基于Dreamlet变换的地震数据压缩理论与方法
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摘要
为达到更加有效地表示地震数据的目的,仅仅将地震数据当作普通的图像数据处理是远远不够的,地震数据中蕴含的地震波的运动学特性也应作为重要因素而被考虑到.本文讨论了利用Dreamlet变换方法实现地震数据压缩的方法,并针对地震数据本身所蕴含的频散关系特性进一步提出了多尺度Dreamlet变换压缩方法.Dreamlet变换由2个一维局部谐波变换的张量积构成,它在提供地震波场时间-空间局部化性质的同时可以保留波场的运动学特性.通过对二维SEG/EAGE叠前、叠后数据的算例说明了Dreamlet变换用于地震数据压缩的有效性.利用压缩后的数据进行成像的结果更表明,与Curvelet变换方法相比,Dreamlet与多尺度Dreamlet方法可以提供更高的压缩比;在相同压缩比的条件下,使用Dreamlet与多尺度Dreamlet方法压缩重建后的数据进行成像能更好地保留成像结果中的重要结构.
For sparse representation of seismic data,simply treating the seismic data as picture is not enough,considering the physical feature of the seismic data in the procedure is needed as well.In this paper,we first study the seismic data sparse representation using the Dreamlet transform.Combining with the dispersion relationship,we then extend the Dreamlet transform to a multi-scale version.The Dreamlet transform is the tensor product of two 1D local harmonic transforms,which can preserve the wave properties in seismic data while providing local information in both time and space domain.2D SEG-EAGE salt model synthetic poststack and prestack data sets are used to demonstrate the validity of both the Dreamlet transform methods.Using the reconstructed data for migration,we can still obtain a high quality image of the sub-salt structure in 2D SEG-EAGE salt model.Meanwhile,numerical tests on 2D SEG-EAGE salt model synthetic prestack data show the potential in propagating the wavefield and imaging directly and efficiently in the Dreamlet domain.The Dreamlet method can outperform the Curvelet method especially for high compression ratios.
For sparse representation of seismic data,simply treating the seismic data as picture is not enough,considering the physical feature of the seismic data in the procedure is needed as well.In this paper,we first study the seismic data sparse representation using the Dreamlet transform.Combining with the dispersion relationship,we then extend the Dreamlet transform to a multi-scale version.The Dreamlet transform is the tensor product of two 1D local harmonic transforms,which can preserve the wave properties in seismic data while providing local information in both time and space domain.2D SEG-EAGE salt model synthetic poststack and prestack data sets are used to demonstrate the validity of both the Dreamlet transform methods.Using the reconstructed data for migration,we can still obtain a high quality image of the sub-salt structure in 2D SEG-EAGE salt model.Meanwhile,numerical tests on 2D SEG-EAGE salt model synthetic prestack data show the potential in propagating the wavefield and imaging directly and efficiently in the Dreamlet domain.The Dreamlet method can outperform the Curvelet method especially for high compression ratios.
引文
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[2]Wang Y Z,Wu R S.Seismic data compression by an adaptivelocal cosine/sine transform and its effects on migration.Geophysical Prospecting,2000,48(6):1009-1031.
[3]Mallat S.A Wavelet Tour of Signal Processing:The SparseWay.New York:Acedemic Press Inc,2009.
[4]朱光明,高静怀,王玉贵.小波变换及其在一维滤波中的应用.石油物探,1993,32(1):1-10.Zhu G M,Gao J H,Wang Y G.Wavelet transform and itsapplication to 1-D filtering.Geophysical Prospecting forPetrole(in Chinese),1993,32(1):1-10.
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[7]Vassiliou A,Wickerhauser M V.Comparison of waveletimage coding schemes for seismic data compression.WaveletApplication in Signal and Image Processing V,1997,3169:118-126.
[8]Candes E J,Donoho D L.New tight frames of curvelets andoptimal representations of objects with piecewise C2singularities.Communications on Pure and Applied Mathematics,2004,57(2):219-266.
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[10]Le Pennec E,Mallat S.Bandelet image approximation andcompression.Multiscale Modeling&Simulation,2005,4(3):992-1039.
[11]Le Pennec E,Mallat S.Sparse geometric imagerepresentations with bandelets.IEEE Transactions on ImageProcessing,2005,14(4):423-438.
[12]Guo K H,Labate D.Sparse shearlet representation ofFourier integral operators.Electronic ResearchAnnouncements in Mathematical Sciences,2007,14:7-19.
[13]Guo K,Labate D.Optimally sparse multidimensionalrepresentation using shearlets.Siam Journal on MathematicalAnalysis,2007,39(1):298-318.
[14]Guo K,Labate D.Analysis and detection of surfacediscontinuities using the 3Dcontinuous shearlet transform.Applied and Computational Harmonic Analysis,2011,30(2):231-242.
[15]Candes E J,Demanet L.The curvelet representation of wavepropagators is optimally sparse.Communications on Pure andApplied Mathematics,2005,58(11):1472-1528.
