Eigenvibrations of the earth excited by finite dislocations-I Toroidal oscillations

Abstract

The expansion of the toroidal Green'sdyad for a radially heterogeneous sphere is obtained in terms of vector spherical harmonics. Volterra'stheory of dislocation is then used to compute the displacement and thereby the strain field due to an internal dislocation of arbitrary size, orientation and depth. Excitation of free oscillations of the sphere due to various sources is derived by evaluating the residues at the poles of the integrand in the ω-plane. Repetition of the above analysis for cylindrical co-ordinates yields the displacement and strain fields in a vertically heterogeneous half-space induced by dislocation sources. The density and rigidity are assumed to be arbitrary functions of the depth. The Green'sdyads obtained are useful in solving various problems concerning a vertically heterogeneous sphere or half-space.