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
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摘要:
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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关键词:
- Hankel预变换 /
- 秩-1矩阵匹配追踪算法 /
- 天然地震数据重建 /
- 加州San Jacinto断层带
Abstract:Restricted by harsh field environment and data collection costs, the natural earthquake data is often irregularly and incompletely distributed in space, which will adversely affect the subsequent seismic data processing and analysis. Therefore, it is necessary to reconstruct and regularize the earthquake data. In this paper, an orthogonal Rank-One Matrix Pursuit (OR1MP) algorithm based on the theory of reduced rank completion is introduced and applied to the reconstruction of natural earthquake data of the San Jacinto fault zone in California. First, Hankel pre-transforms should be performed on each frequency slice of the spatial data, resulting in a pre-transformed matrix with low-rank structure. Missing seismic traces and random noise will increase the rank of the pre-transformed data matrix and the OR1MP algorithm is then used to reduce the rank. Finally, an inverse Hankel transform is conducted to reconstruct data in the frequency domain. The experimental results on 2D and 3D earthquake data from San Jacinto fault zone in California show that the peak signal-to-noise ratio of the seismic data can be greatly improved through the OR1MP algorithm and the earthquake signals can be well reconstructed.
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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 
步骤三: 
end 输出： 
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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
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Anderson J E, Tan L J, Wang D. 2012. Time-reversal checkpointing methods for RTM and FWI. Geophysics, 77(4):S93-S103. doi: 10.1190/geo2011-0114.1
Ben-Zion Y, Vernon F L, Ozakin Y, et al. 2015. Basic data features and results from a spatially dense seismic array on the San Jacinto fault zone. Geophysical Journal International, 202(1):370-380. doi: 10.1093/gji/ggv142
Cadzow J A. 1988. Signal enhancement-a composite property mapping algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing, 36(1):49-62. doi: 10.1109/29.1488
Candès E J, Recht B. 2009. Exact matrix completion via convex optimization. Foundations of Computational Mathematics, 9(6):717-772. doi: 10.1007/s10208-009-9045-5
Cao J J, Wang Y F, Yang C C. 2012. Seismic data restoration based on compressive sensing using the regularization and zero-norm sparse optimization. Chinese Journal of Geophysics (in Chinese), 55(2):596-607, doi:10.6038/j.issn.0001-5733.2012.02.022.
Chen G X, Chen S C, Wang H C, et al. 2013. Geophysical data sparse reconstruction based on L0-norm minimization. Applied Geophysics, 10(2):181-190. doi: 10.1007/s11770-013-0380-6
Chen K, Sacchi M D. 2014. Robust reduced-rank filtering for erratic seismic noise attenuation. Geophysics, 80(1):V1-V11.
Chi B X, Dong L G, Liu Y Z. 2015. Correlation-based reflection full-waveform inversion. Geophysics, 80(4):R189-R202. doi: 10.1190/geo2014-0345.1
Downton J, Holy D, Trad D, et al. 2010. The effect of interpolation on imaging and azimuthal AVO: a nordegg case study.//80th Ann. Internat Mtg., Soc. Expi. Geophys.. Expanded Abstracts.
Fu L H, Zhang M, Liu Z H, et al. 2018. Reconstruction of seismic data with missing traces using normalized Gaussian weighted filter. Journal of Geophysics and Engineering, 15(5):2009, doi:10.1088/1742-2140/aac31c.
Gao J J, Sacchi M D, Chen X H. 2013. A fast reduced-rank interpolation method for prestack seismic volumes that depend on four spatial dimensions. Geophysics, 78(1):V21-V30.
Gierse G, Otto D, Berhorst A, et al. 1949. CRS technique for advanced prestack merging and regularisation of vintage 3D seismic data.//34th Ann. Internat Mtg., Soc. Expi. Geophys.. Expanded Abstracts, 3624-3628.
Hansen S M, Schmandt B. 2015. Automated detection and location of microseismicity at Mount St. Helens with a large-N geophone array. Geophysical Research Letters, 42(18):7390-7397.
