Accuracy of the Hypocenter Location and Fault Plane Orientation for Near Realtime Finite Fault Inversion

Wu-Cheng Chi, Asya Kaverina, and Doug Dreger


Recently there has been a push within the seismological community to produce maps of ground shaking intensity in near real time for emergency response purposes. In densely instrumented regions, such as Southern California, Japan, and Taiwan, these maps can be generated using ground-truth measurements. However, other approaches are needed for regions with sparse station coverage. One of them is to derive finite source parameters in near real time, then forward model the ground shaking in the regions of interest (e.g. Dreger and Kaverina, (2000)). To successfully predict ground motion we need to have good waveform fits at all azimuths from the hypocenter. An initial set of good source parameters will dramatically reduce the time required to derive a good slip model and enable us to generate synthetic ground shaking information. It is also beneficial to have correct finite source information soon after the earthquake. The information then can help to identify the causative fault plane, design temporary portable seismic networks to monitor the aftershocks surrounding the main event, and forward calculate the stress perturbation due to the earthquake.

We inverted strong motion data for the finite source parameters of 6 large aftershocks of the 1999 Chi-Chi, Taiwan earthquake. The locations and origin times are depicted in Figure 1. For each event, we derived a preferred model by testing different focal mechanisms, hypocenters, and other source parameters in more than 1000 inversions. We documented how the fits between the observed waveforms and the corresponding synthetics deteriorated as the hypocenter and focal mechanism deviate from those of the preferred model. These results will help to determine how accurate these parameters must be if we wish to derive slip models in near real-time for generating ShakeMaps.

Data Analyses and Results

More than 6 Chi-Chi, Taiwan Earthquake aftershocks with $M_{w}$ 5.8-6.4 were well-recorded by a strong motion network maintained by the Central Weather Bureau of Taiwan. They provided an unprecedented opportunity to study the finite source process of moderate sized earthquakes. Each aftershock was recorded by more than 200 strong motion stations. We use only data from stations that had no apparent timing errors and provide good azimuthal coverage. We have converted each waveform from digital counts to cm/s$^{2}$, removed the mean offset, integrated from acceleration to velocity, and bandpass filtered between 0.02 and 0.5 Hz with a four-pole acausal Butterworth filter before resampling the data to 10 sps. Using a frequency-wave number code from Chandan Saikia (Saikia, 1994), we calculated a catalog of Green's functions for an average 1D velocity model taken from a 3D tomographic study by Rau and Wu (1995). This 1D model had been tested in routine regional moment tensor studies of local and regional events and performed well for the finite fault inversions of Chi-Chi mainshock and aftershock. The Green's functions were then subjected to the same signal processing as the observed waveforms. We used strong motion data to invert the representation theorem for parameters of the finite source using a method pioneered by Hartzell and Heaton (1983). For each event we tested a range of values for each of the source parameters: the slip vector, fault orientation, location, hypocentral depth, rupture velocity, and dislocation rise time. In this modeling we assumed that the rupture velocity and dislocation rise time were constant and did not vary spatially. For each event, we performed more than 1000 sensitivity tests by varying the source parameters used in the inversions and we documented the influence these parameters have on the slip model and the waveform fits. The preferred models derived after these extensive tests usually gave more than 20% improvement in waveform fits.

We found that, if the deviation in hypocenters and focal mechanisms were less than 5 km and 20$^{o}$, respectively, we generally recovered more than 80% of the preferred model's synthetic waveform fit, measured by variance reduction. The length of 5 km (Figure 14.1) is similar, and maybe related, to the widths of the slip patches we modeled. For the thrust events, the input dip angle of the fault must be correct to within 20$^{o}$. For the strike-slip event, the input fault strike must also be within 20$^{o}$ of the true strike (Figure 14.2).


For each of the six Chi-Chi, Taiwan aftershock events, we performed more than 1000 sensitivity tests by varying the source parameters used in the inversions and we documented the influence these parameters have on the slip model and the waveform fits. Good waveform fits can mostly be achieved if the errors in hypocenters and focal mechanisms are within 5 km and 20$^{o}$, respectively. However, in some cases good waveform fits can also be achieved outside of the preferred ranges of the input source parameters. These results provide the criteria needed to evaluate the performance of the seismic network if we want to invert the finite fault parameters of magnitude 6 earthquakes in real time and use the source model to forward-model the ShakeMaps, which can be used by the seismic response authorities for seismic mitigation purposes.


We thank Dr. Willie Lee for providing the strong motion data from Central Weather Bureau (CWB) of Taiwan and Dr. Win-Gee Huang for the strong motion data from IES, Academia Sinica of Taiwan. We thank CWB for providing their aftershock seismicity data. This research is funded by NSF Grant EAR-0000893 and PEER Lifelines 1E06.


Dreger, D., and A. Kaverina, Seismic remote sensing for the earthquake source process and near-source strong shaking: A case Study of the October 16, 1999 Hector Mine Earthquake, Geophys. Res. Lett., it 27, 13,1941-1944, 2000.

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.

Rau, R.-J., and F. Wu, Tomographic imaging of lithospheric structures under Taiwan, Earth Planet. Sci. Lett., 133, 517-532, 1995.

Saikia, C.K., Modified frequency-wave-number algorithm for regional seismograms using Filon's quadrature-modeling of L(g) waves in eastern North America, Geophys. J. Int., 118, 142-158, 1994.

Figure 14.1: Preferred locations of the aftershock events studied are marked as stars. The origin times for these events are shown at the upper left corner. The dot color shows the variance reduction derived from inversions using that particular location as epicenter. It shows how rapidly the waveform fits, measured by variance reduction (VR), deteriorate if the epicentral information is incorrect. In general, the VR will drop 20% if the epicenter is off by 5 km. Results for Event 5 are shifted to the east for clear presentation. The blue rectangles are the fault dimensions of the preferred slip models. The cross section in the upper right corner shows a schematic with possible rupture scenarios for the aftershocks we studied.
\epsfig{file=chi03_1_1.eps, width=8cm}\end{center}\end{figure}

Figure 14.2: The results of sensitivity tests on the focal mechanism for each event. The P axis of each focal mechanism tested is plotted in lower hemisphere stereonet projection. The left stereonets show the east-dipping fault planes, the right ones the west-dipping planes. The color shows the variance reduction. Note VR deteriorates fastest when the plunge of the P axis changes, implying the waveform fits are most sensitive to the dip, and possibly rake, of the focal mechanism for the thrust events. For the strike-slip aftershock (Event 3), VR is more sensitive to strike. We interpreted this to be the result of the amplitude of the S wave radiation pattern, which controls the inversion results. The star shows the P axis of the preferred focal mechanism. Overall, the waveform fits are pretty good if the fault orientation is accurate within 20 degrees.
\epsfig{file=chi03_1_2.eps, width=15cm}\end{center}\end{figure*}

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