A flattening transformation forP-SVwaves in a transversely isotropic Earth

Abstract

AbstractWe solve the equations of P-SV motion in a transversely isotropic non-gravitating spherical shell with elastic parameters being proportional to rp and density being proportional to rp−2, where p is an arbitrary constant and r is the radial distance from the center of the Earth. The solutions are obtained in terms of exponential functions. The expression for the displacement-stress matrix becomes similar to that used in an isotropic flat-layered Earth. Thus, the existing formulations of this isotropic flat Earth can be used to study wave propagation in a transversely istropic spherical-layered Earth. As an example, one of the existing formulations of the isotropic flat Earth has been used successfully to find phase velocity and eigenfunctions of Rayleigh wave in a transversely isotropic spherical Earth.