基于seislet变换的反假频迭代数据插值方法
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摘要
许多地震资料处理方法需要完整的数据信息,但是受野外施工条件等因素的影响,观测系统很难记录完整的地震波场,如空间采样率不足和地震道缺失等现象,尤其是缺失的叠前地震数据时常产生空间假频现象,给后续处理流程中很多重要环节带来严重的影响.传统数据插值方法通常很难同时解决数据缺失和空间假频问题,因此开发有效的反空间假频数据插值方法具有重要的意义.本文通过同时改变时间和空间方向采样比例,利用预测误差滤波器的尺度缩放不变性,计算反空间假频地震倾角模式,构建可有效压缩含空间假频不完整地震数据的反假频seislet变换方法,通过压缩感知Bregman迭代算法,对缺失地震数据进行反假频插值.理论模型和实际数据的处理结果验证了基于seislet变换的迭代插值方法可以有效地恢复含有假频的缺失地震信息.
Many seismic data processing methods need complete data information.However,an ideal uniform coverage is rarely achieved because of practical and economic constraints,e.g.,spatial undersampling and seismic trace missing,especially,missing seismic data always cause spatial aliasing and affect the following data processing workflow.Traditional interpolation methods hardly solve both data missing and spatial aliasing.Therefore,it is important to develop an effective data interpolation technique to realize antialiasing interpolation.In this paper,we rescale both time and spatial axes and use the scale invariance property of prediction-error filter(PEF)s to calculate the antialiasing dip pattern of seismic data.The dip pattern is used to develop antialiasing seislet transform,which compresses missing data with spatial aliasing.By employing the Bregman iterative algorithm belonging to compressive sensing,the proposed method can interpolate the missing information by aliasing.The synthetic and field-data examples demonstrate that the proposed method based on seislet transform and compressive sensing theory is suitable for recovering missing seismic data even with spatial aliasing.
Many seismic data processing methods need complete data information.However,an ideal uniform coverage is rarely achieved because of practical and economic constraints,e.g.,spatial undersampling and seismic trace missing,especially,missing seismic data always cause spatial aliasing and affect the following data processing workflow.Traditional interpolation methods hardly solve both data missing and spatial aliasing.Therefore,it is important to develop an effective data interpolation technique to realize antialiasing interpolation.In this paper,we rescale both time and spatial axes and use the scale invariance property of prediction-error filter(PEF)s to calculate the antialiasing dip pattern of seismic data.The dip pattern is used to develop antialiasing seislet transform,which compresses missing data with spatial aliasing.By employing the Bregman iterative algorithm belonging to compressive sensing,the proposed method can interpolate the missing information by aliasing.The synthetic and field-data examples demonstrate that the proposed method based on seislet transform and compressive sensing theory is suitable for recovering missing seismic data even with spatial aliasing.
引文
[1]Gardner G H F,Canning A.Effects of irregular sampling on3-D prestack migration.SEG Extended Abstract,1994:1553-1556.
[2]Verschuur D J,Berkhout A J,Wapenaar C P A.Adaptivesurface-related multiple elimination.Geophysics,1992,57(9):1166-1177.
[3]Zhang Y,Zhang G Q,Bleistein N.True amplitude waveequation migration arising from true amplitude one-way waveequations.Inverse Problems,2003,19(5):1113-1138.
[4]Morice S,Ronen S,Canter P,et al.The impact of positioningdifferences on 4D repeatability.SEG Extended Abstract,2000:1611-1614.
[5]Mazzucchelli P,Rocca F.Regularizing land acquisitions usingshot continuation operators:effects on amplitudes.SEGExtended Abstract,1999:1995-1998.
[6]辛可锋,王华忠,王成礼等.叠前地震数据的规则化.石油地球物理勘探,2002,37(4):311-317.Xin K F,Wang H Z,Wang C L,et al.Regularization of pre-stack seismic data.Oil Geophysical Prospecting(in Chinese),2002,37(4):311-317.
[7]管路平,唐亚勋,王华忠.共偏移距道集平面波叠前时间偏移与反偏移.地球物理学报,2009,52(5):1301-1309.Guan L P,Tang Y X,Wang H Z.Common-offset plane-wave prestack time migration and demigration.Chinese J.Geophys.(in Chinese),2009,52(5):1301-1309.
[8]Claerbout J F.Earth Soundings Analysis:Processing VersusInversion.Boston:Blackwell Scientific Publications,1992.
[9]李信富,李小凡.分形插值地震数据重建方法研究.地球物理学报,2008,51(4):1196-1201.Li X F,Li X F.Seismic data reconstruction with fractalinterpolation.Chinese J.Geophys.(in Chinese),2008,51(4):1196-1201.
