the dynamics of thrust and normal faults over …...1623 bulletin of the seismological society of...

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Bulletin of the Seismological Society of America, Vol. 95, No. 5, pp. 1623–1636, October 2005, doi: 10.1785/0120040234

The Dynamics of Thrust and Normal Faults over Multiple Earthquake

Cycles: Effects of Dipping Fault Geometry

by Benchun Duan and David D. Oglesby

Abstract We perform dynamic simulations of thrust and normal faults over mul-tiple earthquake cycles. Our goal is to explore effects of asymmetric fault geometryon the long-term seismicity and dynamics of dipping faults. A dynamic finite-elementmethod is used to model the interseismic and coseismic processes, with a dynamicrelaxation technique for the former. The faults are loaded by stable sliding along thedownward continuation of the faults. The asymmetric fault geometry of dipping faultswith respect to the free surface cause changes in normal stress during the interseismicand coseismic periods. These changes are of opposite sign in the two periods, re-sulting in a stabilization of the normal and shear stresses over many earthquakecycles. Both faults develop relatively stable event patterns, in which a large eventthat ruptures the entire fault is preceded by a number of small events with variousrupture lengths. A strong asymmetry in fault and ground motion exists between thrustand normal faults, and between the hanging wall and the footwall of both faults onfaults dipping less than 70�. In both normal and thrust faults, the horizontal com-ponent of ground motion dominates on the footwall, while the vertical componentdominates on the hanging wall. The above results may have implications in seismichazard analysis and building design in regions where dip-slip faults predominate.

Introduction

There is observational evidence that thrust faults pro-duce higher ground motion than normal faults for compa-rable hypocentral depths and equivalent magnitudes (Mc-Garr, 1984; Cocco and Rovelli, 1989; Margaris andHatzidimitriou, 2002). McGarr (1984) has ascribed this dif-ference to the state of stress (the compressional stress statefor thrust faults and the extensional stress state for normalfaults), showing a factor of 4 contrast in crustal strengthbetween the compressional and extensional tectonic regimes.Cocco and Rovelli (1989) and Margaris and Hatzidimitriou(2002) have shown evidence for the variation of stress dropbetween thrust and normal faulting earthquakes in Italy andin Greece, respectively. Also, a strong asymmetry of groundmotion has been observed between the hanging wall and thefootwall for dip-slip earthquakes. The 1971 San Fernando(Nason, 1973; Steinbrugge et al., 1975; Allen et al., 1998),the 1994 Northridge (Abrahamson and Someville, 1996),and the 1999 Chi-Chi (Taiwan) (Shin et al., 2000) earth-quakes produced systematically higher ground motion on thehanging wall than on the footwall. This phenomenon hasalso been seen in the foam rubber models of Brune (1996).

Recent dynamic models of thrust faulting and normalfaulting have reproduced the above asymmetric strongground motion between thrust and normal faulting earth-quakes and between the hanging wall and the footwall. Us-

ing numerical models, Nielsen (1998), Oglesby et al. (1998,2000a,b), and Shi et al. (1998, 2003) have shown that theasymmetric geometry of surface-rupturing dip-slip faultswith respect to the free surface causes an interaction betweenthe rupture process on the fault and the radiated stress field,caused by the traction-free boundary condition of the freesurface. The effect of this interaction is to cause changes innormal stress on the fault, which would be absent in theabsence of the free surface. These variations in normal stressare opposite for thrust and normal faults, which results inhigher peak slip rate and higher ground motion for thrustfaults than for equivalent normal faults. The asymmetric ge-ometry also directly leads to higher ground motion on thehanging walls of such faults than on the footwalls. In thepresence of lithostatic normal stress and depth-dependentinitial stresses, Aagaard et al. (2001) also observed higherground motion on the hanging wall of a low-angle thrustfault.

The above dynamic models of thrust faulting and nor-mal faulting provide us with insight into the physics of dip-slip faulting. Although Shi et al. (1998, 2003) reported theaccumulated slip on dipping faults over periodic large eventsin their lattice models, these dynamic models mainly focuson dynamic features of single earthquakes, with a simple setof assumed initial stresses on the fault. Some important

1624 B. Duan and D. D. Oglesby

Figure 1. A dip-slip fault model with fixed veloc-ity loading at the base. The direction of loading ve-locity shown is for the thrust fault; it is opposite indirection to that of the normal fault.

questions remain to be answered. These questions includewhether dip-slip faulting effects such as amplified thrust mo-tion near the free surface will have cumulative effects overmultiple earthquakes, and whether the variations in normalstress on the fault will accumulate or stabilize over multipleearthquake cycles.

The current study explores the long-term effects ofasymmetric fault geometry on the dynamics of dip-slipfaults. Also, the difference in seismicity, due to differentfaulting mechanisms between thrust and normal faults andasymmetric fault geometry, is examined. As a first step to-ward understanding the long-term behavior of geometricallycomplex fault systems with the dynamic rupture process in-cluded, we restrict this study to a single pre-existing fault.In this way, the effects of the dipping fault geometry areisolated from other effects, for example, fault interactionswithin a complex fault system, and may be added into a morecomplete model in the future. One distinguishing feature ofthis study, compared with previous dynamic studies of dip-slip faults in which an ad hoc assumed initial stress has usu-ally been used, is that the initial stress for dynamic eventsis a result of both the tectonic loading stress and the residualstress from the previous events.

