Single isotropic scattering model including wave conversions simple theoretical model of the short period body wave propagation

Abstract

The elastic energy propagation in a three dimensional elastic medium, in which scatterers are distributed homogeneously and randomly, is studied from the point of view of the scattering theory. The isotropic scattering is assumed and the scattering process is considered up to the first order. It is assumed that not only the P-wave to P-wave scattering and the S-wave to S-wave scattering but also the S-wave to P-wave conversion scattering and the P-wave to S-wave conversion scattering take place. Green functions corresponding to these single isotropic scatterings are obtained and their properties are exhibited when the elastic energy is radiated sphericaUy from a source. A space-time distribution of the energy density of the single scattered ela.stic waves is obtained. This model is applied to the short period body wave propagation of a small local earthquake near a hypocenter in the earth, when heterogeneities are interpreted as the scatterers. The temporal development of the seismic energy density, which is closely related to the seismogram, may be explained qualitatively. © 1977, The Seismological Society of Japan, The Volcanological Society of Japan, The Geodetic Society of Japan. All rights reserved.