On propagation in continuous random media

Abstract

Abstract The analysis of wave propagation in continuous random media typically proceeds from the parabolic wave equation with back scatter neglected. A closed hierarchy of moment equations can be obtained by using the Novikov–Furutsu theorem. When the same procedure is applied in the spatial Fourier domain, one obtains a closed hierarchy of coupled moment equations for the forward- and back-scattered wavefields that is not restricted to narrow scattering angles nor to small local perturbations. The general equations are difficult to solve, but a Markov-like approximation is suggested by the form of the scattering terms. Simple algebraic solutions can be obtained if a narrow-angle-scatter approximation is then invoked. Thus, three distinct approximations are explicit in this analysis, namely closure, Markov and narrow-angle scatter. The results show that the extinction of the coherent wavefield has a distinctly different form from the corresponding result for propagation in a sparse distribution of discret...