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Curvelet reconstruction of non-uniformly sampled seismic data using the linearized Bregman methodNormal access

Authors: H. Zhang, S. Diao, W. Chen, G. Huang, H. Li and M. Bai
Journal name: Geophysical Prospecting
Issue: Vol 67, No 5, June 2019 pp. 1201 - 1218
DOI: 10.1111/1365-2478.12762
Organisations: Wiley
Language: English
Info: Article, PDF ( 9.77Mb )

Summary:
Seismic data reconstruction, as a preconditioning process, is critical to the perfor-mance of subsequent data and imaging processing tasks. Often, seismic data are sparsely and non-uniformly sampled due to limitations of economic costs and field conditions. However, most reconstruction processing algorithms are designed for the ideal case of uniformly sampled data. In this paper, we propose the non-equispaced fast discrete curvelet transform-based three-dimensional reconstruction method that can handle and interpolate non-uniformly sampled data effectively along two spatial coordinates. In the procedure, the three-dimensional seismic data sets are organized in a sequence of two-dimensional time slices along the source–receiver domain. By in-troducing the two-dimensional non-equispaced fast Fourier transform in the conven-tional fast discrete curvelet transform, we formulate an L1 sparsity regularized prob-lem to invert for the uniformly sampled curvelet coefficients from the non-uniformly sampled data. In order to improve the inversion algorithm efficiency, we employ the linearized Bregman method to solve the L1-norm minimization problem. Once the uniform curvelet coefficients are obtained, uniformly sampled three-dimensional seismic data can be reconstructed via the conventional inverse curvelet transform. The reconstructed results using both synthetic and real data demonstrate that the proposed method can reconstruct not only non-uniformly sampled and aliased data with missing traces, but also the subset of observed data on a non-uniform grid to a specified uniform grid along two spatial coordinates. Also, the results show that the simple linearized Bregman method is superior to the complex spectral projected gradient for L1 norm method in terms of reconstruction accuracy.

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