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

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