Model and Method

For simplicity, we model 2D dip-slip faults in a half-space. Figure 1 shows the fault geometry and the loadingmechanism. A pre-existing dip-slip fault intersects the freesurface and extends 20 km in the down-dip direction. Alongthe downward continuation (30 km long) of the above stick-slip main fault, an imposed velocity between the two wallsof the fault loads the system. The loading velocity directionin Figure 1 is for a thrust fault. For a normal fault, the di-rection of loading velocity is opposite. This loading mech-anism has been widely used in geodetic studies of interseis-mic deformation (e.g., Scholz, 1990) as well as nucleationstudies (Zhang et al., 2004). This model for loading has alsobeen used in earthquake cycle simulations on strike-slipfaults (e.g., Tse and Rice, 1986; Lapusta et al., 2000). In thismodel, the upper part of a fault is locked and undergoesstick-slip, whereas the lower part of the fault undergoes sta-ble sliding at the tectonic loading rate. We remark that thisloading mechanism has been mainly used to study interplateearthquakes, and we focus on this type of earthquake in thisstudy. We use the same lengths of the main stick-slip faultand the velocity loading part for different dip angles to in-vestigate the effects of dip angle on fault evolution and rup-ture dynamics.

In Figure 1, the fault is assumed to be infinitely longalong the strike (z direction), with no variations in propertiesor deformation in this direction. Thus, the problem is re-duced to two dimensions. This model region is surroundedby a large buffer region in our numerical models. This bufferregion extends from the model region in both the negative

and positive x directions and in the negative y direction(Fig. 1) The outside boundary of this buffer region is treatedas a free surface in our model, but this buffer region is largeenough to prevent artificial reflections at the boundary fromtraveling back to the model region within the dynamic simu-lation time. Although stable sliding on the 30-km-long load-ing segment causes stress concentration at both its ends, thestress concentration at the lower end has no obvious effecton dynamic rupture of the stick-slip fault segment or groundmotion. This claim is verified by simulations with the modelsin which the stable sliding segment continually extendsdownward to the bottom of the buffer region. The stressconcentration at the upper end is an important feature of thecurrent model.

For the stick-slip main fault, we use a linear slip-weakening friction law (Ida, 1972; Andrews, 1976). Thisfriction law can be expressed as

s � l r (s � 0)s N

s � [l � (l � l )(1� s/d )]r (0 � s � d )d s d 0 N 0

s � l r (s � d )d N 0

where s is the frictional shear stress, rN is the normal stressacross the fault, s is slip on the fault, lS and ld are the staticand sliding frictional coefficients, and d0 is the critical dis-tance in the linear slip-weakening friction law. The frictionalproperties (static and sliding frictional coefficients) are as-sumed to be uniform on the fault. The material on the twosides of the fault is elastic, and the material properties arehomogenous. In this manner, we can isolate geometrical ef-fects from the effects of material heterogeneity. The materialand computational parameters are listed in Table 1.

A 2D version of DYNA3D (Whirley and Engelman,1993; Oglesby, 1999) is used to model multicycle dynamicsof dip-slip faulting. An explicit finite element code,DYNA3D, has been used to model fault dynamics and wavepropagation (e.g., Oglesby et al., 2000a,b; Oglesby and Day,2001). DYNA3D can capture fully the dynamic effects of

The Dynamics of Thrust and Normal Faults over Multiple Earthquake Cycles: Effects of Dipping Fault Geometry 1625

Table 1Model Parameters

Parameter Value

Fault dip 20�, 45�, 70�Loading rate (Vload) 0.01 m/sec (quasistatic process)

35 mm/yr (dynamic process)Static frictional coefficient 0.7Sliding frictional coefficient 0.55Critical slip-weakening distance d0 0.15 m (rupture initiation)

0.3 m (rupture propagation)Fault element size 500 mDensity 3000 kg/m3

Shear modulus 30,000 MPaPoisson’s ratio 0.25Vp 5480 m/secVs 3160 m/secTime step in simulation 0.005 sec (approximately)

the earthquake rupture process. It also provides a means toachieve a quasistatic solution for the interseismic loadingprocess. By using a dynamic relaxation algorithm that dampsparticle velocity, DYNA3D can perform quasistatic analysis(Whirley and Engelman, 1993). The dynamic relaxationmethod is based on the observation that the long-term limitof a damped dynamic solution is the quasistatic solution.Thus, we perform multicycle simulation within one codeframework. We remark that the dynamic relaxation here ismerely a numerical technique to achieve the quasistatic so-lution from a dynamic analysis. The material in the modelis still elastic, and there is no viscoelastic stress relaxationin the model.

The multicycle simulation starts from an assumed initialshear stress and normal stress on a fault. We then imposethe interseismic loading using the dynamic relaxation algo-rithm and a specified slip rate at the base of the fault. Aftershear stress on the fault exceeds the failure level, we thenmodel coseismic rupture with the slip-weakening frictionlaw using the undamped dynamic method. After the seismicwaves propagate away from the model region, this cycleends. Before the next cycle, we reset the frictional coefficientto the static level on the stick-slip fault. This action can beconsidered a proxy for a healing mechanism in the currentmulticycle models. Also, the numerical mesh is reset to theoriginal mesh. This implies that there is no evolution of thefault geometry, and we do not allow creation of new faultsin our models (i.e., we assume that rock strength is infiniteoff the fault). This assumption is consistent with our currentobjective, which is to investigate long-term effects of asym-metric fault geometry on dynamics of a single dip-slip fault.After this process, the interseismic loading process is startedfor the next cycle, with the stress output of the previous cycleon the fault used as the initial condition. The above processrepeats to perform multicycle simulations. The key point inthis procedure is that the output stresses on the fault froman event are used as initial stresses for the next earthquakecycle. Thus, except for the first event, the initial stresses on

the fault for an earthquake are the result of both the tectonicloading stress field and the residual stress from previousearthquakes. The omission of additional faulting and stressrelaxation in the interseismic period may be a significantapproximation and will be addressed later in this work.

