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2 results

  • 4 - Radiative Transfer Theory for Scalar Wavelet Propagation through Random Media

  • Haruo Sato, Tohoku University, Japan, Kentaro Emoto, Kyushu University
  • Book:
    Seismic Wave Propagation Through Random Media
    Published online:
    31 October 2024
    Print publication:
    14 November 2024, pp 58-84

  • Summary

    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.