IV Wave Propagation Theories in Random Media Based on the Path-Integral Approach

Abstract

Publisher Summary This chapter discusses the wave propagation theories in random media based on the path-integral approach. The chapter focuses on the connection between the path-integral technique and different analytical approximations for solutions of the statistical moment equations and other heuristic approaches that are based on the various plane wave expansions. A treatment of the path integral helps to realize the nature of the two-scale approximation. This approximation is not asymptotic. The chapter also examines the probabilistic interpretation of the path-integral representation, and an approach using orthogonal expansions for the path variables is developed on this basis. The orthogonal expansion is obtained, which leads to the Huygens-Fresnel formula for its zero-order term. The same idea of orthogonal expansions can be used for an improvement of any other approximate solution. The whole set of these approximations with the orthogonal expansion corrections will be a good instrument for analytical and numerical solutions for problems connected with fourth and perhaps higher moments.