A Nonlinear Differential Semblance Strategy for Waveform Inversion: Experiments in Layered Media

This paper proposes an alternative approach to the output leastsquares (OLS) seismic inversion for layered-media. The latter cannot guarantee a reliable solution for either synthetic or field data, because of the existence of many spurious local minima of the objective function for typical data, which lack low-frequency energy. To recover the low-frequency lacuna of typical data, we formulate waveform inversion as a differential semblance optimization (DSO) problem with artificial low-frequency data as control variables. This version of differential semblance with nonlinear modeling properly accounts for nonlinear effects of wave propagation, such as multiple reflections. Numerical experiments with synthetic data indicate the smoothness and convexity of the proposed objective function. These results suggest that gradient-related algorithms may successfully approximate a global minimizer from a crude initial guess for typical band-limited data.