the SAF; the Pacific plate moves as acoherent, rigid block relative to the fixed North Americanplate; and the shear stress is uniformly distributed outsidethe fault zone.[14] Using this simple model as the reference, we can see

how the fragmentation of the California borderland, espe-cially the rotation of the Transverse Ranges (Figure 2b),influences the crustal dynamics in the SAF plate boundaryzone. To illustrate the basic effects of the changing con-figuration of the SAF, we tested a simplified restrainingbend of the SAF (Figure 5). As expected, in the NorthAmerica fixed reference framework, the restraining bendimpedes the motion of the Pacific plate while pushes theNorth American side of the bend to move with the Pacificplate (Figure 5a). In this case the long‐term slip rate onthe SAF is less than the relative plate motion, so someof the plate motion has to be accommodated by crustaldeformation (simulated as plastic strain) outside the SAF(Figure 5b). The plastic strain is concentrated around therestraining bend and along two belts extending from thebend. These belts of localized strain are not artifacts ofboundary conditions but results from the changes of bothshear and normal stresses caused by the restraining bend,as detailed in the study of Li et al. [2009]. In essence, therestraining bend causes stress buildup in its surroundings.While shear stress moves the crust toward plastic failure,increasing of pressure, or the compressive normal stress,inhibits plastic deformation. Hence, the highest plastic strainrates do not simply conform to regions of the highest shearstress (Figure 5c). Rather, the plastic strain is localizedwhere the shear stress is high, but the mean normal stress

Figure 3. Numerical mesh and boundary conditions of thefinite element model. The entire San Andreas Fault, the SanJacinto Fault (SJF), the Garlock Fault (GF), and the easternCalifornia shear zone (ECSZ) are included in the model.

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is relatively low. Note that the localized plastic strain inFigure 5b is optimally oriented to accommodate the relativeplate motion.[15] The restraining bend causes high shear stresses

around it (Figure 5c). However, once the crust has reachedthe plastic yield strength, the stress is capped, and furtherloading is accommodated by plastic deformation in thecrust. Thus, our model avoids the pathogenic stress buildupencountered by viscoelastic models when used to simulatelong‐term lithospheric deformation [Li et al., 2009].

3.2. Impact of the Big Bend

[16] The development of the Big Bend was related to theopening of the Gulf of California between 12 and 5 Ma[Holt et al., 2000; Oskin and Stock, 2003; Stock and Hodges,1989], which caused inland jump of the plate boundary(Figure 2). Around the same time, the Sierra Nevada‐GreatValley block changed from moving westerly to its modernNW‐directed motion, perhaps also related to the inlandjump of the SAF plate boundary. From the results shown in

Figure 5, we expect significant impact on crustal dynamicsby the formation of the Big Bend.[17] To illustrate the impact of the Big Bend, we started

with a model that includes only the SAF proper, with thefirst‐order geometry of its surface trace. The model setting isthe same as that in the study of Li and Liu [2006], exceptthat we now focus on the role of the Big Bend in theinception of the ECSZ. This case also serves as a test of thenumerical stability of the codes because the models in thisstudy use different finite element meshes and rheologicalstructures than those in our previous models [Li and Liu,2006; Li and Liu, 2007]. Furthermore, this case serves asa reference model for comparison with subsequent caseswhich include more fault zones.[18] Figure 6a shows the predicted velocity of long‐term

crustal motion. Away from the plate boundary, the Pacificplate moves coherently relative to the fixed North Americanplate, as expected for rigid plates. However, near the plateboundary the relative velocity changes within both platesbecause of the irregular geometry of the SAF, especially the

Figure 5. Results of a simplified restraining bend. (a) Predicted surface velocity relative to the fixedNorth American Plate. (b) Predicted plastic strain rates outside the fault. (c) Predicted maximum shearstress.

Figure 4. The test model with a straight transform fault parallel to the direction of relative plate motion.(a) Predicted surface velocity relative to the fixed North American Plate. (b) Predicted maximum shearstress. In this case the two plates move as coherent rigid blocks, and the stress is uniformly distributedoutside the plate boundary fault.

