Accelerated Bayesian Inversion of Transient Electromagnetic Data Using MCMC Subposteriors

Transient electromagnetic method (TEM) is one of the major tools to image the subsurface resistivity. The gradient-based inversion of TEM data only provides a unique solution using a subjectively defined regularization penalty, leaving the uncertainty of the solution unaddressed. The Bayesian method can be used to estimate the model parameters, as well as quantify their uncertainty. However, it requires far higher computational costs than gradient-based inversion, which limits the Bayesian inversion of TEM data to 1-D assumptions. We propose an accelerated Bayesian method based on Markov chain Monte Carlo (MCMC) subposteriors to perform full 2-D inversion of TEM data. A robust scheme is designed to divide the model space of a TEM profile into subspaces so that independent MCMC chains can be used to update the parameters in each subspace in parallel. The division is based on the coverage of the source loops using a cumulative sensitivity matrix. Then, the subposteriors obtained at each subspace are merged to approximate the full posterior of the model space using a weighting strategy. A numerical test of a 2-D valley model is used to validate the proposed method. The Bayesian inversion successfully obtained posterior that converges to the true model. The median model makes a good inference of the model parameters, while the probability density function gives their uncertainty estimates. The statistical model of interest can be further extracted from the model ensemble. The proposed method provides an effective framework for Bayesian inversion of TEM data with a multidimensional forward operator.