Quasi-geometrical optics methods in the theory of wave propagation through a randomly inhomogeneous layer

Some possibilities of using asymptotic methods, such as the Maslov method and the interference-integral method, in problems of wave propagation in randomly inhomogeneous media are considered. It is shown that using the Maslov method and the interference-integral method in a small-angle approximation, and neglecting amplitude fluctuations of partial waves, provides results of heuristic spectral methods that utilize expansions in terms of incoming or outgoing waves. The combined use of these asymptotic methods gives a third heuristic method, a mixed-integral representation obtained earlier by applying the method of two-scale expansions. It is pointed out that results of a mixed-integral representation change to those of the method of smooth disturbances and of the phase-screen method. Unlike the method of two-scale expansions, the proposed approach based on the combined use of asymptotic methods facilitates the process of taking into account the heterogeneity of a background medium.