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Big Bend. To the south of the Big Bend, the motion of thePacific plate is impeded; to its north, the Sierra Nevada‐Great Valley block within the North American plate isbeing pushed to move with the Pacific plate. This resultsuggests a causative relationship between the developmentof the Big Bend and the switch from westerly motion ofSierra Nevada‐Great Valley block to its presently NW‐directed motion [Wernicke and Snow, 1998].[19] Note that the predicted surface velocities differ from

those measured by the GPS (Global Positioning System)[e.g., Bennett et al., 1999] because what we calculated hereis the long‐term crustal motion; the fault motion is approxi-mated by steady state plastic creeping. The results aresimilar to those of a simple straining bend (Figure 5).[20] Because of the Big Bend’s impedance to the relative

plate motion, high shear stresses concentrate in the sur-rounding crust (Figure 6b). The broad region of high shearstresses spatially correlates to the diffuse seismicity insouthern California. These results are similar to those in ourearlier model [Li and Liu, 2006].[21] The predicted long‐term slip rates vary significantly

along the strike of the SAF (Figure 6c) as a result of thevariable geometry of the San Andreas Fault. The values of

the predicted slip rates depend on the fault strength andviscosity of the model. The fault strength is given by theplastic yield strength in the fault elements, measured by thecohesion and international friction coefficient [Li and Liu,2006; Li et al., 2009]. Increasing fault strength reducesslip rates; hence, more relative plate motion would be ab-sorbed by plastic deformation in crust outside the fault.Similarly, a higher viscosity for the viscoelastic layer(ductile lower crust and upper mantle) tends to lower sliprates along the SAF [Li and Liu, 2006] and vise versa. Inthis simple model, we assumed a homogeneous viscosityof 2 × 1020 Pa s for the entire model domain and adjustedthe fault strength to fit the observed geological slips rates onthe SAF (CGS, Probablistic Seismic Hazards Assessment,2002, http://www.consrv.ca.gov/CGS/rghm/psha/index.htm).The spatial patterns of the slip rates, however, are notaffected by the chosen fault strength and viscosity values.The highest slip rates are always found in the central andnorthern segments of the SAF, while the lowest slip ratesare over the Big Bend. This is generally consistent withgeological estimates of slips rates along the SAF, whichvary from ∼34 mm/y along central California to less than18 mm/y over the Big Bend (CGS, Probablistic Seismic

Figure 6. Results with only the SAF proper included in the model. (a) Predicted surface velocity relativeto the fixed North America. (b) Predicted maximum shear stress. (c) Predicted slip rates at varioussegments of the SAF proper. Also shown here is the predicted shearing rate along the eastern Californiashear zone, which is not included in the model. (d) Predicted plastic strain outside the SAF proper. Circlesare seismicity explained in Figure 1.

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Hazards Assessment, 2002, http://www.consrv.ca.gov/CGS/rghm/psha/index.htm).[22] Figure 6c shows that <70% of the relative plate

motion is accommodated by the San Andreas Fault; therest has to be taken up by other parts of the plate boundaryzone, simulated as plastic deformation in crust outside thefaults (Figure 6d). Note that high plastic strain is associatedwith each bend of the San Andreas Fault but most notice-ably in two broad belts of localized plastic strain associatedwith the Big Bend, similar to those around the restrainingbend in Figure 5b. One of the high‐strain belts extendsoffshore of southern California, roughly aligned with thePalos Verdes Fault and the Coronado Bank Fault (Figure 1);the other extends along the eastern California shear zone.[23] Because no lateral variations of lithospheric rheology

or fault properties are considered in this case, the predictedlocalization of plastic strain along the ECSZ is entirely dueto the geometrical impact of the Big Bend. To ensure thatthis strain localization along the ECSZ is not an artifact ofthe boundary conditions of the model, we tested cases withthe fixed eastern boundary 100 km further away from theSan Andreas Fault, and the results remain the same. The pair

of high‐strain belts always starts from the two ends of theBig Bend and extend subparallel to the direction of relativeplate motion. These results indicate that the inception of theECSZ was a consequence of the formation of the Big Bend.

3.3. Impact of the Garlock Fault

[24] The Garlock Fault probably formed around thesame time as the Big Bend [Burbank and Whistler, 1987;Monastero et al., 1997]. Figure 7 shows the effects ofincluding the Garlock Fault in the model. Whereas thegeneral results are similar to those in Figure 6 (no GarlockFault), the impact of the Garlock Fault is noticeable. First,the Garlock Fault further impedes the relative plate motion,causing a broader velocity gradient across the plate bound-ary zone (Figure 7a). Second, with the Garlock Fault, thehigh shear stresses are more concentrated in the MojaveDesert (Figure 7b). Third, because of the stronger imped-ance to relative plate motion, the predicted long‐term sliprates on the SAF proper are reduced, while the dextralshearing along the ECSZ increased (Figure 7c). This is alsoevident from the predicted plastic strain rates outside thefaults (Figure 7d).

