Bulletin of the Seismological Society of America, Vol. 95, No. 5, pp. 1604–1622, October 2005, doi: 10.1785/0120050058
The Dynamics of Strike-Slip Step-Overs with Linking Dip-Slip Faults
by David D. Oglesby
Abstract Fault step-overs with linking dip-slip faults are common features on
long strike-slip fault systems worldwide. It has been noted by various researchers
that under some circumstances, earthquakes can jump across fault step-overs to cascade into large events, while under other circumstances rupture is arrested at stepovers. There is also evidence that fault step-overs may be preferential locations for
earthquake nucleation. The present work uses the 3D finite element method to model
the dynamics of strike-slip fault systems with step-overs and linking dip-slip faults.
I find that the presence of a linking normal or thrust fault greatly increases the ability
of earthquake rupture to propagate across the step-over, leading to a larger event.
Additionally, dilational step-overs with linking normal faults are more prone to
through-going rupture than compressional step-overs with linking thrust faults. This
difference is due to the sign of the normal stress increment on the dip-slip fault
caused by slip on the strike-slip segments: Slip on the strike-slip segments causes a
negative (unclamping) normal stress increment on the linking normal fault in a dilational step-over, whereas the opposite effect occurs on the linking thrust fault in a
compressional step-over. Even in cases for which both dilational and compressional
step-overs can experience through-going rupture, dilational step-overs typically experience higher slip, particularly on the linking normal fault. In the compressional
case, rupture nucleation on the linking thrust fault may increase the likelihood of
through-going rupture compared to nucleation on one of the strike-slip segments.
Near the intersections between the fault segments, the stress interaction between the
fault segments also causes a significant rotation of rake away from that which would
be inferred from the regional stress field. The results help to emphasize the importance of two-way interactions between nearby fault segments during the earthquake
rupture process. The results also may have implications for the probability of large
earthquakes along geometrically complex strike-slip fault systems, and may help
explain why step-overs sometimes act as barriers and other times as nucleation locations for large earthquakes.
Introduction
Geologists have long known that faults are not simple
planar features, but typically have complex three-dimensional
geometry. In particular, faults often consist of multiple offset
segments. These offsets can range in scale from meters to
tens of kilometers (e.g., Wesnousky, 1988; Courboulex et
al., 1999; Geist and Zoback, 1999; Zoback et al., 1999; Yule
and Sieh 2003; Zampier et al., 2003; Brankman and Aydin,
2004; Lin et al., 2004). In such fault systems, the fault geometry may play a key role in many aspects of the earthquake process. Segment offsets may serve both as preferred
hypocenter locations and as barriers against rupture propagation. For example, The M 7.9 1906 San Francisco, California earthquake is believed to have nucleated in a stepover region and propagated bilaterally (Zoback et al., 1999),
while the M 5.0 1996 Epagny-Annecy, France earthquake
most likely terminated at a restraining step-over (Courboulex
et al., 1999). An important practical issue that arises in the
study of offset fault segments is whether rupture may propagate across step-overs, leading to a larger earthquake. Wesnousky (1988) cited many earthquakes on major strike-slip
faults that both were bounded by and ruptured through compressional and dilational step-overs. In analyzing the seismic
hazard of the San Francisco Bay region, Parsons et al. (2003)
studied the potential interaction of the Hayward and Rodgers
Creek faults at the extensional step-over that separates the
two faults underneath San Pablo Bay. One of the important
issues that they addressed is whether normal faults exist in
the step-over region, under the assumption that such linking
normal faults could increase the probability of rupture propagating across the step-over. In this work I model the dy-
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The Dynamics of Strike-Slip Step-Overs with Linking Dip-Slip Faults
namics of fault systems consisting of strike-slip fault stepovers linked by dip-slip faults in hopes of delineating some
of the general features of such systems, with an eye toward
both theoretical and practical (seismic hazard) applications.
Many researchers (e.g., Harris et al., 1991; Harris and
Day, 1993; Yamashita and Umeda, 1994; Kase and Kuge,
1998; Harris and Day, 1999; Kase and Kuge, 2001) have
modeled the dynamics of strike-slip faults with step-overs
in the absence of linking faults. In general, these studies
show that the ability of rupture to jump across a step-over
depends strongly on the width of the step-over and the degree of overlap between the segments, with closer segments
and positive (i.e, with no along-strike gap) overlaps allowing
rupture to jump more easily. Another important factor is the
direction of the step-over with respect to the sense of slip
on the strike-slip faults: right-lateral faults with right stepovers and left-lateral faults with left step-overs produce extension/dilation in the step-over region, whereas left-lateral
faults with right step-overs and right-lateral faults with left
step-overs produce compression in the step-over region. The
studies cited above, as well as the quasi-static analysis of
Segall and Pollard (1980), indicate that it is much easier for
rupture to jump across dilational step-overs than compressional step-overs. This effect is due to the dependence of
friction on the normal stress: A compressive normal stress
increment such as that produced in a compressive step-over
increases the frictional strength (failure stress) on nearby
fault segments, inhibiting rupture propagation, while a dilational normal stress increment such as that produced in an
extensional step-over brings nearby faults closer to failure.
In many cases, the normal stress increment can be even more
important than the shear stress increment in aiding or inhibiting nucleation on the secondary fault segment (Harris et
al., 1991; Harris and Day, 1993). In contrast, Sibson (1985,
1986) has argued that the above dilational normal stress increment in dilational step-overs should lead to a sudden
opening of fluid-filled tension cracks, creating suction forces
that inhibit rupture propagation across the step-over. An
analogous effect is also seen in some of the models of Harris
and Day (1993), where models with a nonzero Skempton
coefficient decrease the ability of rupture to propagate across
a dilational step-over compared with the fluid-free case.
There is reason to believe that the presence of linking
faults can have a significant effect on the ability of rupture
to propagate across segment step-overs. Magistrale and Day
(1999) investigated the dynamics of a system of thrust faults
linked by strike-slip tear faults. In their models, they assumed that the linking faults were essentially passive features, with their prestress levels set to the sliding frictional
strength. They found that in spite of the fact that the linking
faults had a net energy release of zero, the presence of a
linking fault allowed rupture to jump across larger step-overs
between the thrust faults than was possible with no linking
fault. The physical mechanism for this effect is that a linking
fault allows a continuous rupture evolution across the entire
fault system. In such a fault system, the rupture front, rather
than rapidly decaying seismic waves, can carry the “failure”
signal across the step-over, increasing the distance over
which rupture can propagate.
While the Magistrale and Day (1999) study helps to
explain some of the results seen in the current work (such
as the observation that linking faults aid in propagation of
rupture across the step-over), one must bear in mind that the
current faulting configuration is quite different from that of
linked thrust segments. In the present work, slip on the
strike-slip segments changes the normal stress on the linking
fault, unlike in the case of the linked thrust segments. Figure
1 shows a schematic picture of two strike-slip segments that
have a right step-over occupied by a linking dip-slip fault.
