Uncertainty Quantification of the Fresh-Saltwater Interface from Time-Domain Electromagnetic Data

Abstract

Geophysical methods provide a cost-effective way to characterize the subsurface for hydrogeological projects, but they rely on solving an inverse problem. Traditionally, deterministic approaches are used, which face challenges due to non-uniqueness. Stochastic methods offer uncertainty quantification but demand high computational resources. Bayesian Evidential Learning (BEL) bypasses full stochastic inversion by approximating the posterior distribution at lower cost. However, as with Monte Carlo techniques, efficiency depends on the number of inversion parameters. We show that incorporating prior knowledge into parameterization reduces unknowns and computational burden. Using time-domain electromagnetic data, we identify fresh - saltwater interfaces in the Flemish coastal aquifer. Conventional blocky or smooth deterministic inversions often misrepresent this transition zone as too sharp or too gradual. To address this, we parameterize the zone with two variables - depth and thickness - assuming a linear transition. This retains the compactness of parametric inversion while allowing sharp or gradual interfaces like voxel-based methods. To assess reliability, we invert these parameters stochastically using BEL with Thresholding (BEL1D-T). Results indicate this approach effectively captures uncertainty for synthetic and field data. The transition zone remains uncertain due to survey design and inherent non-uniqueness, yet our probabilistic method achieves this without the heavy computational cost of traditional stochastic approaches.