Seismic data regularization, which spatially transforms irregularly sampled acquired data to regularly sampled data, is a long-standing problem in seismic data processing. Data regularization can be implemented using Fourier theory by using a method that estimates the spatial frequency content on an irregularly sampled grid. The data can then be reconstructed on any desired grid. Difficulties arise from the nonorthogonality of the global Fourier basis functions on an irregular grid, which results in the problem of “spectral leakage”: energy from one Fourier coefficient leaks onto others. We investigate the nonorthogonality of the Fourier basis on an irregularly sampled grid and propose a technique called “antileakage Fourier transform” to overcome the spectral leakage. In the antileakage Fourier transform, we first solve for the most energetic Fourier coefficient, assuming that it causes the most severe leakage. To attenuate all aliases and the leakage of this component onto other Fourier coefficients, the data component corresponding to this most energetic Fourier coefficient is subtracted from the original input on the irregular grid. We then use this new input to solve for the next Fourier coefficient, repeating the procedure until all Fourier coefficients are estimated. This procedure is equivalent to “reorthogonalizing” the global Fourier basis on an irregularly sampled grid. We demonstrate the robustness and effectiveness of this technique with successful applications to both synthetic and real data examples.

The image quality of 3D pre-stack depth migration in areas of complex geology depends strongly on the accuracy of the velocity model. Velocity updating by seismic tomography, in the form of either traveltime tomography or residual curvature analysis (RCA), has become an important component of the depth imaging process. In this paper, we describe the components of tomography, discussing RCA in detail. These components include: building of the tomographic updating equations; regularization in both data and model spaces; and application of the least-squares solver. Numerical examples show that the RCA algorithm works well, producing velocity models that improve the quality of depth-migrated images over models produced by vertical updating schemes.

We develop a novel procedure to solve the famous old problem of water column statics. Our procedure consists of automatic picking of the relative statics shift between the sail lines and solving this problem as a global nonlinear inversion problem. Like most of inversion problems, the solutions are not unique. So, we introduce a priori constraints to limit the final solution. The constraints require the least movement of traces when statics are derived. Furthermore, we implement the hybrid l 1 /l 2 norm in our algorithm for a robust inversion; it is relatively insensitive to the big residuals, which may occur as the existence of wrong picks in the automatic picking. Both the results on synthetic and real data sets show that our method is robust and powerful.

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