基于压缩感知的加权MCA地震数据重构方法
|
摘要
地震数据规则化重构是地震资料处理十分重要的基础性工作.压缩感知理论打破了香农采样定理的制约,利用信号在某个变换域的稀疏特性重构出完整的信号,在地震数据重构领域得到了很好的应用.深反射地震剖面大都布置在地质构造比较复杂的区段,复杂的地质构造使深反射地震剖面上的波阻特征复杂,采用单一稀疏变换不能最有效地表征数据的内部结构特征.MCA(形态成分分析)方法将信号分解为几种形态特征区别明显的分量来逼近数据的内部复杂结构,但是对各成分简单的叠加仍然无法有效地描述复杂构造数据的各种特征.结合两种方法的优点,本文提出了一种新的基于压缩感知的重构算法框架,在MCA方法的基础上对各稀疏字典进行加权,在迭代中不断更新各个稀疏字典的权值系数,对信号内部的各种特征进行最优描述,从而实现对信号的高质量重构.模型测试和实际资料处理结果表明:基于压缩感知的加权MCA方法不仅可以对地质构造复杂的地震数据进行高效的插值重建,而且可以很好的消除空间假频.
The regularized reconstruction of seismic data is one of the most important and fundamental task in seismic data processing.The compressed sensing(CS)theory has been successfully applied in the reconstruction of seismic data,because it breaks the restriction of Shannon sampling theorem and can obtain a complete reconstructed signal by using the sparsity property in a certain transformation domain.Deep reflection seismic profiles commonly deployed in areas with complicated geological structure,resulted in complicated wave impedance characteristics on deep reflection seismic profiles.Consequently,the internal structure characteristics of data cannot be represented effectively by using a single sparse transformation.The morphological component analysis(MCA)method decomposes a signal into several components with distinguished morphological features toapproximate the complex internal structure of data.However,the various characteristics of the complex data still cannot be described effectively through a simple summation of the signal components.To solve these problems,a new iterative algorithm frame was proposed based on the combination of the merits of the CS and MCA methods.The sparse dictionaries were weighted on the basis of the MCA method,and then the weight coefficients of each sparse dictionary was updated continuously in the process of iteration.Finally an optimal description of the various internal features of signals was obtained and a high-quality reconstruction was achieved for those complex signals.Model tests and real data processing results show that the weighted MCA method based on CS can not only reconstruct the seismic data from the complicated geological structure through interpolation efficiently,but also eliminate the space aliasing very well.
The regularized reconstruction of seismic data is one of the most important and fundamental task in seismic data processing.The compressed sensing(CS)theory has been successfully applied in the reconstruction of seismic data,because it breaks the restriction of Shannon sampling theorem and can obtain a complete reconstructed signal by using the sparsity property in a certain transformation domain.Deep reflection seismic profiles commonly deployed in areas with complicated geological structure,resulted in complicated wave impedance characteristics on deep reflection seismic profiles.Consequently,the internal structure characteristics of data cannot be represented effectively by using a single sparse transformation.The morphological component analysis(MCA)method decomposes a signal into several components with distinguished morphological features toapproximate the complex internal structure of data.However,the various characteristics of the complex data still cannot be described effectively through a simple summation of the signal components.To solve these problems,a new iterative algorithm frame was proposed based on the combination of the merits of the CS and MCA methods.The sparse dictionaries were weighted on the basis of the MCA method,and then the weight coefficients of each sparse dictionary was updated continuously in the process of iteration.Finally an optimal description of the various internal features of signals was obtained and a high-quality reconstruction was achieved for those complex signals.Model tests and real data processing results show that the weighted MCA method based on CS can not only reconstruct the seismic data from the complicated geological structure through interpolation efficiently,but also eliminate the space aliasing very well.
引文
Aharon M,Elad M,Bruckstein A.2006.rmK-SVD:An algorithm for designing overcomplete dictionaries for sparse representation.IEEE Transactions on Signal Processing,54(11):4311-4322,doi:10.1109/TSP.2006.881199.
Bai L S,Liu Y K,Lu H Y,et al.2014.Curvelet-domain joint iterative seismic data reconstruction based on compressed sensing.Chinese Journal of Geophysics(in Chinese),57(9):2937-2945,doi:10.6038/cjg20140919.
