Methodology

The inversion method used is discussed in detail by Ji et al. (2002a, 2003). This unique method performs a waveform inversion in the wavelet domain rather than in the traditional time or frequency domain (Ji et al., 2002a). Both synthetic and observed waveforms are decomposed into wavelets, and the differences between individual wavelet coefficients are minimized. Consequently, we are able to weight the seismic signals on a 2D time-frequency plane instead of a 1D time or frequency axis. The frequency content is usually associated with the earthquake rupture process, and the time information can tell us when this process occurred. Our approach, therefore, takes full advantage of the broadband characteristics of modern seismic records and provides a very efficient environment for simultaneously extracting useful information while depressing noise. Even though constraints on the earthquake rupture process are greatly improved by this approach, it is still difficult to reconstruct the slip history, or the so-called rise time function (RTF) of each subfault in great detail. Rather than representing the RTF with multiple time windows, which increases the number of free parameters several times, we use simple analytic functions (Ji et al. 2002ab, 2003). All of the above are integrated into a simulated annealing inverse procedure to guarantee a global optimal result (Ji et al. 2002a).