Robust Bayesian moment tensor inversion with optimal transport misfits: layered medium approximations to the 3-D SEG-EAGE overthrust velocity model

A velocity model is generally an imperfect representation of the subsurface, which cannot precisely account for the 3-D inhomogeneities of Earth structure. We present a Bayesian moment tensor inversion framework for applications where reliable, tomography-based, velocity model reconstructions are not available. In particular, synthetic data generated using a 3-D model (SEG-EAGE Overthrust) are inverted using a layered medium model. We use a likelihood function derived from an optimal transport distance - specifically, the transport-Lagrangian distance introduced by Thorpe et al. - and show that this formulation yields inferences that are robust to misspecification of the velocity model. We establish several quantitative metrics to evaluate the performance of the proposed Bayesian framework, comparing it to Bayesian inversion with a standard Gaussian likelihood. We also show that the non-double-couple component of the recovered mechanisms drastically diminishes when the impact of velocity model misspecification is mitigated.