initiation of the san jacinto fault and its interaction...

Initiation of the San Jacinto Fault and its Interaction with the

San Andreas Fault: Insights from Geodynamic Modeling

QINGSONG LI1,2 and MIAN LIU

1

Abstract—The San Andreas Fault (SAF) is the Pacific-North American plate boundary, yet in

southern California a significant portion of the relative plate motion is accommodated by the San Jacinto

Fault (SJF). Here we investigate the initiation of the SJF and its interaction with the SAF in a three-

dimensional visco-elasto-plastic finite-element model. The model results show that the restraining bend of

the southern SAF causes strain localization along the SJF, thus may have contributed to its initiation. Slip

on the SJF tends to reduce slip rate on the SAF and enhance deformation in the Eastern California Shear

Zone. The initiation of the SJF and its interaction with the SAF reflect the evolving plate boundary zone as

it continuously seeks the most efficient way to accommodate the relative plate motion.

Key words: Strain localization, fault interaction, San Andreas Fault, restraining bend, finite-element

model.

1. Introduction

The San Andreas Fault (SAF) is the boundary between the Pacific and the North

American plates, but in southern California the relative plate motion is distributed

over a complex fault system. In particular, the San Jacinto Fault (SJF) slips at

� 15� 9 mm/yr (BECKER et al., 2005), comparable to southern SAF (SHARP, 1981;

ROCKWELL et al., 1990; MORTON and MATTI, 1993; BENNETT et al., 2004; BECKER et

al., 2005; MEADE and HAGER, 2005; VAN DER WOERD et al., 2006) (Fig. 1).

The initiation of the SJF and other secondary faults in the SAF system and their

interactions with the SAF are of fundamental importance for understanding the plate

boundary zone dynamics and the associated earthquake hazards. The SJF initiated

between 1.5 and 1.0 Ma, based on geological and stratigraphic evidence (MORTON

and MATTI, 1993; ALBRIGHT, 1999; DORSEY, 2002). The timing roughly coincided

with the formation of a major restraining bend in southern SAF, suggesting a

1 Department of Geological Sciences, University of Missouri, Columbia, MO 65211, U.S.A.E-mail: [email protected]

2 Lunar and Planetary Institute, Houston, TX 77058, U.S.A.

Pure appl. geophys. (2007)DOI 10.1007/s00024-007-0262-z

� Birkhauser Verlag, Basel, 2007

Pure and Applied Geophysics

causative relationship between the SAF and the SJF (MATTI and MORTON, 1993;

MORTON and MATTI, 1993).

Here we test this relationship and explore the dynamic interaction between the

SAF and the SJF in a three-dimensional (3-D) visco-elasto-plastic finite-element

model. The model is similar to that in a preceding paper (LI and LIU, 2006), where we

simulated the first-order geometrical impact of the entire SAF on regional stress field

and strain partitioning. In this study we focus exclusively on southern California,

including both the SAF and the SJF in the model. Our results confirm the notion that

development of the restraining bend along the San Bernardino Mountain segment of

the SAF (Fig. 1) contributed to the initiation of the SJF, and slip on the SJF has

broad impact on strain partitioning in southern California.

2. Numerical Model

The 3-D finite-element model of lithospheric dynamics used in this study was

discussed by LI and LIU (2006). We have modified the model to focus on southern

California (Fig. 2). The first-order geometry of the SJF and SAF, including both the

Big Bend and the smaller restraining bends, is represented in the model, with both

faults dipping at 90 degrees. The model consists of a 20-km thick upper crust (the

240°E

240°E

242°E

242°E

244°E

244°E

32°N 32°N

34°N 34°N

36°N 36°N

6-7 7-7.5 7.5-

Mw

5-6

SAF(Carrizo)

SJF

IMF

SAF(Indio)

SAF(Mojave)SAF(SBM)

restraining bend

34±3 (27±8)

30±7 (16±12)24±6 (1±12)

25±5 (23±8)12±6 (15±9)

20±5 (39±5)

Figure 1

Active faults and seismicity in southern California. Numbers on segments of the San Andreas Fault (SAF),

the San Jacinto Fault (SJF), and the Imperial Fault (IMF) are fault slip rates estimated from geological

data (California Geological Survey, http://www.consrv.ca.gov/CGS/rghm/psha/index.htm) and from

geodetic measurements (in parenthesis) (BECKER et al., 2005). Circles show epicenters of earthquakes

(M > 5.0) from 1800 to present from NEIC catalog.