In the above procedure for multicycle simulations, thetransition from the interseismic quasistatic simulation (usingthe dynamic relaxation algorithm in DYNA3D) to the co-seismic dynamic simulation requires further discussion.There have been several previous studies to explore this tran-sition. Lapusta et al. (2000) used a variable time-step schemewith a rate- and state-dependent friction law to treat thistransition smoothly. Fukuyama et al. (2002) dealt with thistransition in a more approximate way by using the stressoutput from a quasistatic simulation as the initial stress andimposing an amount of initial triggering slip within the re-gion of rupture initiation for dynamic simulations. In thecurrent study, we continuously run simulations for both theinterseismic and coseismic processes of the earthquake cycleand allow the nucleation location and timing to be the cal-culated results of the models. In addition, we adopt a two-d0 scheme to deal with the initiation and propagation of rup-ture within the framework of the slip-weakening law. In thisscheme, a small value of d0 is used in the nucleation zoneand a larger value of d0 is used for propagation of rupture.To a first-order approximation, this two-d0 scheme is con-sistent with the argument that d0 increases with the rupturelength (Andrews, 2004). Experiments with using one d0

value for both the initiation and propagation of rupture showthat a large d0 makes it difficult for rupture to initiate, whilea small d0 can easily lead to extreme rupture speed. Addi-tionally, we find that large events easily develop and smallevents are suppressed if we use a time-weakening frictionlaw (Andrews, 2004), in which the stress drops over a timeinterval T rather than d0. These experiments on initiation ofrupture using the slip-weakening and time-weakening fric-tion laws demonstrate that a more complete friction law suchas a rate- and state-dependent friction law (Dieterich, 1979,1981; Ruina, 1983) may be required to capture the nuclea-tion phase of an earthquake. We will progress in this direc-tion in our future work.

By using the above two-d0 scheme, the nucleation phaseof an earthquake is not simulated accurately in this study,and our multicycle models are approximate. The transitionfrom the small d0 to the large d0 may pose an artificial barrierfor rupture. To minimize this effect on the results, the sizeof the nucleation zone should be as small as possible. In thecurrent study, we define our nucleation region to be 1 kmwide, but as mentioned previously, the location and timingof the nucleation are not prescribed; rather, they are deter-mined by stress evolution on faults spontaneously.

Another approximation in our multicycle models is thata high loading rate relative to the tectonic loading rate isused during the interseismic process for computational ef-ficiency. This high loading rate is still very small comparedto the coseismic velocities. To avoid the possible effect of


Figure 2. Magnitude of initial stresses on faultsfor multicycle simulations. The normal stress is incompression. The shear stress is opposite in sign forthe thrust and normal faults.

this high loading rate on rupture dynamics, we reduce theloading rate to the tectonic rate level when any node on afault fails. Simultaneously, we turn off the dynamic relaxa-tion in DYNA3D to perform a fully dynamic analysis. Thus,the tectonic loading rate, rather than the higher loading ratefor the interseismic process, is used during the dynamic rup-ture process.

To examine the effects of the residual stress from theprevious earthquake cycles on the dynamics of dip-slipfaults, we start from relatively homogeneous initial faultstresses, as shown in Figure 2, which are consistent with theobservation that the stress drop in earthquakes does not varysystematically with depth. The relatively constant normalstress at depth can be considered as the effective normalstress, which is a result of the lithostatic load and the porepressure. However, we do not model pore pressure variationsin this study. The linear decrease to the free surface in initialstresses at shallow depth allows our models to be consistentwith a low stress level near the free surface. Note that Fig-ure 2 gives the amplitude of the initial normal and shearstresses only for the initial earthquake cycle. The normalstress for both thrust and normal faults is in compression.The sign of the shear stress is opposite for a thrust fault anda normal fault. Together with the frictional coefficients givenin Table 1, the initial stresses given in Figure 2 will producea value of 10 MPa for the strength excess (the differencebetween the initial yield stress and the initial shear stress)and a value of 5 MPa for the stress drop (the differencebetween the initial shear stress and the final shear stress inan event) on most of the fault if the entire fault fails fromthe initial stresses. These values are within reasonable rangesfor typical crustal earthquakes. As will be seen later, stressheterogeneity develops on the fault through small events,which results in nonuniform strength excess and stress dropon the fault over multiple earthquake cycles.

Results

We simulate multicycle dynamics of thrust and normalfaults with dips of 20�, 45�, and 70�. We give particular focuson the 45� dip case, as the 20� normal fault and the 70� thrustfault are not common in nature. Having the same dip anglefacilitates comparisons between thrust and normal faults.

Multicycle Dynamics of 45�-Dipping Thrustand Normal Faults

We first explore the evolution of 45�-dipping thrust andnormal faults over multiple earthquake cycles, includingevent patterns and stress variations. Then we examine dy-namic behavior of the two faults in typical small and largeevents, including fault slip and near-source ground motion.

Figures 3 and 4 show the stress evolution of the 45�thrust and normal faults over 30 earthquake cycles, respec-tively. The black curves denote stress on the faults, and thered curves represent slip and displacement (amplitude) on

the fault in 30 sequential events. In the slip-weakening lawused in this study, the yield stress is a proxy for the normalstress. In these figures, except for the first event, the stressesbefore an event are the result of all previous earthquake cy-cles and the interseismic loading. The difference in shearstress before and after an event is the static stress drop in theevent. The location at which the shear stress is at the yieldstress level before an event is the initiation (nucleation) po-sition of the event, which is typically near the down-dip edgeof the fault.

We observe that a relatively stable event pattern devel-ops on both faults over multiple earthquake cycles. For sim-plicity, we differentiate large events from small events bydefining events rupturing the entire fault up to the free sur-face as large events and all others as small events. A generalfeature on both faults is that a large event is preceded by anumber of small events. The small events vary in rupturelength, with a greater number of events having short rupturelengths. Note that the number of small events preceding thelarge ones on the thrust and normal faults is different. Thenormal fault has a relatively simple event pattern in whicha large event is preceded by three small events. Among thethree small events, a relatively longer rupture event separatestwo shorter ruptures. A large event is preceded on the thrustfault by more small events, with more variable rupturelengths.

