Bayesian slip inversion with automatic differentiation variational inference

Abstract

SUMMARY The Bayesian slip inversion offers a powerful tool for modelling the earthquake source mechanism. It can provide a fully probabilistic result and thus permits us to quantitatively assess the inversion uncertainty. The Bayesian problem is usually solved with Monte Carlo methods, but they are computationally expensive and are inapplicable for high-dimensional and large-scale problems. Variational inference is an alternative solver to the Bayesian problem. It turns Bayesian inference into an optimization task and thus enjoys better computational performances. In this study, we introduce a general variational inference algorithm, automatic differentiation variational inference (ADVI), to the Bayesian slip inversion and compare it with the classic Metropolis–Hastings (MH) sampling method. The synthetic test shows that the two methods generate nearly identical mean slip distributions and standard deviation maps. In the real case study, the two methods produce highly consistent mean slip distributions, but the ADVI-derived standard deviation map differs from that produced by the MH method, possibly because of the limitation of the Gaussian approximation in the ADVI method. In both cases, ADVI can give comparable results to the MH method but with a significantly lower computational cost. Our results show that ADVI is a promising and competitive method for the Bayesian slip inversion.