基于正交秩-1矩阵追踪的天然地震数据重建研究:以加州San Jacinto断层密集地震台阵为例

张雪敏, 付丽华, 张海江, 彭佳明. 2019. 基于正交秩-1矩阵追踪的天然地震数据重建研究:以加州San Jacinto断层密集地震台阵为例. 地球物理学报, 62(4): 1427-1439, doi: 10.6038/cjg2019M0352
引用本文: 张雪敏, 付丽华, 张海江, 彭佳明. 2019. 基于正交秩-1矩阵追踪的天然地震数据重建研究:以加州San Jacinto断层密集地震台阵为例. 地球物理学报, 62(4): 1427-1439, doi: 10.6038/cjg2019M0352
ZHANG XueMin, FU LiHua, ZHANG HaiJiang, PENG JiaMing. 2019. Reconstruction of natural earthquake data based on Orthogonal Rank-one Matrix Pursuit and its application to dense seismic array around the San Jacinto Fault Zone in California. Chinese Journal of Geophysics (in Chinese), 62(4): 1427-1439, doi: 10.6038/cjg2019M0352
Citation: ZHANG XueMin, FU LiHua, ZHANG HaiJiang, PENG JiaMing. 2019. Reconstruction of natural earthquake data based on Orthogonal Rank-one Matrix Pursuit and its application to dense seismic array around the San Jacinto Fault Zone in California. Chinese Journal of Geophysics (in Chinese), 62(4): 1427-1439, doi: 10.6038/cjg2019M0352

基于正交秩-1矩阵追踪的天然地震数据重建研究:以加州San Jacinto断层密集地震台阵为例

  • 基金项目:

    国家自然科学基金项目(61601417,617012212),湖北省教育厅科学技术研究项目(B2017597)和"地球内部多尺度成像"湖北省重点实验室开放基金项目(SMIL-2018-06)资助

详细信息
    作者简介:

    张雪敏, 女, 1992年生, 硕士, 主要从事地震数据处理研究.E-mail:xmzhang@cug.edu.cn

    通讯作者: 付丽华, 女, 1979年生, 教授, 主要从事地震数据处理研究.E-mail:lihuafu@cug.edu.cn
  • 中图分类号: P631

Reconstruction of natural earthquake data based on Orthogonal Rank-one Matrix Pursuit and its application to dense seismic array around the San Jacinto Fault Zone in California

More Information
  • 由于受地理环境和采集成本等因素的影响,采集到的天然地震数据往往呈现不规则和不完整分布,将直接影响到后续的天然地震数据处理效果,因此需要对缺失数据进行重建.本文将一种基于降秩补全理论的正交秩-1矩阵追踪算法(Orthogonal Rank-One Matrix Pursuit,OR1MP)应用于加州San Jacinto断层带的天然地震数据重建.首先将空间数据的每个频率切片进行Hankel预变换,获取具有低秩结构特征的预变换矩阵,缺失地震道和随机噪声会增加数据预变换矩阵的秩,然后运用OR1MP算法进行降秩处理,最后做反Hankel变换,得到频域上的重建数据.OR1MP算法对2D和3D的加州San Jacinto断层带的天然地震数据实验结果表明,OR1MP算法能够有效地增加地震体的峰值信噪比,能较好地实现对天然地震信号的重建.

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  • 图 1 

    块Hankel矩阵的构造

    Figure 1. 

    The construction of block Hankel matrix

    图 2 

    加州San Jacinto断层1108个垂直分量ZLand传感器空间上密集的节点阵列图

    Figure 2. 

    Spatially dense nodal array diagram with 1108 vertical component ZLand sensors near San Jacinto fault zone, California

    图 3 

    数据缺失20%情况下San Jacinto断层带基于OR1MP算法的2D数据重建测试结果

    Figure 3. 

    The test of 2D data reconstruction by the OR1MP algorithm for the San Jacinto fault zone in the case of 20% missing traces

    图 4 

    数据缺失40%情况下San Jacinto断层带基于OR1MP算法的2D数据重建测试结果

    Figure 4. 