Figure 7. Results with the SAF proper and the Garlock Fault included in the model. (a) Predictedsurface velocity relative to the fixed North America. (b) Predicted maximum shear stress. (c) Predictedslip rates along the SAF proper, the Garlock Fault, and the eastern California shear zone (not includedin this model). (d) Predicted plastic strain outside the SAF proper and the Garlock Fault. Circles areseismicity explained in Figure 1.

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3.4. Rheological Contribution to the Initiationof the ECSZ

[25] Lithospheric rheology may be another important fac-tor for the initiation of the ECSZ. The Walker Lane part ofthe ECSZ straddles on the boundary between the extendingBasin and Range province and the relatively rigid SierraNevada‐Great Valley block (Figure 1). At present, the SierraNevada‐Great Valley block moves as a rigid microplate,producing a high gradient of surface crustal motion as mea-sured by the GPS [Dixon et al., 2000]. In the past fewmillion years, extension in the Basin and Range provincehas been encroaching into the Sierra Nevada‐Great Valley,causing maximum thinning of the lithosphere under theECSZ [Fliedner et al., 1996; Lachenbruch et al., 1994;Surpless, 2002; Wernicke et al., 1996].[26] To explore the rheological influence on the initiation

and development of the ECSZ, we modified the referencemodel (Figure 6), which has a homogeneous lithosphere,by reducing the viscosity from 2 × 1020 to 1 × 1020 Pa sbeneath the Basin and Range and 1 × 1019 Pa s beneath theECSZ. The weak rheology under the ECSZ and the Basinand Range promotes strain localization along the ECSZ(Figure 8a), which is further enhanced by including the Gar-lock Fault in the model (Figure 8b). As the ECSZ absorbsmore relative plate motion, the slip rates are reduced alongthe northern and central segments of the SAF but increasedon the southern SAF (not shown here), presumably becausethe activation of the ECSZ easies the impedance of the BigBend on slip along the southern SAF.[27] The lateral rheological variations are difficult to quan-

tify, but their role is clear from the model results. Both therheological contrast across the ECSZ and rheological weak-ening under the ECSZ help to localize strain in the ECSZ,hence, promoting its initiation and development.

3.5. Impact of the San Jacinto Fault

[28] In all the cases shown in Figures 6–8, the SJF isnot included, yet the location of the SJF is shown as a belt

of localized strain. Such strain localization results from thebending of the SAF along the San Bernardino Mountainssegment and near the southern end of the Coachella Valleysegment [Li and Liu, 2007]. Theses restraining bends weredeveloped 1.5–2 Ma, about the same time the SJF initiated(1.5–1.0 Ma) [Albright, 1999; Dorsey, 2002; Morton andMatti, 1993]. Hence, the results from this regional scalemodel confirm the conclusion we drew from a local scalemodel [Li and Liu, 2007] that the SJF is genetically relatedto the development of the restraining bend over the SanBernardino Mountains segment of the SAF.[29] To show how the initiation of the SJF may have

impacted on the SAF and the ECSZ, we use the model inFigure 8a and added the SJF (Figure 9). To isolate theeffects of the SJF, the Garlock Fault is not included here.We found that, once initiated, the SJF accommodates someof the relative plate motion, hence, reducing slip rates onthe southern SAF. Assuming the same fault properties forthese two faults, the model predicts much higher slip rateson the SJF than on the southern SAF [Li and Liu, 2007]because the SJF is better oriented for accommodating therelative plate motion. The present‐day slip rates on the SJFis ∼15±9 mm/y [Becker et al., 2005], comparable to but lessthan those on the southern SAF [Meade and Hager, 2005;Morton and Matti, 1993; Rockwell et al., 1990]. To fit theobserved slip rates, we have to make the SJF stronger(higher plastic yield strength) than the SAF. This is con-sistent with the notion that the nascent secondary faults insouthern California are stronger than the mature SAF [Birdand Kong, 1994].[30] In this regional scale model with the ECSZ explic-

itly included as a rheological weak zone, we can alsosee the impact of the SJF on the ECSZ. With a strongSJF as required to fit the present‐day slip rates on the SJFand the southern SAF, the SJF’s impact on strain locali-zation along the ECSZ is insignificant (compare Figures 9aand 8a). However, if the SJF is as weak as the southernSAF, more relative plate motion will be accommodated by

Figure 8. Results showing the impact of lithospheric weakening in the Basin and Range and theeastern California shear zone (bounded by the dashed lines). The viscosity is 2 × 1019 Pa s under theECSZ, 1 × 1020 Pa s under the Basin and Range, 2 × 1020 Pa s for the rest area of the model domain.(a) Predicted plastic strain rates outside the faults. (b) Same as Figure 8a but with the Garlock Faultincluded in the model.

