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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 Es (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 Es 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 Es corresponds to the power spectrum of coda waves.
Haruo Sato (Sat,) studied this question.