Baraniuk R.2007.A lecture on compressive sensing.IEEE Signal Processing Magazine,24(4):118-121.
Baraniuk R,Davenport M,DeVore R,et al.2008.A simple proof of the restricted isometry property for random matrices.Constructive Approximation,28(3):253-263,doi:10.1007/s00365-007-9003-x.
Cai J F,Ji H,Shen Z W,et al.2014.Data-driven tight frame
construction and image denoising.Applied and Computational Harmonic Analysis,37(1):89-105,doi:10.1016/j.acha.2013.10.001.
Candès E J,Romberg J,Tao T.2006.Robust uncertainty principles:Exact signal reconstruction from highly incomplete frequency information.IEEE Transactions on Information Theory,52(2):489-509,doi:10.1109/TIT.2005.862083.
Candès E J,Tao T.2006.Near-optimal signal recovery from random projections:Universal encoding strategies?IEEE Transactions on Information Theory,52(12):5406-5425,doi:10.1109/TIT.2006.885507.
Candès E J.2008.The restricted isometry property and its implications for compressed sensing.Comptes Rendus Mathematique,346(9-10):589-592,doi:10.1016/j.crma.2008.03.014.
Candès E J,Eldar Y C,Needell D,et al.2011.Compressed sensing with coherent and redundant dictionaries.Applied and Computational Harmonic Analysis,31(1):59-73,doi:10.1016/j.acha.2010.10.002.
Cao J J,Wang B F.2015.An improved projection onto convex sets method for simultaneous interpolation and denoising.Chinese Journal of Geophysics(in Chinese),58(8):2936-2947,doi:10.6038/cjg20150826.
Chen Y K,Ma J W,Fomel S.2016.Double-sparsity dictionary for seismic noise attenuation.Geophysics,81(2):V193-V206,doi:10.1190/GEO2014-0525.1.
Cheng B J,Xu T J,Li S G.2012.Research and application of frequency dependent AVO analysis for gas recognition.Chinese Journal of Geophysics(in Chinese),55(2):608-613,doi:10.6038/j.issn.0001-5733.2012.02.023.
Cui X F,Liu D Q,Zhang G Q.2003.Wavelet transform to achieve seismic trace interpolation.Oil Geophysical Prospecting(in Chinese),38(S1):93-97,doi:10.13810/j.cnki.issn.1000-7210.2003.s1.019.
Donoho D L.2006.Compressed sensing.IEEE Transactions on Information Theory,52(4):1289-1306,doi:10.1109/TIT.2006.871582.
Donoho D L,Kutyniok G.2013.Microlocal analysis of the geometric separation problem.Communication on Pure and Applied Mathematics,66(1):1-47,doi:10.1002/cpa.21418.
Du Z Y,Wu G C.2015.Theory and application of irregular seismic data reconstruction based on MCA.∥85th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts 3880-3884,doi:10.1190/segam2015-5854455.1.
Duijndam A J W,Schonewille M A,Hindriks C O H.1999.Reconstruction of band-limited signals,irregularly sampled along one spatial direction.Geophysics,64(2):524-538,doi:10.1190/1.1444559.
Elad M,Starck J L,Querre P,et al.2005.Simultaneous cartoon and texture image inpainting using morphological component analysis(MCA).Applied and Computational Harmonic Analysis,19(3):340-358,doi:10.1016/j.acha.2005.03.005.
Fadili M J,Starck J L,Murtagh F.2009.Inpainting and zooming using sparse representations.Computer Journal,52(1):64-79,doi:10.1093/comjnl/bxm055.
Figueiredo M A T,Nowak R D.2003.An EM algorithm for wavelet-based image restoration.IEEE Transactions on Image Processing,12(8):906-916,doi:10.1109/TIP.2003.814255.
Guo N M,Li H S,Feng X M,et al.2014.Pre-stack seismic data reconstruction based on the undecimated wavelet transform.Oil Geophysical Prospecting(in Chinese),49(3):508-516,doi:10.13810/j.cnki.issn.1000-7210.2014.03.014.
Hampson D.1986.Inverse velocity stacking for multiple elimination.∥56th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,doi:10.1190/1.1893060.