Simple kinematic analysis argues that if such a fault system
slips in the right-lateral (dilational) sense, clamping normal
stress will be decreased on the linking fault. In such a case,
we would predict that the linking normal fault would become
more favorable for rupture as slip accumulates on the strikeslip segment(s). Conversely, left-lateral slip will tend to increase the clamping normal stress on the linking thrust fault,
Figure 1. (a) Schematic diagram of fault geometry
consisting of two vertical strike-slip segments (labeled 1 and 3) linked by a 45⬚-dipping dip-slip fault
in the step-over region (labeled 2). Nucleation is typically on strike-slip segment 1, but in certain models
nucleation is on dip-slip segment 2 or strike-slip segment 3 (stars). (b) Cross-sectional view of the fault
geometry in Figure 1a. The reader is looking directly
toward the fault system along a line perpendicular to
the strike of the strike-slip segments and parallel to
the strike of the dip-slip segment. Thus, strike-slip
segment 3 is closer to the reader than strike-slip segment 1.
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leading to this fault becoming less favorable for rupture as
slip accumulates on the strike-slip segment(s). As will be
shown, this normal stress increment is responsible for many
of the effects seen in the current study.
Other works that investigate the dynamics of linked
fault step-overs are few. Aochi and Fukuyama (2002) modeled the dynamics of the 1992 Landers, California, earthquake, in which rupture propagated across many dilational
step-overs that were linked by strike-slip faults. However,
their work focused on fitting the known slip data and used
the mapped fault geometry; it did not directly deal with the
specific effect of the linking fault on rupture propagation.
There does exist some modeling research on fault systems
that share some aspects of the current fault geometry. Studies
that investigate how rupture transfers from strike-slip faults
to dip-slip faults and vice versa include static and dynamic
models of fault rupture in the Los Angeles, California, area
(Anderson et al., 2003), dynamic models of the 2002 Denali
fault, Alaska, earthquake (Aagaard et al., 2004; Dreger et
al., 2004; Oglesby et al., 2004), and static models of intersecting fault segments (Muller and Aydin, 2004). These
works in general show that the ability of rupture to jump
between dip-slip faults and strike-slip faults depends
strongly (and in a complex manner) on the applied prestress
field, as well as the dynamic stress field radiated from the
propagating rupture. This general result is consistent with
dynamic models of bent and branched fault systems as well
(Bouchon and Streiff, 1997; Aochi et al., 2000a,b; Aochi et
al., 2002; Harris et al., 2002; Kame et al., 2003; Oglesby et
al., 2003; Duan and Oglesby, 2005). Depending on the relative orientations of the fault segments, it can be very difficult
to obtain through-going ruptures with complex fault geometry. This point is made even more strongly by H. Aochi et
al. (unpublished manuscript, 2005), who performed more
general models of rupture propagating from a strike-slip
fault to a thrust or normal fault. They found that only under
certain rather extreme triaxial prestress fields could rupture
propagate across both fault segments. Both Muller and Aydin (2004) and H. Aochi et al. (unpublished manuscript,
2005) also note that the intersection of noncoplanar fault
segments with different focal mechanisms can induce significant spatial rotation of rake on both segments.
The present work analyzes the ability of rupture to propagate across linked dilational and compressional step-overs,
as well as the slip patterns resulting from earthquakes on
such systems. Key variables include the stress pattern on the
fault segments, the hypocenter location, the dip and strike
of the linking dip-slip fault, and the degree of overlap of the
strike-slip faults. The fault geometry and stress patterns assumed are quite simplified compared with those seen in natural settings (as cited previously), and only begin to cover
the range of parameters available. However, they illustrate
many potentially significant behaviors that may be present
in real fault systems. It is hoped that the results may help to
qualitatively constrain the behavior of such fault systems for
seismic hazard evaluation, as well as illustrate some impor-
D. D. Oglesby
tant general features of fault segment interactions during
seismic rupture.
Method and Model Setup
The basic fault geometry is shown in Figure 1. Two
vertical strike-slip faults (labeled 1 and 3) are connected by
a linking dip-slip fault (labeled 2). This work focuses primarily on linking dip-slip faults with dips of 45⬚ so that one
may directly compare results for compressional and dilational step-overs. However, the models also include stepovers with more realistic dips of 60⬚ for normal faults and
30⬚ for thrust faults in the compressional and dilational stepovers, respectively. For simplicity, the models focus primarily on linking faults whose strikes are 90⬚ from the
strikes of the strike-slip segments, but the models also include more realistic cases in which the linking faults have
strikes 45⬚ from those of the strike-slip segments. The final
geometrical variable is the degree of overlap between the
strike-slip faults. Figure 1 illustrates the case with zero overlap, but the present work also investigates cases in which
the strike-slip faults overlap by as much as 14 km along their
mutual strike. In all cases, the linking dip-slip fault terminates 500 m (1 element) away from the planes of the strikeslip faults. Thus, the strike-slip faults are not offset by slip
on the linking dip-slip fault. This configuration is motivated
by computational necessities, but given that the details of
fault intersections at depth (especially to 500-m resolution)
are not well constrained, it is not inconsistent with natural
fault systems. The details of the fault geometry, material
properties, and numerical mesh are summarized in Table 1.
Note that the step-over width of 10 km is constant among
all the models. This width ensures that the results are not
complicated too much by direct interactions between the
strike-slip segments (i.e., not mediated by the linking faults).
Potential effects of varying the step-over width are briefly
addressed in the Discussion section.
Much of this work is focused on comparing dilational
and compressional step-overs with identical fault geometry
but with different initial tectonic stress fields. Figure 2 shows
Table 1
Geometrical, Material, Frictional, and Numerical Parameters
Length of Strike-Slip Segments
Depth of Bottom Fault Edges
Width of Step-Over
Linking Fault Dips
Linking Fault Strikes
VP
VS
Density
Static Frictional Coefficient
Sliding Frictional Coefficient
Slip Weakening Parameter
Nucleation Radius
Approximate Element Size
40 km
20 km
10 km
30⬚, 45⬚, 60⬚
45⬚, 90⬚
5477 m/s
3162 m/s
3000 kg/m3
0.7
0.5
0.3 m
6000 m
500 m ⳯ 500 m
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The Dynamics of Strike-Slip Step-Overs with Linking Dip-Slip Faults
Figure 2. Map view cartoon of dilational and
compressional step-overs showing the principle
stresses that lead to slip on the fault system. The
dashed lines indicate the surface projection of the buried down-dip extent of the linking faults. Note that
while the amplitudes of horizontal stresses can be the
same in the two cases, the amplitude of the vertical
stress cannot.
the two cases in cartoon form, with the dilational step-over
shown on top and the compressional step-over on the bottom. For simplicity, most of the current models assume
depth-independent stresses. The strike-slip faults are assumed to be inclined 35⬚ from the maximum compressive
stress. Thus, for the strike-slip segments, the difference in
the prestress field between the dilational and compressional
cases lies only in the sign of the initial applied shear stress.
Constructing comparable initial stress fields for the linking faults in these two cases is more complicated, however,
due to the linking faults’ nonzero dip. Therefore, different
assumptions are used for two different classes of models:
(1) To facilitate comparisons between dilational and compressional cases, I assume the same initial shear and normal
stress magnitudes on the linking faults as on the strike-slip
faults. This assumption implies that only dynamically induced effects (i.e., stress perturbations due to slip) introduce
differences between the dilational and compressional cases.
This assumption is somewhat difficult to justify physically,
but could correspond to a situation in which the linking
faults are essentially passive features whose stress fields are
determined more by slip on the strike-slip segments than by
the overall tectonic loading. (2) To determine how the compressional and dilational cases might differ in nature, I assume a regional stress field that is resolved onto all fault
segments, including the linking dip-slip faults. Unfortunately, this assumption requires very different vertical
stresses in the dilational and compressional cases, and consequently different shear and normal stresses on the linking
faults in the two cases.
