Geometrical impact of the San Andreas Fault on stress and seismicity

in California

Qingsong Li1 and Mian Liu1

Received 30 December 2005; revised 4 March 2006; accepted 13 March 2006; published 18 April 2006.

[1] Most large earthquakes in northern and centralCalifornia clustered along the main trace of the SanAndreas Fault (SAF), the North American-Pacific plateboundary. However, in southern California earthquakeswere rather scattered. Here we suggest that such along-strike variation of seismicity may largely reflect thegeometrical impact of the SAF. Using a dynamic finiteelement model that includes the first-order geometricfeatures of the SAF, we show that strain partitioning andcrustal deformation in California are closely related to thegeometry of the SAF. In particular, the Big Bend is shownto reduce slip rate on southern SAF and cause high shearstress and strain energy over a broad region in southernCalifornia, and a belt of high strain energy in the EasternCalifornia Shear Zone. Citation: Li, Q., and M. Liu (2006),

Geometrical impact of the San Andreas Fault on stress and

seismicity in California, Geophys. Res. Lett., 33, L08302,

doi:10.1029/2005GL025661.

1. Introduction

[2] As the plate boundary, the San Andreas Fault (SAF)accommodates a large portion of the �49 mm/yr relativemotion between the Pacific and North American plates[Bennett et al., 1996; DeMets et al., 1994; Meade andHager, 2005] and hosts many of the large earthquakes inCalifornia (Figure 1). However, both slip rate and seismicityshow large along-strike variations. In northern and centralCalifornia, up to �34 mm/yr of the plate motion is accom-modated by the SAF and some of the closely subparallelfaults (California Geological Survey, http://www.consrv.ca.gov/CGS/rghm/psha/index.htm, hereinafter referred to asCGS); most large earthquakes occurred on or clustered tothe main trace of the SAF. However, in southern Californiathe relative plate motion is distributed among a complexsystem of faults. Slip rate on the main-trace of the SAFdrops to 24–25 mm/yr (CGS). Recent estimates based onGPS and seismicity [Becker et al., 2005] indicate low sliprate on the Big Bend segments of the SAF: 15.7 ± 12 mm/yrfor the Mojave segment, 11 ± 12 (combined normal andstrike-slip components) for the San Bernardino Mountainssegment. Seismicity in southern California is much diffuse,with many of the large earthquakes occurred off the main-trace of the SAF.[3] Although along-strike variations of seismicity and

slip rate may have numerous causes, such as stressing rate[Parsons, 2006] and distribution and properties of active

secondary faults [Bird and Kong, 1994], a particularlyimportant cause may be the geometry of the SAF, especiallythe Big Bend, a �25� counterclockwise bending in southernCalifornia (Figure 1). Numerous studies have suggested thata non-planar fault geometry may have significant impact onfault slip, stress, and deformation in surrounding regions[Du and Aydin, 1996; Duan and Oglesby, 2005; Fialko etal., 2005; Fitzenz and Miller, 2004; Griffith and Cooke,2005; Smith and Sandwell, 2003; Williams and Richardson,1991]. However, many of these studies were either based ontwo-dimensional models or with oversimplified fault geom-etry. Some are kinematic models with prescribed slip rates[Smith and Sandwell, 2003; Williams and Richardson,1991], thus the effect of fault geometry on slip rates cannotbe directly tested. In previous dynamic models [Du andAydin, 1996; Duan and Oglesby, 2005; Fitzenz and Miller,2004], fault slip rates were not explicitly calculated. Fur-thermore, most studies have focused on the fault zone; theanelastic deformation outside the fault zone, hence theeffects of fault geometry on off-main-trace seismicity,remain to be explored.[4] In this study, we developed a three-dimensional

dynamic finite element model to investigate how the par-ticular geometry of the SAF may have impacted on long-term fault slip, stress pattern, and seismicity in California.

2. Model Description

[5] The finite element model encompasses most ofCalifornia and the entire length of the SAF with realisticfirst-order features of the surface-trace geometry (Figure 2).A 300-km wide extra model domain is added to both endsof the SAF to minimize artificial boundary effects. Themodel includes a 20-km thick upper crust with an elasto-plastic rheology (non-associated Drucker-Prager model),and a 40-km thick viscoelastic (Maxwell model) layerrepresenting both the lower crust and the uppermost mantle.Viscosity for the lower crust and upper mantle between 1019

Pa s and 1021 Pa s [Hager, 1991; Kenner and Segall, 2000;Pollitz et al., 2001] are explored. For both crust and mantle,the Young’s Modulus is 8.75 � 1010 N/m2 and the Poisson’sratio is 0.25. The SAF has a cohesion of 10 MPa, which isclose to the upper bound permitted by heat flow data[Lachenbruch and Sass, 1980], and an effective frictionalcoefficient of 0. Outside the fault zone, the upper crust isrelatively strong, with a cohesion of 50 MPa and effectivefrictional coefficient of 0.4.[6] The model SAF has a uniform dip angle of 90�. It is

simulated with a 4-km thick layer of special fault elements,which deform plastically when reaching the yield criterion.This process simulates relative crustal motion across thefault zone. We developed the finite element codes based on

