The split-step solution in random wave propagation

摘要

This paper considers the accuracy of the split-step solution for wave propagation in random media, both analytically and numerically. The main interest lies in finding the statistical moments of the wavefield, averaged over time of realizations of the random medium. The perturbation error is found explicitly as a function of operators acting on the wavefield. The accuracy of the wave and its moments is then examined, in terms of the error and its autocorrelation function. It is shown that both step-wise and cumulative accuracy of the moments is greater than it is for the wavefield itself. A model is also described in which the random medium may be represented, using a series of correlated phase-screens in arbitrarily fine detail. This is used to examine the convergence of the split-step solution as the step-size is reduced. It is shown that the independent phase-screen model is valid for small scattering when the scale-size of the medium is less than the step-size in the direction of propagation.