2001 Volume 54 Issue 1 Pages 109-125
It is widely accepted that coda waves are composed of incoherent scattered waves for high frequencies. Using the random phase approximation, approaches based on the radiative transfer theory (energy transport theory) have been adopted instead of wave propagation theory itself for the construction of models which describe the envelopes of coda waves. The radiative transfer theory deals directly with the transport of energy through a medium containing scatterers. Since the first paper in 1960s on the single scattering model for cases of weak scattering and that on the diffusion model for cases of strong scattering, a number of improved models have been proposed to expand these models into more complicated cases, e. g., non isotropy in scattering, non spherical source radiation, and the case of separated locations of source and receiver. The single scattering model satisfies causality but does not energy conservation law; on the other hand the diffusion model satisfies the energy conservation law but does not causality. Multiple scattering models have been proposed in 1980s to consider an interpolation between the weak and strong scattering cases. The multiple scattering model can be applicable without assuming the strength of scattering, and satisfies both energy conservation law and causality, but has no simple analytical expression in 3 dimensional space. In parallel with the analytical development, several approaches using Monte Carlo technique were conducted to simulate multiple scattering processes and synthesize the coda wave envelope. Using Monte Carlo simulation the coda wave envelope can be synthesized even in the case of complicated structure having depth dependence on both scattering strength and velocity, beyond mathematical difficulties in analytical studies. The radiative transfer approach has provided a framework for measurements of scattering attenuation and intrinsic absorption, and the comparison of the theory with observation has led us to understand the stochastic inhomogeneity in the real Earth.