To minimize the differences between the dilational and
compressional cases (and thus to facilitate evaluation of the
dynamic differences between them), the vertical stress in
model class (2) above is scaled such that the linking fault
has the same relative fault strength S ⳱ 1.0 as the strikeryield ⳮ rinitial
slip segments, where S ⳱
(Andrews,
rinitial ⳮ rsliding
1976b). Thus, the linking faults in the dilational and compressional cases have the same relative potential for failure.
This assumption results in different stress drops between the
different cases, however. Another possibility for equalizing
stress between the dilational and compressional cases is to
scale the vertical stress so that the linking fault has the same
static stress drop (i.e., in the absence of dynamic effects) as
the rest of the fault segments. This method then produces
linking faults with different values of S in the two cases, and
it was used in a few models as a check of the robustness of
the results using equivalent S. The initial stress values are
summarized in Table 2. It is important to note that the
stresses in these models are defined to facilitate comparisons
between the different faulting cases; they are not designed
necessarily to approximate the real regional stress field of
any particular location on the Earth. Another important point
is that during the rupture process both the shear and normal
stresses vary significantly; thus, the true stress drops on each
segment may be very different from what would be calculated from the initial static stress field alone.
To model spontaneous rupture propagation and slip on
the fault systems, I use the 3D explicit finite-element method
(Whirley and Engelmann, 1993; Oglesby, 1999). For simplicity, the material model is a homogenous half-space so
that one may isolate the dynamic effects of the fault geometry from material heterogeneity. The fault boundary condition is of the “traction at split nodes” type (Andrews,
1976a; Day, 1982; Andrews, 1999), with a Coulomb friction
law
|s| ⱕ lrn ,
(1)
where s is the shear stress on the fault, rn is the normal stress
(positive in compression), and l is the coefficient of friction.
As the fault slips, l decreases from lstatic to lsliding via a slipweakening law (Ida, 1972; Palmer and Rice, 1973; Andrews,
1976a):
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D. D. Oglesby
Table 2
Stress Parameters
r1 (larger horizontal stress)
r3 (smaller horizontal stress)
Stress on Strike-Slip Faults (All Cases)
Normal Stress
Shear Stress
3 ⳯ 107 Pa
1.8 ⳯ 107 Pa
Stress on Linking Normal Fault, Case SM
(DILAdp45sk90stSM)
Normal Stress
Shear Stress
3 ⳯ 107 Pa
1.8 ⳯ 107 Pa
Stress on Linking Thrust Fault, Case SM
(COMPdp45sk90stSM)
Normal Stress
Shear Stress
3 ⳯ 107 Pa
1.8 ⳯ 107 Pa
Stress on Linking Normal Fault, Case TC,
45⬚ Dip, 90⬚ Strike
(DILAdp45sk90stTC)
r2 (vertical stress)
Normal Stress
Shear Stress
1.66 ⳯ 108 Pa
1.05 ⳯ 108 Pa
6.27 ⳯ 107 Pa
Stress on Linking Thrust Fault, Case TC,
45⬚ Dip, 90⬚ Strike
(COMPdp45sk90stTC)
r2 (vertical stress)
Normal Stress
Shear Stress
1.03 ⳯ 107 Pa
3.02 ⳯ 107 Pa
1.81 ⳯ 107 Pa
Stress on Linking Normal Fault, Case TC,
45⬚ Dip, 45⬚ Strike
(DILAdp45sk45stTC)
r2 (vertical stress)
Normal Stress
Shear Stress
7.2 ⳯ 107 Pa
4.54 ⳯ 107 Pa
2.72 ⳯ 107 Pa
Stress on Linking Thrust Fault, Case TC,
45⬚ Dip, 45⬚ Strike
(COMPdp45sk45stTC)
r2 (vertical stress)
Normal Stress
Shear Stress
1.43 ⳯ 107 Pa
3.44 ⳯ 107 Pa
2.06 ⳯ 107 Pa
Stress on Linking Normal Fault, Case TC,
45⬚ Dip, 45⬚ Strike, Same Stress Drop
r2 (vertical stress)
Normal Stress
Shear Stress
6.59 ⳯ 107 Pa
4.22 ⳯ 107 Pa
2.41 ⳯ 107 Pa
Stress on Linking Thrust Fault, Case TC,
45⬚ Dip, 45⬚ Strike, Same Stress Drop
r2 (vertical stress)
Normal Stress
Shear Stress
1.48 ⳯ 107 Pa
3.47 ⳯ 107 Pa
2.04 ⳯ 107 Pa
冢d 冣 (s ⱕ d )
l ⳱ lstatic ⳮ (lstatic ⳮ lsliding)
s
0
0
l ⳱ lsliding
5.57 ⳯ 107 Pa
1.74 ⳯ 107 Pa
Regional Stress Field (All Cases)
(2)
(s ⬎ d0)
where s is the slip at a point, and d0 is the slip-weakening
parameter. The values of the frictional parameters are summarized in Table 1. This frictional boundary condition allows slip in any shear direction on all fault segments, so
spatial and temporal rake rotation is accommodated. Since
equation (1) explicitly includes the dependence of the frictional stress on (time-dependent) normal stress, variations in
normal stress affect both the prerupture strength of the material and the sliding frictional level.
Ruptures are nucleated by artificially forcing failure in
a circular region on one of the faults at a rupture velocity of
3 km/sec, until spontaneous rupture propagation is achieved.
Prior experiments indicate that the results are relatively insensitive to the details of the nucleation process. Most ruptures are nucleated on the left strike-slip segment (segment
1), at a depth of 10 km and a distance of 5 km along strike
from the left edge of the segment. This location is depicted
by the left star in Figure 1. In some cases, rupture is nucleated on the linking fault (segment 2), at a depth of 10 km
and halfway along strike, or on the right strike-slip segment
(segment 3), at a depth of 10 km and a distance 5 km along
strike from the right edge of the segment. These locations
are marked by the central and right star, respectively, in Figure 1. It should be noted that with a nucleation radius of
6 km, the zone of imposed rupture propagation persists to
the edge of the 10-km-wide dip-slip fault segment for models that nucleate on that segment. However, experiments
with models with dip-slip fault widths of 15 km display results essentially identical to those shown here, indicating that
the size of the nucleation zone is not an important factor in
the current results.
The order in which the results will be presented is the
following: The initial fault geometry to be modeled is that
of 45⬚ dipping normal and thrust faults (with strikes 90⬚ from
the strikes of the strike-slip segments) in the dilational and
compressional step-overs, respectively. The first results are
for models in which the same shear and normal stress amplitudes are used on all fault segments. Next, using the same
geometry, I explore the effect of using a regional stress field
resolved onto the various fault segments. I then investigate
the effect of changing the dip of the linking fault, the overlap
of the strike-slip segments, and the strike of linking fault. I
will use the following naming convention for the models:
WWWWdpXXskYYstZZ. WWWW represents the sense of
slip on the offset fault system and takes the values DILA for
The Dynamics of Strike-Slip Step-Overs with Linking Dip-Slip Faults
a dilational system or COMP for a compressional system
(corresponding to right-lateral and left-lateral slip on the
fault system, respectively). XX denotes linking fault dip, and
can take the values 45⬚, 30⬚, or 60⬚. YY denotes linking fault
strike, and can take the values 45⬚ or 90⬚. ZZ denotes the
assumption on stress, which is either SM (same shear and
normal stresses on all segments) or TC (tectonic stress resolved on all segments). Other attributes of the models, such
as the nucleation location and the degree of overlap of the
strike-slip fault segments, will be noted separately.
