Waveform inversion for seismic source processes with uncertainty of Green's function

Errors in observation equations generally consist of observation errors and modeling errors, though modeling errors have been commonly neglected in seismic waveform inversion analyses. As for modeling errors, terms originated from uncertainty of Green's function seem to be most important, because it is well recognized that errors of Green’s function can severely bias the result of the seismic waveform inversion. In the present study, we introduced uncertainty of Green's function into the seismic source inversion analyses. Here, as a typical characteristic of modeling errors, uncertainty of Green's function results in covariance components (off-diagonal components) of the data covariance matrix. By applying the developed inverse method to the teleseismic P-wave data of the 2006 Java, Indonesia tsunami earthquake, we succeeded in obtaining a plausible slip distribution and moment rate function without the non-negative slip condition. If we neglect the covariance components as in the conventional formulation, the total slip distribution contains large slip areas with unrealistic slip directions. If we use a stronger smoothing constraint, we can obtain a more plausible slip distribution, but then the moment rate function becomes too smooth. By comparing the observed waveforms with the synthetic waveforms computed from the new and the conventional formulations, the superiority of the new formulation is even clearer, particularly in high frequency components. Thus, the effect of correlated errors originated from uncertainty of Green's function is crucial for seismic waveform inversion. This fact may contribute to the discrepancy between seismic source models among researchers.