Conditional Diffusion Models for Hydrogeologic Parameter Estimation from Electrical Resistivity Tomography Time-lapse Data

• Introduced Conditional Diffusion Model (CDM) for robust, uncertainty-aware inversion of time-lapse Electrical Resistivity Tomography (ERT) data to estimate hydrogeological parameters. • Designed a robust inversion framework that effectively handles the ill-posed nature of subsurface geophysical inversion while providing reliable uncertainty quantification. • Evaluated the CDM using accuracy, precision, and goodness metrics, confirming its reliability in quantifying uncertainty for 29 hydrogeological parameters. • Demonstrated the ability of forward simulations to accurately reproduce conditional ERT responses based on the estimated hydrogeological parameters. Estimating hydrogeologic parameters from time-lapse electrical resistivity tomography (ERT) monitoring data is challenging due to the inherent non-uniqueness and ill-posed nature of mapping measured geophysical responses to subsurface flow and transport properties. In this work, we present an artificial intelligence (AI)-driven methodology employing conditional diffusion models to robustly estimate hydrogeologic simulation parameters while explicitly quantifying uncertainty. Our approach uses a reverse diffusion process that starts with a Gaussian random vector and gradually denoises it conditioned on time-lapse ERT monitoring data to recover a 29-dimensional parameter vector. The trained AI model generates ensembles of subsurface models that honor the conditional data, providing a mechanism for assessing uncertainty. A goodness-of-fit metric assesses the accuracy and precision of the uncertainty distribution for each parameter, avoiding unreliable or overconfident solutions. Experimental results modeled after an in-situ soil flushing treatment conducted at the Hanford 100K East site in Washington State, USA, demonstrate that the recovered parameter sets produce simulated ERT data in close agreement with the given conditional ERT data, highlighting that conditional diffusion models offer a robust solution for geophysical inversion, including parameter uncertainty estimation.