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Finite Fault Inversion of the September 25, 1999 ($M_{w}$=6.4) Taiwan Earthquake

Wu-Cheng Chi and Douglas Dreger


More than six $M_{w}$ 6 and greater aftershocks of the 1999, Chi-Chi, Taiwan earthquake ($M_{w}$=7.6) were well-recorded. In this study we invert for the finite source rupture process for one of the largest aftershocks (23.86N, 121.01E) that occurred on 1999/9/25 at 23:52:49.5 UTC, 5 days after the mainshock. Through inversions we hope to discriminate the causative fault plane from the auxiliary plane. There are 3 scenarios for the ruptured plane: down-dip extension of the mainshock on the detachment, backthrust above the detachment, and a basement-involved fault below the detachment (Figure 28.1). Although the hypocenter is located in the vicinity of the proposed major shallow east-dipping fault, previous data could not exclude the possibility of a high-angle, west-dipping conjugate fault (backthrust). If true, a backthrust scenario will give us an important constraint on the deep crustal geometry under Taiwan. In addition, recent seismicity studies (e.g. Carena et. al., EOS 82(47), p1176, 2001) show a steep, west-dipping fault below the detachment and the aftershock might have occurred on this fault, if the aftershock focal depth is actually deeper than reported. This scenario implies that large seismic strains can be stored in the footwall of the detachment and future geodynamic studies might need to consider a deformable footwall block that can generate $M_{w}$ $>$ 6 earthquakes. If the rupture was on the proposed detachment, we can delineate its attitude and slip distribution, which can be compared to the mainshock.

Figure 28.1: (a) Location map. The large star shows the epicenter of the Chi-Chi mainshock and its surface rupture is shown as the thick solid lines. The small star is the epicenter of the 9/25 event from this study. The 11 stations we used to invert the 9/25 event are plotted as triangles. The dense vectors show the 9/25 slip derived from this study. The maximum slip is 1.8 m. The sparse vectors show the mainshock model (Chi et al., 2001), where the maximum slip is  10 m. (b) A schematic cross section along AA', showing 3 possible 9/25 rupture scenarios as discussed in the text.
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Method and Results

We used strong motion data from the Central Weather Bureau of Taiwan (Lee at al., 2001) to invert the representation theorem for finite source parameters by using the method of Hartzell and Heaton (1983). We used a linear least-squares inversion of observed velocity seismograms to compute the spatio-temporal slip distribution. To improve inversion stability, we have applied the following additional constraints: slip-positivity, Laplacian smoothing, and moment minimization. We have performed a grid-search over a range of focal parameters to find the optimal orientation using the variance reduction measure. In total, 1036 inversions were performed and we chose 5/30/100 (variance reduction 73 percent) as our preferred model.

Interpretation and Conclusion

One surprising outcome from this study is that the strike of our preferred focal mechanism (5) is different from that of teleseismic results (28). An initial teleseismic moment tensor inversion for the Chi-Chi mainshock also gave a strike of 26, compared with the strike of 5 derived from the mainshock surface rupture, thus this discrepancy could be systematic and relate to complex crustal velocity structures underneath Taiwan. The dip is 30 to the east.

The relatively large moment release from this aftershock indicates that its effects should be incorporated into the ongoing aftershock/afterslip studies. Our results might help recalibrate the coseismic/postseismic GPS data. Here we forward modeled the GPS displacements using our slip model in an elastic half space (c.f. Okada, 1992). For stations near the aftershock epicenter, most of the horizontal surface displacements are about 1/500 of the observed GPS data from the mainshock. The small displacements are due to the greater depth of this aftershock. However, the displacements can still be up to 3.3 cm at some GPS stations, and thus need to be taken into account in afterslip studies.


We thank Roland Burgmann and David Schmidt for their constructive discussions. This research is partially funded by NSF Grant EAR-0105998.


Chi, Wu-Cheng, D. Dreger, and A. Kaverina, Finite-source modeling of the 1999 Taiwan (Chi-Chi) Earthquake derived from a dense strong-motion network, Bull. Seism. Soc. Am., 91, 1144-1157, 2001.

Hartzell, S.H., and T.H. Heaton, Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California, Earthquake, Bull. Seism. Soc. Am., 73, 1553-1583, 1983.

Lee, W. H.K., T.C. Shin, K.W. Kuo, and K.C. Chen, CWB free-field strong-motion data from the 921 Chi-Chi Earthquake: Volume 1. digital acceleration files on CD-ROM, pre-publication Version (December 6, 1999), Seismology Center, CWB, Taipei, Taiwan, 1999.

Okada, Y., Internal deformation due to shear and tensile faults in a half-space, Bull. Seism. Soc. Am., 82, 1018-1040, 1992.

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