    The test of 2D data reconstruction by the OR1MP algorithm for the San Jacinto fault zone in the case of 40% missing traces

    图 5 

    数据缺失20%情况下的San Jacinto断层带2D数据重建结果频谱比较图

    Figure 5. 

    Comparison of the spectrograms for original and reconstructed 2D data results around the SJFZ in the case of 20% missing traces

    图 6 

    缺失40%数据情况下的San Jacinto断层带2D数据重建结果频谱比较图

    Figure 6. 

    Comparison of the spectrograms for original and reconstructed 2D data results around the SJFZ in the case of with 40% missing traces

    图 7 

    原始数据和利用OR1MP重建的第36道单道图

    Figure 7. 

    Comparison of the 36th trace for the original and reconstructed data via the OR1MP algorithm

    图 8 

    2D天然地震数据随着欠采样率从10%增加到50%,OR1MP和SSA两个不同算法重建数据SNR的变化

    Figure 8. 

    Variations of SNR for reconstructed 2D earthquake data by OR1MP and SSA algorthms along with the increase of the missing data ratios from 10% to 50%

    图 9 

    San Jacinto断层带缺失50%数据情况下利用OR1MP算法的重建结果切片图(y=5)

    Figure 9. 

    Thetest of the OR1MP algorithm on 3D earthquake data in the case of 50% data missing for San Jacinto fault zone

    图 10 

    San Jacinto断层带缺失50%数据情况下利用OR1MP算法天然地震重建结果切片图(y=10)

    Figure 10. 

    The test of the OR1MP algorithm on 3D earthquake data in the case of 50% data missing for San Jacinto fault zone

    图 11 

    San Jacinto断层带缺失50%数据情况下利用OR1MP算法天然地震数据重建结果切片图(y=16)

    Figure 11. 

    The test of the OR1MP algorithm on 3D earthquake data in the case of 50% data missing for San Jacinto fault zone

    图 12 

    3D天然地震数据随着欠采样率从10%增加到70%OR1MP和MSSA两个不同算法的重建SNR的变化

    Figure 12. 

    Variations of SNR for reconstructed 3D earthquake data by OR1MP and MSSA algorthms along with the increase of the missing data ratios from 10% to 70%

    算法:基于OR1MP的低秩矩阵补全算法
    输入:S,秩k.
          初始化:L0=0,θ0=0,l=1.
          for l=1:k
          步骤一:找到公式(10)残差的一对左上和右上的奇异向量(ul, vl),令Bl=ulvlT.
          步骤二:用公式更新权重θl.
          步骤三:
          end
          输出:
    下载: 导出CSV

    表 1 

    2D天然地震数据不同缺失率下重建数据的SNR

    Table 1. 

    The SNRs of the reconstructed data at different data missing ratios in the case of the 2D seismic data

    缺失率
    (%)
    SNR_before
    (dB)
    SNR_after_OR1MP
    (dB)
    SNR_after_SSA
    (dB)
    10% 10.0116 27.2199 19.0948
    20% 6.9727 23.3876 17.7292
    30% 5.2182 21.1293 15.3048
    40% 3.9750 19.9332 14.7027
    50% 3.0049 18.4174 14.1793
    下载: 导出CSV

    表 2 

    3D天然地震数据不同缺失率下OR1MP和MSSA算法重建数据的SNR的比较

    Table 2. 

    Comparison of SNRs of the reconstructed 3D earthquake data by OR1MP and MSSA algorithms at different data missing rates

    缺失率
    (%)
    SNR_before
    (dB)
    SNR_after _OR1MP
    (dB)
    SNR_after_MSSA
    (dB)
    10% 10.0071 27.0771 22.0657
    20% 6.9833 23.6627 21.8008
    30% 5.2274 21.8079 18.1214
    40% 3.9811 20.3970 17.8119
    50% 2.9100 19.2680 14.7548
    60% 2.2175 18.0043 13.5535
    70% 1.5475 17.0727 11.0614
    下载: 导出CSV
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出版历程
收稿日期:  2018-06-10
修回日期:  2018-10-25
上线日期:  2019-04-05

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