On propagation in continuous random media

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 discrete scatteres. Furthermore, when the scatter is constrained to narrow forwardand back-scattered cones, there is no back-scatter enhancement. These results are discussed within the context of the extension of the spectral-domain formalism to discrete random media. The general continuous-media moment equations are developed but not solved. The results correct and extend an earlier analysis that used a perturbation approach to compute the scattering functions rather than the Novikov-Furutsu theorem.