Rapid Discriminative Variational Bayesian Inversion of Geophysical Data for the Spatial Distribution of Geological Properties

We present a new, fully probabilistic and nonlinear inversion method to estimate the spatial distribution of geological properties (depositional facies, diagenetic rock types, or other rock properties) from geophysical data (e.g., seismic data). Contrary to the conventional generative approach that models solution probabilities via the likelihood of observed data, our method uses a discriminative approach that directly models the posterior distribution of the geological properties given the data. This reduces the modeling effort significantly and allows machine learning algorithms such as neural networks to be deployed to solve large geophysical inference problems. We show that our method honors spatial distributions of geological parameters supplied as prior information about local geology and can be trained using supervised learning to be robust against noise present in the data as long as we can provide statistical characteristics of the noise. Exact Bayesian inference is almost always infeasible in practice because it requires normalization of the posterior distribution; this is intractable for large models and must therefore be approximated. Most existing probabilistic inversion methods use stochastic sampling (e.g., Markov chain Monte Carlo, McMC) for approximate inference. However, McMC involves the use of subjective criteria to detect convergence. We use the variational Bayes method to transform probabilistic inference into numerical optimization. This is a more efficient, deterministic alternative to McMC‐based inference for suitably structured problems. Our method thus avoids extensive sampling during inference, yet provides fully probabilistic Bayesian results, and is therefore scalable to higher dimensional problems.