[10]Wang Y B,Luo Y,Schuster G T.Interferometricinterpolation of missing seismic data.Geophysics,2009,74(3):SI37-SI45.
[11]高建军,陈小宏,李景叶等.基于非均匀Fourier变换的地震数据重建方法研究.地球物理学进展,2009,24(5):1741-1747.Gao J J,Chen X H,Li J Y,et al.Study on reconstruction ofseismic data based on nonuniform Fourier transform.Progressin Geophys.(in Chinese),2009,24(5):1741-1747.
[12]Xu S,Zhang Y,Pham D,et al.Antileakage Fouriertransform for seismic data regularization.Geophysics,2005,70(4):V87-V95.
[13]孟小红,郭良辉,张致付等.基于非均匀快速傅里叶变换的最小二乘反演地震数据重建.地球物理学报,2008,51(1):235-241.Meng X H,Guo L H,Zhang Z F,et al.Reconstruction ofseismic data with least squares inversion based on nonuniformfast Fourier transform.Chinese J.Geophys.(in Chinese),2008,51(1):235-241.
[14]张红梅,刘洪.基于稀疏离散τ-p变换的叠后地震道内插.石油地球物理勘探,2006,41(3):281-285.Zhang H M,Liu H.Interpolation of poststack seismic tracesbased on sparse discreteτ-p transform.Oil GeophysicalProspecting(in Chinese),2006,41(3):281-285.
[15]王维红,裴江云,张剑锋.加权抛物Radon变换叠前地震数据重建.地球物理学报,2007,50(3):851-859.Wang W H,Pei J Y,Zhang J F.Prestack seismic datareconstruction using weighted parabolic Radon transform.Chinese J.Geophys.(in Chinese),2007,50(3):851-859.
[16]Candés E.Compressive sampling.Proceedings of InternationalCongress of Mathematicians,2006:1433-1452.
[17]Donoho D L.Compressed sensing.IEEE Transactions onInformation Theory,2006,52(4):1289-1306.
[18]Abma R,Kabir N.3Dinterpolation of irregular data with aPOCS algorithm.Geophysics,2006,71(6):E91-E97.
[19]Zwartjes P M,Sacchi M D.Fourier reconstruction ofnonuniformly sampled,aliased seismic data.Geophysics,2007,72(1):V21-V32.
[20]唐刚,杨慧珠.基于泊松碟采样的地震数据压缩重建.地球物理学报,2010,53(9):2181-2188.Tang G,Yang H Z.Seismic data compression andreconstruction based on Poisson Disk sampling.Chinese J.Geophys.(in Chinese),2010,53(9):2181-2188.
[21]刘国昌,陈小宏,郭志峰等.基于Curvelet变换的缺失地震数据插值方法.石油地球物理勘探,2011,46(2):237-246.Liu G C,Chen X H,Guo Z F,et al.Missing seismic datarebuilding by interpolation based on Curvelet transform.OilGeophysical Prospecting(in Chinese),2011,46(2):237-246.
[22]曹静杰,王彦飞,杨长春.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,2012,55(2):596-607.Cao J J,Wang Y F,Yang C C.Seismic data restorationbased on compressive sensing using the regularization andzero-norm sparse optimization.Chinese J.Geophys.(in Chinese),2012,55(2):596-607.
[23]Fomel S,Liu Y.Seislet transform and seislet frame.Geophysics,2010,75(3):V25-V38.
[24]刘洋,Fomel S,刘财等.高阶seislet变换及其在随机噪声消除中的应用.地球物理学报,2009,52(8):2142-2151.Liu Y,Fomel S,Liu C,et al.High-order seislet transformand its application of random noise attenuation.Chinese J.Geophys.(in Chinese),2009,52(8):2142-2151.
[25]Liu Y,Fomel S.OC-seislet:seislet transform constructionwith differential offset continuation.Geophysics,2010,75(6):WB235-WB245.
[26]Fomel S.Applications of plane-wave destruction filters.Geophysics,2002,67(6):1946-1960.
[27]Tikhonov A N.Solution of incorrectly formulated problemsand the regularization method.Soviet Mathematics-Doklady,1963.
[28]Fomel S.Shaping regularization in geophysical estimationproblems.Geophysics,2007,72(2):R29-R36.
[29]Crawley S.Seismic trace interpolation with nonstationaryprediction error filters[Ph.D.thesis].California:StanfordUniversity,2000.
