Estimating moment tensor solutions and related uncertainties through MCMTpy waveform inversion package
Authors: Mancuso Thomas , Totaro Cristina , Orecchio Barbara 
Published: March 2024

Earthquake focal mechanism inversion is a seriously non-linear problem having a fundamental role in several seismological studies. Accurate focal mechanism estimations are helpful for interpreting the style of faulting in active tectonic settings, as well as to obtain good constraints on regional stress field. Waveform inversion methods have so far demonstrated to be capable to furnish stable and reliable solutions (Presti et al., 2013), even if they need accurate estimates of the related uncertainties usually underestimated by linearized techniques (Scolaro et al., 2018). Given the existence of measurement and theoretical errors (Tarantola and Valette, 1982), the inversion uncertainties are inevitable and are important in assessing the reliability of inverted results. Bayesian inference is increasingly being applied to solve these problems as it has the advantage of quantifying uncertainties of parameters (Vasyura-Bathke et al., 2020).
In this work we present the application of a new inversion package MCMTpy (Yin &amp; Wang, 2022), which exploits the &#8216;Cut-And-Paste&#8217; waveform inversion algorithm (CAP, Zhao &amp; Helmberger, 1994; Zhu &amp; Helmberger, 1996) and Bayesian inference. The MCMTpy approach uses Markov Chain to implement the source location and focal mechanism inversion in a unique workflow, also providing a way to quantify uncertainties by statistical inference.
To explore the effectiveness of the package, we applied the MCMTpy to synthetic and real seismic events (2016 Mw 6.0 Amatrice earthquake and a smaller event of the same sequence). We performed several tests by varying the starting solution, number of iterations, and network geometry. We analysed the results obtained in order to evaluate reliability of moment tensor solutions and estimated uncertainties in different inversion settings.
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