| 2D地震数据规则化中随机稀疏采样方案 |
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| 引用本文： | 蔡瑞,赵群,佘德平,杨丽,曹辉,杨勤勇.2D地震数据规则化中随机稀疏采样方案[J].应用地球物理,2014,11(3):321-330. |
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| 作者姓名： | 蔡瑞 赵群 佘德平 杨丽 曹辉 杨勤勇 |
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| 作者单位： | 中石化地球物理重点实验室,中石化石油物探技术研究院,南京211103 |
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| 基金项目： | financially supported by The 2011 Prospective Research Project of SINOPEC（P11096） |
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| 摘 要： | 地震数据规则化是地震信号处理中一个重要步骤,近年来受到广泛关注的压缩感知技术已经被应用到地震数据规则化中。压缩感知技术突破了传统的Shannon-Nyqiust采样定理的限制,可以用采集的少量地震数据重构完整数据。基于压缩感知技术的地震数据规则化质量主要受三个因素影响,除了受地震信号在不同变换域的稀疏表达和11范数重构算法的影响外,极大地取决于地震道随机稀疏采样方式。尽管已有学者开展了2D地震数据离散均匀分布随机采样方式研究,但设计新的稀疏采样方案仍然很有必要。在本文中,我们提出满足Bernoulli分布规律的Bernoulli随机稀疏采样方式和它的抖动形式。对2D数值模拟数据进行四种随机稀疏采样方案和两种变换（Fourier变换和Curvelet变换）实验,对获取的不完整数据应用11范数谱投影梯度算法（SPGL1）进行重构。考虑到不同随机种子点产生不同约束矩阵R会有不同的规则化质量,对每种方案和每个稀疏采样因子进行10次规则化实验,并计算出相应信噪比（SNR）的平均值和标准偏差。实验结果表明,我们提出的新方案好于或等于已有的离散均匀分布采样方案。
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| 关 键 词： | 插值 稀疏采样 变换 重构 稀疏性 |
Bernoulli-based random undersampling schemes for 2D seismic data regularization |
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| Rui Cai,Qun Zhao,De-Ping She,Li Yang,Hui Cao,Qin-Yong Yang.Bernoulli-based random undersampling schemes for 2D seismic data regularization[J].Applied Geophysics,2014,11(3):321-330. |
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| Authors: | Rui Cai Qun Zhao De-Ping She Li Yang Hui Cao Qin-Yong Yang |
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| Institution: | 1. Sinopec Geophysical Research Institute and Sinopec Key Laboratory of Geophysics, Nanjing, 211103, China
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| Abstract: | Seismic data regularization is an important preprocessing step in seismic signal processing. Traditional seismic acquisition methods follow the Shannon-Nyquist sampling theorem, whereas compressive sensing (CS) provides a fundamentally new paradigm to overcome limitations in data acquisition. Besides the sparse representation of seismic signal in some transform domain and the 1-norm reconstruction algorithm, the seismic data regularization quality of CS-based techniques strongly depends on random undersampling schemes. For 2D seismic data, discrete uniform-based methods have been investigated, where some seismic traces are randomly sampled with an equal probability. However, in theory and practice, some seismic traces with different probability are required to be sampled for satisfying the assumptions in CS. Therefore, designing new undersampling schemes is imperative. We propose a Bernoulli-based random undersampling scheme and its jittered version to determine the regular traces that are randomly sampled with different probability, while both schemes comply with the Bernoulli process distribution. We performed experiments using the Fourier and curvelet transforms and the spectral projected gradient reconstruction algorithm for 1-norm (SPGL1), and ten different random seeds. According to the signal-to-noise ratio (SNR) between the original and reconstructed seismic data, the detailed experimental results from 2D numerical and physical simulation data show that the proposed novel schemes perform overall better than the discrete uniform schemes. |
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| Keywords: | Seismic data regularization compressive sensing Bernoulli distribution sparse transform undersampling 1-norm reconstruction algorithm |
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