Results
Presence versus Absence of Linking Fault
In all cases, in the absence of a linking fault, rupture
does not propagate across the dilational or compressional
step-over, and thus slip is confined to the initially nucleating
strike-slip segment. This result is consistent with 2D and 3D
dynamic models of parallel strike-slip fault segments without linking faults (Harris et al., 1991; Harris and Day, 1993;
Kase and Kuge, 1998; Harris and Day, 1999; Kase and
Kuge, 2001). As will be noted later, rupture can propagate
across the step-over under certain circumstances in which a
linking fault is present. Thus, a primary result of this study
is that the presence of a linking thrust or normal fault can
significantly increase the probability of through-going rupture at a fault step-over, and can increase the maximum
event size.
Same Shear and Normal Stress on All Segments
The simplest case analyzed is that of DILAdp45sk90stSM and COMPdp45sk90stSM. As noted above, this
simple case is chosen because there is no difference in the
static stress amplitudes between the dilational and compressive cases. Thus, differences between these two cases can
be attributed to the effects of stress interactions between the
fault segments during the rupture and slip process. Figure 3a
shows that when rupture nucleates on segment 1 of model
DILAdp45sk90stSM, it propagates across the step-over region and causes slip on all segments. Note that even though
the initial static stresses are the same amplitude on all segments, the linking normal fault has significantly more slip
than the strike-slip faults. This effect is due to the change in
normal stress caused by slip on the strike-slip segments, as
predicted earlier: Slip on the strike-slip segments tends to
reduce the clamping normal stress on the linking fault. The
complex stress interaction between the strike-slip and dipslip fault segments is illustrated in Figure 4. At 6.5 sec into
the simulation, the rupture front is propagating on segment
1 toward the linking normal segment. It reaches the edge of
segment 1 at 9.4 sec, at which point one can see that stress
waves radiated by slip on segment 1 have increased the shear
stress and decreased the normal stress near the surface on
the linking normal segment, bringing the segment closer to
failure. By 11.9 sec, the rupture front is propagating over
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the linking normal segment, and by 14.1 sec, the rupture
front has propagated to strike-slip segment 3. At 34.9 sec,
the entire fault system has slipped, leaving greatly reduced
normal stress over most of the linking normal fault. Thus,
we see that stress waves radiated by the strike-slip segments
weaken the linking normal fault, aiding the propagation of
rupture across the step-over, and amplifying slip. Figure 4
also shows the competing effects of the strike-slip fault segments and the normal fault’s own nonvertical geometry on
its stress field. Between 9.4 sec and 11.9 sec, the decreased
normal stress near the surface on the linking fault (due to
slip on segment 1) is replaced by a zone of increased normal
stress. This small zone of increased normal stress near the
surface is consistent with analog and numerical models of
dip-slip faults (Brune, 1996; Nielsen, 1998; Oglesby et al.,
1998; Shi et al., 1998; Bonafede and Neri, 2000; Oglesby
et al., 2000a,b), which predict that near the surface, slip on
a normal fault will result in a compressional normal stress
increment on the fault owing to a stress interaction with the
Earth’s traction-free surface. However, this effect is confined
only to the top few kilometers; over the rest of the normal
fault, the normal stress is significantly decreased by slip on
the strike-slip segments. It should be noted that the downdip directed “stripes” of slightly higher and slightly lower
slip on the linking fault in Figure 3a and other figures are
numerical noise, which appears when this segment ceases
slipping, near the end of the simulations. As can be seen
from the slip snapshots above, this noise does not affect the
process of rupture propagation, so it has little effect on the
results of this study.
The effect of changing the sign of the shear prestress
on this fault system is dramatic. As shown in Figure 3b, in
the compressional (left-lateral slipping) case COMPdp45sk90stSM, slip is confined to the nucleating strike-slip
segment 1; it does not propagate to the linking thrust fault
or the second strike-slip segment. The reason for rupture
dying out at this point is seen in Figure 5, which shows
snapshots of stress on the compressional step-over. At
6.5 sec, the compressional case is essentially identical to the
dilational case because the nonplanar nature of this fault system has not yet manifested itself. However, at 9.4 sec, the
stress waves radiated by segment 1 have caused a significant
increase in the normal stress near the surface on the linking
thrust fault. As the rupture covers all of segment 1 (14.1 sec
to 34.9 sec), this zone of increased normal stress on the linking thrust fault grows, clamping it down and preventing it
from slipping. Without slip on the linking thrust fault, rupture cannot propagate to the other strike-slip segment. Thus,
a change in the sign of the shear stress is enough to completely change the qualitative character of the rupture and
slip process, resulting in a much larger earthquake in the
dilational case.
Another effect of the fault geometry of this fault system
is a significant rotation of rake away from the direction that
one would infer from the prestress direction alone. Figure 6
shows the increment in rake away from the prestress direc-
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D. D. Oglesby
Figure 3. (a) Final slip distribution on dilational fault system for case DILAdp45sk90stSM. In this case, the rupture propagates over the entire fault system. (b) Final slip
distribution on compressional fault system for case COMPdp45sk90stSM. In this case, the
rupture is confined to the nucleating fault segment (strike-slip segment 1).
tion in the dilational case DILAdp45sk90stSM. In this
model, the prestress direction corresponds to a rake of 180⬚
on strike-slip segments 1 and 2, and 270⬚ degrees on the
linking normal fault segment 3. We see a rake rotation of up
to 23⬚ and 29⬚ in the dip-slip direction on strike-slip segments 1 and 2, respectively, near where they intersect the
linking normal fault. In contrast, models of equivalent strikeslip faults in isolation (i.e., with no linking fault or secondary
strike-slip fault) show that the strike-slip segments exhibit
peak rake rotation of less than ⬃10⬚.
To determine the effect of hypocenter location on the
dynamics of this simple system, I experimented with hypocenters located on strike-slip segment 3 and linking fault 2.
For brevity I do not present the results for the case with
nucleation on fault 3; they are quite similar (but not identical) to those with nucleation on segment 1, with throughgoing rupture in the dilational case and rupture restricted to
the nucleating segment (3) in the compressional case. However, the case of earthquake nucleation on the linking fault
(2) produced significantly different results. Figure 7 shows
the slip on the fault system in both the dilational and compressional cases. The slip in the dilational case is qualitatively similar to the model with nucleation on segment 1.
The slip in the compressional case, however, is completely
different from the model with nucleation on segment 1: with
nucleation on the linking thrust fault, rupture is able to propagate to both strike-slip segments, leading to slip on the entire fault system. In this case, rupture is able to propagate
over the entire fault system because rupture proceeds initially on the linking thrust fault without any stress increment
from the strike-slip segments. In the first seconds of the
earthquake, there is no clamping effect on the thrust fault,
so it is able to slip over its whole area. After rupture propagates to the strike-slip faults, however, there is a strong
increase in normal stress over most of the linking thrust fault,
as shown in Figure 8. The thrust fault experiences a positive
increment of normal and shear stress owing to slip on the
strike-slip segments, as well as a negative normal stress increment near the surface owing to its own nonvertical orientation with respect to the free surface. It is important to
note that even though both the dilational and compressional
fault systems slipped over their entire areas in the case of
nucleation on the linking dip-slip fault, the slip patterns in
these two cases are not equivalent: the dilational case has
significantly more slip, particularly on the linking fault, than
the compressional case (Table 3).
