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 band‐limited seismic signals that are irregularly sampled along one spatial coordinate. A simple and efficient diagonal weighting scheme, based on the distance between the 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 for each temporal frequency component allows the specification of a varying spatial bandwidth dependent on the minimum apparent velocity. This parameterization improves the reconstruction capability for the lower temporal frequencies. In practical circumstances, the maximum size of the gaps in which the signal can be reconstructed is three times the (temporal frequency dependent) Nyquist interval. Reconstruction in the wavenumber domain allows a very efficient implementation of the algorithm, and takes a total number of operations a few times that of a 2-D fast Fourier transform corresponding to the size of the output data set. Quality control indicators of the reconstruction procedure can be computed which may also serve as decision criteria on in‐fill shooting during acquisition. The method can be applied to any subset of seismic data with one varying spatial coordinate. Applied along the cross‐line direction, it can be used to compute a 3-D stack with improved anti‐alias protection and less distortion of the signal within the bandwidth.

The nonuniform discrete Fourier transform (NDFT) can be computed with a fast algorithm, referred to as the nonuniform fast Fourier transform (NFFT). In L dimensions, the NFFT requires [Formula: see text] operations, where M𝓁 is the number of Fourier components along dimension 𝓁, N is the number of irregularly spaced samples, and ε is the required accuracy. This is a dramatic improvement over the [Formula: see text] operations required for the direct evaluation (NDFT). The performance of the NFFT depends on the lowpass filter used in the algorithm. A truncated Gauss pulse, proposed in the literature, is optimized. A newly proposed filter, a Gauss pulse tapered with a Hanning window, performs better than the truncated Gauss pulse and the B-spline, also proposed in the literature. For small filter length, a numerically optimized filter shows the best results. Numerical experiments for 1-D and 2-D implementations confirm the theoretically predicted accuracy and efficiency properties of the algorithm.

Seismic reservoir monitoring has become an important tool in the management of many fields. Monitoring subtle changes in the seismic properties of a reservoir caused by production places strong demands on seismic repeatability. A lack of repeatability limits how frequently reservoir changes can be monitored or the applicability of seismic monitoring at all. In this paper we show that towing many streamers with narrow separation, combined with cross‐line interpolation of data onto predefined sail lines, can give highly repeatable marine seismic data. Results from two controlled zero time lag monitoring experiments in the North Sea demonstrate high sensitivity to changing water level and variations in lateral positions. After corrections by deterministic tidal time shifts and spatial interpolation of the irregularly sampled streamer data, relative rms difference amplitude levels are as low as 12% for a deep, structurally complex field and as low as 6% for a shallow, structurally simple field. Reducing the degree of nonrepeatability to as low as 6% to 12% allows monitoring of smaller reflectivity changes. In terms of reservoir management this has three important benefits: (1) reservoirs with small seismic changes resulting from production can be monitored, (2) reservoirs with large seismic changes can be monitored more frequently, and (3) monitoring data can be used more quantitatively.

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A good choice of the sampling in the transform domain is essential for a successful application of the parabolic Radon transform. The parabolic Radon transform is computed for each temporal frequency and is essentially equivalent to the nonuniform Fourier transform. This leads to new and useful insights in the parabolic Radon transform.Using nonuniform Fourier theory, we derive a minimum sampling interval for the curvature parameter and a maximum curvature range for which stability is guaranteed for general (irregular) sampling. A significantly smaller sampling interval requires stabilization. If diagonal stabilization is used, no gain in resolution is obtained.In contrast to conventional implementations, the curvature sampling interval is proposed to be inversely proportional to the temporal frequency. This results in improved quality of the transform and yields significant savings in computation time.