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

Abstract: 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 method called physically structured variational inference, and apply it to 3D acoustic Bayesian FWI. The results 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 deploy variational prior replacement to calculate Bayesian solutions corresponding to different classes of prior information at low additional cost. The results obtained using prior information that models should be smooth show loop-like high uncertainty structures that are consistent with fully nonlinear inversion results presented previously. These structures disappear when smoothing is not imposed, so we conclude that they may be caused by smoothness constraints in tomographic problems. We further analyse a variety of prior hypotheses by constructing Bayesian L-curves, which reveal the sensitivity of the inversion process to different prior assumptions. To our knowledge, this is the first study that allows such prior hypotheses to be compared in probabilistic 3D FWI at feasible computational cost. This work shows that fully probabilistic 3D FWI can be performed and can be used to test different prior hypotheses, at a cost that may be practical, at least in small problems.