Green's dyadics and theoretical amplitudes of the earth's split normal modes

Abstract

Explicit expressions of the Green's dyadics for the toroidal and spheroidal oscillations of the Earth in terms of its normal modes are first obtained. The amplitudes of the split normal modes of the Earth excited by an arbitrary shear dislocation are then derived by making use of the Volterra relation. It is shown that when the normal mode expansion of the Green's dyadic is used, one obtains the amplitudes of the split modes directly and naturally, without requiring transformations of any sort. In particular, the rotation matrix coefficients do not appear in the expressions for the displacements obtained here. Our results highlight once again the elegance and compactness of the Green's function approach to source problems in seismology.