Tectonic Regional Stress Resolved on All Segments
While the preceding results provide insight into how
dynamic changes in normal and shear stress can affect the
propagation of rupture and slip on a simple step-over system,
the assigned prestress field in those results may not reflect
real stress fields seen in natural faults. It has become common in studies of nonplanar fault systems to assign static
prestresses by assuming that they arise from a uniform triaxial compressive stress field. It is this assumption that is
used in models DILAdp45sk90stTC and COMPdp45sk90stTC. As noted by H. Aochi et al. (unpublished manuscript, 2005), rupture propagation between faults with very
different orientation and slip direction often requires rather
extreme assumptions on the stress field. In the current tectonic stress models, the vertical stress must be quite large to
produce normal linking faults with the same S value as the
strike-slip faults in the dilational case, while the vertical
stress must be correspondingly quite small in the compressional case (Table 2). The present work does not address the
question of how such stresses may arise in nature; I merely
The Dynamics of Strike-Slip Step-Overs with Linking Dip-Slip Faults
Figure 4. Snapshots of stress increments from the initial stress field for dilational
fault system case DILAdp45sk90stSM. Right-lateral slip on the strike-slip segments
greatly reduces the clamping normal stress on the linking normal fault, allowing rupture
propagation over the entire fault system. (a) t ⳱ 6.5 sec. (b) t ⳱ 9.4 sec. (c) t ⳱ 11.9
sec. (d) t ⳱ 14.1 sec. (e) t ⳱ 34.9 sec.
(continued)
1611
1612
D. D. Oglesby
Figure 4. Continued.
note that the relative effects seen in the current results may
add to other systematic differences between dilational and
compressional step-overs that exist in the real world; only
by assuming relatively similar stress and fault geometry between the two cases may one isolate the effects of slip direction on the system.
Because DILAdp45sk90stTC and COMPdp45sk90stTC
have very different vertical stresses, they also have quite
different static stress drops on their linking faults, and also
differ from cases DILAdp45sk90stSM and COMPdp45sk90stSM described above (see Table 2). Figure 9 shows the
slip distribution for the dilational case DILAdp45sk90stTC;
note the very high slip on the linking normal fault due to its
much higher static stress drop. As in the cases with the same
shear and normal stresses over all segments, rupture in the
dilational case DILAdp45sk90stTC propagates across the
step-over to cause slip on all fault segments. Similarly, rupture in the compressive case COMPdp45sk90stSM (not
shown) does not propagate beyond the nucleating segment
1, leaving a slip pattern identical to that of the case
COMPdp45sk90stSM (Fig. 3b). The cause of rupture dying
out on COMPdp45sk90stTC is the same as noted before:
slip on segment 1 causes a strongly positive normal stress
increment on the linking fault (segment 2), preventing it
from failing. The final stress in the dilational case DILA-
dp45sk90stTC (Fig. 10) shows that in this case, as in DILAdp45sk90stSM, slip on the strike-slip fault decreases normal
stress on the linking normal fault, facilitating rupture and
slip. Figure 10 also displays an effect that is not present in
DILAdp45sk90stSM or COMPdp45sk90stSM: the effect
that slip on the linking normal fault has on the stress on the
strike-slip segments. In the tectonic regional stress field, the
applied tectonic (static) shear stress on the linking fault in
both the dilational and compressional cases is not purely dipslip directed; the normal fault in DILAdp45sk90stTC is
loaded in the left-lateral sense, and the thrust fault in
COMPdp45sk90stTC is loaded in the right-lateral sense. As
seen in Figure 10, left-lateral slip on normal fault segment
2 causes a decrease in the normal stress on both strike-slip
faults. This effect further amplifies slip on the strike-slip
segments. This effect, coupled with an increase in shear
stress caused by the slip on the normal fault, leads to a large
contrast in the amount of slip on strike-slip segment 1 between the dilational and compressional cases.
The effect of the strike-slip component of prestress on
the linking fault is also seen in models where nucleation is
on the linking fault. Figure 11a displays the slip on model
DILAdp45sk90stTC with nucleation on the normal fault; its
slip pattern is very similar to the case in which nucleation is
on strike-slip segment 1 (Fig. 9). However, as shown in Figure 11b, the compressional case COMPdp45sk90stTC (with
nucleation on the thrust fault) does not result in rupture propagation to the strike-slip segments at all. The reason for this
contrasting behavior with COMPdp45sk90stSM (with nucleation on segment 2) is shown in Figure 12. Right-lateral
slip on the linking thrust fault causes a large increase in
normal stress on the neighboring strike-slip segments. These
stress buildups serve as barriers to further rupture. Thus, we
see that the tectonic stress field introduces a two-way interaction between the linking faults and the strike-slip faults:
there is a positive feedback in the normal stress for the dilational case, leading to amplified slip on all segments, and
a negative feedback in the compressional case, which tends
to hinder fault rupture and slip on all segments in the system.
Effect of Strike-Slip Fault Overlap
To investigate how the degree of overlap between
strike-slip fault segments affects the ability of rupture to
propagate across the step-over, we use the same stress field
as in cases DILAdp45sk90stTC and COMPdp45sk90stTC,
and extend the strike-slip segments along strike beyond the
intersection with the linking dip-slip fault. For brevity, I do
not include figures showing these results, as they qualitatively look very similar to the results for DILAdp45sk90stTC and COMPdp45sk90stTC with nucleation on
segment 1. For all fault overlaps, in the compressional cases
the rupture dies out on the nucleating segment, whether it is
segment 1, 2, or 3. I find that in the dilational case with
nucleation on segment 1, rupture can propagate across the
step-over for overlaps of up to 6 km (i.e., each strike-slip
The Dynamics of Strike-Slip Step-Overs with Linking Dip-Slip Faults
Figure 5. Snapshots of stress increments from the initial stress field for dilational fault
system case COMPdp45sk90stSM. Left-lateral slip on the strike-slip segments greatly increases the clamping normal stress on the linking normal fault, prohibiting rupture propagation
to segments 2 and 3. (a) t ⳱ 6.5 sec. (b) t ⳱ 9.4 sec. (c) t ⳱ 14.1 sec. (d) t ⳱ 34.9 sec.
1613
1614
D. D. Oglesby
ate rupture on the linking normal segment, which has already
had its normal stress decreased by slip on the nucleating
segment. However, for longer overlaps, these stopping
phases decay too much as they propagate, and do not cause
renucleation on the linking fault. In the dilational case, nucleation on the linking fault (segment 2) results in rupture
propagating over the entire fault system for all the strikeslip fault overlaps.
More Realistic Linking Fault Dip
Figure 6.
Change in rake with respect to the initial
rake of the static prestress field on the dilational fault
system DILAdp45sk90stSM (180⬚ for the strike-slip
fault segments, 270⬚ for the linking normal fault).
Note that slip on the linking normal fault induces a
strong dip-slip component of motion on the nearby
edges of the strike-slip segments.
segment extends 3 km beyond the linking normal fault).
However, for overlaps greater than this value, rupture does
not propagate to the linking fault or to the neighboring
strike-slip segment. This result indicates that for the small
overlaps, the stress waves radiated as the rupture terminates
on segment 1 (stopping phases) are strong enough to nucle-
Normal and thrust faults typically have different ranges
of dip angles: normal faults usually have dips steeper than
45⬚, while thrust faults usually have dips shallower than 45⬚.
