Bayesian bootstrapping extension of GISOLA automatic moment tensor inversion software

Moment tensor (MT) determination is a key component of real-time seismology, with applications in moment magnitude estimation, tsunami early warning, volcano monitoring and shake map generation. Despite its importance, the reliable inversion of MT components, especially the non-double-couple ones, presents significant challenges. Indeed, the non–DC components are highly sensitive and often exhibit large fluctuations, making reliable estimation of the full moment tensor difficult. These limitations highlight the need for robust uncertainty quantification of MTs.  To efficiently address this issue, we propose a Bayesian bootstrapping approach. The approach assumes that Signal to Noise Ratio (SNR) is fair and the velocity model is not systematically biased. The method relies on a series of weighted inversions, in which station contributions are stochastically varied using Bayesian weights. This procedure produces an ensemble of plausible MT solutions enabling statistical characterization of the inversion results (e.g., median MT, confidence intervals of ISO and CLVD components, etc.). This approach, free of the assumption of Gaussianity of data error, provides meaningful uncertainty estimates and improves the interpretability of non–double-couple components. The proposed methodology has been integrated into GISOLA, an open-source, highly efficient near–real-time MT inversion software, currently in routine operation in several seismic networks. The resulting automated operational framework handles multiple data streams in heterogeneous formats, interfaces with diverse processing modules, applies a systematic preprocessing workflow to identify the most reliable stations and corresponding signals, performs parallelized inversions, and provides robust uncertainty quantification. This enhances the reliability of source characterization in operational environments and supports more informed use of MT results in time-critical seismic monitoring.

This work is supported by TRANSFORM²  which is funded by the European Union under project number 101188365 within the HORIZON-INFRA-2024-DEV-01-01 call