Improving moment tensor solutions under Earth structure uncertainty with simulation-based inference
This work addresses a specific issue in seismology for earthquake source mechanism analysis, representing an incremental improvement with a novel method for a known bottleneck.
The paper tackled the problem of biased moment tensor solutions in seismology due to Earth structure uncertainty by introducing a simulation-based inference method, which produced more reliable and better calibrated posteriors compared to standard Gaussian approaches, particularly for shallow events and short-period data.
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.