Trans-dimensional Bayesian inversion for airborne EM data in sparse domain

Abstract

The conventional trans-dimensional Bayesian inversion uses Monte Carlo method to search the model space for a solution that satisfies both the acceptance probability and data fitting. With this method one can get the inverse model based on the maximum probability and determine the model uncertainty. However, because the search space is too big, the conventional Bayesian method can only invert simple models, which means that it may not be well applied to the inversion of actual geophysical survey data. In this paper, we propose a new inversion framework based on sampling via a deformed binary-tree structure and take the wavelet coefficients for sparsely constrained Bayesian inversions. This method has the advantages that in the inversion process, the change of the number of wavelet coefficients results in the change of the number of layers, while a slight perturbation of the wavelet coefficients can lead to a big change to the model in the space-domain, so that we avoid updating each individual model parameter, and the inversion process is largely speeded up. We validate our method with both synthetic data and survey data.