A comparative study of multidimensional Fourier reconstruction of 2D prestack seismic data

Although 3D seismic data are being acquired in larger volumes than ever before, the spatial sampling of these volumes is not always adequate for certain seismic processes. This is especially true of marine and land wide-azimuth acquisitions, leading to the development of multidimensional data interpolation techniques. Simultaneous interpolation in all five seismic data dimensions (inline, crossline, offset, azimuth, and frequency) has great utility in predicting missing data with correct amplitude and phase variations. Although there are many techniques that can be implemented in five dimensions, this study focused on sparse Fourier reconstruction. The success of Fourier interpolation methods depends largely on two factors: (1) having efficient Fourier transform operators that permit the use of large multidimensional data windows and (2) constraining the spatial spectrum along dimensions where seismic amplitudes change slowly so that the sparseness and band limitation assumptions remain valid. Fourier reconstruction can be performed when enforcing a sparseness constraint on the 4D spatial spectrum obtained from frequency slices of five-dimensional windows. Binning spatial positions into a fine 4D grid facilitates the use of the FFT, which helps on the convergence of the inversion algorithm. This improves the results and computational efficiency. The 5D interpolation can successfully interpolate sparse data, improve AVO analysis, and reduce migration artifacts. Target geometries for optimal interpolation and regularization of land data can be classified in terms of whether they preserve the original data and whether they are designed to achieve surface or subsurface consistency.

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Assisted History Matching of 4D Seismic Data - A Comparative Study

10.3997/2214-4609.201902180 ◽

2019 ◽

Author(s):

K. Fossum ◽

R.J. Lorentzen

Keyword(s):

Comparative Study ◽

Seismic Data ◽

History Matching ◽

Assisted History Matching ◽

4D Seismic

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Seismic data compression: a comparative study between GenLOT and wavelet compression

10.1117/12.366837 ◽

1999 ◽

Cited By ~ 5

Author(s):

Laurent C. Duval ◽

Truong Q. Nguyen

Keyword(s):

Comparative Study ◽

Data Compression ◽

Seismic Data ◽

Wavelet Compression ◽

Seismic Data Compression

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Fourier reconstruction of marine-streamer data in four spatial coordinates

Geophysics ◽

10.1190/1.2348633 ◽

2006 ◽

Vol 71 (6) ◽

pp. V171-V186 ◽

Cited By ~ 25

Author(s):

P. Zwartjes ◽

A. Gisolf

Keyword(s):

Seismic Data ◽

Time Lapse ◽

Computationally Efficient ◽

Nonuniform Grids ◽

Uniform Grids ◽

Spatial Dimensions ◽

Spatial Coordinates ◽

Fourier Reconstruction ◽

Multiple Prediction ◽

Streamer Data

Many methods exist for interpolation of seismic data in one and two spatial dimensions, but few can interpolate properly in three or four spatial dimensions. Marine multi-streamer data typically are sampled relatively well in the midpoint and absolute offset coordinates but not in the azimuth because the crossline shot coordinate is significantly under sampled. We approach the problem of interpolation of marine-streamer data in four spatial dimensions by splitting the problem into a 1D interpolation along the densely sampled streamers and a 3D Fourier reconstruction for the remaining spatial coordinates. In Fourier reconstruction, the Fourier coefficients that synthesize the nonuniformly sampled seismic data are estimated in a least-squares inversion. The method is computationally efficient, requires no subsurface information, and can handle uniform grids with missing data as well as nonuniform grids or random sampling. The output grid of the 1D interpolation in the first step is arbitrary. When the output grid has uniform inline midpoints spacing, the 3D Fourier reconstruction in the second step is performed in the crossline midpoint, absolute offset, and azimuth coordinates. When the first step outputs to uniform absolute offset, the 3D Fourier reconstruction handles the crossline/inline midpoint and the azimuth coordinates. In both cases, the main innovation is the inclusion of the azimuthal coordinate in the Fourier reconstruction. The azimuth multiplicity must be increased for the method to be successful, which means that overlap shooting is required. We have tested the algorithm on synthetic streamer data for which the proposed method outperforms an approach where the azimuthal coordinate is ignored. Potential applications are interpolation of marine streamer data to decrease the crossline source sampling for the benefit of 3D multiple prediction and regularization to reduce sampling-related differences in processing of time-lapse data.

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Fourier reconstruction of nonuniformly sampled, aliased seismic data

Geophysics ◽

10.1190/1.2399442 ◽

2007 ◽

Vol 72 (1) ◽

pp. V21-V32 ◽

Cited By ~ 106

Author(s):

P. M. Zwartjes ◽

M. D. Sacchi

Keyword(s):

Seismic Data ◽

Fourier Coefficients ◽

A Priori ◽

Nonuniform Sampling ◽

Second Step ◽

Fourier Domain ◽

Sampled Data ◽

Underlying Assumption ◽

Fourier Reconstruction ◽

Step Algorithm

There are numerous methods for interpolating uniformly sampled, aliased seismic data, but few can handle the combination of nonuniform sampling and aliasing. We combine the principles of Fourier reconstruction of nonaliased, nonuniformly sampled data with the ideas of frequency-wavenumber [Formula: see text] interpolation of aliased, uniformly sampled data in a new two-step algorithm. In the first step, we estimate the Fourier coefficients at the lower nonaliased temporal frequencies from the nonuniformly sampled data. The coefficients are then used in the second step as an a priori model to distinguish between aliased and nonaliased energy at the higher, aliased temporal frequencies. By using a nonquadratic model penalty in the inversion, both the artifacts in the Fourier domain from nonuniform sampling and the aliased energy are suppressed. The underlying assumption is that events are planar; therefore, the algorithm is applied to seismic data in overlapping spatiotemporal windows.

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