In our step-over models, we would expect more steeply dipping normal faults and more shallowly dipping thrust faults
both to increase each fault’s tendency to rupture. In the former case, a steeper dip should result in a greater decrease in
normal stress owing to slip on the strike-slip faults, and in
the latter case, a shallower dip should minimize the corresponding increase in normal stress. The slip patterns for
cases DILAdp60sk90stTC and COMPdp30sk90stTC are
shown in Figure 13. The slip for case DILAdp60sk90stTC
is qualitatively similar to that of case DILAdp45sk90stTC.
The reason there is less slip on the linking normal fault in
DILAdp60sk90stTC is that linking fault is required to have
an S value of 1.0; with the new fault geometry, such a stress
field results in a smaller static stress drop on this segment.
The slip pattern for case COMPdp30sk90stTC is significantly different from that of COMPdp45sk90stTC. In particular, slip in COMPdp30sk90stTC propagates from the nu-
Figure 7. (a) Final slip distribution on dilational fault system for case DILAdp45sk90stSM with nucleation on the linking normal fault (segment 2). As in the case
of nucleation on strike-slip segment 1, the rupture propagates over the entire fault
system. (b) Final slip distribution on compressional fault system for case
COMPdp45sk90stSM with nucleation on the linking thrust fault (segment 2). Unlike
the case with nucleation on strike-slip segment 1, rupture propagates over the entire
fault system.
1615
The Dynamics of Strike-Slip Step-Overs with Linking Dip-Slip Faults
Figure 8.
Final stress increment from initial stress
field for compressional fault system case COMPdp45sk90stSM with nucleation on the linking thrust
fault (segment 2). Slip on the linking thrust fault initially takes place without any stress increment from
the strike-slip faults, allowing rupture to propagate
over the entire fault system. After rupture propagates
to the strike-slip segments, a strong normal stress increase is induced on the thrust fault, inhibiting slip.
cleating strike-slip segment (segment 1) to the linking thrust
fault (segment 2). However, the strike-slip motion of the
linking thrust fault causes enough of a positive increment in
normal stress on strike-slip segment 3 to lock that segment
up and extinguish rupture. Thus, changing the dip angle to
more realistic values increases the ability of rupture to propagate in the compressive case, but does not eliminate the
difference between the dilational and compressional cases.
45⬚-Striking Linking Faults
Unlike the previous simplified models, linking faults in
nature typically have strikes significantly less than 90⬚ from
their nearby strike-slip faults (e.g., Courboulex et al., 1999;
Zampier et al., 2003; Brankman and Aydin, 2004; Wakabayashi et al., 2004). To investigate this potentially more
realistic fault geometry, I modeled dilational and compressional step-overs where the linking faults have dips of 45⬚
and strikes of 45⬚ (rather than 90⬚), greater than their corresponding strike-slip faults. The slip patterns associated
with these models (DILAdp45sk45stTC and COMPdp4545sk45stTC) are shown in Figure 14. In both cases, rupture
is able to propagate across the step-over. The differences
between the dilational and compressive cases are the smallest of any of the faulting scenarios. One reason for this similarity is that for 45⬚-striking linking faults, the static stress
field favors left-lateral slip on the linking fault in both the
dilational and compressional cases. Thus, slip on the strikeslip faults would tend to reduce the strike-slip component of
shear stress on the linking normal fault in a dilational stepover, while such slip on the strike-slip segments increases
the shear stress on the linking thrust fault in a compressional
step-over. However, even in this more favorable geometry
and stress scenario, the dilational step-over still has somewhat higher slip than the compressional step-over because
of the normal stress increment discussed earlier (Table 3).
The static stress drop (as predicted by the prestress field in
the absence of dynamic effects) on the linking fault is larger
for the dilational case than for the compressional case, and
one might argue that this difference in static stress drop
might be responsible for some of the difference in the absolute amount of slip on the two fault systems. To explore
this issue, I produced models of this fault geometry for
which the predicted static stress drop (prior to dynamic effects) on the linking faults was equal to 30 bars for both
systems (matching the stress drop on the strike-slip segments). This assumption leads to an S value of 1.8 on the
dilational system and 1.3 on the compressional system.
Thus, in isolation, the thrust fault and normal fault should
have equal slips, but the thrust fault should be more likely
to fail. However, the results for this model indicate that rupture propagates across the entire dilational system, but is
unable to propagate to the linking thrust fault in the compressional case. Taken together with the earlier results for
this fault geometry, these results indicate that regardless of
the strike and dip angle, the effects of the normal stress increment caused by the strike-slip faults are still significant.
Discussion
The results of current models are summarized in Table
3, with the exception of the models with nonzero strike-slip
fault overlap, which are described in the Results section.
There are two important general results of the present work.
First, it is much easier for rupture to propagate across stepovers between strike-slip faults if there is a linking dip-slip
fault in the step-over region. This result is consistent with
the work of Magistrale and Day (1999) on linked thrust
faults, even though the static and dynamic stress fields in the
present work are quite distinct from this earlier work. The
second general result is that it is much easier for rupture to
propagate across a dilational step-over with a linking normal
fault than across a compressional step-over with a linking
thrust fault. This result is consistent with the work of a num-
1616
D. D. Oglesby
Table 3
Summary of Results
Model
Nature of
Step-Over
Linking Fault
Dip, Strike
DILAdp45sk90stSM
dilational
COMPdp45sk90stSM
Total Seismic
Moment (N m)
and Magnitude
Stress Assumption
Nucleation
Segment
Rupture
Propagation
Avg. Slip
(m)
45⬚, 90⬚
same shear/normal
stress on all segments
strike-slip
segment 1
through-going
Seg. 1: 2.2
Seg. 2: 3.0
Seg. 3: 2.3
1.3 ⳯ 1020
7.4
compressional
45⬚, 90⬚
same shear/normal
stress on all segments
strike-slip
segment 1
confined to
segment 1
Seg. 1: 1.8
Seg. 2: 0
Seg. 3: 0
4.3 ⳯ 1019
7.1
DILAdp45sk90stSM
dilational
45⬚, 90⬚
same shear/normal
stress on all segments
normal
segment 2
through-going
Seg. 1: 2.4
Seg. 2: 3.0
Seg. 3: 2.2
1.3 ⳯ 1020
7.4
COMPdp45sk90stSM
compressional
45⬚, 90⬚
same shear/normal
stress on all segments
thrust
segment 2
through-going
Seg. 1: 2.0
Seg. 2: 1.4
Seg. 3: 2.0
1.1 ⳯ 1020
7.4
DILAdp45sk90stTC
dilational
45⬚, 90⬚
tectonic stress resolved
on all segments
strike-slip
segment 1
through-going
Seg. 1: 2.8
Seg. 2: 6.4
Seg. 3: 3.1
1.9 ⳯ 1020
7.5
COMPdp45sk90stTC
compressional
45⬚, 90⬚
tectonic stress resolved
on all segments
strike-slip
segment 1
confined to
segment 1
Seg. 1: 1.8
Seg. 2: 0
Seg. 3: 0
4.3 ⳯ 1019
7.1
DILAdp45sk90stTC
dilational
45⬚, 90⬚
tectonic stress resolved
on all segments
normal
segment 2
through-going
Seg. 1: 3.1
Seg. 2: 6.5
Seg. 3: 3.0
2.0 ⳯ 1020
7.5
COMPdp45sk90stTC
compressional
45⬚, 90⬚
tectonic stress resolved
on all segments
thrust
segment 2
confined to
segment 2
Seg. 1: 0
Seg. 2: 0.9
Seg. 3: 0
6.9 ⳯ 1018
6.6
DILAdp60sk90stTC
dilational
60⬚, 90⬚
tectonic stress resolved
on all segments
strike-slip
segment 1
through-going
Seg. 1: 2.3
Seg. 2: 3.8
Seg. 3: 2.4
1.4 ⳯ 1020
7.4
COMPdp30sk90stTC
compressional
30⬚, 90⬚
tectonic stress resolved
on all segments
strike-slip
segment 1
confined to
segments
1 and 2
Seg. 1: 1.5
Seg. 2: 0.8
Seg. 3: 0
4.6 ⳯ 1019
7.1
DILAdp45sk45stTC
dilational
45⬚, 45⬚
tectonic stress resolved
on all segments
strike-slip
segment 1
through-going
Seg. 1: 1.9
Seg. 2: 2.2
Seg. 3: 2.1
1.3 ⳯ 1020
7.4
COMPdp45sk45stTC
compressional
45⬚, 45⬚
tectonic stress resolved
on all segments
strike-slip
segment 1
through-going
Seg. 1: 1.7
Seg. 2: 1.6
Seg. 3: 1.8
1.1 ⳯ 1020
7.4
ber of researchers on fault step-overs with no linking faults
(Harries et al., 1991; Harris and Day, 1993; Kase and Kuge,
1998; Kase and Kuge, 2001). These results appear to be
robust with respect to linking fault strike and dip, as well as
to assumptions about the stress field on the fault segments.
