Generalized Two-Dimensional Model Seismology with Application to Anisotropic Earth Models

Abstract

The theory of two-dimensional seismic modeling is generalized to include the effect of anisotropy. The elastic coefficient matrix for a plate with orthorhombic symmetry is derived and is used to convert three-dimensional anisotropic problems into corresponding two-dimensional model problems. This is equivalent to replacing directional body velocities by the directional plate velocities. In addition to the application to seismic modeling, this can be considered a contribution to the basic theory of long waves in anisotropic plates. As such it has application to such problems as long waves in floating ice sheets. A model consisting of an anisotropic layer over an anisotropic half-space is constructed using a formica layer and a grooved aluminum plate. It is shown that rolled metal sheets can be made appreciably anisotropic by machining grooves in the surface. The experimental Rayleigh wave phase velocities are compared with the theoretical dispersion curves computed using isotropic and anisotropic theories. Two-layer circular models of the earth, one with an isotropic and the other with an anisotropic upper mantle, are fabricated, and a comparative study of body and surface waves is made. It is found that the relative effect of anisotropy is greater on surface waves than on body waves.