Pure appl. geophys. (2007)
DOI 10.1007/s00024-007-0262-z
Ó Birkhäuser Verlag, Basel, 2007
Pure and Applied Geophysics
Initiation of the San Jacinto Fault and its Interaction with the
San Andreas Fault: Insights from Geodynamic Modeling
QINGSONG LI1,2 and MIAN LIU1
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 threedimensional 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: li@lpi.usra.edu
2
Lunar and Planetary Institute, Houston, TX 77058, U.S.A.
Q. Li and M. Liu
240°E
242°E
Pure appl. geophys.,
244°E
Mw
6-7
5-6
7.5-
36°N
SA
8) )
7± o
(2 r r i z
±3 a
34 F(C
36°N
7-7.5
3
SA 0±7 (1
F(M 6±1
oja 2)
ve)
24±6 (1±12)
SAF(SBM)
S
8)
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(2 dio
±5 (In
25 A F
34°N
restraining bend
12 S
±6 J
(1 F
5±
9)
34°N
(
F )
IM39±5
±5
20
32°N
240°E
242°E
32°N
244°E
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.
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
San Jacinto and San Andreas Faults
SA
F
SAF
SA
SJ
49
F
F
IM
F
mm
/yr
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.
schizosphere) with an elasto-plastic (non-associated Drucker-Prager model) rheology, 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
Q. Li and M. Liu
Pure appl. geophys.,
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 southernmost 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°
242°
244°
240°
(a)
242°
244°
KJ/m2/yr
(b)
600.0
0.0
36°
36°
36°
34°
34°
~35mm/a
~22mm/a
~17mm/a
34°
~30mm/a
~0mm/a
Fault slip rate
Mw
50mm/a
~36mm/a
32°
5-6
6-7
7-7.5
7.5-
32°
240°
242°
244°
32°
240°
242°
244°
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.
San Jacinto and San Andreas Faults
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
240°
242°
240°
244°
(a)
242°
244°
KJ/m2/yr
(b)
0.0
36°
600.0
36°
36°
34°
34°
~33mm/a
~26mm/a
~5mm/a
34°
~14mm/a
~26mm/a
Fault slip rate
Mw
50mm/a
~43mm/a
32°
5-6
6-7
7-7.5
7.5-
32°
32°
240°
242°
244°
240°
242°
244°
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.
Q. Li and M. Liu
Pure appl. geophys.,
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°
242°
240°
244°
242°
(b)
(a)
244°
KJ/m2/yr
0.0
36°
600.0
36°
36°
34°
34°
~35mm/a
~23mm/a
~14mm/a
34°
~24mm/a
~11mm/a
Fault slip rate
Mw
50mm/a
~38mm/a
32°
5-6
6-7
7-7.5
7.5-
32°
32°
240°
242°
244°
240°
242°
244°
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.
San Jacinto and San Andreas Faults
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
Q. Li and M. Liu
Pure appl. geophys.,
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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(Received October 26, 2006, accepted January 25, 2007)
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