Reconstruction of 3-D seismic signals irregularly sampled along two spatial coordinates

Seismic signals are often irregularly sampled along spatial coordinates, leading to suboptimal processing and imaging results. Least-squares estimation of Fourier components is used for the reconstruction of bandlimited seismic signals that are irregularly sampled along two spatial coordinates. A simple and efficient diagonal weighting scheme, based on the areas surrounding the spatial samples, takes the properties of the noise (signal outside the bandwidth) into account in an approximate sense. Diagonal stabilization based on the energies of the signal and the noise ensures robust estimation. Reconstruction by temporal frequency component allows the specification of varying bandwidth in two dimensions, depending on the minimum apparent velocity. This parameterization improves the reconstruction capability for lower temporal frequencies. The shape of the spatial aperture affects the method of sampling the Fourier domain. Taking into account this property, a larger bandwidth can be recovered. The properties of the least-squares estimator allow a very efficient implementation which, when using a conjugate gradient algorithm, requires a modest number of 2-D fast Fourier transforms per temporal frequency. The method shows significant improvement over the conventionally used binning and stacking method on both synthetic and real data. The method can be applied to any subset of seismic data with two varying spatial coordinates.