A spectral domain method for multiple scattering in discrete random media

In an earlier paper (see ibid., vol.36, p.1114-28, 1988) a spectral-domain method was developed for analyzing multiply scattered scalar wavefields propagating in continuous random media. This method is extended to accommodate vector wavefields propagating in discrete random media. The two-dimensional Fourier spectra of vector wavefields propagating in the forward and backward directions are characterized by a pair of coupled first-order differential equations. Dyadic scattering functions characterize the local interaction of the wavefields with the random medium. The results are restricted to sparse distributions whereby the dyadic scattering functions are easily computed. The first- and second-order moments of the vector wavefields can be computed by invoking an assumption essentially equivalent to the Markov approximation as it is applied to scalar wavefields propagating in continuous random media. A complete solution for the coherent wavefield is derived and compared to known results. The results are essentially equivalent to those obtained by using the effective field approximation