Representation of the Elastic ‐ Gravitational Excitation of a Spherical Earth Model by Generalized Spherical Harmonics

Abstract

The generalized spherical harmonics, which arise as representations of the rotation group, provide a natural basis for the expansion of tensors of any order in spherical co‐ordinates. By using the covariant differentiation rules of Burridge, it is possible to obtain economically the separated differential equations of elastic vibration in a radially symmetric sphere. Derivation of the excitation of an Earth model by a point force or point dislocation is also carried out with the aid of these functions. While all the results obtained are known, the methods used have a substantially greater simplicity than conventional methods. Copyright © 1973, Wiley Blackwell. All rights reserved