Geostatistical Inversion for Subsurface Characterization Using Stein Variational Gradient Descent With Autoencoder Neural Network: An Application to Geologic Carbon Sequestration

Abstract Geophysical subsurface characterization plays a key role in the success of geologic carbon sequestration (GCS). While deterministic inversion methods are commonly used due to their computational efficiency, they often fail to adequately quantify the model uncertainty, which is essential for informed decision‐making and risk mitigation in GCS projects. In this study, we propose the SVGD‐AE method, a novel geostatistical inversion approach that integrates geophysical data with prior geological knowledge to estimate subsurface properties. SVGD‐AE combines Stein Variational Gradient Descent (SVGD) for sampling high‐dimensional distributions with an autoencoder (AE) neural network for re‐parameterizing reservoir models, aiming to accurately preserve geologic characteristics of reservoir models derived from prior knowledge. Through a synthetic example of pre‐stack seismic inversion, we demonstrate that the SVGD‐AE method outperforms traditional probabilistic methods, particularly in inverse problems with complex posterior distributions. Then, we apply the SVGD‐AE method to the Illinois Basin—Decatur Project (IBDP), a large‐scale CO 2 storage initiative in Decatur, Illinois, USA. The resulting petrophysical models with quantified uncertainty enhance our understanding of subsurface properties and have broad implications for the feasibility, decision making, and long‐term safety of CO 2 storage at the IBDP.