Hennenfent G,Herrmann F.2005.Sparseness-constrained data continuation with frames:applications to missing traces and aliased signals in 2/3-D.∥75th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,24:2162-2165,doi:10.1190/1.2148142.
Hennenfent G,Herrmann F J.2006.Seismic denoising with nonuniformly sampled curvelets.Computing in Science&Engineering,8(3):16-25,doi:10.1109/MCSE.2006.49.
Herrmann F J,Hennenfent G.2008.Non-parametric seismic data recovery with curvelet frames.Geophysical Journal International,173(1):233-248,doi:10.1111/j.1365-246X.2007.03698.x.
Kirachaiwanich D,Liang Q L.2011.Compressive sensing:to compress or not to compress.∥Proceedings of 2011Conference Record of the Forty Fifth Asilomar Conference on Signals,Systems and Computers.Pacific Grove,CA,USA:IEEE,809-813,doi:10.1109/ACSSC.2011.6190119.
Kittipoom P,Kutyniok G,Lim W Q.2012.Construction of compactly supported shearlet frames.Construction Approximation,35(1):21-72,doi:10.1007/s00365-011-9142-y.
Kutyniok G.2013.Theory and applications of compressed sensing.GAMM-Mitteilungen,36(1):79-101,doi:10.1002/gamm.201310005.
Li H S,Wu G C,Yin X Y.2012.Morphological component analysis in seismic data reconstruction.Oil Geophysical Prospecting(in Chinese),47(2):236-243,doi:10.13810/j.cnki.issn.1000-7210.2012.02.020.
Liang J W,Ma J W,Zhang X Q.2014.Seismic data restoration via data-driven tight frame.Geophysics,79(3):V65-V74,doi:10.1190/geo2013-0252.1.
Lin C Y,Dong C M,Ren L H,et al.2013.Development of reservoir characterization and its stimulation.Journal of China University of Petroleum(Edition of Natural Science)(in Chinese),37(5):22-27,doi:10.3969/j.issn.1673-5005.2013.05.004.
Ma J W.2011.Improved iterative Curvelet thresholding for compressed sensing and measurement.IEEE Transactions on Instrumentation and Measurement,60(1):126-136,doi:10.1109/TIM.2010.2049221.
Meng X H,Guo L H,Zhang Z F,et al.2008.Reconstruction of seismic data with least squares inversion based on nonuniform fast Fourier transform.Chinese Journal of Geophysics(in Chinese),51(1):235-241,doi:10.3321/j.issn:0001-5733.2008.01.029.
Naghizadeh M,Sacchi M D.2010.Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data.Geophysics,75(6):WB189-WB202,doi:10.1190/1.3509468.
Starck J L,Elad M,Donoho D.2004.Redundant multiscale transforms and their application for morphological component separation.Advances in Imaging and Electron Physics,132:287-348,doi:10.1016/S1076-5670(04)32006-9.
Starck J L,Murtagh F,Fadili J M.2010.Sparse Image and Signal Processing:Wavelets,Curvelets,Morphological Diversity.Cambridge:Cambridge University Press.
Studer C,Kuppinger P,Pope G,et al.2012.Recovery of sparsely corrupted signals.IEEE Transactions on Information Theory,58(5):3115-3130,doi:10.1109/TIT.2011.2179701.
Trifunac M D.1971.Response envelope spectrum and interpretation of strong earthquake ground motion.Bulletin of the Seismological Society of America,61(2):343-356.
Vogel C R.2002.Computational Methods for Inverse Problems.Philadelphia:Society for Industrial and Applied Mathematics.
Xiong Z.2012.Seismic exploration for strati-lithologic reservoirs.Oil Geophysical Prospecting(in Chinese),47(1):1-18,doi:10.13810/j.cnki.issn.1000-7210.2012.01.009.
Yang P L,Fomel S.2015.Seislet-based morphological component analysis using scale-dependent exponential shrinkage.Journal of Applied Geophysics,118:66-74,doi:10.1016/j.jappgeo.2015.04.003.
