Edge Waves in Boundary Layers
Published:January 01, 2008
2008. "Edge Waves in Boundary Layers", Edge and Tip Diffractions: Theory and Applications in Seismic Prospecting, Kamill Klem-Musatov, Arkady M. Aizenberg, Jan Pajchel, Hans B. Helle
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The descriptions of edge diffraction that one can use to solve practical problems depend on the character of the problem considered. In some cases, consideration of an individual edge wave can be of practical importance. It is often sufficient in such situations to describe the edge wave in the framework of the geometric theory of diffraction. Sometimes it is necessary to use a more complicated description, which involves combining the formulas of the geometric theory of diffraction and the boundary-layer approximation. However, of greatest practical importance is the case in which edge waves can be regarded as factors interfering with regular reflections/transmissions representing basic geophysical information. In such situations, it is possible to use the simplest description of edge-diffraction phenomena. All the following sections deal only with that kind of situation. Let us begin with general considerations on the representation of wavefields in media consisting of regions and interfaces. Description of a stationary wavefield in such media is based on separation of the wavefield into individual waves caused by the consecutive reflection/transmission phenomena at the interfaces. It can be written in the form of the superposition of individual waves: where m is the index of the individual wave fm, Φm is its amplitude, τm is its eikonal, cm is the propagation velocity, and ω is the frequency of oscillations. If there are diffracting edges at the interfaces, this description is not sufficient because of shadow zones in the individual
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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.