Q. Li and M. Liu Pure appl. geophys.,

schizosphere) with an elasto-plastic (non-associated Drucker-Prager model) rheol-

ogy, and a 40-km thick visco-elastic layer (Maxwell model) representing lower crust

and uppermost mantle (the plastosphere). The young’s modulus and Poisson’s ratio

are 8:75� 1010 Pa and 0.25, respectively, for the whole entire region. We explored the

viscosity of the plastosphere in the range between 1019 Pa s and 1021 Pa s that has

been suggested for southern California (HAGER, 1991; KENNER and SEGALL, 2000;

POLLITZ et al., 2001). The schizosphere outside the fault zone has a cohesion of

50 MPa and an internal frictional coefficient of 0.4. The faults in the upper crust are

simulated with 4-km thick plastic layers with zero internal frictional coefficients

(BIRD and KONG, 1994). The cohesion for the SAF is assumed to be 10 MPa, perhaps

the upper bound permitted by the surface heat flux measurements (LACHENBRUCH

and SASS, 1980). We used various cohesion values for the SJF to explore the effect of

changing fault strength as the SJF evolves. The boundary condition simulates motion

of the Pacific plate relative to the fixed North American plate (Fig. 2). The two sides

that cross the SAF are free in the direction normal to the boundary plane and fixed in

the other two directions. The surface is a free boundary and the bottom is a free-slip

boundary.

The model calculates plastic deformation both within the fault zones (plastic

sliding) and outside fault zones (plastic deformation) when stress reach their

respective yield criteria. Allowing plastic deformation outside fault zones prevents

pathological stress buildup that would occur in elastic and viscoelastic models when

simulating long-term deformation. To reduce the impact of the arbitrary initial

conditions (zero initial stress), the model is run more than 20,000 years at 10-year

time steps until the system approaches a steady state. Thereafter, the predicted fault

49 mm/yr

SAF

SAF

SAF

SJF IMF

Figure 2

Numerical mesh and boundary conditions of the finite-element model. Abbreviations are explained in the

caption of Figure 1. On both ends of the SAF an extra 300-km model domain with a straight fault zone is

added to minimize the effects of artificial boundary conditions.

San Jacinto and San Andreas Faults

slip rates reflect the secular slip rates that depend mainly on the specified tectonic

loading rate and fault properties.

3. Model Results

3.1. Initiation of the SJF

To test the idea that the restraining bend of the SAF may have caused the

initiation of the SJF (MATTI and MORTON, 1993), we started with a model that

includes only the main trace of the SAF; both the Big Bend and the restraining bend

along the San Bernardino Mountain (SBM) segment are included (Fig. 2). Figure 3a

shows the predicted secular slip rates on various segments of the SAF. In general the

predicted rates are higher in central (the Carrizo plain segment) and the southern-

most segments of the SAF than around the Big Bend. The values depend mainly on

the viscosity of the plastosphere: lower viscosity causes higher slip rates on the SAF.

Using 2� 1020 Pa s produces �35 mm/yr on the Carrizo plain segment, close to the

geological rate (Fig. 1). The predicted slip rates on other segments are close to the

upper bounds of geological estimates (KELLER et al., 1982; WELDON and SIEH, 1985;

HARDEN and MATTI, 1989; POWELL and WELDON, 1992). Using different viscosity

and yield strengths affects the absolute values but not the general pattern of the

predicted fault slip rates. In essence, the bends of the SAF hamper the relative plate

240°

240°

242°

242°

244°

244°

32° 32°

34° 34°

36° 36°

50mm/a

~35mm/a

~22mm/a

~17mm/a

~30mm/a

~36mm/a

~0mm/a

Fault slip rate

(a) (b)

