Using deep generative neural networks to account for model errors in Markov chain Monte Carlo inversion

Most geophysical inverse problems are nonlinear and rely upon numerical forward solvers involving discretization simplified representations of the underlying physics. As a result, modeling errors inevitable. In practice, such model tend to be either completely ignored, which leads biased over-confident inversion results, or only partly taken into account using restrictive Gaussian assumptions. Here, we on deep generative neural networks learn problem-specific low-dimensional probabilistic discrepancy between high-fidelity low-fidelity solvers. These then used probabilistically invert for error jointly with target property field, computationally-cheap, solver. To this end, combine Markov-chain-Monte-Carlo (MCMC) algorithm trained convolutional network spatial adversarial (SGAN) type, whereby at each MCMC step, simulated response is corrected proposed model-error realization. Considering crosshole ground-penetrating radar traveltime tomography problem, train SGAN images between: (1) curved-ray (high fidelity) straight-ray (low solvers; (2) finite-difference-time-domain We demonstrate that able statistics suitable both subsurface can recovered by MCMC. comparison results obtained when ignored approximated distribution, find our method has lower posterior parameter bias better explains observed data.[...]