局部平面波模型约束下的迭代加权最小二乘反演三维地震数据规则化
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摘要
数据规则化是地震数据处理中一项十分重要的内容,本文提出一种基于迭代加权最小二乘反演的数据规则化方法。该方法的思路是:在Cauchy模意义下引入与模型有关的加权算子对数据拟合剩余量进行加权,可有效避免野值对插值结果的影响;采用平面波解构滤波器估计的局部倾角信息作为约束条件,不仅可保证反演过程稳定,而且能对假频数据有效插值;通过预条件共轭梯度法迭代求解,提高收敛速度;采用分时间切片并行化处理,可进一步提高三维地震数据规则化处理的效率。理论模型和实际地震数据的插值试验结果验证,本文提出的地震数据规则化处理方法速度快,效果好,具有较高实用价值和广泛应用前景。
Regularization of irregular spaced seismic data is a crucial step of data processing.In this paper,a data regularization method based on iteratively re-weighted least-squares inversion is proposed,which can eliminate the effect of burst noise on the interpolated data.The weighting operator is introduced to weight the data fit residual under Cauchy norm.Local slope field estimated by plane wave destructor is used as prior information to make the process of inversion stable and interpolate the aliased data correctly.The inverse problem is solved by the preconditioning conjugate gradient method with fast convergence.Parallel processing along time slices for three dimensional data cube can promote the efficiency of three dimensional data regularization further.Experimental results on theoretical model and real seismic data show that the proposed method is fast,efficient and applicable.
Regularization of irregular spaced seismic data is a crucial step of data processing.In this paper,a data regularization method based on iteratively re-weighted least-squares inversion is proposed,which can eliminate the effect of burst noise on the interpolated data.The weighting operator is introduced to weight the data fit residual under Cauchy norm.Local slope field estimated by plane wave destructor is used as prior information to make the process of inversion stable and interpolate the aliased data correctly.The inverse problem is solved by the preconditioning conjugate gradient method with fast convergence.Parallel processing along time slices for three dimensional data cube can promote the efficiency of three dimensional data regularization further.Experimental results on theoretical model and real seismic data show that the proposed method is fast,efficient and applicable.
引文
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[3]Biondi B.3-D Seismic Imaging.Stanford Explora-tion Project,2004
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[6]Legott R J,Williams R G,Skinner M.Co-location of4Dseismic data in the presence of navigational andtiming errors.SEG Technical Program ExpandedAbstracts,1999,18:1699～1702
[7]Morice S,Ronen S,Canter P et al.The impact of po-sitioning differences on 4Drepeatability.SEG Tech-nical Program Expanded Abstracts,2000,19:1611～1614
[8]Fomel S and Bleistein N.Amplitude Preservationfor Offset Continuation:Confirmation for Kirch-hoff Data.1996,SEP-92:219～227
[9]Bagaini C and Spagnolini U.2-D continuation opera-tors and their applications.Geophysics,1996,61(6):1846～1858
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[13]Trad D,Ulrych T,Sacchi M.Latest views of thesparse Radon transform.Geophysics,2003,68(1):386～399
[14]Sacchi M and Ulrych T.Estimation of the discreteFourier transform,a linear inversion approach.Geo-physics,1996,61(4):1128～1136
[15]Liu B,Sacchi M.Minimum weighted norm interpola-tion of seismic records.Geophysics,2004,69(4):1560～1568
[16]Spitz S.Seismic trace interpolation in the f-xdomain.Geophysics,1991,56(6):785～794
[17]国九英,周兴元,俞寿朋.F-X域等道距内插.石油地球物理勘探,1996,31(1):28～34Guo Jiuying,Zhou Xingyuan,Yu Shoupeng.Iso-inter-val trace interpolation in F-X domain.OGP,1996,31(1):28～34
[18]Sean Crawley.Interpolation with Smoothly Non-sta-tionary Prediction-error Filters[D],Stanford Uni-versity,1999
