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
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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.
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(OR1 MP)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,resultingin 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 OR1 MP 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 2 Dand 3 Dearthquake 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 OR1 MP algorithm and the earthquake signals can be well reconstructed.
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(OR1 MP)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,resultingin 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 OR1 MP 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 2 Dand 3 Dearthquake 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 OR1 MP algorithm and the earthquake signals can be well reconstructed.
引文
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Hansen S M,Schmandt B.2015.Automated detection and location of microseismicity at Mount St.Helens with a large-Ngeophone 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.
Hua Y.1992.Estimating two-dimensional frequencies by matrix enhancement and matrix pencil.IEEE Transactions on Signal Processing,40(9):2267-2280.
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.
Lai M J,Xu Y Y,Yin W T.2013.Improved iteratively reweighted least squares for unconstrained smoothedq minimization.SIAM Journal on Numerical Analysis,51(2):927-957.
Li,V,Tsvankin L,Alkhalifah T.2016.Analysis of RTM extended images for VTI media.Geophysics,81(3),S139-S150.
Lin F C,Li D Z,Clayton R W,et al.2013.High-resolution 3Dshallow crustal structure in Long Beach,California:Application of ambient noise tomography on a dense seismic array.Geophysics,78(4):Q45-Q56.
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Naghizadeh M,Sacchi M D.2009.f-x adaptive seismic-trace interpolation.Geophysics,74(1):V9-V16.
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.
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-reductionbased 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.
Zhang J H,Hao J L,Zhao X,et al.2016.Restoration of clipped seismic waveforms using projection onto convex sets method.ScientificReports,6(1):39056.
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 3Dsubsurface angle gathers for subsalt velocity update and image optimization:Case study at Shenzi field.Geophysics,76(5):WB27-WB39.
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.
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.
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.
Cadzow J A.1988.Signal enhancement-a composite property mapping algorithm.IEEE Transactions on Acoustics,Speech,and Signal Processing,36(1):49-62.
Candès E J,Recht B.2009.Exact matrix completion via convex optimization.Foundations of Computational Mathematics,9(6):717-772.
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.
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.
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 3Dseismic 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-Ngeophone 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.
Hua Y.1992.Estimating two-dimensional frequencies by matrix enhancement and matrix pencil.IEEE Transactions on Signal Processing,40(9):2267-2280.
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.
Lai M J,Xu Y Y,Yin W T.2013.Improved iteratively reweighted least squares for unconstrained smoothedq minimization.SIAM Journal on Numerical Analysis,51(2):927-957.
Li,V,Tsvankin L,Alkhalifah T.2016.Analysis of RTM extended images for VTI media.Geophysics,81(3),S139-S150.
Lin F C,Li D Z,Clayton R W,et al.2013.High-resolution 3Dshallow crustal structure in Long Beach,California:Application of ambient noise tomography on a dense seismic array.Geophysics,78(4):Q45-Q56.
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,Ylmaz.2013.Improved wavefield reconstruction from randomized sampling via weighted onenorm minimization.Geophysics,78(5):V193-V206.
Naghizadeh M,Sacchi M D.2009.f-x adaptive seismic-trace interpolation.Geophysics,74(1):V9-V16.
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.
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-reductionbased 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.
Zhang J H,Hao J L,Zhao X,et al.2016.Restoration of clipped seismic waveforms using projection onto convex sets method.ScientificReports,6(1):39056.
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 3Dsubsurface angle gathers for subsalt velocity update and image optimization:Case study at Shenzi field.Geophysics,76(5):WB27-WB39.
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.
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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