The event pattern in which a large event is preceded bya number of small ones can be understood by examining thefault stress evolution over multiple earthquake cycles. Thesteady applied slip on the downward continuation of a stick-slip fault during the interseismic process builds up shearstress on the fault, concentrating on the lower end of thefault. Thus, earthquakes tend to initiate at the lower end ofthe fault. After a large event, the shear stress is relativelylow over the entire fault. At this stage, earthquakes tend to


Figure 3. Shear stress (dashed black) and yield stress (dot-dash black) before eachevent, shear stress (solid black) after each event, slip (solid red), amplitude of displace-ment of hanging wall (dashed red) and footwall (dot-dash red) for events 1–30 on a 45�-dipping thrust fault. Zero on the horizontal axis corresponds to the free surface, and20 km on the horizontal axis corresponds to the down-dip edge of the stick-slip fault.

be small deep events, because the shear stress over most ofthe fault is not high enough to support self-sustaining rup-ture. A small event results in a shear stress peak at the ter-mination of rupture on the fault along the up-dip direction.A relatively longer rupture leads to a shear stress peak closerto the free surface (e.g., events 5, 15, and 24 in Figure 3).A number of small events with various rupture lengths re-sults in a highly heterogeneous shear stress with a relativelyhigh average stress level over the fault. This high stress level

facilitates a large event that ruptures the entire fault. Afterthis large event, the shear stress on the fault is again rela-tively low and homogenous on most of the fault. Then thefault roughly repeats the above event pattern.

In this discussion on fault stress evolution, we mainlyfocus on the shear stress, as the yield stress (a proxy for thenormal stress) does not appear to change significantly overmultiple cycles (see Figs. 3 and 4). However, as emphasizedby Oglesby et al. (1998, 2000a,b), the normal stress can


Figure 4. Shear stress (dashed black) and yield stress (dot-dash black) before eachevent, shear stress (solid black) after each event, slip (solid red), amplitude of displace-ment of hanging wall (dashed red) and footwall (dot-dash red) for events 1–30 on a 45�-dipping normal fault. Zero on the horizontal axis corresponds to the free surface, and20 km on the horizontal axis corresponds to the down-dip edge of the stick-slip fault.

change significantly during dynamic rupture on dippingfaults, owing to the asymmetric fault geometry with respectto the free surface. An immediate result of the present workis that the variations in normal stress in a single dynamicevent do not appear to accumulate over multiple earthquakecycles. Figure 5 illustrates why this is the case. It displaysnormal stress variations on the thrust and normal faults inthe first earthquake cycle and after 30 cycles, starting froman almost homogenous initial stress level. Figure 5a dem-

onstrates that the normal stress increases on the lower partand decreases on the upper part of the normal fault duringthe interseismic process, while the normal stress varies inthe opposite manner on the thrust fault. Figure 5b shows thatthe normal stress decreases on the lower part and increaseson the upper part of the normal fault after a large event, whilethe normal stress varies in the opposite manner on the thrustfault. The comparison between Figures 5a and 5b illustratesthat the normal stress changes in opposite directions in the


Figure 5. Normal stress variation on 45�-dippingthrust and normal faults (a) after the first interseismicloading, (b) after the first coseismic rupture, and (c)after 30 cycles. For both the interseismic and coseis-mic processes, the normal stress increment is in theopposite direction on the thrust and normal faults. Forboth the thrust and normal faults, the normal stressincrement is in the opposite direction after the inter-seismic and coseismic processes for large events.Note finer scale for stress in (a).

interseismic process and the coseismic process of a largeevent on both the normal and thrust faults. The amplitude ofchange in normal stress after an interseismic process is muchsmaller than that after a coseismic process of a large event.Further, we find that the change in normal stress after a smallevent (not shown) is similar in magnitude and sign to thatduring the interseismic process for the same fault. As shownabove, there are more small events than large ones on boththe thrust and normal faults. Thus, the relatively large vari-ations in normal stress that take place in the few large eventsare counteracted by the small variations in this stress due tothe interseismic process and the large number of small

events. The consequence is that the normal stress on bothnormal and thrust faults is relatively stable on average overmultiple earthquake cycles, as shown in Figure 5c.

Although the variations in normal stress during the in-terseismic process on both normal and thrust faults are smallin amplitude, they appear to play a critical role in stabilizingthe normal stress on the faults in the long term. Furthermore,the difference in these variations between the normal andthrust faults results in the difference in event patterns be-tween the two faults. On the normal fault, an increase in thenormal stress on the lower edge of the fault during the inter-seismic process leads to a longer interseismic loading period,and thus a higher initial shear stress on the fault at nuclea-tion. A decrease in the normal stress on the shallow part ofthe normal fault facilitates rupture propagation. As a result,it is easier to develop large events on the normal fault. Onthe thrust fault, a decrease in the normal stress on the loweredge of the fault during the interseismic process leads to ashorter loading period, and thus a lower initial shear stresson the fault at nucleation. An increase in the normal stresson the shallow part of the thrust fault inhibits rupture prop-agation. The above two factors result in more small eventson the thrust fault, compared with the normal fault.

Another observation in Figures 3 and 4 is that asym-metry in displacement between two walls on a dipping fault(larger displacement on the hanging wall) is obvious forlarge surface-rupturing events, while not obvious for smallerburied events. This is consistent with the previous studieson a single event (Oglesby et al., 2000a; Aagaard et al.,2001). As shown in these studies, the free-surface effect de-creases rapidly with burial depth of ruptured faults.

In the interest of ground-motion prediction and seismichazard analysis, we examine dynamic behavior of the twofaults in typical large and small events. Although these top-ics have been the focus of previous studies (Oglesby et al.,1998, 2000a,b; Shi et al., 1998, 2003; Aagaard et al., 2001),the current study is unique in the sense that the initial stressesfor events are the result of both the long-term interseismicloading process and residual stress from previous earth-quakes, rather than ad hoc assumptions. We choose thetwenty-fourth event on the thrust fault and the twenty-seventh event on the normal fault as typical small events,and the twenty-ninth event on both faults as typical largeevents.

