Deriving the response of an array is one thing, designing an array to match a desired response is quite another. The first is easy, the second is not. Given a selected pass and reject requirement in the spatial frequency domain, an array can be obtained that best matches such requirement within the limits of available hardware.
Optimum spatial arrays for 2-D and 3-D/4-D seismic surveys can be designed using the technique of spatial convolution. Such a technique relies upon uniform arrays of differing shapes and sizes as building blocks. These building blocks are convolved in space because their selected responses matching notch points against side lobes to achieve a desired end result in the spatial frequency domain. The final array design can be made optimum for a given set of requirements, such as signal preservation within the passband, attenuation within the reject band, and azimuthal distribution for 3-D/4-D seismic surveys. For any given design, solely the number and the spacing of the elements limit the optimization.
A rule of thumb has been observed which shows that the required number of elements in a 2-D array for 3-D/4-D seismic is equal to the square of the number of elements in a 1-D equivalent array for 2-D seismic. It is also observed that for a given number of elements, narrow azimuth designs can offer greater attenuation than wide azimuth designs.