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

Summary 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.