Wave propagation in strongly scattered random elastic media: Energy equilibration and crossover from ballistic to diffusive behavior

We studied the energy equilibration process of elastic wave propagation through a strong-scattering random medium via multiple-scattering theory and the radiative transfer equation. The equilibration of the shear and compressional energy densities due to the mode conversions is clearly observed in both calculations, although the ratio of the shear energy density to the compressional energy density obtained from the multiple-scattering theory is higher than that obtained from the radiative transfer equation, which has the value predicted by the principle of the equipartition of wave modes. The discrepancy is due to the presence of a negative interference energy inside the sample. This is in contrast to the common belief that the interference energy density of a weak-scattering random medium always averages to zero inside the medium except near its boundaries. We also showed that the negative interference energy is concentrated near the boundary of each scatterer and, therefore, cannot be averaged to zero. In addition, we studied various distribution functions of the transmitted waves in thin samples before the establishment of the energy equilibration. We found that these distribution functions are described well by a random-phasor-sum model and they exhibit crossover behavior from ballistic to diffusive transport.