Theoretical amplitudes of body waves from a dislocation source in the earth. I. Core reflections

Abstract

Expressions are obtained for the ray-theoretical spectral amplitudes of body waves induced by a shear dislocation of arbitrary orientation and depth situated in a radially heterogeneous model of the Earth. Account is taken of the azimuthal and colatitudinal radiation patterns of the source, the geometrical spreading, and the reflections and refractions at the free surface and at the mantle-core boundary. Spectral amplitudes are calculated for PcP, PcS, ScP, ScSV and ScSH. The results are presented in the form of tables for a source of strength U₀dS = 10¹⁵ cm³, where U₀ is the amount of the dislocation and dS is the fault area. Given the slip and dip angles of the source, the amplitudes of the five core reflected phases can be obtained from these tables for all azimuths, for most of the epicentral distances at which a particular phase is observable, and for all the fourteen focal depths included in the Jeffreys-Bullen tables. It is found that the depth of the source has a strong effect on the amplitudes of the body wave signals. It is the first time that detailed numerical results are given for the core reflected body wave amplitudes for a realistic source in a realistic model of the Earth. In most of the studies made so far, the asymmetry of the radiations from the source was not taken into account. The results of computation for other important phases and the application of the theoretical amplitudes to source studies will be given in subsequent publications.