Antileakage Fourier transform for seismic data regularization

TLDR

Seismic data regularization converts irregularly sampled data into a regularly sampled grid, typically via Fourier theory, but the nonorthogonality of the global Fourier basis on irregular grids causes spectral leakage where energy from one coefficient contaminates others. This study investigates the nonorthogonality of the Fourier basis on irregular grids and introduces the antileakage Fourier transform to mitigate spectral leakage. The antileakage Fourier transform iteratively estimates the most energetic Fourier coefficient, subtracts its contribution from the input to suppress its leakage, and repeats this reorthogonalization until all coefficients are recovered. The method proved robust and effective on both synthetic and real seismic data, demonstrating successful regularization without spectral leakage.

Abstract

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.