Yin X Y,Zhang S X,Zhang F.2013.Two-term elastic impedance inversion and Russell fluid factor direct estimation method for deep reservoir fluid identification.Chinese Journal of Geophysics(in Chinese),56(7):2378-2390,doi:10.6038/cjg20130724.
Yu S W,Ma J W,Zhang X Q,et al.2015.Interpolation and denoising of high-dimensional seismic data by learning a tight frame.Geophysics,80(5):V119-V132,doi:10.1190/geo2014-0396.1.
Yu S W,Ma J W,Osher S.2016.Monte Carlo data-driven tight frame for seismic data recovery.Geophysics,81(4):V327-V340,doi:10.1190/geo2015-0343.1.
Yu S W.2017.Seismic data reconstruction based on adaptive sparse inversion[Ph.D.thesis](in Chinese).Harbin:Harbin Institute of Technology.
Zhang H,Chen X H,Wu X M.2013.Seismic data reconstruction based on CS and Fourier theory.Applied Geophysics,10(2):170-180,doi:10.1007/s11770-013-0375-3.
Zhang L,Han L G,Xu D X,et al.2017a.Seismic data reconstruction with Shearlet transform based on compressed sensing technology.Oil Geophysical Prospecting(in Chinese),52(2):220-225,doi:10.13810/j.cnki.issn.1000-7210.2017.02.004.
Zhang L,Han L G,Liu Z G,et al.2017b.Seismic data reconstruction based on compressed sensing and Contourlet transform.Geophysical Prospecting for Petroleum(in Chinese),56(6):804-811,doi:10.3969/j.issn.1000-1441.2017.06.005.
白兰淑,刘伊克,卢回忆等.2014.基于压缩感知的Curvelet域联合迭代地震数据重建.地球物理学报,57(9):2937-2945,doi:10.6038/cjg20140919.
曹静杰,王本锋.2015.基于一种改进凸集投影方法的地震数据同时插值和去噪.地球物理学报,58(8):2936-2947,doi:10.6038/cjg20150826.
程冰洁,徐天吉,李曙光.2012.频变AVO含气性识别技术研究与应用.地球物理学报,55(2):608-613,doi:10.6038/j.issn.0001-5733.2012.02.023.
崔兴福,刘东奇,张关泉.2003.小波变换实现地震道内插.石油地球物理勘探,38(S1):93-97,doi:10.13810/j.cnki.issn.1000-7210.2003.s1.019.
郭念民,李海山,冯雪梅等.2014.非抽样离散小波变换叠前地震数据重建方法.石油地球物理勘探,49(3):508-516,doi:10.13810/j.cnki.issn.1000-7210.2014.03.014.
李海山,吴国忱,印兴耀.2012.形态分量分析在地震数据重建中的应用.石油地球物理勘探,47(2):236-243,doi:10.13810/j.cnki.issn.1000-7210.2012.02.020.
林承焰,董春梅,任丽华等.2013.油藏描述技术发展及启示.中国石油大学学报(自然科学版),37(5):22-27,doi:10.3969/j.issn.1673-5005.2013.05.004.
孟小红,郭良辉,张致付等.2008.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,51(1):235-241,doi:10.3321/j.issn:0001-5733.2008.01.029.
熊翥.2012.地层、岩性油气藏地震勘探方法与技术.石油地球物理勘探,47(1):1-18,doi:10.13810/j.cnki.issn.1000-7210.2012.01.009.
印兴耀,张世鑫,张峰.2013.针对深层流体识别的两项弹性阻抗反演与Russell流体因子直接估算方法研究.地球物理学报,56(7):2378-2390,doi:10.6038/cjg20130724.
于四伟.2017.基于自适应稀疏反演的地震数据重构[博士论文].哈尔滨:哈尔滨工业大学.
张良,韩立国,许德鑫等.2017a.基于压缩感知技术的Shearlet变换重建地震数据.石油地球物理勘探,52(2):220-225,doi:10.13810/j.cnki.issn.1000-7210.2017.02.004.
张良,韩立国,刘争光等.2017b.基于压缩感知和Contourlet变换的地震数据重建方法.石油物探,56(6):804-811,doi:10.3969/j.issn.1000-1441.2017.06.005.
