Moment Tensor Inversion Using Empirical Green’s Functions: a Methodological Approach in Complex Media for Seismotectonic and Volcanic Studies

Obtaining reliable moment tensor (MT) solutions for earthquakes is particularly challenging due to their strong dependence on station geometry, accurate hypocentral locations, and a well-constrained seismic velocity model. The estimation of seismic moment and magnitude, as well as the decomposition of the source mechanism into double-couple (DC), isotropic (ISO), and compensated linear vector dipole (CLVD) components, strongly depend on the assumed velocity model, which also controls the minimum resolvable magnitude. The limited availability of detailed three-dimensional crustal models often restricts MT inversions to low-frequency data, reducing resolution and negatively affecting both source parameter accuracy and inversion stability.

Recent improvements in seismic network coverage and instrument sensitivity have increased the resolving power, leading to a growing demand for MT solutions of progressively lower-magnitude earthquakes. This evolution imposes stricter requirements on the accuracy of 3D velocity models, which must properly represent small-scale heterogeneities, attenuation, and seismic anisotropy. In this context, Empirical Green’s Functions (EGFs) provide a practical approach to reduce the impact of simplified velocity models, empirically incorporating path and site effects, and improving high-frequency waveform fits.

In this study, we propose a methodological approach for earthquake MT inversion that includes EGFs into time-domain waveform inversion using the ISOLA code (Zahradník and Sokos, 2018). The methodology is based on the concept introduced by Plicka and Zahradník (1998), which enables the estimation of spatial derivatives of the EGF tensor directly from seismic observations, without requiring an a priori similarity among the focal mechanisms of weak earthquakes. Within this conceptual framework, a selected set of well-recorded small earthquakes within the same focal volume is first inverted for MTs using a standard waveform inversion procedure. These independently obtained MT solutions are combined with the corresponding observed waveforms to retrieve empirical Green’s tensor spatial derivatives, which are subsequently used to invert other earthquakes occurring in the same source region.

Within this framework, the use of EGFs significantly reduces modeling errors associated with simplified velocity structures and unresolved small-scale heterogeneities, while preserving sufficient resolution capability to extend MT analysis toward lower-magnitude earthquakes. The ISOLA code further enables systematic exploration of source parameters, quantitative assessment of solution quality through variance reduction and stability analysis, and consistent comparison among different inversion setups, providing an additional criterion for evaluating the reliability of the obtained solutions.

The proposed methodology is applied to the 2024–2025 seismic crisis at Campi Flegrei, a volcanically active area in Southern Italy, characterized by strong lateral heterogeneity and complex wave propagation effects. This dataset provides a representative test case to evaluate and validate the robustness of this approach under challenging geological and observational conditions, where complex rupture processes may be influenced by crustal fluids.

References

Plicka, V., and J. Zahradník (1998). Inverting seismograms of weak events for empirical Green’s tensor derivatives, Geophys. J. Int. 132, 471–478.

Zahradník, J., & Sokos, E. (2018). ISOLA code for multiple-point source modeling. In Moment tensor solutions: A useful tool for seismotectonics (pp. 1-28). Cham: Springer International Publishing.