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Seismic prospecting for oil and gas has undergone a digital revolution during the past decade. Most stages of the exploration process have been affected: the acquisition of data, the reduction of this data in preparation for signal processing, the design of digital filters to detect primary echoes (reflections) from buried interfaces, and the development of technology to extract from these detected signals information on the geometry and physical properties of the subsurface. The seismic reflection is genenlly weak, and it must be strengthened by the use of signal summing (stacking) procedures. The determination of depths to a target horizon requires knowledge of the propagational velocities of seismic stress waves, and a wealth of technology has evolved for this purpose. More recently, it has been possible to relate signal amplitude to the physical properties of the medium traversed and, in particular, to make inferences about the oil and gas content of the buried rocks. Much of the exploration effort occurs in offshore areas, where reverberations in the water layer mask reflections from below. The method of predictive deconvolution has been most effective in its ability to attenuate these reverberations, making it possible to detect reflections from structures at depth. Seismic signal processing is neither pure science nor pure art, and offers a continuing challenge to the practitioners of both cultures.