Sampling 3‐D seismic data

Abstract

AbstractA 3‐D seismic survey is usually achieved by recording a parallel profile network. The 3‐D data thus obtained are sampled and processed in a cubic grid for which the sampling requirements are generally derived from the usual 1‐D viewpoint. The spectrum of 3‐D seismic data has a support (the region of the Fourier space in which the spectrum is not zero) that can be approximated by a domain bounded by two cones. Considering the particular shape of this support, we use a 3‐D sampling theory to obtain results applicable to the recording and processing of 3‐D seismic data. This naturally leads to weaker sampling requirements than the 1‐D viewpoint does. We define the hexagonal non‐cubic sampling grid and the triangular non‐cubic sampling grid and show that fewer sample points are needed to represent 3‐D seismic data with the same degree of accuracy. Thus, using the hexagonal non‐cubic sampling grid we point out that the maximum value of the spatial sampling interval along the profiles is larger by 15.6% than the one of the cubic sampling grid. We also point out that the triangular non‐cubic sampling grid requires a number of sample points equal to half the number required by a cubic sampling grid.