Energy propagation including scattering effects single isotropic scattering approximation

Abstract

The elastic energy propagation in a three dimensional infinite elastic medium, in which scatterers are distributed homogeneously and randomly, is investigated by a statistical method. A single isotropic scattering process is investigated. The elastic medium is characterized by the wave velocity V and the distribution of the scatterers is characterized by the mean free path I. It is assumed that the elastic energy is radiated spherically from the source at a time t=0 in a short time duration. A space-time distribution of the mean energy density of the scattered waves is obtained as Es(r,t)= (W0/4πlVtr)ln((Vt+r)/(Vt-r)) for Vt⁥tr where r is the distance from the source and W0 is the total energy radiated. A uniform spatial distribution is constructed far behind the wave front and near the source. The mean energy density Es is proportional to t-2 for t-2⁥r/V and independent of r and W0. Several important properties of coda waves observed near the hypocenter are explained qualitatively by this solution when heterogeneities in the earth are interpreted. © 1977, The Seismological Society of Japan, The Volcanological Society of Japan, The Geodetic Society of Japan. All rights reserved.