Alternative Misfit Functions for FWI Applied to Surface Waves

Abstract

The aim of this study is to determine the advantages and limitations of different misfit functions for an application of Full Waveform Inversion (FWI) to surface waves. The difference-based L2 norm, classically used in FWI and sensitive to both amplitude and phase information, suffers from cycle-skipping and local minima. For slow surface waves propagating in the low velocity near surface, the problem of cycle-skipping is even greater due to their small wavelengths. In the absence of low frequencies, convergence may not be possible when starting from a smooth initial mode. Alternative misfit functions applied in various data domains are therefore investigated with the aim of overcoming this issue. Taking the difference-based L2 norm as a basis for comparison, simple synthetic tests are conducted to evaluate a weighted cross-correlation and a singular value decomposition approach as alternative misfit functions, as well as investigating the effect of calculating the residual in different data domains such as the (omega-k), (tau-p) and (omega-p) domains.