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.

中文翻译：

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使用机制复杂性的矩量度来表征震源场的应力-应变

总结 地震破裂和地震序列可能非常复杂，包括在不同方向的表面上的不同方向的滑动。地震能量释放的这种几何复杂性，这里称为机制复杂性，是如何受构造应力控制的？我们使用双偶分布的概率模型来解决这个问题，该模型与区域应力反演中常用的三个假设一致：构造应力是恒定的，滑动矢量与滑动平面中的最大剪切牵引力对齐，以及更高剪切牵引促进更多的地震能量释放。我们根据一组有序的主应力方向、应力形状因子 R 和应变敏感性参数 $\kappa $ 来表征应力对齐源过程的矩张量场。后者控制地震力矩密度对剪切牵引幅度的依赖性，因此参数化了地震应变对驱动应力的响应。这些应力-应变表征 (SSC) 参数可以通过在大地震和地震序列中观察到的机制复杂性的矩量度来确定。这里考虑的力矩测量是 Aki 力矩与总地震力矩的比值，以及由力矩张量场线性映射到五个偏转机制的正交基上定义的总力矩的五个部分。我们通过选择其主要成员作为质心力矩张量（CMT）机构和其他三个代表 CMT 机构的正交旋转来构建这个基础以应力导向。从应力对齐场到这个应力导向基础上的投影，我们推导出矩分数积分的期望值作为 R 和 $\kappa $ 的函数的显式表达式。我们将 SSC 方法应用于 San Jacinto 断层 (SJF) 带的 39 年震源机制目录以及 Graves-Pitarka 随机破裂模型的实现。SJF 数据与 SSC 模型一致，恢复的参数 $R = {\rm{ }}0.45 \pm 0.050$ 和 $\kappa = {\rm{ }}5.7 \pm 1.75$ 表明机制复杂度适中. Graves–Pitarka 实现的参数 $R = {\rm{\ }}0.49 \pm 0.005,{\rm{\ \ }}\kappa = {\rm{\ }}9.5 \pm 0.375,$ 意味着更低机构比 SJF 目录复杂，