Bai L S,Liu Y K,Lu H Y,et al.2014.Curvelet-domain joint iterative seismic data reconstruction based on compressed sensing.Chinese Journal of Geophysics(in Chinese),57(9):2937-2945,doi:10.6038/cjg20140919.
Baraniuk R.2007.A lecture on compressive sensing.IEEE Signal Processing Magazine,24(4):118-121.
Baraniuk R,Davenport M,DeVore R,et al.2008.A simple proof of the restricted isometry property for random matrices.Constructive Approximation,28(3):253-263,doi:10.1007/s00365-007-9003-x.
Cai J F,Ji H,Shen Z W,et al.2014.Data-driven tight frame
construction and image denoising.Applied and Computational Harmonic Analysis,37(1):89-105,doi:10.1016/j.acha.2013.10.001.
Candès E J,Romberg J,Tao T.2006.Robust uncertainty principles:Exact signal reconstruction from highly incomplete frequency information.IEEE Transactions on Information Theory,52(2):489-509,doi:10.1109/TIT.2005.862083.
Candès E J,Tao T.2006.Near-optimal signal recovery from random projections:Universal encoding strategies?IEEE Transactions on Information Theory,52(12):5406-5425,doi:10.1109/TIT.2006.885507.
Candès E J.2008.The restricted isometry property and its implications for compressed sensing.Comptes Rendus Mathematique,346(9-10):589-592,doi:10.1016/j.crma.2008.03.014.
Candès E J,Eldar Y C,Needell D,et al.2011.Compressed sensing with coherent and redundant dictionaries.Applied and Computational Harmonic Analysis,31(1):59-73,doi:10.1016/j.acha.2010.10.002.
Cao J J,Wang B F.2015.An improved projection onto convex sets method for simultaneous interpolation and denoising.Chinese Journal of Geophysics(in Chinese),58(8):2936-2947,doi:10.6038/cjg20150826.
Chen Y K,Ma J W,Fomel S.2016.Double-sparsity dictionary for seismic noise attenuation.Geophysics,81(2):V193-V206,doi:10.1190/GEO2014-0525.1.
Cheng B J,Xu T J,Li S G.2012.Research and application of frequency dependent AVO analysis for gas recognition.Chinese Journal of Geophysics(in Chinese),55(2):608-613,doi:10.6038/j.issn.0001-5733.2012.02.023.
Cui X F,Liu D Q,Zhang G Q.2003.Wavelet transform to achieve seismic trace interpolation.Oil Geophysical Prospecting(in Chinese),38(S1):93-97,doi:10.13810/j.cnki.issn.1000-7210.2003.s1.019.
Donoho D L.2006.Compressed sensing.IEEE Transactions on Information Theory,52(4):1289-1306,doi:10.1109/TIT.2006.871582.
Donoho D L,Kutyniok G.2013.Microlocal analysis of the geometric separation problem.Communication on Pure and Applied Mathematics,66(1):1-47,doi:10.1002/cpa.21418.
Du Z Y,Wu G C.2015.Theory and application of irregular seismic data reconstruction based on MCA.∥85th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts 3880-3884,doi:10.1190/segam2015-5854455.1.
Duijndam A J W,Schonewille M A,Hindriks C O H.1999.Reconstruction of band-limited signals,irregularly sampled along one spatial direction.Geophysics,64(2):524-538,doi:10.1190/1.1444559.
Elad M,Starck J L,Querre P,et al.2005.Simultaneous cartoon and texture image inpainting using morphological component analysis(MCA).Applied and Computational Harmonic Analysis,19(3):340-358,doi:10.1016/j.acha.2005.03.005.
Fadili M J,Starck J L,Murtagh F.2009.Inpainting and zooming using sparse representations.Computer Journal,52(1):64-79,doi:10.1093/comjnl/bxm055.
Figueiredo M A T,Nowak R D.2003.An EM algorithm for wavelet-based image restoration.IEEE Transactions on Image Processing,12(8):906-916,doi:10.1109/TIP.2003.814255.
Guo N M,Li H S,Feng X M,et al.2014.Pre-stack seismic data reconstruction based on the undecimated wavelet transform.Oil Geophysical Prospecting(in Chinese),49(3):508-516,doi:10.13810/j.cnki.issn.1000-7210.2014.03.014.
