Solution of the Wave Equation in the Boundary Layer
where the wave velocity depends on point M of an inhomogeneous medium. We look for high-frequency solutions of this equation in a narrow vicinity of the shadow boundary of an individual reflected/transmitted wave, where the geometrical theory of diffraction fails. In Section V.3.2 we identified such a domain as the boundary layer. Here we extend this concept to the case of 3-D inhomogeneous media. To do so, we have to consider a geometrical scheme of rays and wave fronts that follows from the kinematic law of edge diffraction (see Chapter I, Section 6).
Let us take two families of rays, determined by two corresponding sets of parameters individual ray of the first family. Each pair of gives a ray of the second family. We call the families and the congruencies of reflected/transmitted and diffracted rays, respectively.
Any of the expressions gives a surface, formed by the rays of the congruence. Any of the expressions gives a surface, formed by the rays of the congruence. We will consider the specific case when the congruencies under consideration have acommonsurface.Wesuppose the latter can be given simultaneously