[30]Liu Y,Fomel S.Seismic data interpolation beyond aliasingusing regularized nonstationary autoregression.Geophysics,2011,76(5):V69-V77.
[31]Fomel S.Three-dimensional seismic data regularization[Ph.D.thesis].California:Stanford University,2001.
[32]Gao J,Chen X H,Li J,et al.Irregular seismic datareconstruction based on exponential threshold model of POCSmethod.Applied Geophysics,2010,7(3):229-238.
[33]Osher S,Burger M,Goldfarb D,et al.An iterativeregularization method for total variation-based image restoration.Multiscale Modeling&Simulation,2005,4(2):460-489.
[34]Yin W,Osher S,Goldfarb D,et al.Bregman iterativealgorithms for L1minimization with applications to compressedsensing.SIAM Journal on Imaging Sciences,2008,1(1):143-168.
[35]Daubechies I,Defries M,de Mol C.An iterativethresholding algorithm for linear inverse problems with asparsity constraint.Communications on Pure and AppliedMathematics,2004,57(11):1413-1457.
[36]Donoho D L.De-noising by soft-thresholding.IEEETransactions on Information Theory,1995,41(3):613-627.
[37]Sweldens W.Lifting scheme:A new philosophy in biorthogonalwavelet constructions.Wavelet Applications in Signal andImage Processing III,Proceedings of SPIE 2569,1995:68-79.
[38]Sweldens W,Schroder P.Building your own wavelets athome,Wavelets in Computer Graphics.ACM SIGGRAPHCourse notes,1996:15-87.
[2]Verschuur D J,Berkhout A J,Wapenaar C P A.Adaptivesurface-related multiple elimination.Geophysics,1992,57(9):1166-1177.
[3]Zhang Y,Zhang G Q,Bleistein N.True amplitude waveequation migration arising from true amplitude one-way waveequations.Inverse Problems,2003,19(5):1113-1138.
[4]Morice S,Ronen S,Canter P,et al.The impact of positioningdifferences on 4D repeatability.SEG Extended Abstract,2000:1611-1614.
[5]Mazzucchelli P,Rocca F.Regularizing land acquisitions usingshot continuation operators:effects on amplitudes.SEGExtended Abstract,1999:1995-1998.
[6]辛可锋,王华忠,王成礼等.叠前地震数据的规则化.石油地球物理勘探,2002,37(4):311-317.Xin K F,Wang H Z,Wang C L,et al.Regularization of pre-stack seismic data.Oil Geophysical Prospecting(in Chinese),2002,37(4):311-317.
[7]管路平,唐亚勋,王华忠.共偏移距道集平面波叠前时间偏移与反偏移.地球物理学报,2009,52(5):1301-1309.Guan L P,Tang Y X,Wang H Z.Common-offset plane-wave prestack time migration and demigration.Chinese J.Geophys.(in Chinese),2009,52(5):1301-1309.
[8]Claerbout J F.Earth Soundings Analysis:Processing VersusInversion.Boston:Blackwell Scientific Publications,1992.
[9]李信富,李小凡.分形插值地震数据重建方法研究.地球物理学报,2008,51(4):1196-1201.Li X F,Li X F.Seismic data reconstruction with fractalinterpolation.Chinese J.Geophys.(in Chinese),2008,51(4):1196-1201.
[10]Wang Y B,Luo Y,Schuster G T.Interferometricinterpolation of missing seismic data.Geophysics,2009,74(3):SI37-SI45.
[11]高建军,陈小宏,李景叶等.基于非均匀Fourier变换的地震数据重建方法研究.地球物理学进展,2009,24(5):1741-1747.Gao J J,Chen X H,Li J Y,et al.Study on reconstruction ofseismic data based on nonuniform Fourier transform.Progressin Geophys.(in Chinese),2009,24(5):1741-1747.
[12]Xu S,Zhang Y,Pham D,et al.Antileakage Fouriertransform for seismic data regularization.Geophysics,2005,70(4):V87-V95.
[13]孟小红,郭良辉,张致付等.基于非均匀快速傅里叶变换的最小二乘反演地震数据重建.地球物理学报,2008,51(1):235-241.Meng X H,Guo L H,Zhang Z F,et al.Reconstruction ofseismic data with least squares inversion based on nonuniformfast Fourier transform.Chinese J.Geophys.(in Chinese),2008,51(1):235-241.
[14]张红梅,刘洪.基于稀疏离散τ-p变换的叠后地震道内插.石油地球物理勘探,2006,41(3):281-285.Zhang H M,Liu H.Interpolation of poststack seismic tracesbased on sparse discreteτ-p transform.Oil GeophysicalProspecting(in Chinese),2006,41(3):281-285.
