Static Stress Transfer and Aftershock Triggering by the 1999 Chi-Chi Earthquake in Taiwan

The static stress changes caused by the Chi-Chi mainshock with ML =7.3 were analyzed with an elastic dislocation model in a homogenous half-space. The results show that most aftershocks in the fold-and-thrust belt might best be interpreted as the re-activation of pre-existing thrust faults trig­ gered by the mainshock. Strike-slip motions near the terminations of the Chelungpu fault are also likely to have been enhanced by the static stress transfer. The Chukou fault, on the other hand, fell in a stress shadow; as a result, few aftershocks occurred there. The Chia-Yi earthquake sequence which occurred a month after the Chi-Chi earthquake turns out to have been an exception in this study. No evidence of static stress enhancement was found in that area. Unless the large aftershocks which followed the Chi-Chi earthquake altered the stress field and promoted failure, the time lag of the Chia-Yi earthquake might well be attributed to the influence of a stress shadow. (key words: Chi-Chi earthquake, Coulomb failure stress, Static stress changes)


INTRODUCTION
Taiwan is located at the active convergent boundary between the Eurasian and Philippine Sea plates.Collision of the two plates have frequently induced many large earthquakes and caused serious damage especially in eastern, northwestern and southwestern Taiwan.Com pared to these highly vulnerable areas, central Taiwan, on the other hand, had been relatively inactive in terms of seismicity until 21 September, 1999 (local time), when a major earthquake with local magnitude of 7 .3struck the Taichung-Nantou area killing more than 2,500 people.
In many places, this strong shock lasted more than 40 seconds and more than 980 gal.ground acceleration was experienced.With the mainshock, the Chelungpu fault, a reactive thrust fault, extending nearly 77 km in the North-south (NS) direction, ruptured the ground with a maxi-1 Institute of Applied Geophysics, National Chung Cheng University, Chia-Yi, Taiwan, ROC *Corresponding author address: Prof. Wei-Hau Wang, Institute of Applied Geophysics, National Chung Cheng University, Chia-Yi, Taiwan, ROG; E-mail: seiwhwg@eq.ccu.edu.twmum surface displacement of up to 3.4 mi n the vertical direction and 9 mi n the horizontal direction (Chung and Shin 1999).In the first three months after the mainshock, thousands of earthquakes occurred over a vast area as shown in Fig. 1.Why were these aftershocks distrib uted over such a wide area?Could they have been the result of the same kind of rupture mechanism?Were all of them triggered by the mainshock?These are the issues which are addressed in this paper.
Recent studies have indicated that static stress changes due to mainshocks would likely induce aftershocks on nearby faults where the Coulomb failure stress is increased (e.g., Reasenberg and Simpson 1992;King et al. 1994;Toda et al. 1998)

1998).
If so, analyzing the static stress changes induced from the Chi-Chi earthquake would be one key to answering the above questions.However, previous studies have also indicated that not all cases follow the static stress change triggering model.For instance, the N orthridge (Hardebeck et al. 1998) and Lorna Prieta earthquakes (Beroza and Zoback,. 1993;Kilb et al. 1997) show few signs of static stress triggering in aftershock sequences.Therefore, in order to better understand the effect of static stress transfer, this paper adopted a statistical method to test the hypothesis of static stress triggering in the Chi-Chi earthquake sequence.