Hampson D.1986.Inverse velocity stacking for multiple elimination.∥56th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,doi:10.1190/1.1893060.
Hennenfent G,Herrmann F.2005.Sparseness-constrained data continuation with frames:applications to missing traces and aliased signals in 2/3-D.∥75th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,24:2162-2165,doi:10.1190/1.2148142.
Hennenfent G,Herrmann F J.2006.Seismic denoising with nonuniformly sampled curvelets.Computing in Science&Engineering,8(3):16-25,doi:10.1109/MCSE.2006.49.
Herrmann F J,Hennenfent G.2008.Non-parametric seismic data recovery with curvelet frames.Geophysical Journal International,173(1):233-248,doi:10.1111/j.1365-246X.2007.03698.x.
Kirachaiwanich D,Liang Q L.2011.Compressive sensing:to compress or not to compress.∥Proceedings of 2011Conference Record of the Forty Fifth Asilomar Conference on Signals,Systems and Computers.Pacific Grove,CA,USA:IEEE,809-813,doi:10.1109/ACSSC.2011.6190119.
Kittipoom P,Kutyniok G,Lim W Q.2012.Construction of compactly supported shearlet frames.Construction Approximation,35(1):21-72,doi:10.1007/s00365-011-9142-y.
Kutyniok G.2013.Theory and applications of compressed sensing.GAMM-Mitteilungen,36(1):79-101,doi:10.1002/gamm.201310005.
Li H S,Wu G C,Yin X Y.2012.Morphological component analysis in seismic data reconstruction.Oil Geophysical Prospecting(in Chinese),47(2):236-243,doi:10.13810/j.cnki.issn.1000-7210.2012.02.020.
Liang J W,Ma J W,Zhang X Q.2014.Seismic data restoration via data-driven tight frame.Geophysics,79(3):V65-V74,doi:10.1190/geo2013-0252.1.
Lin C Y,Dong C M,Ren L H,et al.2013.Development of reservoir characterization and its stimulation.Journal of China University of Petroleum(Edition of Natural Science)(in Chinese),37(5):22-27,doi:10.3969/j.issn.1673-5005.2013.05.004.
Ma J W.2011.Improved iterative Curvelet thresholding for compressed sensing and measurement.IEEE Transactions on Instrumentation and Measurement,60(1):126-136,doi:10.1109/TIM.2010.2049221.
Meng X H,Guo L H,Zhang Z F,et al.2008.Reconstruction of seismic data with least squares inversion based on nonuniform fast Fourier transform.Chinese Journal of Geophysics(in Chinese),51(1):235-241,doi:10.3321/j.issn:0001-5733.2008.01.029.
Naghizadeh M,Sacchi M D.2010.Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data.Geophysics,75(6):WB189-WB202,doi:10.1190/1.3509468.
Starck J L,Elad M,Donoho D.2004.Redundant multiscale transforms and their application for morphological component separation.Advances in Imaging and Electron Physics,132:287-348,doi:10.1016/S1076-5670(04)32006-9.
Starck J L,Murtagh F,Fadili J M.2010.Sparse Image and Signal Processing:Wavelets,Curvelets,Morphological Diversity.Cambridge:Cambridge University Press.
Studer C,Kuppinger P,Pope G,et al.2012.Recovery of sparsely corrupted signals.IEEE Transactions on Information Theory,58(5):3115-3130,doi:10.1109/TIT.2011.2179701.
Trifunac M D.1971.Response envelope spectrum and interpretation of strong earthquake ground motion.Bulletin of the Seismological Society of America,61(2):343-356.
Vogel C R.2002.Computational Methods for Inverse Problems.Philadelphia:Society for Industrial and Applied Mathematics.
Xiong Z.2012.Seismic exploration for strati-lithologic reservoirs.Oil Geophysical Prospecting(in Chinese),47(1):1-18,doi:10.13810/j.cnki.issn.1000-7210.2012.01.009.
Yang P L,Fomel S.2015.Seislet-based morphological component analysis using scale-dependent exponential shrinkage.Journal of Applied Geophysics,118:66-74,doi:10.1016/j.jappgeo.2015.04.003.