Figure 6 shows the peak slip velocity on the two faultsand the peak particle velocity on each of the two walls ofeach fault in typical small events and large events. The ve-locity peaks at depth in these curves appear to correlate withthe peaks in the initial shear stress before these events inFigure 3 and 4. Higher peak slip rate on the thrust fault, aswell as higher motion of the hanging wall of both faults, isobserved in the large events. Very large peak slip velocityand very large hanging wall peak particle velocity at the freesurface on the thrust fault are observed in the large event(the bottom left panel), even with a very low stress levelnear the free surface, indicating that the amplification effect


Figure 6. Peak slip velocity (solid curves) and peak particle velocity (amplitude)on hanging wall (dashed curve) and footwall (dot-dash curve) in typical large eventsand small events on 45�-dipping thrust and normal faults.

of the free surface on the thrust fault during dynamic ruptureobserved in the homogeneous prestress studies (Oglesby etal., 1998, 2000a,b) is present even with depth-dependentfault stress. In the large event on the normal fault (the bottomright panel), the maximum peak slip velocity (and also peakparticle velocity) occurs at a down-dip distance of about2.5 km. The presence of this peak slightly below the freesurface may result from the combined effects of the deam-plification effect of the free surface on the normal fault (Og-lesby et al., 1998, 2000a,b), the reduced shear stress nearthe surface, and the rupture directivity as rupture propagatesupward from depth. The above difference in peak velocityat the surface between the thrust and normal faults is con-sistent with the observation that a greater peak ground mo-tion is usually reported on thrust faults (e.g., Nason, 1973;Steinbrugge et al., 1975; Abrahamson and Somerville, 1996;Allen et al., 1998; Shin et al., 2000). In large events, the slipis also larger on the thrust fault than on the normal fault, andthe displacement is larger on the hanging wall than on thefootwall for both faults, as shown in Figures 3 and 4.

Asymmetry between the thrust and normal faults, andbetween the hanging wall and footwall, in large events isalso seen in the peak particle displacements (Fig. 7) and thepeak particle velocities (Fig. 8) on the free surface near thefaults. This observation is consistent with the previous stud-ies on a single event (Oglesby et al., 1998, 2000a,b; Shi etal., 1998, 2003; Aagaard et al., 2001).

In addition to the overall asymmetry of the amplitude

of near-source ground motion, we also observe that the par-tition of ground motion between horizontal and vertical com-ponents is different for the hanging wall and footwall of bothfaults. In Figures 7 and 8, the dashed curves denote the hor-izontal components and the dot-dash curves represent thevertical components. In the vicinity of both thrust and nor-mal faults, the vertical component dominates on the hangingwall, while the horizontal component dominates on the foot-wall. Also note that the total peak ground motion at a certainpoint often occurs at a different time than the peak horizontalor peak vertical components, so the total peak ground motionis typically not equal to the vector combination of the peakhorizontal and peak vertical components in these figures. Allthese asymmetries in ground motion near the faults can alsobe clearly seen from synthetic seismograms at two symmet-ric locations relative to the fault trace, as shown in Figure 9.The asymmetry in magnitude of ground motion between thehanging wall and the footwall is almost entirely due to theamplified vertical motion on the hanging wall.

Effects of the Dip Angle

Previous studies on single earthquake events (Oglesbyet al., 1998, 2000a,b) have shown that the dip angle has animportant effect on the dynamics of dipping faults. We per-formed multicycle dynamic simulations on faults with ashallow dip angle (20�) and a steep dip angle (70�), in ad-dition to the above 45� dip angle. Except for the dip angles


Figure 7. Peak particle displacement along the free surface above 45�-dipping thrustand normal faults in typical large events and small events. Solid curves denote ampli-tude of the total displacement; dashed curves denote the horizontal (x) component anddot-dash curves denote the vertical (y) component. Footwall is on left with negativecoordinate; hanging wall is on right with positive coordinate. Note finer scale for dis-placement in the small events.

and the different loading directions between thrust and nor-mal faults, all parameters were the same for all faults. In thismanner, we could isolate the effect of dip angle on our faultsystems. We acknowledge that the 20� normal fault and the70� thrust fault are somewhat artificial. We include them forcompleteness and to help illustrate the dependence of theresults on fault geometry.

Figure 10 shows maximum final slip and maximumpeak slip velocity on all simulated faults for the 30 sequentialevents. We observe that a relatively stable event patterntends to develop on all faults. A general feature of all dippingfaults is that a large event, which is usually characterized bya large maximum slip or a large maximum peak slip velocity,or both, is preceded by a number of small events. For ashallow dip angle (20�), peak slip velocity is slightly higheron the thrust fault than on the normal fault in large eventsover multiple cycles, even though maximum slip may be lesson the thrust fault. This suggests that at the shallower dipangles, the asymmetric fault geometry tends to have largereffects on fault dynamics. We remark that the slip on the 20�normal fault in large events becomes stable after the faultdevelops the stable event pattern (a large event is precededby three small events as shown by events 24–27), althoughthis slip appears to decrease at the early stage of the sequence

of events. This is confirmed by continuing the simulation tofiftieth event (not shown). For a moderate dip angle (45�),peak slip velocity is higher on the thrust fault than on thenormal fault in large events, and maximum slip is also largeron the thrust fault. For a high dip angle (70�), the thrust andnormal faults have similar peak slip velocity and maximumslip in large events over multiple earthquake cycles, eventhough the thrust fault has significantly higher peak slip ve-locity and greater maximum slip in the first event in whichthe two faults have similar initial stress. The observation ofasymmetry in the first event here is consistent with the re-sults of previous studies (Oglesby et al., 1998, 2000a,b). Thecurrent multicycle results for the 70� case suggest that twofaults of this dip tend to organize themselves to behave sim-ilarly in the long term. In this way, we see that in the longterm, the effect of asymmetric fault geometry tends to besmall for faults that are close to vertical, and large for moreshallow-dipping faults. Of course, a real-world comparisonbetween normal and thrust faults would most closely cor-respond to a comparison between the 20�-dipping thrust faultand the 70�-dipping normal fault. This comparison in Figure10 indicates a much larger peak slip and slip rate in largeevents on the thrust fault, even with all other aspects of thefaults equal.


