Bayesian Inference for Subsurface Geophysical Inverse Problems

Abstract In subsurface studies, geophysical inverse modeling aims to infer key Earth physical properties, such as deep geological structures, lithology, and fluid distribution from indirect observations, particularly geophysical data, while rigorously quantifying uncertainty. These inverse problems are typically high‐dimensional and computationally demanding, requiring efficient probabilistic inference methods. Bayesian inversion provides a coherent statistical framework that integrates prior geological knowledge with observed data, enabling systematic uncertainty quantification in subsurface characterization. Gradient‐free Bayesian sampling methods have long been used to characterize complex posterior distributions and remain foundational in geophysical inversion. Recently, in scenarios where gradient information can be efficiently obtained, gradient‐informed Bayesian inference methods have emerged as effective alternatives. By leveraging the local geometry of the posterior, these methods enable more efficient exploration of high‐dimensional parameter spaces. Concurrently, deep learning has further enhanced Bayesian inversion by facilitating implicit geological priors, surrogate forward modeling, and automatic differentiation for efficient gradient computation. This review provides a comprehensive synthesis of both gradient‐free and gradient‐informed Bayesian inference techniques, with an emphasis on the latter, and examines their applications in seismic, electromagnetic, gravity, and multiphysics inverse problems. Building on these developments, we introduce Differentiable Bayesian Inversion as a potential unifying conceptual framework that integrates deep‐learning‐based geological prior parameterization, physics‐based or surrogate forward modeling, and probabilistic reasoning within a modular, differentiable architecture. We conclude by outlining open challenges and future research directions toward developing robust, interpretable, and uncertainty‐aware inversion frameworks for increasingly complex geoscientific applications.