形态分量分析在去除地震资料随机噪声中的应用
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摘要
以数学形态学和稀疏信号理论为依据,采用形态分量分析(MCA)方法去除地震数据中的随机噪声。应用MCA方法的关键在于选取合适的字典,从地震数据的特点和计算复杂性出发,选取UWT字典和Curvelet字典,一个用来稀疏表示地震数据的局部奇异部分,一个用来稀疏表示地震数据的线状变化部分。采用BCR算法求解目标函数,通过将数据分解为形态特征不同的2个分量,舍弃在字典中不能有效稀疏表示的随机噪声来达到去噪目的。作为一种二维去噪方法,MCA去噪方法在时间和空间方向上都具有很强的随机噪声抑制能力;由于UWT字典和Curvelet字典能够比传统的小波变换有更强的稀疏表示能力,MCA去噪方法对有效信息的损害较小,是一种保真保幅的去噪方法。模型测试和实际资料处理验证了该方法的有效性。
According to the morphology and sparse signal theory,morphological component analysis(MCA) method is used for random noise attenuation in seismic data.The key of MCA is to select the appropriate dictionaries.In view of the characteristics of seismic data and computational complexity,UWT dictionary and Curvelet dictionary are selected.One sparsely represents for local singular part of the seismic data,the other sparsely represents for smooth and linear part of seismic data.BCR algorithm is used to solve objective function,and the denoised results are obtained by decomposing the seismic data into two morphologically different components and discarding the random noise which can't be sparsely represented in dictionaries efficiently.As a 2D denoising method,MCA denoising method can efficiently suppress random noise both in time and spatial directions;Because the sparse representation abilities of UWT dictionary and Curvelet dictionary are stronger than traditional wavelet transform,MCA denoising is an amplitude and fidelity preserved denoising method,its damage to effective information is quite smaller.Theoretical and real data processing verified the efficiency of MCA method.
According to the morphology and sparse signal theory,morphological component analysis(MCA) method is used for random noise attenuation in seismic data.The key of MCA is to select the appropriate dictionaries.In view of the characteristics of seismic data and computational complexity,UWT dictionary and Curvelet dictionary are selected.One sparsely represents for local singular part of the seismic data,the other sparsely represents for smooth and linear part of seismic data.BCR algorithm is used to solve objective function,and the denoised results are obtained by decomposing the seismic data into two morphologically different components and discarding the random noise which can't be sparsely represented in dictionaries efficiently.As a 2D denoising method,MCA denoising method can efficiently suppress random noise both in time and spatial directions;Because the sparse representation abilities of UWT dictionary and Curvelet dictionary are stronger than traditional wavelet transform,MCA denoising is an amplitude and fidelity preserved denoising method,its damage to effective information is quite smaller.Theoretical and real data processing verified the efficiency of MCA method.
引文
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[18]Wang Run-qiu,Li Qing,Zhang Ming.Application ofMulti-Scaled Morphology in Denoising Seismic Data[J].Applied Geophysics,2008,5(3):197-203.
[19]Starck J L,Elad M,Donoho D L.Redundant Multi-scale Transform and Their Application for Morpho-logical Component Analysis[J].Advance in Imagingand Electron Physics,2004,132(82):278-348.
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[21]Sardy S,Bruce A,Tseng P.Block Coordinate Relaxa-tion Methods for Nonparametric Wavelet Denoising[J].Journal of Computational and Graphical Statis-tics,2000,9(2):361-379.
[22]Starck J L,Elad M,Donoho D L.Redundant Multi-scale Transform and Their Application for Morpho-logical Component Analysis[J].Advance in Imagingand Electron Physics,2004,132:288-348.
[23]Elad M,Starck J L,Querreb P,et al.SimultaneousCartoon and Texture Image Inpainting Using Mor-phological Component Analysis(MCA)[J].Appliedand Computational Harmonic Analysis,2005,19:340-358.
[24]Starck J L,Fadili M J,Murtagh F.The UndecimatedWavelet Decomposition and Its Reconstruction[J].IEEE Transactions on Image Processing,2007,16(2):297-309.
[25]Candes E J,Donoho D L.Recovering Edges in Ill-Posed Inverse Problems:Optimality of CurveletFrames[J].Ann Statist,2002,30:784-842.
[26]Candes E J,Demanet L,Donoho D L,et al.FastDiscrete Curvelet Transforms[J].Multiscale Mode-ling and Simulation,2006,5(3):861-899.
[2]Canales L L.Random Noise Reduction[C]//Presentedat the 54th SEG Mtg.Tulsa:SEG,1984:525-527.
[3]Alsdorf D.Noise Reduction in Seismic Data UsingFourier Correlation Coefficient Filtering[J].Geophysics,1997,62(5):1617-1627.
[4]Zhu Wei-hong,Liu Qing-lin,Panos G K.LinearNoise Attenuation Using Local Radial Trace MedianFiltering[J].The Leading Edge,2004,23(8):728-730.
[5]王润秋,郑桂娟,付洪洲,等.地震资料处理中的形态滤波去噪方法[J].石油地球物理勘探,2005,40(3):277-282.Wang Run-qiu,Zheng Gui-juan,Fu Hong-zhou,et al.Noise-Eliminated Method by Morphologic Filtering inSeismic Data Processing[J].Oil GeophysicalProspecting,2005,40(3):277-282.
[6]吴招才,刘天佑.地震数据去噪中的小波方法[J].地球物理学进展,2008,23(2):493-499.Wu Zhao-cai,Liu Tian-you.Wavelet TransformMethods in Seismic Data Noise Attenuation[J].Progress in Geophysics,2008,23(2):493-499.
