Published:January 01, 2008
Interfaces in 3D block media are represented by the surfaces of curvilinear polyhedrons. Such surfaces include vertices where several diffracting edges can converge. This means that edges are not smooth in 3D block media. Each smooth part of the edge has two terminal points called tips. A joint of two tips is called a breakpoint of the edge. A joint of two or more tips is a vertex. The existence of such points puts some limitations on the previous discussion of edge diffraction. The essence of these limitations becomes clear from the following example. Figure 1a shows the geometry of the shadow boundary of a reflected/transmitted wave in the case of a broken edge. The edge consists of two semi-infinite parts, RA and RB. Point R is a breakpoint because the tangent to the edge is not single valued. The shadow boundary consists of two smooth parts, RAT and RBT. Figure 1b and 1c shows the edge wavefronts arising at semiedges RB and RA. The diffracted rays, generated by each individual semiedge, form a congruence. However, the unification of two sets of diffracted rays emanating from both semiedges is not a congruence. Each of these congruences exists only on one side of the cone of diffracted rays spreading from point R. Such a cone acts as a shadow boundary of the corresponding edge wave generated by the semiedge. The edge wavefield has a discontinuity because there is no edge wave in the region where diffracted rays do not exist. The
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Edge and Tip Diffractions: Theory and Applications in Seismic Prospecting
In Edge and Tip Diffractions: Theory and Applications in Seismic Prospecting (SEG Geophysical Monograph Series No. 14), the theoretical framework of the edge and tip wave theory of diffractions has been elaborated from fundamental wave mechanics. Seismic diffractions are inevitable parts of the recorded wavefield scattered from complex structural settings and thus carry back to the surface information that can be exploited to enhance the resolution of details in the underground. The edge and tip wave theory of diffractions provides a physically sound and mathematically consistent method of computing diffraction phenomena in realistic geologic models. In this book, theoretical derivations are followed by their numerical implementation and application to real exploration problems. The book was written initially as lecture notes for an internal course in diffraction modeling at Norsk Hydro Research Center, Bergen, Norway, and later was used for a graduate course at Novosibirsk State University in Russia. The material is drawn from several previous publications and from unpublished technical reports. Edge and Tip Diffractions will be of interest to geoscientists, engineers, and students at graduate and Ph.D. levels.