[19]William Curry.Interpolation with Prediction-errorFilters and Training Data[D],Stanford University,2008
[20]Sergey Fomel.Three Dimension Seismic Data Regu-larization[D],Stanford University,2001
[21]Sergey Fomel.Applications of plane-wave destructionfilters.Geophysics,2002,67(6):1946～1960
[22]Paul Sava,Sergey Fomel.Spectral Factorization Re-visited.Stanford Exploration Project,1999,SEP100,227～235
[23]Claerbout J F.Earth Soundings Analysis:Processingversus Inversion.Blackwell Scientific Publications,2004
[24]Claerbout J F.Geophysical Estimation by Example:Geophysical Soundings Image Construction and Mul-tidimensional Auto-regression.Stanford ExplorationProject,2009
[25]Unser M,Aldroubi A,Eden M.B-spline signal pro-cessing:PartⅠ-Theory.IEEE Transactions on Sig-nal Processing,1993,41(1):821～832
[2]Biondi B and Palacharla G.3-D prestack migration ofcommon-azimuth data.Geophysics,1996,61(6):1822～1832
[3]Biondi B.3-D Seismic Imaging.Stanford Explora-tion Project,2004
[4]Verschuur D J,Berkhout A J.Estimation of multiplescattering by iterative inversion,PartⅡ:Practical as-pects and examples.Geophysics,1997,62(5):1596～1611
[5]van Dedem E J,Verschuur D J.3-D surface-relatedmultiple elimination and interpolation.SEG Techni-cal Program Expanded Abstracts,1998,17:1321～1324
[6]Legott R J,Williams R G,Skinner M.Co-location of4Dseismic data in the presence of navigational andtiming errors.SEG Technical Program ExpandedAbstracts,1999,18:1699～1702
[7]Morice S,Ronen S,Canter P et al.The impact of po-sitioning differences on 4Drepeatability.SEG Tech-nical Program Expanded Abstracts,2000,19:1611～1614
[8]Fomel S and Bleistein N.Amplitude Preservationfor Offset Continuation:Confirmation for Kirch-hoff Data.1996,SEP-92:219～227
[9]Bagaini C and Spagnolini U.2-D continuation opera-tors and their applications.Geophysics,1996,61(6):1846～1858
[10]Biondi B,Fomel S and Chemingui N.Azimuth move-out for 3-D prestack imaging.Geophysics,1998,63(2):574～588
[11]Chemingui N.Imaging Irregularly Sampled 3 DPrestacked Data[D],Stanford University,1999
[12]Sacchi M and Ulrych T.High-resolution velocitygathers and offset space reconstruction.Geophysics,1995,60(4):1169～1177
[13]Trad D,Ulrych T,Sacchi M.Latest views of thesparse Radon transform.Geophysics,2003,68(1):386～399
[14]Sacchi M and Ulrych T.Estimation of the discreteFourier transform,a linear inversion approach.Geo-physics,1996,61(4):1128～1136
[15]Liu B,Sacchi M.Minimum weighted norm interpola-tion of seismic records.Geophysics,2004,69(4):1560～1568
[16]Spitz S.Seismic trace interpolation in the f-xdomain.Geophysics,1991,56(6):785～794
[17]国九英,周兴元,俞寿朋.F-X域等道距内插.石油地球物理勘探,1996,31(1):28～34Guo Jiuying,Zhou Xingyuan,Yu Shoupeng.Iso-inter-val trace interpolation in F-X domain.OGP,1996,31(1):28～34
[18]Sean Crawley.Interpolation with Smoothly Non-sta-tionary Prediction-error Filters[D],Stanford Uni-versity,1999
[19]William Curry.Interpolation with Prediction-errorFilters and Training Data[D],Stanford University,2008
[20]Sergey Fomel.Three Dimension Seismic Data Regu-larization[D],Stanford University,2001
[21]Sergey Fomel.Applications of plane-wave destructionfilters.Geophysics,2002,67(6):1946～1960
[22]Paul Sava,Sergey Fomel.Spectral Factorization Re-visited.Stanford Exploration Project,1999,SEP100,227～235
[23]Claerbout J F.Earth Soundings Analysis:Processingversus Inversion.Blackwell Scientific Publications,2004
[24]Claerbout J F.Geophysical Estimation by Example:Geophysical Soundings Image Construction and Mul-tidimensional Auto-regression.Stanford ExplorationProject,2009
[25]Unser M,Aldroubi A,Eden M.B-spline signal pro-cessing:PartⅠ-Theory.IEEE Transactions on Sig-nal Processing,1993,41(1):821～832
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