3-D symmetric 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 considerable, 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 designed. 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 geometry design and analysis. Methods and theories for the design of 2-D surveys were developed in the 1980s. Anstey proposed the stack‐array approach, Ongkiehong and Askin the hands‐off acquisition technique, and Vermeer introduced symmetric sampling theory. In this paper, the theory of symmetric sampling for 2-D geometries is expanded to the most important 3-D geometries currently in use. Essential elements in 3-D symmetric sampling are the spatial properties of a geometry. Spatial aspects are important because most seismic processing programs operate in some spatial domain by combining neighboring traces into new output traces, and because it is the spatial behavior of the 3-D seismic volume that the interpreter has to translate into maps. Over time, various survey geometries have bee devised for the acquisition of 3-D seismic data. All geometries constitute some compromise with respect to full sampling of the 5-D prestack wavefield (four spatial coordinates describing 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 spatial coordinates. The spatial attributes of the traces in each subset vary slowly and regularly, and this property provides spatial continuity to the 3-D survey. The spatial continuity can be exploited optimally if the subsets are properly sampled and if their extent is maximized. The 2-D symmetric sampling criteria—equal shot and receiver intervals, 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 orthogonal geometry (geometry with parallel shotlines orthogonal to parallel receiver lines) is to ensure that the maximum cross‐line offset is equal to the maximum inline offset. Three‐dimensional symmetric sampling simplifies the design of 3-D acquisition geometries. A simple checklist of geophysical requirements (spatial continuity, resolution, mappability of shallow and deep objectives, and signal‐to‐noise ratio) limits the choice of survey parameters. In these consideration, offset and azimuth distributions are implicitly being taken care of. The implementation in the field requires careful planning to prevent loss of spatial continuity.