Reconstruction of 3D non-uniformly sampled seismic data along two spatial coordinates using non-equispaced curvelet transform

Abstract

Seismic data acquisition often faces the challenge of non-uniformly sampled data with missing traces. Only a few existing multitrace reconstruction methods can natively handle non-uniformly sampled data with missing traces. In this paper, we propose the non-equispaced fast discrete curvelet transform (NFDCT)-based reconstruction method designed for 3D seismic data that are non-uniformly sampled along two spatial coordinates. By partitioning 3D seismic datasets into time slices along source-receiver coordinates, we introduce 2D non-equispaced fast Fourier transform in the conventional fast discrete curvelet transform and formulate a regularised inversion of operator that links the uniformly sampled curvelet coefficients to non-uniformly sampled data. Numerically, the uniform curvelet coefficients are calculated by solving the L1-norm problem via the spectral projected-gradient algorithm. With the uniform curvelet coefficients, the NFDCT is formed via the conventional inverse curvelet transform and is used to reconstruct 3D non-uniformly sampled seismic data along two spatial coordinates. At the hand of reconstructed results from synthetic and field data, we demonstrate that the proposed method shows significant improvement over the conventional anti-leakage Fourier transform-based reconstruction method. The method we propose, which has a strong anti-aliasing and anti-noise ability, can be used to reconstruct the subset of observed data to a specified uniform grid along two spatial coordinates.

We propose the non-equispaced fast discrete curvelet transform-based reconstruction method designed for 3D seismic data that are non-uniformly sampled along two spatial coordinates. The method we propose, which has a strong anti-aliasing and anti-noise ability, can be used to reconstruct the non-uniform sampled data to a specified uniform grid.

• L1 norm
• data reconstruction
• non-equispaced curvelet transform
• non-equispaced fast Fourier transform

Acknowledgements

This paper was prepared using NFFT (https://www-user.tu-chemnitz.de/~potts/nfft/); CurveLab (curvelet.org); SPGL1 (cs.ubc.ca/laboratories/scl/spgl1); and relevant software in SLIM (https://www.slim.eos.ubc.ca). We thank them for their free available codes. We thank Dr Haneet Wason for helpful discussion about this paper. Hua Zhang sincerely thanks Felix J. Herrmann for supporting his visiting to the Seismic Laboratory for Imaging and Modelling (SLIM) of University of British Columbia (UBC). This research is sponsored by the National Natural Science Foundation of China (Nos. 41304097, 41664006, 41504095, 41604104), Distinguished Young Talent Foundation of Jiangxi Province (20171BCB23068), the Natural Science Foundation of Jiangxi Province (20151BAB203044, 20171BAB203031) and the science and technology project of Jiangxi Provincial Education Department (GJJ170486). We thank Professor Linping Song and Professor David Nobes for help in improving the English writing. We also appreciate the valuable comments and suggestions from two anonymous reviewers and one associate editor.