STATIC STRESS CHANGES CAUSED BY THE CHI-CHI EARTHQUAKE
This study adopted the unilateral rupture model of Yagi and Kikuchi (1999) which had been derived from the inversion of teleseismic body waveforms.The rupture model was fur ther simplified to 50 slip patches 10 by 10 km in size as shown in Fig. 2. The source mecha nism of the mainshock given by the CMT short reference results suggests that the Chelungpu fault is oriented N26°E, 27°E with fault slip along a rake of 82°.With this information, the static stress changes can be calculated by applying the finite source dislocation model (Okada 1992) on each fault patch in an elastic half-space with a shear modulus of 3X1010 Nm-2 and Poisson's ratio of 0.25.The changes in static stress obtained from the above calculations were then converted into stress increments onto the fault planes in orthogonal directions (normal stress increments) and in the slip directions (shear stress increments) of the triggered earth quakes.
In the Coulomb failure criterion, failure occurs on a plane when the Coulomb failure stress (CFS) is zero; that is, where Uc is the Coulomb failure stress; T is the shear stress on the objective plane (in the slip direction); µ is the friction coefficient; Un is the normal stress on the objective plane; p is the pore fluid pressure; C is the cohesion.If µ and C are constant over time, the Coulomb failure stress changes ( Ll CFS) on a fault plane can then be determined as follows: (2) Longitude(0E)  This equation is usually simplified to the following equivalent form by introducing the Skempton's coefficient j3: where µ' is the effective friction coefficient.
Theoretically, f3 may range from 0 to 1, but iri fact it is usually from 0.7 to 1.0 (e.g., Green and Wang 1986).Strictly speaking, µ' is not a constant but instead changes with time due to fluctuations in the pore fluid pressures induced by the stress step from the mainshock.Nevertheless, µ' tends to be small in value (e.g., Gross and Burgmann 1998;Kagan and Jackson 1998).Deng and Sykes (1997) suggested a range ofµ' between 0 and 0.6.In this study , µ' was assumed to be 0.4, following King et al. (1994).Positive values of the �CFS promote failure or, in terms of rate-and-state dependent friction, increase the seismicity rate and vice versa (Dieterich 1994).
The attitude of the objective fault plane and the slip direction can be determined either from estimations based on geological observations and historical earthquake records, or from focal mechanisms of the aftershocks.Alternatively, if the background stress field prior to the mainshock is available with small faults distributed regionally in all orientations, the "opti mal" fault planes that are most likely triggered by the static stress changes can be determined.However, because limited knowledge of the regional stress is currently available, this study tested the �CFS on three types of faults, namely those with attitudes ofN10°E, 30°E (thrust), N75°W, 90° (left-lateral strike-slip), and N75°W, 80°S (right-lateral strike-slip).These are the most commonly observed faults in the field and were inferred from focal mechanisms (e.g., Kao and Chen 2000).For each case, it was assumed that micro-faults with the same attitude were distributed all over the study area.Apparently, though, this is not the case in reality; as a result, none of these models alone could fully describe the rupture mechanisms for all the aftershocks even though thrust faults are more frequently observed in the mountain belt than are strike-slip faults.The relative significance among the models in a specific area relies on the agreement between the modeled ruptures and the focal mechanisms of the aftershocks.
Figures 3 to 5 illustrate the �CFS for thrusts at depths of 2.5, 7 .5,and 12.5 km, respec tively.The common feature of these diagrams is that the Ll CFS greatly increases in the area to the east of the Chelungpu fault.In other words, it was very likely that thrust faulting was triggered by the mainshock in this area.This inference is consistent with the focal mechanism suggested by Kao and Chen (2000).West of this stress-elevated zone, the �CFS becomes negative, indicative of a local stress shadow.Noteworthy is that the Chukou fault falls within this shadow zone, implying that the seismicity rate on the Chukou fault would decrease.In fact, fewer earthquakes were located in this shadow zone than in the stress-enhanced area.Kao and Chen (2000) have suggested that the Chelungpu fault is bounded by NE trend ing, right-lateral strike-slip faults to the north and NW trending, left-lateral strike-slip faults to the south.Figure 6 shows the �CFS for the right-lateral strike-slip faults.Unlike previous calculations, the �CFS in this case is positive in the area near the northern termination of the Chelungpu fa ult.As a result, more earthquakes agree with the static stress triggering model.It is also worth noting that the Meishan fault, southwest of the Chelungpu fault, has the same orientation but falls in a stress shadow.This implies that right-lateral strike-slip movement Similarly, the Li CFS for left-lateral strike-slip faults at the depth of 7 .5km (Fig. 7) suggests a stress-enhanced belt associated with a cluster of aftershocks near the southern end of the Chelungpu fault.This feature supports Kao and Chen's findings.Although most aftershocks were distributed in the stress-enhanced region, there were exceptions.For instance, northwest of the mainshock, a cluster of earthquakes in the foreland near the central portion of the Chelungpu fault fell into a stress shadow zone (see Fig. 4).This inconsistency may be from some error in identifying the type of objective fault that was as sumed in the stress calculations.Kao and Chen (2000) found several normal rather than thrust ing events in this area, which suggests that this area was experiencing extension, and not compression.The unexpected number of normal events, likely in response to the elastic re-   and October 22, 1999 had the Chi-Chi earthquake not disturbed the region.Alternatively, the Chia-Yi earthquake might not have been triggered by the Chi-Chi mainshock, as implied by its static stress changes, but by the following large aftershocks.For instance, four hours after the mainshock, a large aftershock with ML =6.5 was located in the region about 40 km to the east of the Chia-Yi earthquake.This event might have further disturbed the stress field around Chia-Yi and induced the earthquake.This puzzle will be clarified when subsequent distur bance from the aftershocks of the Chi-Chi earthquake is quantitatively evaluated.
Still another inconsistency comes from the NNE-trending earthquake cluster in the east ern flank of the Central Range, which is separated from the stress-enhanced zone in the fold and-thrust belt by an aseismic zone along the crest of the Central Range.Kao and Chen (2000) have found that both normal and strike-slip faulting instead of thrusting have occurred in this belt.The complexity of the rupture mechanisms would cause the failure of any triggering model proposed earlier that calculates the �CFS on just one kind of rupture.

