3D Bayesian Variational Full Waveform Inversion

TL;DR

This paper evaluates three variational inference methods for 3D seismic full-waveform inversion, demonstrating their trade-offs in computational efficiency and uncertainty quantification, and establishing the practical applicability of 3D Bayesian FWI.

Contribution

It applies and compares three variational inference techniques to 3D FWI, analyzing their performance and computational costs, and demonstrates the feasibility of Bayesian FWI in three dimensions.

Findings

ADVI is the most computationally efficient but underestimates uncertainty.

SVGD provides biased results with high computational cost.

sSVGD offers accurate results at intermediate computational expense.

Abstract

Seismic full-waveform inversion (FWI) provides high resolution images of the subsurface by exploiting information in the recorded seismic waveforms. This is achieved by solving a highly nonnlinear and nonunique inverse problem. Bayesian inference is therefore used to quantify uncertainties in the solution. Variational inference is a method that provides probabilistic, Bayesian solutions efficiently using optimization. The method has been applied to 2D FWI problems to produce full Bayesian posterior distributions. However, due to higher dimensionality and more expensive computational cost, the performance of the method in 3D FWI problems remains unknown. We apply three variational inference methods to 3D FWI and analyse their performance. Specifically we apply automatic differential variational inference (ADVI), Stein variational gradient descent (SVGD) and stochastic SVGD (sSVGD), to a 3D FWI problem, and compare their results and computational cost. The results show that ADVI is the most computationally efficient method but systematically underestimates the uncertainty. The method can therefore be used to provide relatively rapid but approximate insights into the subsurface together with a lower bound estimate of the uncertainty. SVGD demands the highest computational cost, and still produces biased results. In contrast, by including a randomized term in the SVGD dynamics, sSVGD becomes a Markov chain Monte Carlo method and provides the most accurate results at intermediate computational cost. We thus conclude that 3D variational full-waveform inversion is practically applicable, at least in small problems, and can be used to image the Earth's interior and to provide reasonable uncertainty estimates on those images.