Subsurface uncertainty quantification with deep geologic priors: A variational Bayesian framework

Abstract

Recent years have seen surging interest in the area of geophysical inversion and uncertainty quantification (UQ) using data-driven priors for geologic domains. In particular, deep generative models, e.g., variational autoencoders (VAEs) and generative adversarial networks (GANs), have been employed in a number of studies to either regularize deterministic sub-surface inversion, or to act as prior distributions for Bayesian inversion. These models offer a low-dimensional representation of high-dimensional property fields, by capturing intrinsic structural features observed in nature, thus providing a common prior for the concomitant assimilation of data of different modalities such as seismic, fluid flow, electromagnetism, gravity etc. On one hand, this low-dimensionality is an important enabler for Bayesian methods, which are generally deemed impractical for industrial-scale subsurface UQ applications. On the other hand, the computational burden of evaluating expensive forward models and the non-convexity/multi-modality of the resulting inverse problems continue to present a formidable challenge for Bayesian methods. Towards the goal of scalable subsurface Bayesian inversion, we present a framework that considerably mitigates the aforementioned challenges of expensive physics and complex posteriors. The proposed framework exploits the low-dimensionality provided by deep generative priors, and approximates the posterior using deep mixture models via variational inference. The efficacy of our proposal is demonstrated on a joint inverse problem employing gravity and seismic data within a synthetic testbed.