Narrow Results

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.

Statistical boundary value problem of a scattering of sound pulses incident on the randomly fluctuating layered medium is considered on the basis of an exact wave formulation in the spatial-time domain. To solve this problem we developed an analytical-numerical approach in earlier papers, and results of a statistical simulation were presented both for various durations of the incident pulses and for various thickness of a random medium layer. Analysis for the statistical moments, correlation functions and power spectral densities of the backscattered wave field has been carried out. Comparison with the results of this problem approximate asymptotical analysis, previously carried out by the other authors, finds out the number of differences. In this paper we examine both the results of an exact statistical simulation and the approximate analytical ones and propose, as a generalization, some quite simple approximations to describe statistical moments of the backscattered field in the region of nonstationarity. Studying the problem considered is of a fundamental interest for theoretical acoustics as well as its outcomes can be applied to interpret the data on the ocean water and bottom sediments probing with the time pulse.