[15]王维红,裴江云,张剑锋.加权抛物Radon变换叠前地震数据重建.地球物理学报,2007,50(3):851-859.Wang W H,Pei J Y,Zhang J F.Prestack seismic datareconstruction using weighted parabolic Radon transform.Chinese J.Geophys.(in Chinese),2007,50(3):851-859.
[16]Candés E.Compressive sampling.Proceedings of InternationalCongress of Mathematicians,2006:1433-1452.
[17]Donoho D L.Compressed sensing.IEEE Transactions onInformation Theory,2006,52(4):1289-1306.
[18]Abma R,Kabir N.3Dinterpolation of irregular data with aPOCS algorithm.Geophysics,2006,71(6):E91-E97.
[19]Zwartjes P M,Sacchi M D.Fourier reconstruction ofnonuniformly sampled,aliased seismic data.Geophysics,2007,72(1):V21-V32.
[20]唐刚,杨慧珠.基于泊松碟采样的地震数据压缩重建.地球物理学报,2010,53(9):2181-2188.Tang G,Yang H Z.Seismic data compression andreconstruction based on Poisson Disk sampling.Chinese J.Geophys.(in Chinese),2010,53(9):2181-2188.
[21]刘国昌,陈小宏,郭志峰等.基于Curvelet变换的缺失地震数据插值方法.石油地球物理勘探,2011,46(2):237-246.Liu G C,Chen X H,Guo Z F,et al.Missing seismic datarebuilding by interpolation based on Curvelet transform.OilGeophysical Prospecting(in Chinese),2011,46(2):237-246.
[22]曹静杰,王彦飞,杨长春.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,2012,55(2):596-607.Cao J J,Wang Y F,Yang C C.Seismic data restorationbased on compressive sensing using the regularization andzero-norm sparse optimization.Chinese J.Geophys.(in Chinese),2012,55(2):596-607.
[23]Fomel S,Liu Y.Seislet transform and seislet frame.Geophysics,2010,75(3):V25-V38.
[24]刘洋,Fomel S,刘财等.高阶seislet变换及其在随机噪声消除中的应用.地球物理学报,2009,52(8):2142-2151.Liu Y,Fomel S,Liu C,et al.High-order seislet transformand its application of random noise attenuation.Chinese J.Geophys.(in Chinese),2009,52(8):2142-2151.
[25]Liu Y,Fomel S.OC-seislet:seislet transform constructionwith differential offset continuation.Geophysics,2010,75(6):WB235-WB245.
[26]Fomel S.Applications of plane-wave destruction filters.Geophysics,2002,67(6):1946-1960.
[27]Tikhonov A N.Solution of incorrectly formulated problemsand the regularization method.Soviet Mathematics-Doklady,1963.
[28]Fomel S.Shaping regularization in geophysical estimationproblems.Geophysics,2007,72(2):R29-R36.
[29]Crawley S.Seismic trace interpolation with nonstationaryprediction error filters[Ph.D.thesis].California:StanfordUniversity,2000.
[30]Liu Y,Fomel S.Seismic data interpolation beyond aliasingusing regularized nonstationary autoregression.Geophysics,2011,76(5):V69-V77.
[31]Fomel S.Three-dimensional seismic data regularization[Ph.D.thesis].California:Stanford University,2001.
[32]Gao J,Chen X H,Li J,et al.Irregular seismic datareconstruction based on exponential threshold model of POCSmethod.Applied Geophysics,2010,7(3):229-238.
[33]Osher S,Burger M,Goldfarb D,et al.An iterativeregularization method for total variation-based image restoration.Multiscale Modeling&Simulation,2005,4(2):460-489.
[34]Yin W,Osher S,Goldfarb D,et al.Bregman iterativealgorithms for L1minimization with applications to compressedsensing.SIAM Journal on Imaging Sciences,2008,1(1):143-168.
[35]Daubechies I,Defries M,de Mol C.An iterativethresholding algorithm for linear inverse problems with asparsity constraint.Communications on Pure and AppliedMathematics,2004,57(11):1413-1457.
[36]Donoho D L.De-noising by soft-thresholding.IEEETransactions on Information Theory,1995,41(3):613-627.
[37]Sweldens W.Lifting scheme:A new philosophy in biorthogonalwavelet constructions.Wavelet Applications in Signal andImage Processing III,Proceedings of SPIE 2569,1995:68-79.
[38]Sweldens W,Schroder P.Building your own wavelets athome,Wavelets in Computer Graphics.ACM SIGGRAPHCourse notes,1996:15-87.
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