Seismic modelling by methods of the theory of edge waves
K.D. Klem-Musatov, A.M. Aizenberg, 2016. "Seismic modelling by methods of the theory of edge waves", Seismic Diffraction, Kamil Klem-Musatov, Henning Hoeber, Michael Pelissier, Tijmen Jan Moser
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This paper deals with the computation of wavefields in 3-D inhomogeneous media Containing structural elements such as pinch-outs, vertical and oblique contacts, faults, etc. The approach is based on the theory of edge waves. The total wavefield is considered as the superposition or two parts. The first part is described by the ray method. It has discontinuities because of its shadow boundaries. The second part is a superposition of two types of diffracted w:aves. caused by the edges and vertices of interfaces. This part smooths the above-mentioned discontinuities so lhat the total wavefield is continuous. Of special importance is the mathematical farm of the amplitudes of diffracted waves, described with unified functions of eikonals. In fact, it allows all additional computalions 10 be considered by finding the eikonals of diffracled waves. A modification or 1 lie ray method including diffraction by edges and vertices is described. A generalization of ihe concept of edge waves for caustic situations is given the method of superposition of edge,tip waves. The result of such a generalization no longer supplements the geometrical seismic description, but completely replaces il by a new description valid for a broader class of wave phenomena (reflection refraction, diffraction on edges and vertices, formation of caustics, etc.).
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The use of diffraction imaging to complement the seismic reflection method is rapidly gaining momentum in the oil and gas industry. As the industry moves toward exploiting smaller and more complex conventional reservoirs and extensive new unconventional resource plays, the application of the seismic diffraction method to image sub-wavelength features such as small-scale faults, fractures and stratigraphic pinchouts is expected to increase dramatically over the next few years. “Seismic Diffraction” covers seismic diffraction theory, modeling, observation, and imaging. Papers and discussion include an overview of seismic diffractions, including classic papers which introduced the potential of diffraction phenomena in seismic processing; papers on the forward modeling of seismic diffractions, with an emphasis on the theoretical principles; papers which describe techniques for diffraction mathematical modeling as well as laboratory experiments for the physical modeling of diffractions; key papers dealing with the observation of seismic diffractions, in near-surface-, reservoir-, as well as crustal studies; and key papers on diffraction imaging.