240°

240°

242°

242°

244°

244°

32°

34°

36°

6-7 7-7.5 7.5-

Mw

5-6

600.00.0

KJ/m2/yr

Figure 3

(a) Predicted slip rates along the SAF. Line thickness is proportional to the slip rates (scale shown in the

lower left corner). Lines are major active faults in the region. Only the SAF main trace is included in the

model. (b) Predicted rate of plastic strain energy release outside the SAF, vertically integrated through the

schizosphere per unit surface area. Note the high-energy band in the location of the SJF. Circles show

seismicity explained in Figure 1.


motion and force more strain to be partitioned in the surrounding region, similar to

the results of the regional scale model (LI and LIU, 2006).

The link between the development of the restraining bend and initiation of the

SJF can be seen from the resulting strain distribution. Figure 3b shows the predicted

release rate of plastic strain energy, defined as the product of plastic strain rates and

the deviatoric stress, in the crust outside the fault zone. Such plastic strain is

presumably absorbed mainly by secondary faults not included in the model. A pair of

high energy zones results from relative motion over the Big Bend of the SAF: one is

located roughly along the ECSZ (Eastern California Shear Zone), the other is to the

southwest of the SAF, along the Palos Verdes-Coronado Bank Fault zones and the

San Clemente Fault off the coast. Superimposed on this pattern are two secondary

high-energy zones resulting from the restraining bend of the SBM segment and the

bend between the SAF-Indio segment and the Imperial Fault (Fig. 1). The result is

strain localization along the SJF, although it is not included in this model. Thus the

SJF may have initiated to accommodate the high strain energy resulting from the

development of the SBM restraining bend, as suggested previously based on the

timing of these two events (MATTI and MORTON, 1993; MORTON and MATTI, 1993).

3.2. Interaction between the SJF and the SAF

We then included both the SJF and the SAF in the model to explore their

dynamic interaction. Figure 4a shows the predicted slip rates when the SJF and the

SAF have the same strength. In this case the slip rate on the SJF (�26 mm/yr) is

much higher than on the sub-parallel Indio segment of the SAF, where the slip rate

decreased from �30 mm/yr (Fig. 3a) to �14 mm/yr. Initiation of the SJF also

34°

240°

240°

242°

242°

244°

244°

32° 32°

34°

36° 36°

50mm/a

Fault slip rate

~33mm/a

~26mm/a

~5mm/a

~14mm/a

~43mm/a

~26mm/a

(a)

240°

240°

242°

242°

244°

244°

32°

34°

36°

6-7 7-7.5 7.5-

Mw

5-6

600.00.0

KJ/m2/yr(b)

Figure 4

Predicted slip rates (a) and plastic strain energy release outside the SAF and the SJF (b). Both the SAF and

the SJF are included in the model with the same strength. Legends are explained in Figure 3.


reduces the predicted slip rates on the SBM segment of the SAF from �17 mm/yr

(Fig. 3a) to �5 mm/yr. In essence, the straighter SJF provides an easier path than the

bended SAF to accommodate the Pacific-North American relative plate motion.

The SJF could also influence regional crustal deformation in southern California.

A comparison of Figure 4b with Figure 3b shows that activation of the SJF tends to

increase plastic strain energy along the ECSZ and over the Mojave Desert, at the

expense of strain energy along the coast of southern California.

The impact of the SJF depends on its relative slip rate. Most studies suggest that

the modern slip rates on the SJF are lower than, or at most close to, that on the Indio

segment of the SAF (ROCKWELL et al., 1990; POWELL and WELDON, 1992; BOURNE et

al., 1998; MEADE and HAGER, 2005; FIALKO, 2006). This is generally consistent with

most geological estimates (Fig. 1), although the long-term slip rates between these

two faults remain debatable (BENNETT et al., 2004; VAN DER WOERD et al., 2006).

