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Seismic Wave Propagation Through Random Media Published online by Cambridge University Press: 31 October 2024
Chapter 4 introduces phenomenologically the radiative transfer equation of the directional distribution of the energy density for a given anisotropic scattering coefficient of scalar waves in random media. We solve the radiative transfer equation analytically by using the Legendre expansion for isotropic radiation from a point source. By probabilistically interpreting the Born scattering coefficient and the Eikonal angular spectrum function and the traveling distance fluctuation for scalar waves, we construct the corresponding pseudo-random number generators, where the rejection sampling method is introduced. Then, we synthesize the space–time distribution of the energy density for isotropic radiation from a point source using the MC simulation and compare it with the analytical solution of the radiative transfer equation.
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