Stochastic Seismic Waveform Inversion Using Generative Adversarial Networks as a Geological Prior

Abstract

We present an application of deep generative models in the context of partial differential equation constrained inverse problems. We combine a generative adversarial network representing an a priori model that generates geological heterogeneities and their petrophysical properties, with the numerical solution of the partial-differential equation governing the propagation of acoustic waves within the earth’s interior. We perform Bayesian inversion using an approximate Metropolis-adjusted Langevin algorithm to sample from the posterior distribution of earth models 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 Metropolis-adjusted Langevin sampling allows an 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.