Bayesian Inversion of Time Domain Electromagnetic (TDEM) Synthetic Data using Langevin Monte Carlo (LMC)

Abstract

The inversion of time domain electromagnetic (TDEM) data is an ill-posed problem. This makes the standard inversion procedure, which is to linearize the related objective function. Then take a deterministic approach to determine a solution that can minimize the said objective function, which has the potential to be trapped in a local minimum. In this study, we solved the problem of TDEM data inversion using the Bayesian framework by generating a sample from the posterior distribution. The posterior distribution contains information related to the uncertainty of the TDEM data and the results of the forward modeling formulation, and prior information about the subsurface parameter model. In conducting the sampling process, we use the Langevin Monte Carlo (LMC) algorithm, one of many gradient-based Markov chain Monte Carlo (MCMC) sampling algorithms. Bayesian inversion was performed on synthetic data generated through the forward modeling of several test models. We used a model with varying thickness and resistivity values for inversion. We also added a prior probability distribution related to the smoothness constraint between resistivity values in adjacent layers allowing sharp and smooth transitions.