However, it is important to note that the models in this article
are for a narrow range of fault geometry and stress pattern.
The models are not designed to represent exactly what fault
step-overs look like in nature, where they commonly have
multiple linking faults, variations in strike and dip, and many
other complicated geometrical features (e.g., Courboulex et
al., 1999; Geist and Zoback, 1999; Zoback et al., 1999; Yule
and Sieh 2003; Zampier et al., 2003; Brankman and Aydin,
2004; Lin et al., 2004). Rather, the current study is designed
to isolate some physical processes that may be important in
the dynamics of fault step-overs.
One issue that is not explored in detail in the current
work is the effect of the step-over width. As noted by many
researchers (e.g., Harris et al., 1991; Harris and Day, 1993;
Yamashita and Umeda, 1994; Kase and Kuge, 1998; Harris
and Day, 1999; Kase and Kuge, 2001), large step-over
widths make it much more difficult for rupture to propagate
across a step-over with no linking fault. The same is true for
step-overs that are connected by a linking fault with zero
static stress drop (Magistrale and Day, 1999). In the current
work, however, experiments with wider (15-km) step-overs
show results essentially identical to the 10-km stepovers. I
expect that in general the results will be relatively insensitive
1617
The Dynamics of Strike-Slip Step-Overs with Linking Dip-Slip Faults
Figure 9.
Final slip distribution on dilational fault
system for case DILAdp45sk90stTC. In this case, the
rupture propagates over the entire fault system and
produces high slip on the linking normal fault owing
to its high stress drop. High slip on the linking normal
fault induces high slip on the neighboring strike-slip
segments.
to the step-over width, because the linking fault has a nonzero static stress drop and can support propagating rupture
over large distances. A wider linking fault will experience
less of a normal and shear stress increment from slip on the
nearby strike-slip fault; however, the effect on the stress field
at the edges of the linking fault should be relatively unaffected by its width. Since it is the stress field at the edges of
the linking fault that determine the ability of rupture to propagate across the step-over, I expect that the ability of rupture
to propagate across wider or narrower step-overs will be
similar to those presented here, as long as the step-over is
not narrow enough to allow a direct jump between the strikeslip segments without a linking fault. However, for ruptures
that propagate across the step-overs, the differences in linking-fault slip between the dilational and compressional cases
(e.g., Fig. 7) should decrease with increasing linking-fault
width. The reason is that as the width of the step-over grows,
a larger proportion of the linking fault will be relatively unaffected by the normal stress increment from the strike-slip
segments, and will experience slip that is determined predominantly by the static stress field.
Perhaps importantly, the present results do not include
the effects of pore-fluid migration. Sibson (1985, 1986) has
argued that many strike-slip earthquakes are observed to terminate at dilational step-overs as well as at compressional
step-overs. Upon initial reading, this result would appear to
contradict the results of the current work’s elastodynamic
analysis. Sibson (1985, 1986) explains this observation by
arguing that when rupture hits a dilational step-over, the sudden decrease in normal stress causes small mode-I cracks to
open up in the step-over region. This increase in crack vol-
Figure 10.
Final stress increment from initial
stress field for dilational fault system case DILAdp45sk90stTC. Right-lateral slip on the strike-slip
segments greatly reduces the clamping normal stress
on the linking normal fault, allowing rupture propagation over the entire fault system. The left-lateral
component of slip on the linking normal fault also
greatly reduces the clamping normal stress on the
nearby strike-slip segments, amplifying slip on these
segments.
ume would lead to a suction force that would inhibit the
further propagation of rupture across the step-over, and
could even reduce the ability of rupture to nucleate on secondary faults in the step-over region. Harris and Day (1993)
used a nonzero Skempton coefficient as a proxy for such an
effect in their dynamic models of fault step-overs with no
linking faults. Their analysis confirmed that the coseismic
decrease in pore-fluid pressure in the dilational step-over
region could greatly reduce the probability of through-going
rupture. Modeling this sort of effect is beyond the scope of
the current work. However, reasonable assumptions about
the Skempton coefficient (i.e., being less than unity) would
imply that a dilational step-over should still produce a net
reduction in the normal stress in the step-over region, which
should still relatively favor rupture propagation across a dilational step-over compared to the case of a compressional
step-over, or to cases with no linking dip-slip fault.
1618
D. D. Oglesby
Figure 11. (a) Final slip distribution on dilational fault system for case DILAdp45sk90stTC with nucleation on the linking normal fault (segment 2). As in the case
of nucleation on strike-slip segment 1, the rupture propagates over the entire fault
system. (b) Final slip distribution on compressional fault system for case
COMPdp45sk90stTC with nucleation on the linking normal fault (segment 2). Rupture
only propagates on the linking thrust fault.
There are, however, many reasons why rupture might
terminate at dilational step-overs even though they are relatively more favorable for rupture than compressional stepovers. First, step-overs in nature often have a significant
overlap between the strike-slip fault segments (e.g., Brankman and Aydin, 2004; Wakabayashi et al., 2004). As the
current results show, such an overlap greatly inhibits the
propagation of rupture across the step-over. Also, the current
results assume that the linking dip-slip faults come very
close (within 500 m) to the strike-slip segments. Experiments with larger separation (along the strike of the linking
fault) between the strike-slip and linking faults indicate that
the ability of rupture to propagate through the step-over decreases significantly if there is a large gap between the linking and strike-slip segments. In addition, a normal fault in a
dilational step-over may have a very low average stress
level, which could lead to a very low stress drop on this
segment. Such a low stress drop may not release enough
energy to nucleate slip on the secondary strike-slip segment.
Finally, I note that while there may be many examples of
rupture terminating at dilational stepovers, there are also
many examples (e.g., Wesnousky, 1988) of rupture propagating through dilational step-overs.
