Approximate Bayesian Geophysical Inversion using Generative Modeling and Subset Simulation

We present preliminary work on solving geophysical inverse problems by exploring the latent space of a joint Generative Neural Network (GNN) model by Approximate Bayesian Computation (ABC) based on Subset Simulation (SuS). Given pre-generated subsurface domains and their corresponding solver outputs, the GNN surrogates the forward solver during inversion to quickly explore the input space through SuS and locate regions of credible solutions. Akin to ABC methods, our methodology allows to tune the similarity threshold between observed and candidate outputs. We explore how tuning this threshold influences the uncertainty in the solutions, allowing to sample solutions with a selected diversity level. Our initial tests were carried out with data from straight-ray (linear) tomography with Gaussian priors on slowness fields and Gaussian versus Gumbel observation noise distributions. We are presently testing the methodology on non-linear physics to demonstrate its applicability in more general inversion settings.