How does anisotropy of focal region change structure of moment tensors?

Abstract

ABSTRACTThe invariants of the moment tensor such as its norm, eigenvalues and trace are closely related to the physical properties of the seismic source and the focal region, for example, seismic moment, radiation pattern, non‐double‐couple components. In this study, we investigate the relationship between these invariants and the eigenvalues and eigenvectors of the transversely isotropic elasticity tensor of the focal region. More specifically, we study how these invariants change as the source orientations vary with respect to the symmetry axes of the transversely isotropic elasticity tensor, by plotting these invariants on the stereographic net. Fortunately, one can plot them since they are independent of the strike of the fault when the focal region is a vertical transversely isotropic medium . Eigenvalues of the elasticity tensor control the invariants of the moment tensor; for instance, the ratio of the maximum and minimum norms achieved for some orientations of source is equal to the ratio of the two specific eigenvalues of the elasticity tensor. Moreover, the separation of the eigenvectors of the moment tensor from the eigenvectors of the source tensor is related to the deviation of the eigenvalues of the transversely isotropic elasticity tensor from the eigenvalues of the closest isotropic elasticity tensor. It is also found that this deviation is responsible for the percentages of non‐double‐couple components of the resulting moment tensor. This linear algebra point of view makes it easier to understand why and how the structure of the moment tensor changes for different orientations of sources.