Stress–strain characterization of seismic source fields using moment measures of mechanism complexity

Abstract

SUMMARY Earthquake ruptures and seismic sequences can be very complex, involving slip in various directions on surfaces of variable orientation. How is this geometrical complexity in seismic energy release, here called mechanism complexity, governed by tectonic stress? We address this question using a probabilistic model for the distribution of double couples that is consistent with three assumptions commonly used in regional stress inversions: the tectonic stress is constant, slip vectors are aligned with the maximum shear traction in the plane of slip, and higher shear traction promotes more seismic energy release. We characterize the moment-tensor field of a stress-aligned source process in terms of an ordered set of principal-stress directions, a stress shape factor R, and a strain-sensitivity parameter $\kappa $. The latter governs the dependence of the seismic moment density on the shear-traction magnitude and therefore parametrizes the seismic strain response to the driving stress. These stress–strain characterization (SSC) parameters can be determined from moment measures of mechanism complexity observed in large earthquakes and seismic sequences. The moment measures considered here are the ratio of the Aki moment to the total seismic moment and the five fractions of the total-moment defined by linear mappings of the moment-tensor field onto an orthonormal basis of five deviatoric mechanisms. We construct this basis to be stress-oriented by choosing its leading member to be the centroid moment tensor (CMT) mechanism and three others representing orthogonal rotations of the CMT mechanism. From the projections of the stress-aligned field onto this stress-oriented basis, we derive explicit expressions for the expected values of the moment-fraction integrals as functions of R and $\kappa $. We apply the SSC methodology to a 39-yr focal mechanism catalogue of the San Jacinto Fault (SJF) zone and to realizations from the Graves–Pitarka stochastic rupture model. The SJF data are consistent with the SSC model, and the recovered parameters, $R = {\rm{ }}0.45 \pm 0.050$ and $\kappa = {\rm{ }}5.7 \pm 1.75$, indicate moderate mechanism complexity. The parameters from the Graves–Pitarka realizations, $R = {\rm{\ }}0.49 \pm 0.005,{\rm{\ \ }}\kappa = {\rm{\ }}9.5 \pm 0.375,$ imply lower mechanism complexity than the SJF catalogue, and their moment measures show inconsistencies with the SSC model that can be explained by differences in the modelling assumptions.