Refraction and diffusion of acoustic waves in a random fluid medium

Based upon the asymptotic and stochastic formulation of the acoustic wave equations, this article considers a stochastic wave propagation problem in a random multilayer which is totally refracting. Both the WKB analysis and the diffusion limit theory of stochastic differential equations are used to analyze the interplay of refraction (macrostructure) and diffusion (microstructure) of the propagating waves. The probabilistic distribution of solutions to the resultant Kolmogorov-Fokker-Planck equation is given as a computable form from the pseudodifferential operator theory and Wiener's path integral theory.