Efficient 2-D trans-dimensional Bayesian inversion of MT data using an extended Fourier DeepONet Network

SUMMARY Uncertainty quantification is indispensable for reliable magnetotelluric (MT) data interpretation, given the inherent non-uniqueness of MT inverse problem solutions. However, traditional sampling-based probabilistic schemes often require millions of costly forward predictions, making them computationally prohibitive. To address this, we develop a trans-dimensional Bayesian inversion framework that incorporates a novel forward modelling operator and a reversible-jump Markov chain Monte Carlo algorithm for robust uncertainty quantification. The forward modelling method leverages the extended Fourier DeepONet (EFDO) network. Once trained, the EFDO achieves up to a 300-fold acceleration in forward predictions compared to a conventional finite volume-based solver. Furthermore, we utilize an adaptive Delaunay model parametrization during the sampling process to allow for efficient model space exploration. We demonstrate the efficacy of the proposed approach through numerical experiments and application to the COPROD2 MT field data set. Overall, this work advances Bayesian MT inversion by enabling rapid, high-dimensional inference of subsurface electrical resistivity structures, thereby facilitating reliable geological interpretation.