Geometrical theory of diffraction for high-frequency coherence functions in a weakly random medium

We propose a theory of propagation and diffraction of the statistical moments of high-frequency fields in the presence of interfaces, boundaries, or general scattering objects embedded within a medium with weak large-scale random fluctuations. The formulation utilizes the deterministic ray paths and initial conditions of the geometrical theory of diffraction when stochastic effects are omitted to construct initial conditions for ray-centered transport equations governing appropriate statistical measures of the field when stochastic effects are included. The basic principles of the problem strategy are discussed and demonstrated on canonical examples.