GEOPHYSICAL RESEARCH LETTERS, VOL. 33, L08302, doi:10.1029/2005GL025661, 2006

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

Copyright 2006 by the American Geophysical Union.0094-8276/06/2005GL025661$05.00

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a commercial FE package (www.fegensoft.com) [Li et al.,2005], and run the model on a 16-nodes PC cluster.[7] The eastern side of the model domain is fixed, while

the western side is loaded by a shear velocity of 49 mm/yrrepresenting relative motion between the Pacific and theNorth American plates. Stress evolution is calculated at ten-year time steps. To minimize effects of artificial initialstress, the model is run till it reaches a steady state, whichreflects the long-term slip on the SAF owing to tectonicloading from plate motion. We then calculated stress evo-lution over a period of tens of thousands of years withcontinuous tectonic loading. Over this time scale, the SAFcreeps continuously. This is a long-term approximation ofrepeated rupture and locking on the SAF over shortertimescales. Outside the fault zone, excess stress over theyield strength is released by plastic deformation.

3. Model Results

3.1. Slip Rates on the SAF

[8] Although slip rates along the SAF remain somewhatuncertain [Becker et al., 2005; Meade and Hager, 2005;CGS], the general along-strike variations are clear(Figure 3). The central segments of the SAF have thehighest geological slip rates (�34 mm/yr). Slip rate on thenorthern segments of the SAF are lower (17–24 mm/yr)because some of the slip is taken up by the closelysubparallel faults (the Rodgers Creek Fault, the HaywardFault, and the Calaveras Fault). Adding up slip rates onthese faults brings the total rates to near 34 mm/yr. Over theBig Bend slip rate lowers significantly. The slip rate is�16 mm/yr on the Mojave segment, and even lower on theSan Bernardino segment, with �15 mm/yr slip accommo-dated by the subparallel San Jacinto fault [Becker et al.,2005].[9] The model results indicate that such along-strike

variation of slip rate may be largely explained by thegeometry of the SAF. The relatively straight traces of thenorthern and central segments of the SAF, all subparallel to

the direction of relative plate motion, account for therelatively high slip rate on these segments. Conversely,the Big Bend is shown to significantly hamper fault slip.The absolute values of the predicted slip rates dependon the viscosity of the lower crust and uppermost mantle(Figure 3). A value of 2 � 1020 Pa s provides a close fit forthe northern and central segments of the SAF. For thesouthern segments of the SAF, the predicted slip rates aresignificantly lower than the geological value, but close tothose inverted from GPS data [Becker et al., 2005; Meadeand Hager, 2005]. Incorporating the series of weak faultsand spreading centers to the southeast of the Salton Seawould produce a higher and better-fitting slip rate on thesouthernmost SAF.

3.2. Shear Stress and Seismicity

[10] Figure 4 shows the predicted steady-state maximumshear stress (js1 � s3j/2), where s1 and s3 are first and thirdprinciple stress, respectively. In regions where the stress hasreached the Drucker-Prager yield strength, the maximumshear stress is capped by the yield strength envelope: aI1 +

Figure 2. Numerical mesh and boundary conditions of thefinite element model. The entire San Andreas Fault (blackline) is explicitly included in the model.

Figure 3. Comparison of the predicted slip rates (curvesmarked by viscosity values of the lower crust and uppermantle) and geological and geodetic slip rates (lines witherror bars) along the SAF. Geological slip rates are fromCalifornia Geological Survey (http://www.consrv.ca.gov/CGS/rghm/psha/index.htm). Geological Rates A shows thesum of slip rates on several subparallel faults in northernCalifornia. Geological Rates B shows slip rates on the SAFmain trace alone. Geodetic slip rates are from Becker et al.[2005].

Figure 1. Topographic relief and seismicity in Californiaand surrounding regions. Data of seismicity (includes M >5.0 earthquakes from 1800 to present) are from the NEICcatalog.

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ffiffiffiffiffiJ 02

p� k, where I1 and J02 are first invariant and second

deviatoric invariant of the stress tensor, respectively; a andk are parameters related to cohesion and effective coefficientof friction.[11] The most conspicuous feature in Figure 4 is the

broad area of high stress that spans over much of southernCalifornia where many of the large earthquakes occurred offthe main-trace of the SAF. This is a direct consequence ofthe Big Bend. The small trans-compressive bending of theSAF south of the San Francisco Bay Area also causes aregion of high stress, showing the sensitivity of stress fieldto fault geometry. The low shear stress around the northernpart of the SAF results from the relatively straight SAF anda trans-extensional bend of the SAF near the MendocinoTriple Junction, which allows plastic deformation at lowershear stress. The low shear stress around the central SAFsegments, which include the ‘‘creeping’’ section, arisessolely from the relatively straight SAF. Assuming a weakerfault zone for the ‘‘creeping’’ section would further reducethe maximum shear stress in this part of the SAF.

