Comparison of moment tensor inversion methods in a Bayesian framework

Focal mechanism and moment tensor computation based on regional and local waveforms has become routine task in seismology. These tools are essential for understanding seismotectonic stress regimes and are among the most widely used data for stress inversion, playing a crucial role in identifying deformation zones and tectonically active structures at both local and regional scales (e.g., Totaro et al., GRL 2016; Martínez-Garzón et al., JGR SE 2016).

Many different and similar approaches are available to perform inversion for the double-couple, deviatoric or full moment tensor. However, a key aspect often not fully addressed is the estimation of moment tensor uncertainty. It can be mostly caused by measurement (e.g., data contamination by noise) and theory errors (e.g., mathematical simplifications), and can affect the accuracy of results limiting their interpretation. Over the past decades, considerable efforts have been made in this context, and Bayesian inference is increasingly being applied in moment tensor inversion problems due to the advantage of quantifying parameter uncertainties (Vasyura-Bathke et al., SRL 2020). The Bayesian approach allows for a thorough exploration of the solution space by using appropriate samplers (e.g., Del Moral et al., JRSS 2006) and generates an ensemble of solutions rather than a single optimal one, providing a measure of uncertainty based on the solution distribution.

In this study, we focused on testing the stability of double-couple solutions obtained using two recently developed open-source software packages: BEAT (Bayesian Earthquake Analysis Tool; Vasyura-Bathke et al., SRL 2020) and MCMTpy (Yin and Wang, SRL 2022). These moment tensor inversion algorithms are extremely useful for estimating source parameter uncertainties and the range of acceptable solutions. We applied them to the 2016 Mw 6.0 Amatrice mainshock and a Mw 3.2 earthquake from the same sequence occurred in Central Italy, in order to check the performance of the algorithms at different magnitude levels. We selected this region due to several reasons: it is characterized by active tectonics, it benefits from good azimuthal coverage of seismic stations, and it offers plenty of moment tensor solutions obtained using different approaches (e.g., Scognamiglio et al., BSSA 2009; Artale Harris et al., JGR SE 2022).

For these two earthquakes we compared the results obtained by BEAT and MCMTpy with solutions available in the main seismic catalogs to evaluate the overall coherence of the results and the possible improvements in resolution and robustness. Then, we focused on the performance evaluations by proposing a series of methodological tests which simulate different data setup as not-optimal network geometry, epicentral location errors, biases in the velocity model. By applying these tests on the selected algorithms, we (i) explored their stability, (ii) identified their limitations in resolving double-couple moment tensors and (iii) evaluated the related uncertainty estimates. By doing so, we provide a comprehensive understanding of how these algorithms perform in real-world scenarios and we also suggest an approach useful to verify and eventually compare the performance of moment tensor inversion algorithms also taking into account the uncertainty estimates.