[16]Hennenfent G,Herrmann F J.Seismic denoising withnonuniformly sampled curvelets.Computing in Science&Engineering,2006,8(3):16-25.
[17]Herrmann F J,Wang D L,Hennenfent G,et al.Curvelet-8期耿瑜等:基于Dreamlet变换的地震数据压缩理论与方法based seismic data processing:A multiscale and nonlinearapproach.Geophysics,2008,73(1):A1-A5.
[18]Herrmann F J,Brown C R,Erlangga Y A,et al.Curvelet-based migration preconditioning and scaling.Geophysics,2009,74(1):A41-A46.
[19]Chauris H,Nguyen T.Seismic demigration/migration in thecurvelet domain.Geophysics,2008,73(2):S35-S46.
[20]Douma H,de Hoop M V.Leading-order seismic imagingusing curvelets.Geophysics,2007,72(6):S231-S248.
[21]Lin T T Y,Herrmann F.Compressed wavefield extrapolation.Geophysics,2007,72(5):SM77-SM93
[22]Fomel S,Liu Y.Seislet transform and seislet frame.Geophysics,2010,75(3):V25-V38.
[23]Coifman R,Meyer Y.Remarques sur l'analyse de Fourier afenetre.Comptes Rendus de L Academie Des Sciences,1991,32:259-261.
[24]Wallace G K.The JPEG still picture compression standard.Communications of the Acm,1991,34(4):30-44.
[25]Pascal A,Guido W,Wicherhauser M V.Local Sine andCosine Bases of Coifman and Meyer and the Construction ofSmooth Wavelets.Wavelets:A Tutourial in Theory andApplications,1992.
[26]Averbuch A,Aharoni G,Coifman R,et al.Local cosinetransform—a method for the reduction of the blocking effectin JPEG.Journal of Mathematical Imaging and Vision,1996,3(1):7-38.
[27]Coifman R R,Wickerhauser M V.Entropy-based algorithmsfor best basis selection.IEEE Transactions on InformationTheory,1992,38(2):713-718.
[28]Wu R S,Wang Y Z,Gao J H.Beamlet migration based onlocal perturbation theory.Expanded abstracts,SEG 70thAnnual Meeting,2000:1008-1011.
[29]Wu R S,Wang Y Z,Luo M Q.Beamlet migration using localcosine basis.Geophysics,2008,73(5):S207-S217.
[30]Mao J,Wu R S,Gao J H.Directional illumination analysisusing the local exponential frame.Geophysics,2010,75(4):S163-S174.
[31]毛剑,吴如山,高静怀等.局部指数标架小波束在复杂介质方向照明分析中的应用.地球物理学报,2010,53(12):2955-2963.Mao J,Wu R S,Gao J H,et al.Directional illuminationanalysis for complex medium using local exponential framebeamlet.Chinese J.Geophys.(in Chinese),2010,53(12):2955-2963.
[32]Wu R S,Geng Y,Wu B Y.Physical wavelet defined on anobservation plane and the dreamlet.Expanded abstracts,SEG 81th Annual Meeting,2011,30:3835-3839.
[33]Wu R S,Wu B Y,Geng Y.Seismic wave propagation andimaging using time-space wavelets.Expanded abstracts,SEG78th Annual International Meeting,2008:2983-2987.
[34]Wu R S,Wu B Y,Geng Y.Imaging in copressed domainusing Dreamlets.Expanded Abstracts:Annual InternationalMeeting,Beijing SEG,2009.
[35]Wu B Y,Wu R S,Gao J H.Sourve-receiver prestack depthmigration using dreamlets.Expanded Abstracts,SEG 81thAnnual Meeting,2011,30:3377-3381.
[2]Wang Y Z,Wu R S.Seismic data compression by an adaptivelocal cosine/sine transform and its effects on migration.Geophysical Prospecting,2000,48(6):1009-1031.
[3]Mallat S.A Wavelet Tour of Signal Processing:The SparseWay.New York:Acedemic Press Inc,2009.
[4]朱光明,高静怀,王玉贵.小波变换及其在一维滤波中的应用.石油物探,1993,32(1):1-10.Zhu G M,Gao J H,Wang Y G.Wavelet transform and itsapplication to 1-D filtering.Geophysical Prospecting forPetrole(in Chinese),1993,32(1):1-10.
[5]高静怀,汪文秉,朱光明等.地震资料处理中小波函数的选取研究.地球物理学报,1996,39(3):392-400.Gao J H,Wang W B,Zhu G M,et al.On the choice ofwavelet functions for seismic data processing.Chinese J.Geophys.(in Chinese),1996,39(3):392-400.
[6]Villasenor J D,Ergas R A,Donoho P L.Seismic datacompression using high-dimensional wavelet transforms.Proceedings of the Data Compression Conference,1996:396-405.
[7]Vassiliou A,Wickerhauser M V.Comparison of waveletimage coding schemes for seismic data compression.WaveletApplication in Signal and Image Processing V,1997,3169:118-126.
