A variational inference inversion approach to electrical resistivity tomography

Abstract

We present a particle-based variational inference approach for Electrical Resistivity Tomography (ERT) using the Annealed Stein Variational Gradient Descent (A-SVGD) algorithm. This approach enables efficient approximation of the posterior distribution while addressing common limitations of standard SVGD—such as mode collapse and underestimation of variance—through a temperature-based annealing strategy. To reduce both the dimensionality of the inverse problem and computational cost, we perform the inversion in a compressed model space using the Discrete Cosine Transform (DCT), aligning the number of particles with the number of parameters—an ideal setting for a SVGD algorithm. We validate our method on both synthetic and real datasets, showing improved convergence and lower data misfit compared to standard SVGD and conventional deterministic inversion, along with effective uncertainty quantification comparable to those provided by a well-established gradient-based Markov Chain Monte Carlo algorithm. These results underscore the potential of A-SVGD, especially when combined with model-space compression, as a scalable and robust framework for nonlinear geophysical inversion.