Bayesian subsampling of time-domain electromagnetic data using kernel density product

The Bayesian method is a powerful tool to estimate the resistivity distribution and associated uncertainty from time-domain electromagnetic (TDEM) data. Because the forward simulation of the TDEM method is computationally expensive and a large number of samples are needed to globally explore the model space, the full Bayesian inversion of the TDEM data is limited to layered models. To make the high-dimensional Bayesian inversion tractable, we have adopted a divide-and-conquer strategy to speed up the Bayesian inversion of TDEM data. First, the full data sets and model spaces are divided into disjoint batches based on the coverage of the sources so that the independent and highly efficient Bayesian subsampling can be conducted. Then, the samples from each subsampling procedure are combined to get the full posterior. To obtain an asymptotically unbiased approximation to the full posterior, a kernel density product method is used to reintegrate samples from each subposterior. The model parameters and their uncertainty are estimated from the full posterior. Our method is tested on synthetic examples and applied to a field data set acquired with a large fixed-loop configuration. The 2D section from the Bayesian inversion revealed several mineralized zones, one of which matches well with the information from a nearby drillhole. The field example indicates the ability of the Bayesian inversion to infer reliable resistivity and uncertainty.