Abstract
Two problems in wave propagation governed by the reduced wave equation with a random refractive index are studied. Problem (a) is concerned with radiation from a source in an infinite medium, and problem (b) pertains to the scattering by a random half-space at high frequencies. By transforming the reduced wave equation into a generalized heat equation, it becomes possible to express the moments of solutions in terms of Wiener integrals. Concrete results are obtained for certain special cases. By systematically approximating the functional integral representation for the moments, various perturbation equations come forth. Among them is Kraichnan's direct interaction approximation. By examining the errors involved, the accuracy in each approximation is ascertained and the nature of the approximation becomes transparent.
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