An Asymmetric Micropolar Moment Tensor Derived from a Discrete-Block Model for a Rotating Granular Substructure

Abstract

Abstract I define an asymmetric moment tensor for individual slip events and for an average over multiple slip events using a discrete rigid-block model to account for the brittle deformation of a granular material. For the brittle crust, the grains are taken to be fault-bounded blocks. Permanent deformation accumulates by slip events on the boundaries of the blocks. The deformation is described by two independent motions: the local relative motion of the block centroids and the local rigid rotation of the blocks about their centroids. Averaging each of these local motions over multiple slip events in a volume defines both the macrodeformation, which consists of the macrostrain and macrorotation, and the microrotation. An asymmetric local micropolar moment tensor and an asymmetric micropolar moment-density tensor are defined from the local and the averaged motions, respectively. The model shows (1) the symmetric part of the micropolar moment tensors depends on the constant-volume local shear strain of the block centroids or its averaged equivalent, the macrostrain; (2) the antisymmetric part depends on an objective quantity defined as the difference between the rotational component associated with the centroid deformation and the local block rotation, or their averaged equivalents the macrorotation and the microrotation; and (3) the symmetric and antisymmetric parts of the micropolar moment-density tensor can be inferred up to a scalar magnitude by a micropolar inversion of standard seismic focal mechanisms. Three field tests show consistency with the theory, but definitive tests are thwarted by insufficient quantitative information or insufficient resolution of the available data.