[8]Candes E J,Donoho D L.New tight frames of curvelets andoptimal representations of objects with piecewise C2singularities.Communications on Pure and Applied Mathematics,2004,57(2):219-266.
[9]Candes E,Demanet L,Donoho D,et al.Fast discretecurvelet transforms.Multiscale Modeling&Simulation,2006,5(3):861-899.
[10]Le Pennec E,Mallat S.Bandelet image approximation andcompression.Multiscale Modeling&Simulation,2005,4(3):992-1039.
[11]Le Pennec E,Mallat S.Sparse geometric imagerepresentations with bandelets.IEEE Transactions on ImageProcessing,2005,14(4):423-438.
[12]Guo K H,Labate D.Sparse shearlet representation ofFourier integral operators.Electronic ResearchAnnouncements in Mathematical Sciences,2007,14:7-19.
[13]Guo K,Labate D.Optimally sparse multidimensionalrepresentation using shearlets.Siam Journal on MathematicalAnalysis,2007,39(1):298-318.
[14]Guo K,Labate D.Analysis and detection of surfacediscontinuities using the 3Dcontinuous shearlet transform.Applied and Computational Harmonic Analysis,2011,30(2):231-242.
[15]Candes E J,Demanet L.The curvelet representation of wavepropagators is optimally sparse.Communications on Pure andApplied Mathematics,2005,58(11):1472-1528.
[16]Hennenfent G,Herrmann F J.Seismic denoising withnonuniformly sampled curvelets.Computing in Science&Engineering,2006,8(3):16-25.
[17]Herrmann F J,Wang D L,Hennenfent G,et al.Curvelet-8期耿瑜等:基于Dreamlet变换的地震数据压缩理论与方法based seismic data processing:A multiscale and nonlinearapproach.Geophysics,2008,73(1):A1-A5.
[18]Herrmann F J,Brown C R,Erlangga Y A,et al.Curvelet-based migration preconditioning and scaling.Geophysics,2009,74(1):A41-A46.
[19]Chauris H,Nguyen T.Seismic demigration/migration in thecurvelet domain.Geophysics,2008,73(2):S35-S46.
[20]Douma H,de Hoop M V.Leading-order seismic imagingusing curvelets.Geophysics,2007,72(6):S231-S248.
[21]Lin T T Y,Herrmann F.Compressed wavefield extrapolation.Geophysics,2007,72(5):SM77-SM93
[22]Fomel S,Liu Y.Seislet transform and seislet frame.Geophysics,2010,75(3):V25-V38.
[23]Coifman R,Meyer Y.Remarques sur l'analyse de Fourier afenetre.Comptes Rendus de L Academie Des Sciences,1991,32:259-261.
[24]Wallace G K.The JPEG still picture compression standard.Communications of the Acm,1991,34(4):30-44.
[25]Pascal A,Guido W,Wicherhauser M V.Local Sine andCosine Bases of Coifman and Meyer and the Construction ofSmooth Wavelets.Wavelets:A Tutourial in Theory andApplications,1992.
[26]Averbuch A,Aharoni G,Coifman R,et al.Local cosinetransform—a method for the reduction of the blocking effectin JPEG.Journal of Mathematical Imaging and Vision,1996,3(1):7-38.
[27]Coifman R R,Wickerhauser M V.Entropy-based algorithmsfor best basis selection.IEEE Transactions on InformationTheory,1992,38(2):713-718.
[28]Wu R S,Wang Y Z,Gao J H.Beamlet migration based onlocal perturbation theory.Expanded abstracts,SEG 70thAnnual Meeting,2000:1008-1011.
[29]Wu R S,Wang Y Z,Luo M Q.Beamlet migration using localcosine basis.Geophysics,2008,73(5):S207-S217.
[30]Mao J,Wu R S,Gao J H.Directional illumination analysisusing the local exponential frame.Geophysics,2010,75(4):S163-S174.
[31]毛剑,吴如山,高静怀等.局部指数标架小波束在复杂介质方向照明分析中的应用.地球物理学报,2010,53(12):2955-2963.Mao J,Wu R S,Gao J H,et al.Directional illuminationanalysis for complex medium using local exponential framebeamlet.Chinese J.Geophys.(in Chinese),2010,53(12):2955-2963.
[32]Wu R S,Geng Y,Wu B Y.Physical wavelet defined on anobservation plane and the dreamlet.Expanded abstracts,SEG 81th Annual Meeting,2011,30:3835-3839.
[33]Wu R S,Wu B Y,Geng Y.Seismic wave propagation andimaging using time-space wavelets.Expanded abstracts,SEG78th Annual International Meeting,2008:2983-2987.
[34]Wu R S,Wu B Y,Geng Y.Imaging in copressed domainusing Dreamlets.Expanded Abstracts:Annual InternationalMeeting,Beijing SEG,2009.
[35]Wu B Y,Wu R S,Gao J H.Sourve-receiver prestack depthmigration using dreamlets.Expanded Abstracts,SEG 81thAnnual Meeting,2011,30:3377-3381.
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