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.
Figures & Tables
This book is devoted to one important aspect of development of physical foundations of the seismic method — the theory of edge diffraction phenomena. Thoese phenomena occur when conditions of the regular wave reflection/transmission change sharply. Though these phenomena drew the attention of many scientist for many decades, their real influence on the resolution ability of the seismic method was truly understood rather recently due to interpretation of seismic data in block structures. Clearly, to develop seismic method for investigation of such structures without developing the theory of edge diffraction phenomena is impossible. The latter is the aim of this book.
The seismic method is based on the fundamental laws of continuum mechanics. These laws describe the behavior of wavefields on the microscopic level, i.e., in the form of differential equations of motion. Integrating these equations under some initial conditions or boundary conditions, makes possible acquisition of all necessary information on the wavefield in the given situation. However, the working base of the seismic method consists of not only the differential equations of motion themselves but of some general and simple enough consequences of their solutions, which are formulated in the form of physical principles and l aws. The latter include the concepts of wave, Fermat’s principle, the law of conservation of the energy flux, and the reflection/transmission laws. Essentially these laws and principles must form a system of concepts sufficient for the solution of some class of typical interpretation problems. In fact, these principles and laws form the physical fo ndation of the seismic method.