Approximation of the parabolic equation and the wavefield of a point source in a layered random medium

This paper studies the wavefield of a source in a multidimensional randomly layered medium. They obtained asymptotical expressions of the wave statistical characteristics for different boundary conditions both in the framework of the parabolic equation approximation and the exact formulation of the boundary problem for the Helmholtz equation. It is shown that the presence of a small but finite absorption γ is most important for the statistics. The diffraction effects turn out to be like those of absorption, but γ cannot tend to zero in this problem. In an appendix they give the factorization formulae of the wave equation solution in a layered medium.