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A flattening transformation for P-SV waves in a transversely isotropic Earth

Seismological Observatory India Meteorological Department, Lodi Road, New Delhi 110003 India snb{at}imd.ernet.in (91) (11) 4699216, 4623220
D.A.V. College for Women, Karnal 132001, India

Abstract

We solve the equations of P-SV motion in a transversely isotropic non-gravitating spherical shell with elastic parameters being proportional to r^p and density being proportional to r^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 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.