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 employed 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 parameterizes 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-year focal mechanism catalog 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 catalog, and their moment measures show inconsistencies with the SSC model that can be explained by differences in the modeling assumptions.

Quantitative analysis of crustal deformation, seismic strain, and stress estimation in Iran via earthquake mechanisms

“…Crustal deformations have been investigated using seismic stress and strain analysis in different research, such as tectonic stress and the spectra of seismic shear waves from earthquakes (BRUNE JN, 1970); horizontal stress orientations (Lund and Townend, 2007); active crustal deformation in tow seismogenic zones of the Pannonian region (Bus et al, 2009); crustal deformation map of Iran (Khorrami et al, 2019); Stress-strain characterization of seismic source fields (Jordan and Juarez, 2021); evolution of the Stress and Strain field and Seismic Inversion of fault zone (Khoshkholgh et al, 2022); active deformation Patterns in the Northern Birjand Mountains, Iran (Ezati et al, 2022a); tectonic Evolution of Fault Splays in the East Iran Orogen (Rashidi et al, 2023b); seismic strain and seismogenic stress regimes in the crust of the southern Tyrrhenian region (Neri et al, 2003).…”

A Diffuse Interface Method for Earthquake Rupture Dynamics Based on a Phase‐Field Model

“…Backus and Mulcahy (1976) termed stress glut the stress mismatch of a purely elastic medium and the true physical stress. The stress glut method was first established within the context of kinematic earthquake source descriptions, where the region of non‐zero stress glut is the internal source (Bukchin, 1995; Chen et al., 2005; Clévédé et al., 2004; Jordan & Juarez, 2019, 2020, 2021; McGuire, 2017; McGuire et al., 2001, 2002). The stress glut (Andrews, 1999) and the thick fault zone (Madariaga et al., 1998) methods in the context of dynamic rupture modeling have been implemented in the finite difference method (Andrews, 1976, 1999; Dalguer & Day, 2006; Herrendörfer et al., 2018; Madariaga et al., 1998; Preuss et al., 2019).…”