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the SJF, consequently reducing the shear strain along theECSZ (Figure 9b).

3.6. Present‐Day Crustal Dynamics of the SAF PlateBoundary Zone

[31] In the final case we included the SAF, the SJF, theGarlock Fault, and the ECSZ to simulate the present‐dayregional crustal dynamics of the SAF plate boundary zone(Figure 10). The rheological structure in this case is thesame as that in Figures 8–9, with the ECSZ as a rheologicalweak zone, and the SJF is stronger than the SAF, as inFigure 9b.[32] The model results shows that the ECSZ takes up

∼9.5 mm/y relative plate motion along the Walker Lane andup to 13 mm/y long the eastern Mojave Desert (Figure 10a).Along the SAF proper, the slip rates are around 30 mm/yalong the central and northern segments but less over theBig Bend. South of the Big Bend, the relative plate motionis shared by the SAF (∼26 mm/y) and the SJF (∼11 mm/y),comparable to the geological and geodetic data [Becker etal., 2005; Bennett et al., 1996; Petersen and Wesnousky,1994, CGS, Probablistic Seismic Hazards Assessment, 2002,http://www.consrv.ca.gov/CGS/rghm/psha/index.htm].Although changing local fault properties and lithosphericrheology may improve the fits to the observed slip rates,the general agreement with the regional slip rate patterns,despite of the relatively uniform fault properties and rheo-logical structure in the model, indicates that fault geometryand orientations largely control the present‐day fault sliprates and crustal dynamics in the SAF plate boundary zone.[33] Figure 10b shows the spatial distribution of the

maximum shear stresses. The results are similar to those inFigures 6b and 7b, showing a broad area of high shear stressaround the Big Bend. The stress distribution is furthermodified by the Garlock Fault and the San Jacinto Fault.[34] The predicted strain localizations outside the faults

(Figure 10c), together with results in Figures 7d and 8,indicate that strain localization along the ECSZ is causedby the Big Bend and promoted by the rheological weaken-

ing under the ECSZ and along the western margins of theBasin and Range province. The Garlock fault enhancesstrain localization along the Walker Lane while weakens itacross the eastern Mojave Desert.[35] Finally, the model predicts broad uplift, up to 1.5 mm/y,

around the Transverse Ranges (Figure 10d), consistent withcompressive fault structures around the Transverse Ranges[Spotila et al., 2007] and indicating a causative relationshipbetween the Transverse Ranges and the fault developmentin southern California. The predicted subsidence near thenorthern end of the SAF may be an artifact. By assuminga fixed direction of relative plate motion in the entire modeldomain, the bend near the northern end of the SAF becomesa releasing bend, with opposite impacts to the restrainingbends. In reality the direction of the relative plate motionrotates somewhat to N‐NE near the northern end of the SAF[Bennett et al., 2002; DeMets et al., 1994], so the effects ofthe releasing bend may not be as strong as in the model.Including other faults in northern California (the HaywardFault, the Calaveras Fault, and others; see Figure 1) in themodel may also improve the results.

4. Discussion

[36] The San Andreas Fault system is perhaps the beststudied plate boundary zone in the world [e.g., Powell andWeldon, 1992; Wallace, 1990]. Intensive geological inves-tigation and space‐based geodetic measurements have pro-vided great details of the kinematic evolution of the plateboundary zone. In this study, through modeling a sequenceof “snapshots” of the evolving plate boundary, we haveshown how changes of fault configuration and lithosphericrheology may have influenced subsequent development ofthe SAF plate boundary zone. The opening of the Gulf ofCalifornia between 12 and 5 Ma [Oskin and Stock, 2003],which caused the inland jump of the southern SAF andformed the Big Bend, had hindered fault slip on the SAF andcaused strain localization along the eastern California shearzone. Rheological weakening because of the encroaching

Figure 9. Results showing the impact of the San Jacinto Fault on the predicted plastic strain rates outsidethe faults. (a) The SJF is three times stronger than the SAF. (b) The SJF is as weak as the SAF. In thiscase, more strain can be accommodated by the SJF, hence, less needs to be accommodated by the ECSZ(bounded by the dashed lines).