Figure 8. Peak particle velocity along the free surface above 45�-dipping thrust andnormal faults in typical large events and small events. Solid curves denote amplitudeof the vector velocity; dashed curves denote the horizontal (x) component and dot-dashcurves denote the vertical (y) component. Footwall is on left with negative coordinate;hanging wall is on right with positive coordinate. Note finer scale for velocity in thesmall events.

Discussion

Differences in strong ground motion between thrustfaulting and normal faulting have been studied by a numberof researchers. Campbell (1984) found that accelerationsfrom thrust faults are approximately 30%–40% higher thanthose from other faulting mechanisms. McGarr (1984) no-ticed a strange inverse correlation of earthquake size to dam-age for the Idaho (October 1983, MS 7.3, normal faulting)and Coalinga (May 1983, MS 6.5, thrust faulting), California,earthquakes with a similar hypocenter depth of 10 km. Heargued that the inverse correlation was due to substantiallyhigher near-source peak ground motion from the Coalingashock. He attributed higher ground motion from thrust fault-ing to the larger crustal strength in the compressional regimethan the extensional regime. Cocco and Rovelli (1989) re-ported higher peak ground motions from thrust earthquakesthan from normal earthquakes with similar moment magni-tudes in Italy. They found that the thrust earthquakes exhibithigher stress drop than the normal earthquakes. Margaris andHatzidimitriou (2002) also reported higher stress drop onthrust earthquakes than on normal and strike-slip earth-quakes in Greece. The current study and previous studies(Oglesby et al., 1998, 2000a,b) show that even with similar

strength and stress drop, thrust faults with shallow to mod-erate dip angles produce significantly higher peak groundmotion than normal faults with similar dip angles, especiallyin large events. Thus, the dipping fault geometry appears toplay an important role in the contrast of strong ground mo-tion between thrust and normal faulting earthquakes. Thiseffect may add to the effects of the state of stress and thestress drop in different seismotectonic regimes.

Higher strong ground motion from thrust faults thannormal faults deserves particular attention in seismic hazardanalysis. Another important issue in seismic hazard analysisis how often the large earthquakes occur. Cocco and Rovelli(1989) used the historical catalog of Italian earthquakes toargue that the higher stress drop on thrust faults correlateswith a longer repeat time, compared with normal faults.They cautioned that this correlation in Italian earthquakescannot be generalized simply and noted that some normalfaults have long repeat times (e.g., basin and range earth-quakes). Although comparison between the 45� thrust andnormal faults (Figs. 3, 4, and 10) in this study shows thatwithin 30 sequential events, the normal fault has more largeevents than the thrust fault, the number of large events withina certain time period is similar between these two faults.Figure 11 shows the distribution of 30 simulated sequential


Figure 9. Ground velocity time history in typical large events on 45�-dipping thrustand normal faults. Two points on the surface are symmetric relative to the fault trace,x � �2 km on the footwall and x � 2 km on the hanging wall (see Fig. 1). Note allvertical axes have same length. Differences between thrust and normal faults, betweenhanging wall and footwall, and between horizontal and vertical components are ob-served.

events on all faults in this study over equivalent time periods.To produce this plot, we assumed a slip rate of 35 mm/yrfor all faults. The difference in this plot between thrust andnormal faults with the same dip angle is exclusively due tothe effect of dipping fault geometry on the two differentfaulting mechanisms. The normal faults take more time tohave 30 events than the thrust faults for all dipping anglecases, owing to the differences in normal stress change dur-ing the interseismic loading phase between the two types offaults (Fig. 5). Within a certain time period, the number oflarge events is similar between the thrust and normal faults,although there are more small events on the thrust faults.The differences among different dipping angles can also beattributed to the effect of dipping fault geometry. Detailedexamination of stress evolution during the interseismic load-ing phase shows that the amplitudes of normal stress changeand shear stress buildup on the 45�-dipping faults are muchlarger than those on either the 20�- or 70�-dipping faults,given the same time period with the same slip rate. Also, thebuildup of shear stress is much larger in magnitude than thenormal stress change at the lower end of the 45�-dipping

fault. Thus, the 45�-dipping faults have a shorter repeat timefor large events than the faults with the other two dip angles.This result suggests that the details of fault geometry (e.g.,the dip), whenever available, may need to be taken into ac-count in seismic hazard analysis.

As shown above, the normal stress change due to dip-ping fault geometry plays an important role in fault behavior.The importance of the time-dependent normal stress on dip-ping faults during the earthquake rupture process has beenemphasized in previous studies (Brune, 1996; Oglesby et al.,1998; Shi et al., 1998; Oglesby et al., 2000a,b). The currentstudy further reveals that the normal stress change on dip-ping faults during the interseismic loading phase can alsohave a significant effect on long-term behavior of dippingfaults, including the event pattern and the repeat time oflarge events, although these changes are small over one sin-gle interseismic process. An analysis of typical events withinmultiple earthquake cycles in this study confirms the find-ings in the previous studies, including higher ground motionon thrust faults than on normal faults, and higher motion onthe hanging wall than on the footwall. A new finding in


Figure 10. Maximum final slip and maximum peak slip velocity on thrust andnormal faults with dips of 20�, 45�, and 70� in 30 sequential events.

terms of asymmetric ground motion between thrust and nor-mal faulting is that at high dip angles, the thrust and normalfaults organize themselves over multiple earthquake cyclesto behave similarly, even though they produce significantlydifferent ground motion given the same initial stresses at thebeginning.

