In 3-D block media the interlaces are represented by the surfaces of the curvilinear polyhedrons. Such surfaces include the vertices, where several diffracting edges can converge, and therefore, in 3-D block media the diffracting edges are not smooth. The latter limits the range of applicability of the approach described in Chapter VIll. The gist of the limitations becomes clear from the following example.
Figure 71a shows the geometry of the shadow boundary of the reflected/transmitted wave in the case of a broken edge. The edge consists of two semi-infinite parts RA and RB. Point R is not a regular point of the edge, because the tangent to the edge cannot be determined as a single value at R. The shadow boundary consists of two parts RAT and RBT.
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.