How does anisotropic focal region change the structure of the moment tensor?

Abstract

In this study, we show how the invariants of the moment tensors change for different orientations of sources in a vertical transversely isotropic (TI) focal region. The invariants of the moment tensors, namely their norms, traces and eigenvalues, have physical interpretations such as seismic moment, isotropic-component and radiation pattern, respectively. Hence it is important to know how these values change for a given elasticity tensor of the focal region. These invariants strongly depend on the strength of anisotropy which is related with the variation of the eigenvalues of TI elasticity tensor from its closest-isotropic elasticity tensor. We plotted the values of the projection for each 10-gridded orientations of slip and normal vectors around the unit sphere in order to see the distribution properly. Thus, we plotted the projection of source tensor d onto different eigenspaces. In doing so, various materials were used for data of elastic parameters and eigenvalues such as shale, dry-cracks etc. Then the norms of the elasticity tensors of various materials has been calculated and plotted. The maximum and minimum points in the norm plots and the ratios of the maximum and minimum eigenvalues of various materials were found to be similar to each other. The eigenvalues of moment tensor for different anisotropic focal regions have been shown. Thus, the relation between isotropic component amount and γ values were illustrated. Lastly, the strength of anisotropy is evaluated and related with the invariants of the moment tensors.