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of the expanding Basin and Range extension, as well asthe activation of the Garlock fault, further contributed to thedevelopment of the ECSZ. Similarly, the development ofthe restraining bend along the San Bernardino Mountainssegment of the SAF may have led to the initiation and devel-opment of the San Jacinto Fault. These modeling resultsprovide some insights into the crustal dynamics behind theobserved kinematic evolution of the SAF plate boundaryzone.[37] To better illustrate the impacts of the fault config-

urations, we tried to keep the model simple. Because ourmain goal here is to show how the relative plate motion isaccommodated by the evolving faults in the plate bound-ary zone, we used the relative plate motion as the soledriving force in our model while ignoring tectonic forceswithin the plate (the gravitational potential energy) and onthe base of the North American plate. This is justifiablebecause deformation within the SAF plate boundary zone isdominated by shear coupling across the plate boundary[Choi and Gurnis, 2003; Humphreys and Coblentz, 2007;Yang and Liu, 2010], although gravitational collapse is theprimary cause for the widespread Cenozoic extension inwestern United States [Jones et al., 1996; Liu and Shen,

1998]. Basal shear under the western United States, espe-cially under the SAF plate boundary zone, is likely weak[Flesch et al., 2007; Humphreys and Coblentz, 2007; Yangand Liu, 2010]. In our model, the loading from relativeplate motion is given by the imposed velocity on the sideof the model domain (Figure 3), whereas in some previ-ous models, the loading is prescribed by velocities in thelower crust [Bourne et al., 1998; Roy and Royden, 2000].Whereas these models have their own merits, we preferthe side loading because it is better constrained than thebottom loading.[38] Furthermore, we used uniform lithospheric rheology

and fault properties in most cases; only in a few selectedcases did we vary these model inputs to test their effects. Ingeneral, higher fault strength reduces the slip rates on thegiven fault, hence, increases slip rates on other subparallelfaults and plastic strain rates in unfaulted crust. Higherviscosity for the viscoelastic layer in the model, representingthe ductile lower crust and upper mantle, has similar effects[Li and Liu, 2006; Li et al., 2009].[39] As for any numerical models, the results can be

affected by the chosen boundary conditions. In our numer-ical experiments, we varied the width of the model, including

Figure 10. Model results of present‐day crustal dynamics in the SAF plate boundary zone. The SAFproper, the Garlock Fault, the San Jacinto Fault, and the eastern California shear zone are included inthe model. (a) Predicted slip rates along the faults and the ECSZ. (b) Predicted maximum shear stress.(c) Predicted plastic strain rate outside the SAF, the GF, and SJF. (d) Predicted vertical velocities. Circlesare seismicity explained in Figure 1.

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extending the lateral boundaries hundreds of kilometersfurther away from the SAF, and found that the resultsare not significantly affected by the lateral boundary con-ditions [Li et al., 2009]. Less constrained are the boundaryconditions on the northern and southern ends of the modeldomain. In our model, these two ends are fixed in the tan-gential direction and free in the direction of relative platemotion. To minimize the boundary effects, we added 300 kmlithosphere on both ends of the SAF, within which the SAFis extended straightly, parallel to the direction of relativeplate motion (Figure 3). Using more realistic boundary con-ditions will not change the main results but may improvethem. For instance, considering the Klamath Mountains’resistance to the northward motion of the Sierra Nevada‐Great Valley block may alleviate the problem of predictedsubsidence in northern California (Figure 10d).[40] Our investigation of the evolution of the SAF plate

boundary zone focused on the initiation of the ECSZ whileignoring some other important fault development, such asthe initiation of the Garlock Fault, which was probablyaround the same time as the opening of the Gulf of Cali-fornian and formation of the Big Bend or earlier [Burbankand Whistler, 1987; Monastero et al., 1997], certainly beforethe development of the ECSZ. The bending of the GarlockFault (Figure 1) is thought to result from the dextral shearalong the ECSZ [Dokka and Travis, 1990] and has beenused for estimating the age and slip rate of the ECSZ [Ganet al., 2003]. It is not clear why none of the faults in theECSZ cross cuts the older Garlock Fault (Figure 1).[41] Our results show that initiation of new faults and

