Abstract
Seismic data are usually irregularly and sparsely sampled along the spatial coordinates, which yields suboptimal imaging results. For time-lapse data, differences in the spatial sampling of base and monitor surveys lead to undesired differences between the images of the surveys that are not due to differences in the subsurface. In this paper, an efficient two-step reconstruction method is proposed for irregularly and sparsely sampled 3D seismic data recorded with a dominant azimuth for large offsets. The first step is reconstruction along the receiver lines such that the midpoints are exactly on crosslines. The second step is a 2D reconstruction in the crossline midpoint-offset domain using a least-squares estimation of Fourier components. Sparse sampling can be handled by optimizing the parameterization of the least-squares estimation of the Fourier coefficients, and consequently it is possible to reconstruct data that would be aliased when considering single common-midpoint gathers. The method can be used to do a geometry transformation of the data to any desired spatial grid. Since the method yields consistent results independent of the actual sampling, it is very well suited for 4D processing.