Sampling 3-D Seismic Data

Abstract

A three-dimensional (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 generally are derived from the usual one-dimensional (1-D) viewpoint. The spectrum of 3-D seismic data has a band region (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 the 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. We define the hexagonal noncubic sampling grid and the triangular noncubic 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 noncubic sampling grid, we point out that the maximum value of the spatial sampling interval along the profiles is larger by 15.6% that the one of the cubic sampling grid. We also point out that the triangular noncubic sampling grid requires a number of sample points equal to half the number requiredmore » by a cubic sampling grid.« less