Edge Waves in the Boundary Layers
The most intensive diffraction effects smoothing the discontinuities at shadow boundaries are localized in the boundary layers. Outside the boundary layers the scattering effect has a character of a less intensive diffraction background. The very possibility of dividing the edge-diffracted wave into the boundary layer approximation and the background prompts a simple approximate way to describe wave fields in inhomogeneous block media with diffracting edges. It is based on representation of the wavefieldas the superposition of two parts. The first part is described by the ray method and has discontinuities at the shadow boundaries, which are caused by the edges of interfaces. The second part, which is the superposition of edge-diffractedwaves taken in the boundary layer approximation, smoothes the discontinuities at the shadow boundaries of the reflected/transmitted waves. The existence of the diffraction background is neglected. The total wavefield complies with given conditions at interfaces in the raymethod approximation. Such an approach results in a modification of the ray method by considering the diffraction phenomena only in the boundary layers.
Chapter VIII we consider the special problem of finding edge-diffracted waves in the boundary-layer approximation. It is essential that there is no necessity to deal with the equations of motion to state this problem. Therefore, the final result is equally fair for scalar and vector waves of any physical origin (optics, acoustics, elastodynamics, electrodynamics, etc.). First we consider the statement of this problem for a scalar case.