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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 of 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 waves, caused by the edges and vertices of interfaces. This part smooths the above-mentioned discontinuities so that the total wavefield is continuous. Of special importance is the mathematical form of the amplitudes of diffracted waves, described with unified functions of eikonals. In fact, it allows all additional computations to be considered by finding the eikonals of diffracted waves. A modification of the ray method including diffraction by edges and vertices is described. A generalization of the 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 it 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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