Application of randomized sampling schemes to curvelet‐based sparsity‐promoting seismic data recovery
Application of randomized sampling schemes to curvelet‐based sparsity‐promoting seismic data recovery
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DOI：
10.1111/1365-2478.12050
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发表时间：
2013-09
影响因子：
2.6
通讯作者：
R. Shahidi;Gang Tang;Jianwei Ma;F. Herrmann
中科院分区：
文献类型：
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作者：
R. Shahidi;Gang Tang;Jianwei Ma;F. Herrmann
地震数据重建是从不完整的地震记录中提高地震数据的质量和分辨率的常规方法。基于Curvelet的稀疏度提升反演法是近年来发展起来的一种基于压缩传感理论的恢复方法，特别适用于欠采样地震数据的恢复。与传统的基于傅立叶的方法一样，当与随机化的子采样结合使用时，它的性能最好，随机化的子采样将混叠从通常的规则周期性子采样转换为易于消除的噪声。抖动(亚)采样具有控制间隙大小的能力，其采样模式具有随机性和不规则性，是一种行之有效的方法，已成功地用于确定地震检波器沿线的位置。在本文中，我们将抖动采样扩展到二维采集设计，这是一个更困难的问题，既有笛卡尔网格，也有六边形网格。我们还研究了我们所说的可分离和不可分离的二维抖动采样。我们发现六边形抖动采样的性能优于笛卡尔抖动采样，而完全不可分抖动采样的性能好于可分离抖动采样。另外两种2D随机抽样方法，泊松圆盘抽样和最远点抽样，都具有蓝噪声谱，也被证明执行得很好。
Reconstruction of seismic data is routinely used to improve the quality and resolution of seismic data from incomplete acquired seismic recordings. Curvelet‐based Recovery by Sparsity‐promoting Inversion, adapted from the recently‐developed theory of compressive sensing, is one such kind of reconstruction, especially good for recovery of undersampled seismic data. Like traditional Fourier‐based methods, it performs best when used in conjunction with randomized subsampling, which converts aliases from the usual regular periodic subsampling into easy‐to‐eliminate noise. By virtue of its ability to control gap size, along with the random and irregular nature of its sampling pattern, jittered (sub)sampling is one proven method that has been used successfully for the determination of geophone positions along a seismic line. In this paper, we extend jittered sampling to two‐dimensional acquisition design, a more difficult problem, with both underlying Cartesian and hexagonal grids. We also study what we term separable and non‐separable two‐dimensional jittered samplings. We find hexagonal jittered sampling performs better than Cartesian jittered sampling, while fully non‐separable jittered sampling performs better than separable jittered sampling. Two other 2D randomized sampling methods, Poisson Disk sampling and Farthest Point sampling, both known to possess blue‐noise spectra, are also shown to perform well.