In addition to arguing that dilational step-overs may be
easier for rupture to propagate through than compressional
stepovers, the current results also indicate that there are fault
geometries for which rupture can propagate to a linking
thrust fault and across a compressional step-over. A shallow
fault dip or a smaller change in strike between the strikeslip and thrust fault segments both bring the linking thrust
fault closer to an optimal orientation for failure and slip; in
both cases, the compressive normal stress increment is min-
imized while the shear stress increment is maximized. However, it must be pointed out that even though rupture can
propagate across the compressional step-over in some cases,
the slip on the fault system (especially on the linking fault)
is less than on an equivalent dilational step-over owing to
the stress interaction between the fault segments. The fact
that through-propagating rupture is so strongly suppressed
in the models with orthogonal thrust and strike-slip faults
may help to explain why such a fault geometry is rare in
nature: rather rapidly such an orthogonal fault will lock up,
leading to either the creation of a new, more favorably oriented fault, or simply the production of more anelastic behavior (such as folding) in the step-over region.
Another faulting configuration that aids in the propagation of rupture across compressional stepovers is the case
of nucleation on the linking thrust fault. In such a case, the
linking thrust fault slips before it experiences the compressional stress increment from the strike-slip fault segments.
As long as the strike-slip component of slip on the linking
thrust fault does not clamp the adjacent strike-slip segments,
a centrally nucleating rupture can propagate across a stepover that is impossible to cross for a rupture that nucleates
on one of the strike-slip segments. This observation may
help to explain why compressional step-overs may be both
barriers to rupture and nucleation points for large events, as
argued by Segall and Pollard (1980). The importance of the
hypocenter location and rupture order is a dynamic effect
that is not captured in many static faulting models, such as
that by Muller and Aydin (2004); this effect could be quite
important in evaluating the probability of large events in a
step-over region.
In the current work, stress interaction between the link-
1619
The Dynamics of Strike-Slip Step-Overs with Linking Dip-Slip Faults
Figure 12. Final stress increment from the initial
stress field for compressional fault system case
COMPdp45sk90stTC with nucleation on the linking
thrust fault (segment 2). The right-lateral strike-slip
component of slip on the linking thrust fault raises the
clamping normal stress on the adjacent strike-slip segments, preventing rupture propagation beyond the
linking thrust fault.
rake rotation has also been seen in the quasi-static models
of Muller and Aydin (2004) and the dynamic models of
Guatteri and Spudich (1998), Oglesby and Day (2001) and
H. Aochi et al. (unpublished manuscript, 2005). The results
argue that constraining slip to take place only in the direction
of the static prestress field may be inappropriate for fault
systems with complex geometry and substantial fault–fault
stress interactions.
A final point concerning the current results is the nature
of the assumed stress field. The current stress assumptions
lead to faults with an S value of 1.0 over most of the system.
Experiments with lower S values (not shown) indicate that
a lower S facilitates through-going rupture propagation in
both the compressional and dilational cases. A more complicated issue is heterogeneity in the stress field. While a
regional stress field (which is used in the majority of the
current models) is a common assumption for dynamic models, it may not be the most appropriate assumption for fault
systems with complex geometry. Multicycle dynamic models of a strike-slip fault with a change in strike (Duan and
Oglesby, 2005) indicate that over multiple earthquakes,
stress buildups near geometrical discontinuities take on a
crucial role in rupture and slip evolution. The postevent
stress distribution in the current models (e.g., Fig. 10) is
significantly more heterogeneous than the initial regional
stress field. Unless this incremental stress field is largely
relaxed before the next earthquake, the behavior of the fault
system may be qualitatively different in the long term from
the current models. In particular, the lowered normal stress
in the dilational step-over could lead to the normal fault being a preferred location for nucleation of future large events.
Such long-term models of geometrically complex fault systems are the subject of future work.
Conclusions
ing dip-slip faults and the nearby strike-slip faults lead to
normal faults having significantly higher slip than equivalent
thrust faults. This result is in marked contrast to the behavior
of dip-slip faults in isolation (Brune, 1996; Oglesby et al.,
1998; Shi et al., 1998; Oglesby et al., 2000a,b), for which
the stress interaction with the free surface can produce significantly higher slip on the thrust fault than on an otherwise
equivalent normal fault. The current results serve to emphasize the crucial importance that fault–fault interactions may
have on the dynamics of the rupture process. In this case,
the stress interaction with neighboring faults dominates the
effect of the free surface. The positive feedback between the
strike-slip faults and the linking normal fault in the dilational
step-over leads to amplified slip on all the fault segments,
while the opposite is true for the compressional step-over.
A second effect that emphasizes the two-way interaction between the fault segments is the rotation in rake seen when
rupture propagates across the entire fault system. Analogous
Dynamic models of strike-slip faults with step-overs
and linking dip-slip faults indicate that the presence of a
linking fault can greatly increase the ability of earthquake
rupture to propagate across the step-over and lead to a larger
event. This effect is even stronger for dilational step-overs
than compressional step-overs owing to the sign of the normal stress increment on the linking fault: slip on the strikeslip segments tends to unlock a linking normal fault in a
dilational step-over, while it tends to lock up a linking thrust
fault in a compressional step-over. The current results help
to explain why fault step-overs may serve as both barriers
to rupture propagation and preferred locations for large event
nucleation. Although the current models are quite simplified,
the fundamental results above are robust with respect to assumptions about stress field and fault geometry. The results
may have important implications for evaluating the probability of large earthquake events near step-overs in strikeslip faults, such as numerous locations along the San Andreas fault system in California.
1620
D. D. Oglesby
Figure 13. (a) Final slip distribution on dilational fault system for case DILAdp60sk90stTC. With an even more favorable orientation for the linking fault than in
the 45⬚-dipping case, rupture propagates across the entire fault system. (b) Final slip
distribution on compressional fault system for case COMPdp30sk90stTC. With a more
favorable orientation for the linking fault than in the 45⬚-dipping case, rupture propagates to the linking thrust fault. However, the strike-slip component of slip on the
linking fault causes a clamping normal stress increase on strike-slip segment 3, preventing rupture from continuing beyond the linking thrust fault.
Figure 14.
(a) Final slip distribution on a dilational fault system for case DILAdp45sk45stTC. As in all cases with dilational step-overs, rupture propagates across the
entire fault system. (b) Slip distribution on a compressional fault system for case
COMPdp60sk90stTC. Because of the linking thrust fault’s more favorable orientation
with respect to both the regional stress field and the dynamic stress field from the strikeslip faults, rupture is able to propagate across the entire fault system. However, slip in
this system is still less than in the equivalent dilational fault system, owing to the effect
of the clamping normal stress on sliding frictional stress.
The Dynamics of Strike-Slip Step-Overs with Linking Dip-Slip Faults
Acknowledgments
The author would like to thank David Bowman, James Dieterich,
Benchun Duan, Martin Kennedy, Peter Sadler, and Michael Vredevoogd
for many helpful conversations concerning this project. The manuscript was
greatly improved through reviews by Ruth Harris and an anonymous reviewer. This work was inspired by conversations with Tom Parsons. This
research was supported in part by the Southern California Earthquake Center. SCEC is funded by NSF Cooperative Agreement EAR-0106924 and
USGS Cooperative Agreement 02HQAG0008. The SCEC contribution number for this paper is 923.
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Department of Earth Sciences
University of California, Riverside
Riverside, California 92521
Manuscript received 25 March 2005.