Waveform Inversion via Nonlinear Differential Semblance Optimization

This article describes a nonlinear differential semblance approach to waveform inversion. Nonlinear differential semblance optimization combines the ability of full waveform inversion to account for nonlinear physical effects, such as multiple reflections, with the tendency of differential semblance migration velocity analysis to avoid local minima. It borrows the gather-flattening concept from migration velocity analysis, and updates the velocity by flattening primaries-only gathers obtained via nonlinear inversion. We describe the underlying idea and formulation of this algorithm, and present a layered 2D acoustic inversion excercise for which standard full waveform inversion fails, whereas nonlinear differential semblance succeeds in constructing a kinematically correct model and fitting the data rather precisely.