Differences between the horizontal and vertical com-ponents of near-source ground motion over the dippingfaults in this study may have implications in earthquake en-gineering. To our knowledge, there have not been reports onthis asymmetry in the literature. On the hanging wall nearthe fault trace, the total ground motion is larger, and is dom-inated by the vertical component. Conversely, the totalground motion is smaller on the footwall, and is dominatedby the horizontal component. Typical buildings are designedto withstand horizontal forces. However, our models showthat very large vertical peak ground motion, as shown inFigure 8 (the lower left panel), can occur near the fault traceon the hanging wall of thrust faults. Large vertical groundmotion on the hanging wall near the fault trace has beeninferred from the 1971 San Fernando earthquake (Allen etal., 1998). This very large peak vertical particle velocitycould cause localized high damage owing to buildings notbeing designed to withstand strong vertical motion.

A more theoretical issue for earthquake physics is the

question of how a complex range of earthquake size ariseson a fault. Our models in this study are quite simple, and donot include any heterogeneity in fault properties and materialproperties. However, we still find that the faults in the longterm produce both small events and large events. Thesesmall events appear to play an important role in evolutionof the fault by adjusting the fault stresses. Small events raiseshear stress level around their termini, and generate shearstress heterogeneity on the fault. In this manner, small eventsraise the overall stress level to a critical yet heterogeneousstate. This critical state facilitates a subsequent large, sur-face-rupturing event. Multicycle numerical models may bea way to monitor the approach to a critical state by incor-porating observations of deformation and seismicity intomodels for a system of faults. Other factors not included inthe present models, such as heterogeneities in fault proper-ties and material properties and interactions between differ-ent faults or fault segments, may contribute to the criticalstatus. For example, Lapusta et al. (2000) observed a re-peated pair of larger and smaller events on a vertical strike-slip fault for a certain set of parameters with depth-variablefriction parameters using a rate- and state-dependent frictionlaw.

In this study, we do not take into account the visco-elastic stress relaxation in the medium; the material in our


Figure 11. Distribution of simulated 30 events over time given a slip rate of 35mm/yr. Normal faults take more time for these 30 events than their thrust counterparts.However, the number of large events over a certain time is comparable between 45�-thrust and normal faults.

models is totally elastic, except on the single pre-existingfault. Viscoelastic models have been shown to be importantin studying broad deformation in the upper crust at strike-slip boundaries (Roy and Royden, 2000a,b) and the long-term evolution of nonplanar faults (Duan and Oglesby,2005). However, the faults in this study are planar, and nostress buildup over multiple earthquake cycle occurs on thefaults. Nevertheless, it will be desirable in the future to in-tegrate more realistic material models, for example, visco-elastic and plastic models, into our current earthquake cyclemodel to fully capture the complex behavior of fault sys-tems. Another issue is that our models are two dimensionalin this study for computational simplicity. We expect thatthe main findings in this study will be valid qualitatively inthree dimensions, at least near the centers of relatively widefaults. The large values of the maximum slip and maximumpeak slip velocity on 20�- and 70�-dipping faults in Figures10 and 11 are expected to be smaller in three dimensions,where energy concentration at the crack tip is expected tobe less.

Conclusions

We performed multicycle dynamic simulations of thrustfaults and normal faults within one algorithm framework (afinite-element code for dynamic simulations). We find thatboth thrust and normal faults tend to develop a relativelystable pattern in the long term, in which a large event rup-turing the entire fault is preceded by a number of smallevents. The normal stress change on a dipping fault in asingle large event does not accumulate over multiple earth-quakes because of the opposite change in this stress duringthe interseismic process and during small events on the fault.Higher peak ground motion is observed near the source oflarge thrust earthquakes in the long term for shallow to mod-erate fault dip angles, compared with their normal counter-parts. This asymmetry in ground motion become small inthe long term for faults that are close to vertical.

The multicycle models in the current study are approx-imate in the sense that only the interseismic loading processand the coseismic rupture process are modeled. It is desirableto incorporate other processes into the multicycle models,


such as the nucleation process and the postseismic defor-mation process. These processes may have large effects onlong-term behavior of dipping faults. As discussed in theMethods section of this article, the rate- and state-dependentfriction law may be required to simulate the nucleationphase. We will continue to work on these issues to moreaccurately capture the long-term behavior of dipping faults.

Acknowledgments

The authors gratefully acknowledge the support of the National Sci-ence Foundation through grants EAR-0106828 and EAR-0409836. Thisresearch was also supported by the Southern California Earthquake Center.SCEC is funded by NSF Cooperative Agreement EAR-0106924 and USGSCooperative Agreement 02HQAG0008. The SCEC contribution number forthis paper is 898. We appreciate helpful reviews from Fred F. Pollitz, RuthHarris, Eiichi Fukuyama, and Mitsuhiro Matsu’ura.

References

Aagaard, B. T., T. H. Heaton, and J. F. Hall (2001). Dynamic earthquakeruptures in the presence of lithostatic normal stresses: implicationsfor friction models and heat production, Bull. Seism. Soc. Am. 91,1765–1796.

Abrahamson, N. A., and P. G. Somerville (1996). Effects of the hangingwall and footwall on ground motions recorded during the Northridgeearthquake, Bull. Seism. Soc. Am. 86, 93–99.

Allen, C. R., J. N. Brune, L. S. Cluff, and A. G. Barrows (1998). Evidencefor unusually strong near-field ground motion on the hanging wall ofthe San Fernando fault during the 1971 earthquake, Seism. Res. Lett.69, 524–531.

Andrews, D. (1976). Rupture propagation with finite stress in antiplanestrain, J. Geophys. Res. 81, 3575–3582.

Andrews, D. (2004). Rupture models with dynamically determined break-down displacement, Bull. Seism. Soc. Am. 94, 769–775.

Brune, J. (1996). Particle motions in a physical model of shallow anglethrust faulting, Proc. Indian Acad. Sci. (Earth Planet. Sci.) 105,L197–L206.

