Transport Lagrangian misfit measures and velocity model uncertainty in Bayesian moment tensor inversion

Model error is endemic to full waveform inversion (FWI). Bayesian moment tensor inversion is an example of a linear inverse problem that can be heavily affected by errors in the velocity model. The choice of misfit function plays a crucial role in mitigating the effects of these errors. We explore and quantify the benefits of using a newly introduced optimal transport distance, called the Transport-Lagrangian (TL) distance, through a series of synthetic experiments. We generate earthquake data for a heterogeneous 3D model, the SEG/EAGE Overthrust model. For inference, we test several layered-medium models derived from vertical profiles of velocity at single locations in the 3D model. A consistent Bayesian update is established to integrate the aforementioned distance with FWI. Through an appropriate scoring system, we show that, on average, TL distances produce posterior distributions with less bias and less variance than distributions obtained with a standard `2 misfit.