Open AccessRepresentation of the Elastic ‐ Gravitational Excitation of a Spherical Earth Model by Generalized Spherical Harmonics
Author(s) -
Phinney Robert A.,
Burridge Robert
Publication year - 1973
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1973.tb02407.x
Subject(s) - spherical harmonics , zonal spherical harmonics , spin weighted spherical harmonics , covariant transformation , vector spherical harmonics , solid harmonics , classical mechanics , fuzzy sphere , physics , rotation (mathematics) , gravitational potential , harmonics , representation (politics) , vibration , mathematical analysis , point (geometry) , harmonic , gravitation , mathematics , geometry , mathematical physics , quantum mechanics , voltage , politics , political science , law
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.