Five Dimensional Seismic Data Interpolation

Many seismic processing techniques, for example migration, have strict requirements on the regular spatial distribution of traces. Datasets that do not fulfill these requirements, such as most 3D land surveys, will suffer from poor processing results. Although not a substitute for well-sampled field data, interpolation can provide useful data preconditioning that allows these processing techniques to work better. Interpolation algorithms that use multiple spatial dimensions have many advantages over one-dimensional methods. In particular, simultaneous interpolation in all five seismic data dimensions has the greatest chance to predict missing data with correct amplitude and phase variations. The negative aspect of working in five dimensions is the difficulty of solving the problem in a numerically efficient fashion. In this paper, we discuss an approach that uses Fourier reconstruction in the inline-crossline-offset-azimuth-frequency domain, with a sparseness constraint on the 5D spectrum. The method has been successful for interpolation and regularization of land data in a variety of scenarios, helping on the processing of data with different acquisition problems