change of the configuration of existing faults would changeslip rates on other faults in the plate boundary zone. Thismay provide some explanation for the observed long‐termtemporal variations of fault slip rates in the SAF system.For example, our results show that the initiation of the SanJacinto Fault would reduce slip rate on the southern SAF,consistent with the codependent slip rates between thesetwo faults since the initiation of the SJF around 1 Ma toabout 90 ka [Bennett et al., 2004]. The increasing of sliprate on the SJF during this period is consistent with faultweakening as it matures [Bird and Kong, 1994]. However,the reverse trend of slip rates on these two faults since then,as suggested by Bennett et al. [2004], cannot be readilyexplained by this model. Prediction of decreasing slip rateson the SJF would require either strengthening of the SJF orfurther weakening of the SAF since 90 ka, both are pos-sible but without evidence.[42] In general, our model results show that the part of

the relative plate motion not accommodated by the SAFproper is distributed over the plate boundary zone andabsorbed by slip on subparallel faults or by plastic strainin the unfaulted crust, which in reality would be mainlyin the form of slip on smaller faults not included in ourmodel. These results are consistent with the understandingthat the relative plate motion between the Pacific andNorth American plates is absorbed by slip on the SAF aswell as other faults over a broad boundary zone includingthe ECSZ; the right oblique extension of the Basin andRange may also accommodated some of the relative platemotion [e.g., Powell and Weldon, 1992]. Hence, withinany swath perpendicular to the strike of the plate boundary,the slip rates or rates of seismic moment release on the faults

are expected to be codependent, with the total values equalor close to those of a single plate boundary fault. Thiscodependence follows the simple principles of mass (forslip) and energy (for seismic moment) conservation and isshown by the fault slip between the SJF and the southernSAF over thousands of years [Bennett et al., 2004] and bythe seismic moment release between the ECSZ and faults inthe Los Angeles region over hundreds of years [Dolan et al.,2007].[43] Perhaps the most important insight provided by the

model results is how the plate boundary zone has continu-ously evolved to accommodate the relative plate motion.The most efficient transform fault would be a straight faultparallel to the direction of relative plate motion, but evolv-ing plate boundary conditions and intrinsic lithological het-erogeneities would change the configuration of the plateboundary fault. When the Big Bend formed, it impedesthe relative plate motion on the SAF, causing strain locali-zation along the ECSZ to absorb the extra strain. Similarly,the restraining bend along the San Bernardino Mountainslocalizes strain along the SJF to make up for the reducedslip rates on southern SAF. Both the ECSZ and the SJFprovide an alternative and more optimally oriented pathsfor accommodating the relative plate motion. They are theresults of the evolving SAF plate boundary zone as it con-tinuously seeks the best ways to accommodate the relativeplate motion.

5. Conclusions

[44] We have investigated how changes of fault config-urations may influence the initiation of new faults in theSAF plate boundary zone using a 3‐D viscoelastoplasticfinite element model. Major conclusions we may draw fromthis work include the following.[45] 1. The formation of the Big Bend played a major role

in the inception and development of the eastern Californiashear zone. The Big Bend reduced slip rates on the SAFproper, forced strain partitioning over a broad plate bound-ary zone, and localized strain along the ECSZ to com-pensate for the reduced slip rates on the SAF.[46] 2. Rheological weakening due to the encroaching

of the Basin and Range extension, and the activation of theGarlock Fault, further contributed to the development of theWalker Lane part of the ECSZ.[47] 3. Initiation of the San Jacinto Fault was genetically

related to the development of the restraining bend over theSan Bernardino Mountains segment of the SAF. Slip on theSJF tends to reduce that on the southern SAF.[48] 4. The SAF proper and the secondary faults in the

SAF plate boundary zone, including the ECSZ, collectivelyaccommodate the relative plate motion between the Pacificand the North American plates. Hence, all these faultsare kinematically connected and mechanically coupled. Allfaults within a swath perpendicular to the strike of theplate boundary are expected to show some codependencein terms of slip rates and seismic moment release, whichshould sum up to values close or equal to those for asingle plate boundary fault between these two plates.[49] 5. The initiation of the ECSZ, the SJF, and some

other young faults in the SAF system is the manifestationof a continuously evolving and self‐adjusting plate bound-

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ary zone. When the fault configuration in the plate bound-ary zone is not optimal for accommodating the relativeplate motion, strain is localized where new faults wouldprovide better paths for the relative plate motion.

[50] Acknowledgments. This work was supported by NSF grantsEAR‐0635574, 0948620, and ITR/EAR‐0225546. We thank an anony-mous referee and the associate editor of JGR for helpful suggestions, HuaiZhang for assisting our code development, and Eric Hetland for usefulcomments of an early version of this paper.

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