Considering the inaccurate Green’s functions and the errors of source models during finite fault source inversion

Abstract:

With recent improvements in geophysical observations and computational capability, the rupture processes of large earthquakes are routinely imaged with seismic and geodetic data. However, similar to other geophysical problems, the inverted solutions are contaminated with uncertainties caused by various limitations, such as data coverage, observational noise, inaccurate earth response, fault parameterization, inversion algorithms, etc. While it is difficult to estimate the exact impact that each source of uncertainty has on the inverted solutions, their potential effects should be honored in the data mining procedure, especially in the design of the misfit function. We notice that for most finite fault inversion algorithms using seismic data, the misfit between observed and synthetic seismograms is assumed to be temporally homoscedastic. However, considering the errors of subfault Green’s functions and the inverted model, the error associated with the waveform misfit should be heteroscedastic, gradually increasing with time. As a result, the misfits associated with early stages of a large rupture should be weighted more compared with those associated with the later stages. In this study, we develop a series of new objective functions to measure waveform misfits in a sense of weighted least squares. The weights are defined as the reciprocals of standard deviations of combined synthetic and observed noise, which are functions of time and are numerically estimated after assuming different noise characterizations of subfault Green’s functions, observations, and inverted source itself. Fast algorithms are developed so that the weights can be updated iteratively even during the nonlinear finite fault inversions. The justifications and potential impacts of these new objective functions are addressed using both the SIV examples and the recent earthquakes. In the end, it is noteworthy that the proposed approaches could be incorporated into other linear and nonlinear finite fault algorithms.