Improving moment tensor solutions under Earth structure uncertainty with simulation-based inference

TL;DR

This paper introduces a simulation-based inference method to improve moment tensor solutions by accurately modeling Earth structure uncertainties, overcoming limitations of traditional Gaussian error assumptions, and providing more reliable earthquake source characterizations.

Contribution

The paper develops a novel SBI framework that better captures theory errors in moment tensor inversions, avoiding restrictive Gaussian assumptions and improving uncertainty quantification.

Findings

Gaussian error models can bias solutions under Earth model uncertainty

SBI produces more reliable and calibrated earthquake source posteriors

Method successfully applied to real earthquakes from Long Valley and Zagreb

Abstract

Bayesian inference represents a principled way to incorporate Earth structure uncertainty in full-waveform moment tensor inversions, but traditional approaches generally require significant approximations that risk biasing the resulting solutions. We introduce a robust method for handling theory errors using simulation-based inference (SBI), a machine learning approach that empirically models their impact on the observations. This framework retains the rigour of Bayesian inference while avoiding restrictive assumptions about the functional form of the uncertainties. We begin by demonstrating that the common Gaussian parametrisation of theory errors breaks down under minor ($1-3 \%$) 1-D Earth model uncertainty. To address this issue, we develop two formalisms for utilising SBI to improve the quality of the moment tensor solutions: one using physics-based insights into the theory errors, and another utilising an end-to-end deep learning algorithm. We then compare the results of moment tensor inversion with the standard Gaussian approach and SBI, and demonstrate that Gaussian assumptions induce bias and significantly under-report moment tensor uncertainties. We also show that these effects are particularly problematic when inverting short period data and for shallow, isotropic events. On the other hand, SBI produces more reliable, better calibrated posteriors of the earthquake source mechanism. Finally, we successfully apply our methodology to two well studied moderate magnitude earthquakes: one from the 1997 Long Valley Caldera volcanic earthquake sequence, and the 2020 Zagreb earthquake.