Abstract
A general theory for the elastic-gravitational oscillation of the earth is developed. It is found that a linear vector operator that governs the oscillation is not Hermitian. In this regard the perturbation theory developed by Dahlen is found to be incorrect. However, when the density of the earth is a function of only the radial distance from the center of the earth, the operator becomes Hermitian even if other elastic parameters are asymmetrically distributed.
An adjoint operator that complements the original one is obtained. The two operators enable us to obtain formal solutions for deformations excited by body forces and dislocations. These solutions agree, as they should, with solutions so far obtained for an isotropic, laterally homogeneous earth. Perturbation schemes which allow the first order calculation of eigenfrequencies of any earth model in termsof the solutions of a non-rotating, spherically symmetric earth model are also developed.