[7]巩向博,韩立国,王恩利,等.压制噪声的高分辨率Radon变换法[J].吉林大学学报:地球科学版,2009,39(1):152-157.Gong Xiang-bo,Han Li-guo,Wang En-li,et al.Denoising via High Resolution Radon Transform[J].Journal of Jilin University:Earth Science Edition,2009,39(1):152-157.
[8]张孝珍,董汉强,侯国文,等.地震勘探中的去噪技术新进展[J].勘探地球物理进展,2009,32(3):172-178.Zhang Xiao-zhen,Dong Han-qiang,Hou Guo-wen,etal.Advances in Denoising Technology in SeismicExploration[J].Progress in Exploration Geophysics,2009,32(3):172-178.
[9]聂鹏飞,曾谦,马海涛,等.消减地震勘探随机噪声:导数算子约束下的维纳滤波[J].吉林大学学报:地球科学版,2010,40(6):1471-1478.Nie Peng-fei,Zeng Qian,Ma Hai-tao,et al.ReducingSeismic Random Noise:Derivative OperatorConstrainted Wiener Filtering[J].Journal of JilinUniversity:Earth Science Edition,2010,40(6):1471-1478.
[10]李振春,张军华.地震数据处理方法[M].东营:石油大学出版社,2004:23-54.Li Zhen-chun,Zhang Jun-hua.Seismic Data Proces-sing Methods[M].Dongying:Petroleum UniversityPress,2004:23-54.
[11]査树贵,陈洪堤,龚小金.反偏移技术对叠前资料的噪声消除[J].中外能源,2006,11(3):6-20.Zha Shu-gui,Chen Hong-di,Gong Xiao-jin.Demigration Technolgy used to Eliminate the Noise inPrestack Data[J].China Foreign Energy,2006,11(3):6-20.
[12]Starck J L,Candes E J,Donoho D L.The CurveletTransform for Image Denoising[J].IEEE Trans onImage Processing,2002,11(6):670-684.
[13]赵天姿,宋炜,王尚旭.基于匹配追踪算法的时频滤波去噪方法[J].石油物探,2008,47(4):367-371.Zhao Tian-zi,Song Wei,Wang Shang-xu.Time-Frequency Filtering De-Noise Method Based onMatching Pursuit Algorithm[J].GeophysicalProspecting for Petroleum,2008,47(4):367-371.
[14]彭才,朱仕军,孙建库,等.基于独立成分分析的地震数据去噪[J].勘探地球物理进展,2007,30(1):30-32.Peng Cai,Zhu Shi-jun,Sun Jian-ku,et al.NoiseElimination with Independent Component Analysis[J].Progress in Exploration Geophysics,2007,30(1):30-32.
[15]吕文彪,尹成,张白林,等.利用独立分量分析法去除地震噪声[J].石油地球物理勘探,2007,42(2):132-136.LüWen-biao,Yin Cheng,Zhang Bai-lin,et al.UsingIndependent Component Analysis to EliminateSeismic Noises[J].Oil Geophysical Prospecting,2007,42(2):132-136.
[16]崔屹.图象处理与分析:数学形态学方法及应用[M].北京:科学出版社,2000:1-14.Cui Yi.Image Processing and Analysis:Mathematical Morphology Method and ItsApplication[M].Beijing:Science Press,2000:1-14.
[17]郑桂娟,王润秋.数学形态学在地震资料处理中的应用探索[J].勘探地球物理进展,2003,26(4):277-281.Zheng Gui-juan,Wang Run-qiu.Application ofMathematical Morphology in Seismic Data Processing[J].Progress in Exploration Geophysics,2003,26(4):277-281.
[18]Wang Run-qiu,Li Qing,Zhang Ming.Application ofMulti-Scaled Morphology in Denoising Seismic Data[J].Applied Geophysics,2008,5(3):197-203.
[19]Starck J L,Elad M,Donoho D L.Redundant Multi-scale Transform and Their Application for Morpho-logical Component Analysis[J].Advance in Imagingand Electron Physics,2004,132(82):278-348.
[20]Starck J L,Elad M,Donoho D L.Image Decomposi-tion via the Combination of Sparse Representation anda Variational Approach[J].IEEE Transactions onImage Processing,2005,14(10):1570-1582.
[21]Sardy S,Bruce A,Tseng P.Block Coordinate Relaxa-tion Methods for Nonparametric Wavelet Denoising[J].Journal of Computational and Graphical Statis-tics,2000,9(2):361-379.
[22]Starck J L,Elad M,Donoho D L.Redundant Multi-scale Transform and Their Application for Morpho-logical Component Analysis[J].Advance in Imagingand Electron Physics,2004,132:288-348.
[23]Elad M,Starck J L,Querreb P,et al.SimultaneousCartoon and Texture Image Inpainting Using Mor-phological Component Analysis(MCA)[J].Appliedand Computational Harmonic Analysis,2005,19:340-358.
[24]Starck J L,Fadili M J,Murtagh F.The UndecimatedWavelet Decomposition and Its Reconstruction[J].IEEE Transactions on Image Processing,2007,16(2):297-309.
[25]Candes E J,Donoho D L.Recovering Edges in Ill-Posed Inverse Problems:Optimality of CurveletFrames[J].Ann Statist,2002,30:784-842.
[26]Candes E J,Demanet L,Donoho D L,et al.FastDiscrete Curvelet Transforms[J].Multiscale Mode-ling and Simulation,2006,5(3):861-899.
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