Campbell, K. W. (1984). Near-source attenuation of strong ground motionfor moderate to large earthquakes: an update and suggested applica-tion to the Wasatch fault zone in north-central Utah, in Proceedingsof Workshop on Evaluation of Regional and Urban Earthquake, Haz-ards and Risk in Utah, Salt Lake City, Utah, U.S. Geol. Surv. Open-File Rept. 84-763, 483–499.

Cocco, M., and A. Rovelli (1989). Evidence for the variation of stress dropbetween normal and thrust faulting earthquakes in Italy, J. Geophys.Res. 94, 9399–9416.

Dieterich, J. H. (1979). Modeling of rock friction. 1. Experimental resultsand constitutive equations, J. Geophys. Res. 84, 2161–2168.

Dieterich, J. H. (1981). Constitutive properties of faults with simulatedgouge, in Mechanical Behavior of Crustal Rocks, N. L. Carter, M.Friedman, J. M. Logan, and D. W. Stearns (Editors), American Geo-physical Monograph 24, 103–120.

Duan, B., and D. D. Oglesby (2005). Multicycle dynamics of nonplanarstrike-slip faults, J. Geophys. Res. 110, B03304, doi: 10.1029/2004JB003298.

Fukuyama, E., C. Hashimoto, and M. Matsu’ura (2002). Simulation of thetransition of earthquake rupture from quasi-static growth to dynamicpropagation, Pageoph 159, 2057–2066.

Ida, Y. (1972). Cohesive force across tip of a longitudinal shear crack andGriffith’s specific energy balance, J. Geophys. Res. 77, 3796–3805.

Lapusta, N., J. R. Rice, Y. Ben-Zion, and G. Zheng (2000). Elastodynamicanalysis for slow tectonic loading with spontaneous rupture episodes

on faults with rate- and state-dependent friction, J. Geophys. Res. 105,23,765–23,789.

Margaris, B. N., and P. M. Hatzidimitriou (2002). Source spectral scalingand stress release estimates using strong-motion records in Greece,Bull. Seism. Soc. Am. 92, 1040–1059.

McGarr, A. (1984). Scaling of ground motion parameters, state of stress,and focal depth, J. Geophys. Res. 89, 6969–6979.

Nason, R. (1973). Increased seismic shaking above a thrust fault, in SanFernando, California, Earthquake of February 9, 1971, Volume III,Geological and Geophysical Studies, N. A. Benfer, J. L. Coffman,and J. R. Bernick (Editors), National Oceanic and Atmosphanic Ad-ministration, Washington, D.C., 123–126.

Nielsen, S. B. (1998). Free surface effects on the propagation of dynamicrupture, Geophys. Res. Lett. 25, 125–128.

Oglesby, D. D. (1999). Earthquake dynamics on dip-slip faults, Ph.D. The-sis, University of California, Santa Barbara.

Oglesby, D. D., and S. M. Day (2001). Fault geometry and the dynamicsof the 1999 Chi-Chi (Taiwan) earthquake, Bull. Seism. Soc. Am. 92,3006–3021.

Oglesby, D. D., R. J. Archuleta, and S. B. Nielsen (1998). Earthquakes ondipping faults: the effects of broken symmetry, Science 280, 1055–1059.

Oglesby, D. D., R. J. Archuleta, and S. B. Nielsen (2000a). Dynamics ofdip-slip faulting: exploration in two dimensions, J. Geophys. Res. 105,13,643–13,653.

Oglesby, D. D., R. J. Archuleta, and S. B. Nielsen (2000b). The three-dimensional dynamics of dipping faults, Bull. Seism. Soc. Am. 90,616–628.

Roy, M., and L. H. Royden (2000a). Crustal rheology and faulting at strike-slip plate boundaries. 1. An analytic model, J. Geophys. Res. 105,5583–5597.

Roy, M., and L. H. Royden (2000b). Crustal rheology and faulting at strike-slip plate boundaries. 2. Effects of lower crustal flow, J. Geophys.Res. 105, 5599–5613.

Ruina, A. L. (1983). Slip instability and state variable friction laws, J.Geophys. Res. 88, 10,359–10,370.

Scholz, C. H. (1990). The mechanics of earthquakes and faulting, Cam-bridge University Press, Cambridge, U.K.

Shi, B., A. Anooshehpoor, J. N. Brune, and Y. Zeng (1998). Dynamics ofthrust faulting: 2D lattice model, Bull. Seism. Soc. Am. 88, 1484–1494.

Shi, B., J. N. Brune, Y. Zheng, and A. Anooshehpoor (2003). Dynamicsof earthquake normal faulting: two-dimensional lattice particle model,Bull. Seism. Soc. Am. 93, 1179–1197.

Shin, T. C., K. W. Kuo, W. H. Lee, T. L. Teng, and Y. B. Tsai (2000). Apreliminary report on the 1999 Chi-Chi (Taiwan) earthquake, Seism.Res. Lett. 71, 24–30.

Steinbrugge, K. V., E. E. Schader, and D. F. Moran (1975). Building dam-age in San Fernando Valley, Bulletin California Division of Minesand Geology 196, 323–353.

Tse, S. T., and J. R. Rice (1986). Crustal earthquake instability in relationto the depth variation of frictional slip properties, J. Geophys. Res.91, 9452–9472.

Whirley, R. G., and B. E. Engelmann (1993). DYNA3D: A Nonlinear, Ex-plicit, Three-Dimensional Finite Element Code for Solid and Struc-tural Mechanics. User Manual, University of California, LawrenceLivermore National Laboratory, UCRL-MA-1107254 Rev. 1.

Zhang, C., D. D. Oglesby, and G. Xu (2004). Earthquake nucleation ondip-slip faults, J. Geophys. Res. 109, B11302, doi: 10.1029/2003JB002894.

Department of Earth SciencesUniversity of CaliforniaRiverside, California 92521

Manuscript received 3 December 2004.

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