Michel Schonewille

Reconstruction of band-limited signals, irregularly sampled along one spatial direction

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.

A proven method for acquiring highly repeatable towed streamer seismic data

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 deg...

Parabolic Radon transform, sampling and efficiency

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.

3D surface-related multiple elimination: Acquisition and processing solutions

The removal of free-surface multiples from seismic reflection data remains an essential processing step before the application of prestack migration. Slowly decaying water layer multiples arising from a strong impedance contrast at the sea floor severely degrade the quality of the seismogram. In addition, peg-leg multiples generated from structurally complex 3D geologic bodies create a complex set of reverberations that can easily obscure weak primary reflections. In other areas, diffracted multiples from shallow point diffractors generate a “cloud” of multiple energy masking underlying primaries.

Regularization with azimuth time‐shift correction

Irregular sampling can give problems for time-lapse seismic and imaging. Fourier regularization can be used to regularize the data, but this method does not take into account azimuth variations. For steeply dipping layers (in particular oblique dips), azimuth variations lead to timeshifts which can be significant, in particular for time-lapse surveys. In this paper a new method to correct for timeshifts due to azimuth variations is proposed. The correction for the time shifts is included in a 2D Radon regularization routine. The time-shifts are derived from an equation for the two-way time for a dipping layer in a homogeneous subsurface, but the method is also shown to correct for the time shifts for a point diffractor. For a synthetic time-lapse example, the azimuth time-shift correction leads to a strong improvement of the repeatability.

Data regularization for 3-D SRME: A comparison of methods

Summary This paper discusses and compares different strategies for data regularization prior to the application of 3-D SRME. It is shown that synthetic analysis can be utilized to determine whether azimuth corrections are needed during data regularization. It is shown that only in certain instances this is needed, depending on the azimuth between the dipping reflectors and the acquisition direction. Also, the reflector dips, offset ranges and the reflectors depths are important. For geometries where azimuth corrections are needed, a comparison is made between two well-known solutions: Forward DMO followed by inverse DMO (DMO-DMO -1 ) regularization, and Fourier regularization with azimuth correction. It is shown that the latter shows better performance in terms of amplitude fidelity, as well as dealing with practical issues such as irregular sampling due to feathering of the streamers. Application of the Fourier regularization method to a field data set shows that the method is very capable of predicting complex 3-D multiples in the presence of multiple diffractions.

3D SRME: Acquisition & processing solutions

This paper describes the issues and possible solutions involved in the application of 3D data-driven multiple removal in a marine production environment. The optimization of marine data acquisition for 3D Surface related multiple elimination (SRME) is discussed. Recommendations for acquisition are given to create a dense grid of sail lines and streamers needed to predict the full 3D characteristics of the multiples. A processing sequence is discussed to predict and remove 3D multiples for each sail line using only the recorded data around the output streamer. The processing strategy does not rely on any a priori information or model of the subsurface to remove 3D multiples. The application of 3D SRME to a field data set from the Norwegian Sea leads to results that could not be obtained using its 2D equivalent.

High-resolution transforms and amplitude preservation

High-resolution transforms have several advantages over standard least squares transforms. However, the highresolution transform can show extra artifacts, which may compromise amplitude preservation. In addition, amplitudes may be affected if the induced sparseness is too strong. In this paper the amplitude preservation of high-resolution transforms is studied using synthetic data. Firstly, the high-resolution parabolic Radon transform is shown to improve both the preservation of primary AVO and demultiple efficiency related to standard least squares methods. Secondly it is shown that a high resolution Fourier/Radon regularization provides an improved interpolation of data with large gaps, and less edge effects. Finally, it is shown that that the artifacts can be suppressed by using a frequency independent sparseness prior. This prior can be derived in a cost efficient manner from a previous (adjacent) common midpoint gather.

A modeling study on seismic data regularization for time‐lapse applications

Repeatability of time-lapse data is affected by differences in spatial sampling of the shot and receiver positions. For marine streamer data, repeating shot positions and accurate feather matching is one way to reduce the sampling differences and improve the repeatability. Handling the differences in spatial sampling during processing could be more cost-effective, however conventional processing methods that have been used for legacy data may not be good enough for new, dedicated, high quality time-lapse data.

Comparison of 3D Time-domain Radon and Matching-pursuit Fourier Interpolation

We compare a 3D sparse time-domain Radon interpolator (TDRI) with frequency-domain matching pursuit Fourier interpolation (MPFI) using synthetic data and field data. MPFI and the similar anti-leakage Fourier transform are widely used beyond aliasing interpolators. Though TDRI is not new, it is not widely used, possibly because of its computational cost. It is illustrated with a simple synthetic example that TDRI can provide a sparser representation than MPFI in the transform domain. From compressive sampling theory, we know that this may provide better reconstruction of undersampled data. TDRI and MPFI are applied to complex and highly aliased synthetic and marine data. For both datasets, the results of TDRI are significantly better than the results of MPFI. In particular, steeply dipping events are better reconstructed, continuity of events is improved and artefacts are reduced.We compare a 3D sparse time-domain Radon interpolator (TDRI) with frequency-domain matching pursuit Fourier interpolation (MPFI) using synthetic data and field data. MPFI and the similar anti-leakage Fourier transform are widely used beyond aliasing interpolators. Though TDRI is not new, it is not widely used, possibly because of its computational cost. It is illustrated with a simple synthetic example that TDRI can provide a sparser representation than MPFI in the transform domain. From compressive sampling theory, we know that this may provide better reconstruction of undersampled data. TDRI and MPFI are applied to complex and highly aliased synthetic and marine data. For both datasets, the results of TDRI are significantly better than the results of MPFI. In particular, steeply dipping events are better reconstructed, continuity of events is improved and artefacts are reduced.