Soil electrical conductivity imaging using a neural network-based forward solver: Applied to large-scale Bayesian electromagnetic inversion

Abstract

In recent years, probabilistic solution to the inversion of electromagnetic induction (EMI) data has been progressively developed for non-invasive subsurface characterization. However, Bayesian inversion of EMI data using forward solvers based on full solution of Maxwell's equation is associated with computationally expensive modelings, particularly for large-scale surveys. Here, we incorporated artificial neural network (ANN) with Bayesian inference to obtain subsurface electromagnetic conductivity image (EMCI) from EMI data down to 10 m depth. In this respect, a complex EMI forward model was replaced by a trained neural network (ANN proxy forward function) that can be evaluated comparably rapidly. The accuracy of the ANN-based forward solver was examined using different synthetic subsurface models. The proposed methodology was applied on EMI data measured with a DUALEM-421 s sensor from 10 ha study site in the Alken Enge area of Denmark. We compared the inversely estimated EMCI with the counterpart obtained from a quasi-three-dimensional (quasi-3D) spatially-constrained deterministic algorithm as a standard code. The network training procedure was performed within few minutes, and once it was trained, the ANN-based forward solver returned roughly 150,000 model responses per second. This value for the EMI forward solver was around 400, demonstrating the computational efficiency of the ANN proxy forward function. The theoretical simulations demonstrated that the ANN-based forward solver accurately mimics the EMI response within the training range. Moreover, the proposed inversion strategy successfully delineated the subsurface EMCI from Alken Enge area. This approach thus facilitates rapid and accurate subsurface conductivity imaging using Bayesian inversion of multi-configuration EMI data, which is particularly pertinent for large-scale measurements.