ENERGY TRANSPORTATION IN 1-DIMENSIONAL AND 2-DIMENSIONAL SCATTERING MEDIA - ANALYTIC SOLUTIONS OF THE MULTIPLE ISOTROPIC SCATTERING MODEL

Envelopes of high-frequency seismic waves are well described by the incoherent sum of scattered waves by heterogeneities in the earth medium. Supposing multiple isotropic scattering by point-like scatterers randomly distributed in one- and two-dimensional infinite scattering media, we derive analytic solutions for the space-time distribution of the energy density for an impulsive isotropic radiation based on the energy transportation theory. The analytic solution obtained in two-dimensional space coincides with that of Shang & Gao (1988). Here we show an alternative derivation of analytic solutions by using the Laplace transformation in time and the Fourier transformation in space.