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Edge- and tip-wave theories were developed during a time when computational power was not readily available for verification by comparing with full wave solutions. However, physical modeling of wave propagation was common in several Soviet laboratories, including the Institute of Geophysics in Novosibirsk, where the initial theory and algorithms were developed (Klem-Musatovet al., 1972, 1975, 1976, 1982; Aizenberg and Klem-Musatov, 1980; Aizenberg, 1982). The first section of this chapter reviews experiments made by Russian scientists to compare their theoretical calculations against experimental data in simple 2D and 3D models (Klem-Musatov, 1980; Landa and Maksimov, 1980; Luneva and Kharlamov, 1990). Because theory and applications of edge and tip waves were published in Western journals (Klem-Musatov and Aizenberg, 1984, 1985, 1989), several groups pursued their own implementation, e.g., Pajchel et al. (1987, 1988, 1989) in Norway, Hoffmann et al. (1993) and Klaeschen et al. (1994) in Germany, Hron and Chan (1995) in Canada, and Wang and Waltham (1995) in the United Kingdom. As ray-method applications developed as tools in geophysical prospecting, edge-wave theory was discovered to be a convenient remedy for limitations of the ray approach in handling model discontinuities. We devote the second section of this chapter to one of the first practical implementations of edge-wave theory: the 2D software package of Pajchel et al. (1987). This implementation was used widely for practical exploration problems in the North Sea, where discontinuities in geologic structures and diffractions are common features of seismic sections. Edge-wave theory fails where the ray-theory field changes rapidly

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