A Semi-Empirical Approach for Generating Synthetic Seismograms for use in Matched-Waveform Source Location.

A matched field processor for seismic stations is developed to provide refined locations and source parameters. The concept is to find a synthetic seismogram with the best fit to the observed seismograms. For the seismic location problem, synthetic waveforms are computed on a three dimensional grid. The synthetic waveforms are compared to observed data at each grid point. The best fit between the synthetic waveform and the data in the grid is assumed to be the optimal source location. A limit to this approach is the computation of the synthetic waveform, i.e., errors in the earth model will propagate to errors in the synthetic waveform which appear as errors in the estimated location and source parameters. One method to mitigate this limitation is to insert observed waveforms from "Ground Truth" events into the computation of the synthetic waveforms. The semi-empirical approach is based on the time invariance of the propagation medium, i.e., the seismic waveform from a specific location from one event with a specific source mechanism recorded at a station will be identical to the waveform from a second event at the same location with the same source mechanism recorded at the same station. Typically, seismic events do not have the same source parameters. However, full synthetic waveforms for "Ground Truth" events can be computed. By deconvolving these synthetic waveforms from the observed waveforms, and then convolving with the synthetic waveforms computed for nearby locations with arbitrary source mechanisms, the semi-empirical synthetic waveforms can be generated. Errors in the synthetic waveforms are expected to cancel. The application of this technique to multiple "Ground Truth" events stabilizes the deconvolution by averaging over multiple events. In addition, spectral smoothing is used to further stabilize the deconvolution. Using this approach, semi-empirical synthetic seismograms are computed for the fundamental dislocation 3-D grid. The optimal source parameters (moment tensor) are determined by matching the observed waveforms to the semi-empirical synthetic waveforms at each grid point using an earthquake that was not in the Ground Truth set,. The optimal solution is determined to be the one with the least RMS difference. The overall approach is demonstrated with both simulated data and data from aftershocks of the Hector Mine Earthquake.