3D Bayesian Full Waveform Inversion and Efficient Analysis of Prior Hypotheses

Spatially 3-dimensional seismic full waveform inversion (3D FWI) is a highly nonlinear and computationally demanding inverse problem that constructs 3D subsurface seismic velocity structures using seismic waveform data. To characterise non-uniqueness in the solutions we demonstrate Bayesian 3D FWI using an efficient variational method called physically structured variational inference to 3D acoustic Bayesian FWI. The results contain the true velocity model, and provide reasonable posterior uncertainty estimates, at a computational cost that is only an order of magnitude greater than that of standard, deterministic FWI. Furthermore, we employ a variational prior replacement methodology to calculate Bayesian solutions corresponding to different classes of prior information, and develop an effective approach to analyse those prior hypotheses by constructing Bayesian L-curves. This provides insight into the sensitivity of the inversion process to different prior assumptions. This opens the possibility that fully probabilistic 3D FWI can be performed at a sufficiently low cost to be practical in small FWI problems, and to be used to test different prior hypotheses.