3-D SYMMETRICAL SAMPLING

Three-dimensional seismic surveys have become accepted in the industry as a means of acquiring detailed information on the subsurface. Yet, the cost of 3-D seismic data acquisition is and will always be conside rable, making it highly important to select the right 3-D acquisition geometry. Up till now, no really comprehensive theory existed to tell what constitutes a good 3-D geometry and how such a geometry can be de signed. The theory of 3-D symmetric sampling proposed in this paper is intended to fill this gap and may serve as a sound basis for 3-D geom etry design and analysis. Methods and theories for the design of 2-D s urveys were developed in the 1980s. Anstey proposed the stack-array ap proach, Ongkiehong and Askin the hands-off acquisition technique, and Vermeer introduced symmetric sampling theory. In this paper, the theor y of symmetric sampling for 2-D geometries is expanded to the most imp ortant 3-D geometries currently in use. Essential elements in 3-D symm etric sampling are the spatial properties of a geometry Spatial aspect s are important because most seismic processing programs operate in so me spatial domain by combining neighboring traces into new output trac es. and because it is the spatial behavior of the 3-D seismic volume t hat the interpreter has to translate into maps. Over time, various sur vey geometries have been devised for the acquisition of 3-D seismic da ta. All geometries constitute some compromise with respect to full sam pling of the 5-D prestack wavefield (four spatial coordinates describi ng shot and receiver position. and traveltime as fifth coordinate). It turns out that most geometries can be considered as a collection of 3 -D subsets of the 5-D wavefield, each subset having only two varying s patial coordinates. The spatial attributes of the traces in each subse t vary slowly and regularly, and this property provides spatial contin uity to the 3-D survey. The spatial continuity can be exploited optima lly if the subsets are properly sampled and if their extent is maximiz ed. The 2-D symmetric sampling criteria-equal shot and receiver interv als, and equal shot and receiver patterns-apply also to 3-D symmetric sampling but have to be supplemented with additional criteria that are different for different geometries. The additional criterion for orth ogonal geometry(geometry with parallel shotlines orthogonal to paralle l receiver lines) is to ensure that the maximum cross-line offset is e qual to the maximum in line offset. Three-dimensional symmetric sampli ng simplifies the design of 3-D acquisition geometries. A simple check list of geophysical requirements (spatial continuity, resolution, mapp ability of shallow and deep objectives, and signal-to-noise ratio) lim its the choice of survey parameters. In these considerations, offset a nd azimuth distributions are implicitly being taken care of. The imple mentation in the field requires careful planning to prevent loss of sp atial continuity.