Examples and Applications
Published:January 01, 2008
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
Figures & Tables
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.