Chapter 12 - Wave localization in randomly layered media

Abstract

This chapter analyzes wave localization in randomly layered media. The problem on plane wave propagation in layered media is formulated in terms of the one-dimensional boundary-value problem. In view of the fact that the one-dimensional problem allows an exact asymptotic solution, one can use it for tracing the effect of different models, medium parameters, and boundary conditions on statistical characteristics of the wavefield. The boundary conditions for equation are formulated as the continuity of function and derivative at layer boundaries. The imbedding method provides a possibility of reformulating boundary-value problem, in terms of the dynamic initial value problem with respect to geometric position of the right-hand boundary of the layer, by considering the solution of the problem as a function of this parameter. The case of nonabsorptive medium can be integrated in an analytic form. It is found that complex coefficient of wave reflection from a medium layer satisfies the closed Riccati equation. It is found that the obtained results related to wavefield at fixed spatial points offer a possibility of making certain general conclusions about the behavior of the wavefield average intensity inside the random medium.