On the excitation of the earth's seismic normal modes

Abstract

The excitation of the earth's normal modes is formulated as an initial value problem. The static state of the earth, stressed from its hydrostatic reference situation, is considered as the initial state. The initial state is relaxed, at the time of the earthquake, by the removal of the forces maintaining the departure from hydrostatic equilibrium. Expressions are derived for the coefficients giving the relative excitation of the individual modes for the cases where these forces are compensating volume forces or compensating tractions on the faces of a dislocation. It is demonstrated that a point slip dislocation has a body force equivalent in the form of a double couple with a deviatoric moment tensor. However, for a source with volume change no moment tensor equivalent can be found. The volume change, apart from an elastic effect which can be represented by an isotropic moment tensor, has a direct gravitational effect on the excitation. This effect is due to a balanced force field consisting of a point force at the source and a continuous distribution of volume forces throughout the earth. The latter distribution, if not taken into account, may give rise to artificial phases in the frequency spectrum of the normal modes.