Hassani H, Zhigljavsky A. 2009. Singular spectrum analysis:methodology and application to economics data. Journal of Systems Science and Complexity, 22(3):372-394. doi: 10.1007/s11424-009-9171-9
Hua Y. 1992. Estimating two-dimensional frequencies by matrix enhancement and matrix pencil. IEEE Transactions on Signal Processing, 40(9):2267-2280. doi: 10.1109/78.157226
Jia Y N, Yu S W, Liu L N, et al. 2016. A fast rank-reduction algorithm for three-dimensional seismic data interpolation. Journal of Applied Geophysics, 132:137-145. doi: 10.1016/j.jappgeo.2016.06.010
Lai M J, Xu Y Y, Yin W T. 2013. Improved iteratively reweighted least squares for unconstrained smoothed lq minimization. SIAM Journal on Numerical Analysis, 51(2):927-957. doi: 10.1137/110840364
Li, V, Tsvankin L, Alkhalifah T. 2016. Analysis of RTM extended images for VTI media. Geophysics, 81(3), S139-S150. doi: 10.1190/geo2015-0384.1
Lin F C, Li D Z, Clayton R W, et al. 2013. High-resolution 3D shallow crustal structure in Long Beach, California:Application of ambient noise tomography on a dense seismic array. Geophysics, 78(4):Q45-Q56. doi: 10.1190/geo2012-0453.1
Ling Y, Wang X, Li F, et al. 2016, Application of OVT processing to 3D seismic data in western China. SEG International Geophysical Conference, 353-355.
Mansour H, Herrmann F J, Yılmaz Ö. 2013. Improved wavefield reconstruction from randomized sampling via weighted one-norm minimization. Geophysics, 78(5):V193-V206. doi: 10.1190/geo2012-0383.1
Naghizadeh M, Sacchi M D. 2009. f-x adaptive seismic-trace interpolation. Geophysics, 74(1):V9-V16. http://d.old.wanfangdata.com.cn/NSTLQK/NSTL_QKJJ028441802/
Naghizadeh M, Sacchi M D. 2013. Multidimensional de-aliased Cadzow reconstruction of seismic records. Geophysics, 78(1):A1-A5.
Oropeza V, Sacchi M D. 2011. Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis. Geophysics, 6(3):V25-V32. http://d.old.wanfangdata.com.cn/NSTLQK/NSTL_QKJJ0221970601/
Stanton A, Sacchi M D. 2013. Shear wave splitting parameter estimation using a regular distribution of azimuths.//63th Ann. Internat Mtg., Soc. Expi. Geophys.. Expanded Abstracts, 1-4.
Trickett S, Burroughs L, Milton A, et al. 2010. Rank-reduction-based trace interpolation.//80th Ann. Internat Mtg., Soc. Expi. Geophys.. Expanded Abstracts, 3829-3833.
Wang Z, Lai M, Lu Z, et al. 2014. Orthogonal rank-One matrix pursuit for matrix completion. Proceedings of the 31st International Conference on Machine Learning, 91-99.
Yang Y, Ma J, Osher S. 2014. Seismic data reconstruction via matrix completion. Inverse Problems & Imaging, 7(4):1379-1392. http://d.old.wanfangdata.com.cn/NSTLQK/NSTL_QKJJ0231454446/
Zhang J H, Hao J L, Zhao X, et al. 2016. Restoration of clipped seismic waveforms using projection onto convex sets method. Scientific Reports, 6(1):39056. doi: 10.1038/srep39056
Zhao B, Wang Y, Lu J. 2012. Recent advances of multi-component seismic and some of its key issues. Oil Geophysical Prospecting, 47(3):506-516.
Zhou Z Z, Howard M, Mifflin C. 2011. Use of RTM full 3D subsurface angle gathers for subsalt velocity update and image optimization:Case study at Shenzi field. Geophysics, 76(5):WB27-WB39. doi: 10.1190/geo2011-0065.1
曹静杰, 王彦飞, 杨长春. 2012.地震数据压缩重构的正则化与零范数稀疏最优化方法.地球物理学报, 55(2):596-607, doi:10.6038/j.issn.0001-5733.2012.02.022. http://www.geophy.cn//CN/abstract/abstract8435.shtml
赵波, 王赟, 芦俊. 2012.多分量地震勘探技术新进展及关键问题探讨.石油地球物理勘探, 47(3):506-516.
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