Five Dimensional Interpolation

Many seismic processing techniques have strict requirements on the regular spatial distribution of traces in seismic data. Datasets that do not fulfill these requirements, such as most 3D land surveys, will suffer from poor processing results when these techniques are used. Although not a substitute for well-sampled field data, interpolation can provide useful data preconditioning that allows these techniques to work better, and hence provide a superior result. Interpolation algorithms that use multiple spatial dimensions have many advantages over one-dimensional methods. In particular simultaneous interpolation in all the five seismic data dimensions has the greatest chance to predict missing data with correct amplitude and phase variations. However, the negative aspects of working in five dimensions are both the difficulty of solving the problem in a numerically efficient fashion and the handling of the large volumes of data. The first aspect is a consequence of the nonlinear increasing cost of interpolation with data size. The second aspect arises because of poor data sampling when considering all five seismic dimensions simultaneously. In this paper, we discuss an approach that has been successful for interpolation of land data and contrast it with narrow azimuth marine interpolation.