3.3. Release of Plastic Strain Energy Outside the SAF

[12] In this model plastic deformation occurs both withinand outside the fault zone when stress reaches the yieldcriterion. Figure 5 shows the predicted long-term rates ofenergy release outside the SAF, given by the product ofstress tensor and the tensor of plastic strain necessary toabsorb the excess stress. Again, the results indicate signif-icant impact of the geometry of the SAF; each subtlebending of the SAF causes high plastic energy release inits surrounding. The Big Bend causes two elongated belts ofhigh energy release. One is to the west of the SAF, coincideswith the Palos Verdes Fault and the Coronado Bank Fault;the other coincides with the Eastern California Shear Zone(ECSZ). We have found that, if the San Jacinto fault, whichabsorbs a significant portion of the relative plate motion insouthern California [Bennett et al., 2004], is included in themodel, the predicted energy release in the western beltweakens considerably, while energy release in the ECSZ

amplifies and high energy release is distributed over theentire Mojave desert [Li and Liu, 2005].

4. Discussion and Conclusions

[13] The results are affected by other model inputsbesides the geometry of the SAF, noticeably viscosity ofthe lower crust and uppermost mantle, and the ratio betweenthe cohesion of the upper crust outside and within the faultzone. High viscosity of the lower crust and upper mantle(>1021 Pa s), and low cohesion ratio (<2) tend to cause morerelative plate motion to be absorbed outside the SAF, thusweaken its geometrical impact. Within reasonable ranges ofviscosity (4 � 1019 Pa s–1021 Pa s) and cohesion ratio (>2),the main features of model results remain the same. Thealong-strike variation of the geological slip rates are best fitwith a lower crust and mantle viscosity of �2 � 1020 Pa s(Figure 3), which is higher than the viscosity (�1019 Pa s)estimated from postseismic relaxation studies [Kenner andSegall, 2000; Pollitz et al., 2001]. This may be due to themuch longer timescale (>103 years) considered in thismodel than that for postseismic studies (days to decades).As Pollitz [2003] has shown, the effective viscosity of uppermantle may increase as much as two orders of magnitudewhen the timescale of deformation increases.[14] The model results provide useful insights into the

observed along-strike variation of slip rate, stress, andseismicity, much of those may reflect the geometricalimpact of the SAF. The relatively straight segments ofcentral and northern SAF help to explain the relatively highslip rates and seismicity that clusters to the SAF main-trace.

Figure 4. The predicted maximum shear stress (see textfor definition). The dots show earthquakes (M > 6.0) from1800 to present (data from the NEIC catalog).

Figure 5. The predicted plastic energy release off the SAFmain trace. The energy release is vertically integratedthrough the upper crust per unit surface area. The areas ofhigh energy release coincide with many active faults inCalifornia, including the Maacama-Garberville Fault(MGF), the Rodgers Creek Fault (RC), the Hayward Fault(HF), the Calaveras Fault (CF), the Garlock Fault (GF), theEast California Shear Zone, the San Jacinto Fault (SJF), theElsinore Fault (EF), the Palos Verdes Fault (PVF), andthe Coronado Bank Fault (CBF). Cycles are seismicity asexplained in Figure 4.

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Each trans-compressive bending of the SAF causes highstress and high energy release, which are consistent with theclustered seismicity south of the Bay Area and the broaddistribution of seismicity in southern California.[15] Although the model includes only the main trace of

the SAF, the coincidence of the resulting spatial pattern ofplastic energy release with many of the secondary faults insouthern California and the ECSZ (Figure 5) suggests thatthese faults may be genetically related to the geometry ofthe SAF, as suggested by others [Du and Aydin, 1996]. Thismay reflect the natural evolution of the plate boundary zonein searching for the most efficient way to accommodate therelative plate motion. Thus the initiation of the San Jacintofault straightens the southern SAF and eases plate motion inthis part of California, and the ECSZ, which absorbs 9–23% of the relative plate motion [Dokka and Travis, 1990],makes up some of the fault slip deficiency caused by theBig Bend. If the ECSZ further weakens, it may eventuallyreplace the SAF as a straighter and hence more efficientfault zone to accommodate the North American-Pacificplate motion.

[16] Acknowledgments. We thank Kevin Furlong and Rick Bennettfor helpful discussion and constructive review. This work is partiallysupported by USGS grant 04HQGR0046 and NSF/ITR grant 0225546.

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�����������������������Q. Li and M. Liu, Department of Geological Sciences, University of

Missouri, Columbia, MO 65211, USA. (qlpkd@mizzou.edu)

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