ENERGY PROPAGATION INCLUDING SCATTERING EFFECTS SENGLE 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 l. 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 E_s(r, t)=(W₀/4πlVtr)1n((Vt+r)/(Vt-r)) for Vt≥r, 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 E_s is proportional to t^-2 for t_??_2r/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 as the scatterers and E_s corresponds to the power spectrum of coda waves.