In von Karmam-type random media, when the center wavenumber is higher than the corner wavenumber of the PSDF and the phase shift across the correlation length is not small enough, the conventional Born approximation is not applicable. To overcome this difficulty, Chapter 7 presents an ongoing study of a hybrid MC simulation using the spectrum division method for scalar/vector wavelet propagation. Taking the center wavenumber as a reference, we divide the PSDF into two parts, then we serially use the Born wide-angle scattering for the high-wavenumber spectral component and the Eikonal narrow-angle ray bending and travel distance fluctuation for the low-wavenumber spectral component. For the elastic case, the synthesized three-component RMS velocity amplitude time traces are compared with the ensemble average of the FD simulation results in realized random elastic media.

Chapter 5 presents the realization of random media for a given power spectral density function for FD simulation of scalar wavelet propagation. We verify the MC simulation results with the ensemble average of the FD simulation results in realized random media for a given power spectral density function.

Chapter 6 studies vector wave scattering in random elastic media. The Born approximation leads to PP, PS, SP, and SS scattering coefficients, from each of which we construct the corresponding PRNG of scattering angles. Using these in MC simulations, we synthesize three-component RMS velocity amplitude time traces for the radiation from a point shear dislocation (PSD) source. The simulation results are compared with the ensemble average of FD simulation results in random elastic media for a given power spectral density function.