Application of seismic strain tensor shape analysis to global tectonics

The analysis of earthquake focal mechanisms is a key tool for studying active tectonic deformation. Various stress inversion methods are frequently used based on this data to obtain stress tensors by making a series of assumptions that can compromise the reliability of the results. On the other hand, obtaining seismic deformation tensors from the summation of seismic moment tensors offers a solid alternative for characterising seismic strain tensors without the uncertainties inherent in stress-based approaches. In this work, we study the global distribution and shape of these combined seismic strain tensors, with special emphasis on their geometric properties and non-double-couple (NDC) components. Our results show systematic patterns in the shape of the tensor in different tectonic contexts. Shallow seismicity, predominantly associated with plate boundaries, shows alternating ellipsoid shapes between prolate and oblate along oceanic ridges, while subduction zones show planar-type strains (near the double-couple) in interface events and departures from this double-couple in back-arc zones. In contrast, deep seismicity within subduction slabs shows greater variability, with some slabs characterised by oblate ellipsoids and others by prolate geometries, indicating diverse deformation modes at depth. Continental collision zones, such as the Himalayan front and the Zagros belt, are dominated by oblate tensor shapes, while adjacent regions, such as the Tibetan plateau, exhibit prolate geometries, reflecting a significant component of uniaxial extension or constriction. Error estimation is addressed through probabilistic weighting of focal mechanisms based on uncertainties in event location and through a Monte Carlo perturbation scheme of the tensor components. This characterisation of aleatory errors ensures a robust evaluation of eigenvalues, eigenvectors, and parameters derived from them. The observed correlation between the tensor shape and the tectonic context highlights the usefulness of strain tensor-based approaches for seismotectonic studies. By characterising instantaneous seismic strain, the methodology proposed in this work complements the study of both brittle and ductile finite strain. These results contribute to improving global models of lithospheric deformation and show the importance of incorporating the geometry of seismic strain tensors into tectonic and geodynamic analysis, as well as their potential application to seismic risk.