S. N. Bhattacharya and Swarn Arora
A flattening transforming for P-SV waves in a transversely isotropic Earth
Bulletin of the Seismological Society of America (October 1997), 87(5):1297-1304

Abstract:
We solve the equations of P-SV motion in a transversely isotropic nongravitating spherical shell with elastic parameters being proportional to r ^p and density being proportional to r (super p-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 isotropic 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.