Perturbation Methods in Stochastic Wave Propagation

Several methods of approximation applicable to problems in wave propagation governed by a three-dimensional random reduced wave equation are presented within the framework of perturbation theory. For moderate wave numbers, the methods collected in this paper include the regular perturbation, two-variable method, the smoothing perturbation and the direct interaction approximation. At high frequencies, the parabolic equation approximation, the logarithmic regular perturbation and the geometric optics approximation are described. The validity and accuracy of various approximations are discussed by comparing them with an exact solution constructed through a function space integration.

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