BENNETT et al. (2004) suggested that since the initiation of the SJF around 1.5 Ma, its

slip rates accelerated to 26� 4 mm/yr by 90 ka, while slip rate on the SAF decreased

to 9� 4 mm/yr from �35 mm/yr over the same period. This is consistent with the

predicted impact of the SJF on the SAF (Fig. 4).

However, to produce the modern slip rates on these faults would require a higher

strength of the SJF in the model (Fig. 5a). This would be consistent with the notion

that the nascent secondary faults in southern California are stronger than the mature

SAF (BIRD and KONG, 1994), and the fact that the SJF is composed of numerous

disconnected fault segments (Fig. 1). A low slip rate on the SJF would weaken its

impact on the regional crustal deformation; the corresponding spatial distribution of

240°

240°

242°

242°

244°

244°

32° 32°

34° 34°

36° 36°

50mm/a

~35mm/a

~23mm/a

~14mm/a

~24mm/a

~38mm/a

Fault slip rate

(a)

~11mm/a

240°

240°

242°

242°

244°

244°

32°

34°

36°

6-7 7-7.5 7.5-

Mw

5-6

600.00.0

(b) KJ/m2/yr

Figure 5

Predicted slip rates (a) and plastic strain energy release outside the SAF and the SJF (b). The SJF is

assumed to be 3 times stronger than the SAF. Legends are explained in Figure 3.


plastic strain energy (Fig. 5b) is close to that before the initiation of the SJF

(Fig. 3b).

4. Discussion and Conclusions

Previous studies have suggested that a non-planar fault geometry may affect

fault slip and deformation in surrounding regions (WILLIAMS and RICHARDSON,

1991; DU and AYDIN, 1996; FIALKO et al., 2005). In the preceding study (LI and

LIU, 2006) we showed that the Big Bend of the SAF may be responsible for the

diffuse seismicity in southern California and strain localization in the ECSZ. In

this study we have found that the smaller bends of the southern SAF also matter.

In particular, the restraining bend of the San Bernardino Mountain segment of

the SAF and the bend between the SAF-Indio segment and the Imperial Fault

may have localized strain energy along the SJF, thus having contributed to its

initiation.

Once the SJF is initiated, it tends to slow fault slip on the southernmost SAF

and increase strain localization in the ECSZ. The impact of the SJF on the SAF

depends on their relative slip rates. The predicted slip rates are affected by the

viscosity of the plastosphere and the strength of the faults. Higher viscosity tends

to decrease slip rates on both the faults, and vice versa. The relative slip rates on

these two faults depend mainly on the fault strength. Assuming the SJF gradually

weakens as it matures (BIRD and KONG, 1994), our model predicts increasing slip

rate on the SJF and concurrent decrease of slip rate on the southern SAF,

consistent with the codependent trend between these two faults since the initiation

of the SJF to about 90 ka (BENNETT et al., 2004). However, the reverse trend of

slip rates on these two faults since then, as suggested by BENNETT et al. (2004),

cannot be readily explained by the model. It would require either strengthening of

the SJF or further weakening of the SAF, both are possible but without evidence.

Although the ECSZ is not included in the model, its effects are partially

accounted for by the localized plastic deformation along the ECSZ. Explicitly

including the ECSZ would weaken the impact of the SJF, as less relative plate

motion would be accommodated between the SJF and the SAF. Including other

faults in southern California is unlikely to change the main results of this study

because of the small slip rates on these faults.

The model results illustrate some interesting aspects of fault interactions that may

be fundamental to the evolution of a plate boundary zone. The ECSZ may be formed

in part to accommodate the relative plate motion hampered by the Big Bend of the

SAF. Similarly, the SJF developed in response to the formation of the restraining

bend in the SBM segment of the SAF. Each new fault causes readjustment of

regional stain partitioning. All these may be understood in light of the natural


evolution of the SAF system as the plate boundary zone continues to seek the most

efficient way to accommodate the relative plate motion.

Acknowledgments

We thank Huai Zhang for assistance in model development and for providing a

parallel elastic finite-element code that forms the base of our models, and Zhengkang

Shen for constructive review. This work was supported by USGS grant

04HQGR0046 and NSF/ITR GEON grant 0225546.

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