The effect of block rotations on the global seismic moment tensor and the patterns of seismic P and T axes

Abstract

Distributed brittle deformation of the Earth's crust involving block rotations is comparable to the deformation of a granular material, with fault blocks acting like the grains. The deformation of a granular material is not adequately described using classical continuum mechanics because the individual grains within the material rotate in a manner that is not uniquely determined by the large‐scale average deformation. Thus a theoretical link has not existed between the kinematics of deformation involving block rotation and the associated effects on the seismic moment tensor and focal mechanism solutions. We establish this link using micropolar continuum theory (Eringen, 1964, 1966 a, b; Eringen and Suhubi, 1964) and the analysis of the effect of block rotations on fault slickenline patterns by Twiss et al. (1991). This theory takes into account two separate scales of motion: a large‐scale average motion of the material, the macromotion, composed of a macrodeformation rate (i.e., a macrostrain rate) and a macrospin, and a local motion, the microspin, that describes the average rotation rate of grains in the material. The micropolar kinematic theory allows us to predict the orientations of coseismic slip directions V on local shear planes of any orientation in a large‐scale shear zone. We define a local and a global asymmetric micropolar seismic moment tensor in terms of these slip directions. For a restricted kinematic model, the theory shows that two scalar parameters, D and W, determine the symmetry of the global micropolar seismic moment tensor and the pattern of seismic P (shortening) and T (lengthening) axes. The deformation rate parameter D is defined in terms of the principal values of the deformation rate tensor . The deformation is transtensional (constrictional) if 0 ≤ D ≤ 0.5, plane strain if D = 0.5, and transpressional (flattening) if 0.5 < D ≤ 1. The net vorticity parameter W is a normalized value of the difference between microspin and macrospin . It is an objective variable. W = 0 implies that the global micropolar seismic moment tensor is symmetric and that P and T axis patterns have orthorhombic or higher symmetry. W ≠ implies that the global micropolar seismic moment tensor is asymmetric and that P and T axis patterns have monoclinic symmetry. The antisymmetric part of the global micropolar seismic moment tensor is associated with the net vorticity that characterizes the deformation. W has different values for different models of rigid block rotation and thus could serve to identify the rotation mechanism.