Stochastic seismic waveform inversion using generative adversarial networks as a geological prior

TL;DR

This paper introduces a novel seismic inversion method combining deep generative models with PDE-based wave propagation, enabling efficient Bayesian inference of subsurface structures from seismic data.

Contribution

It integrates GANs as geological priors with PDE solvers and MALA sampling for Bayesian seismic inversion, a novel approach in geophysics.

Findings

Efficient sampling of geological models consistent with seismic data.

Generation of diverse subsurface realizations reflecting observed seismic responses.

Demonstration of the method's capability to incorporate complex geological priors.

Abstract

We present an application of deep generative models in the context of partial-differential equation (PDE) constrained inverse problems. We combine a generative adversarial network (GAN) representing an a priori model that creates subsurface geological structures and their petrophysical properties, with the numerical solution of the PDE governing the propagation of acoustic waves within the earth's interior. We perform Bayesian inversion using an approximate Metropolis-adjusted Langevin algorithm (MALA) to sample from the posterior given seismic observations. Gradients with respect to the model parameters governing the forward problem are obtained by solving the adjoint of the acoustic wave equation. Gradients of the mismatch with respect to the latent variables are obtained by leveraging the differentiable nature of the deep neural network used to represent the generative model. We show that approximate MALA sampling allows efficient Bayesian inversion of model parameters obtained from a prior represented by a deep generative model, obtaining a diverse set of realizations that reflect the observed seismic response.