Probabilistic inversion of electromagnetic data using stein variational gradient descent

Summary

Geophysical inversion is inherently non-unique, and efficient uncertainty quantification remains a major challenge for large-scale applications. Conventional Bayesian approaches, such as Markov chain Monte Carlo (McMC), provide rigorous posterior estimates but are often computationally prohibitive, while deterministic inversion methods lack uncertainty characterization. In this study, we develop a Stein variational gradient descent (SVGD) framework for one-dimensional (1-D) geophysical Bayesian inversion. SVGD is a variational inference method that approximates the posterior distribution using an ensemble of interacting particles, which are iteratively updated through gradient-based optimization. The proposed framework is evaluated using airborne electromagnetic (AEM) data in both synthetic and field scenarios. Synthetic tests demonstrate that SVGD effectively recovers subsurface resistivity structures while capturing associated uncertainty. The influence of particle number on posterior resolution and computational cost is analyzed, and comparison with McMC highlights differences in posterior characteristics and computational efficiency. Application to field data from the Mississippi Alluvial Plain shows that the SVGD posterior mean agrees well with deterministic inversion results, while providing the uncertainty estimates. In addition, noise sensitivity tests are conducted to investigate the impact of data errors on inversion behavior. We find that increasing noise level degrades resolution and shifts the posterior toward prior-dominated regimes. Overall, the SVGD framework provides a flexible and scalable approach to probabilistic geophysical inversion, with strong potential for extension to higher-dimensional problems.