EFFECT OF STRESS TRANSFER ON AFTERSHOCKS
Totally, 6 , 810 aftershocks occurring during the period from September 21 to December 31 were used to evaluate the possibility that the aftershocks had been triggered by the static stress changes due to the Chi-Chi earthquake.The judgement was based on the significance level with which one can reject the null hypothesis that aftershocks are independent of the static stress changes induced by the Chi-Chi earthquake.The null hypothesis implies the pos sibility of 0.5 for an individual event to fall into the region with the positive A CFS and a binomial possibility density function for the number of events that agree with the positive A CFS.Because thrust faulting is the most common type of rupture observed in the fold-and thrust belt, the A CFS referred to below is only for thrusts with attitude of NlOE, 30E.The results indicate that 4,453 out of the 6 , 810 aftershocks fell within the region with the positive A CFS.In other words, 65% of the aftershocks agree with the static stress triggering model.In a standard right-side test (e.g., Kreyszig 1979), the corresponding significance level of the test is less than 0.01 %.This means that the possibility of the number of aftershocks agreeing with a positive A CFS to be equal or larger than 4,453 is less than 0.01 % if the null hypothesis stands.This value of significance level is much smaller than a frequent choice of significance level of 5%; thus, the null hypothesis is rejected.

DISCUSSION
Although static stress triggering seems very promising in the case of the Chi-Chi earth quake sequence, there are several aspects that need to be improved upon in the future.First is the rupture model.The rupture model adopted in this preliminary study was inferred from teleseismic body waveforms.A better rupture model with higher resolution of the rupture characteristics can be derived from near-field strong motions recorded by dense broadband seismograph stations all over the island.Secondly, the Chelungpu fault should be modeled as Other than the fracture model, rock rheology is another aspect to be considered.The aseismic Central Range might reflect ductile deformation within the deep crust.Viscoelastic or elastoplastic analyses need to be applied to that area.This is important especially for long term triggering (e.g., Pollitz and Sacks 1997) which cannot be explained by elastic analyses.

Fig. 1 .
Fig. 1.Subsequent seismicty of the Chi-Chi earthquake from 22 September to 31 December, 1999 (Data provided by the Central Weather Bureau).The open circles indicate the locations of the aftershocks.Two N-S trending clusters of earthquakes east of the Chelungpu fault are separated by an aseismic Central Range.

Fig. 3 .Fig. 4 .
Fig. 3. Coulomb stress changes resolved onto thrust faults with attitude ofN10°E, 30°E by the Chi-Chi earthquake at the depth of 2.5 km.White dots show the locations of the aftershocks with focal depths between 0 and 5 km.The black star indicates the epicenter of the Chi-Chi mainshock.Any stress changes over or under the scale of the color index was automati cally assigned to the same color for positive or negative 5 bars, respec tively.

Fig. 5 .
Fig. 5. Coulomb stress changes resolved onto thrust faults with attitude ofN10°E, 30°E by the Chi-Chi earthquake at the depth of 12.5 km.White dots show the locations of the aftershocks with focal depths between 10 and 15 km.

Fig. 6 .
Fig. 6.Coulomb stress changes resolved onto right-lateral strike-slip faults with attitude of N75°E, 80°S by the Chi-Chi earthquake at the depth of 7 .5km.White dots show the locations of the aftershocks with focal depths between 5 and 10 km.

WeiFig. 7 .
Fig. 7. Coulomb stress changes resolved onto left-lateral strike-slip faults with attitude of N75°W, 90° by the Chi-Chi earthquake at the depth of7.5 km.White dots show the locations of the aftershocks with focal depths be tween 5 and 10 km. 639 a multi-segmented thrust to account for the fact that the strike of the fault changes from N-S to E-W near the northern end of the fault This consideration has not yet been taken into account in this paper, which may have led to a misinterpretation of static stress transfer around the northern termination of the Chelungpu fault.The assumption of unilateral slips on every fault patch of the Chelungpu fault is also not very reasonable in light of the GPS observations by Hwang et al. (1999), who indicated slip vectors changing directions along the Chelungpu fault trace.A variable slip model is therefore required.
but decelerate the seismic ity rate in a region where the Coulomb failure stress is decreased (e.g., Harris and Simpson,.