Yin X Y,Zhang S X,Zhang F.2013.Two-term elastic impedance inversion and Russell fluid factor direct estimation method for deep reservoir fluid identification.Chinese Journal of Geophysics(in Chinese),56(7):2378-2390,doi:10.6038/cjg20130724.
Yu S W,Ma J W,Zhang X Q,et al.2015.Interpolation and denoising of high-dimensional seismic data by learning a tight frame.Geophysics,80(5):V119-V132,doi:10.1190/geo2014-0396.1.
Yu S W,Ma J W,Osher S.2016.Monte Carlo data-driven tight frame for seismic data recovery.Geophysics,81(4):V327-V340,doi:10.1190/geo2015-0343.1.
Yu S W.2017.Seismic data reconstruction based on adaptive sparse inversion[Ph.D.thesis](in Chinese).Harbin:Harbin Institute of Technology.
Zhang H,Chen X H,Wu X M.2013.Seismic data reconstruction based on CS and Fourier theory.Applied Geophysics,10(2):170-180,doi:10.1007/s11770-013-0375-3.
Zhang L,Han L G,Xu D X,et al.2017a.Seismic data reconstruction with Shearlet transform based on compressed sensing technology.Oil Geophysical Prospecting(in Chinese),52(2):220-225,doi:10.13810/j.cnki.issn.1000-7210.2017.02.004.
Zhang L,Han L G,Liu Z G,et al.2017b.Seismic data reconstruction based on compressed sensing and Contourlet transform.Geophysical Prospecting for Petroleum(in Chinese),56(6):804-811,doi:10.3969/j.issn.1000-1441.2017.06.005.
白兰淑,刘伊克,卢回忆等.2014.基于压缩感知的Curvelet域联合迭代地震数据重建.地球物理学报,57(9):2937-2945,doi:10.6038/cjg20140919.
曹静杰,王本锋.2015.基于一种改进凸集投影方法的地震数据同时插值和去噪.地球物理学报,58(8):2936-2947,doi:10.6038/cjg20150826.
程冰洁,徐天吉,李曙光.2012.频变AVO含气性识别技术研究与应用.地球物理学报,55(2):608-613,doi:10.6038/j.issn.0001-5733.2012.02.023.
崔兴福,刘东奇,张关泉.2003.小波变换实现地震道内插.石油地球物理勘探,38(S1):93-97,doi:10.13810/j.cnki.issn.1000-7210.2003.s1.019.
郭念民,李海山,冯雪梅等.2014.非抽样离散小波变换叠前地震数据重建方法.石油地球物理勘探,49(3):508-516,doi:10.13810/j.cnki.issn.1000-7210.2014.03.014.
李海山,吴国忱,印兴耀.2012.形态分量分析在地震数据重建中的应用.石油地球物理勘探,47(2):236-243,doi:10.13810/j.cnki.issn.1000-7210.2012.02.020.
林承焰,董春梅,任丽华等.2013.油藏描述技术发展及启示.中国石油大学学报(自然科学版),37(5):22-27,doi:10.3969/j.issn.1673-5005.2013.05.004.
孟小红,郭良辉,张致付等.2008.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,51(1):235-241,doi:10.3321/j.issn:0001-5733.2008.01.029.
熊翥.2012.地层、岩性油气藏地震勘探方法与技术.石油地球物理勘探,47(1):1-18,doi:10.13810/j.cnki.issn.1000-7210.2012.01.009.
印兴耀,张世鑫,张峰.2013.针对深层流体识别的两项弹性阻抗反演与Russell流体因子直接估算方法研究.地球物理学报,56(7):2378-2390,doi:10.6038/cjg20130724.
于四伟.2017.基于自适应稀疏反演的地震数据重构[博士论文].哈尔滨:哈尔滨工业大学.
张良,韩立国,许德鑫等.2017a.基于压缩感知技术的Shearlet变换重建地震数据.石油地球物理勘探,52(2):220-225,doi:10.13810/j.cnki.issn.1000-7210.2017.02.004.
张良,韩立国,刘争光等.2017b.基于压缩感知和Contourlet变换的地震数据重建方法.石油物探,56(6):804-811,doi:10.3969/j.issn.1000-1441.2017.06.005.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |