基于提升算法和百分位数软阈值的小波去噪技术
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摘要
在地震勘探领域,随机噪声一直是影响地震信号信噪比的主要因素之一,如何从被干扰的地震信号中有效去除随机噪声并保护有用信号具有重要的意义.针对经典小波变换在计算效率方面的缺陷,本文推荐应用提升算法实现第二代小波变换的构建,分析和对比了提升算法(Lifting Scheme)下不同小波变换方法的特性,选取更加符合小波域去噪原理的CDF 9/7双正交小波变换作为基本算法,同时应用了简单、有效的百分位数(Percentiles)软阈值进行信噪分离.通过理论模型处理,本方法可以在去噪能力和保护有用信号之间找到很好的平衡点.实际剖面的处理效果表明,此方法不仅能有效的滤除随机噪声,而且很好地保护有用信号,提高地震数据分析的精确性.
In seismic prospecting,random noise is always one of the foremost factors that affect SNR of seismic signal,so how to eliminatie random noise and protect useful information is very important.Aiming at the shortage of classical wavelet transforms that have lower computational efficiency,the paper recommends a second generation wavelet transform based on lifting scheme.By analyzing and comparing the characteristics of different wavelet transform so with the lifting scheme method,we choose the CDF 9/7 biorthogonal wavelet transform to be the basic algorithm because this method fits the denoising theory in wavelet domain better.At the same time,we apply a simple and effective percentiles soft-threshold to separate the signal from random noise.By processing the model,we find that the recommended method strikes a balance between eliminating random noise and protecting useful information.Processing field data shows that the method can perfectly filter random noise,protect useful information and improve the accuracy of seismic data analysis.
In seismic prospecting,random noise is always one of the foremost factors that affect SNR of seismic signal,so how to eliminatie random noise and protect useful information is very important.Aiming at the shortage of classical wavelet transforms that have lower computational efficiency,the paper recommends a second generation wavelet transform based on lifting scheme.By analyzing and comparing the characteristics of different wavelet transform so with the lifting scheme method,we choose the CDF 9/7 biorthogonal wavelet transform to be the basic algorithm because this method fits the denoising theory in wavelet domain better.At the same time,we apply a simple and effective percentiles soft-threshold to separate the signal from random noise.By processing the model,we find that the recommended method strikes a balance between eliminating random noise and protecting useful information.Processing field data shows that the method can perfectly filter random noise,protect useful information and improve the accuracy of seismic data analysis.
引文
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[2]Ristau J P,Moon W M.Adaptive filtering of random noise in 2-D geophysical data[J].Geophysics,2001,66:342~349.
[3]Liu C,Liu Y,Yang B,Wang D,Sun J.A 2D multistage medianfilter to reduce random seismic noise[J].Geophysics,2006,71:V105~V110.
[4]赵德斌,黄真萍,王春梅.F-X域奇异值分解预测滤波法随机噪声衰减[J].石油物探,1998,37(3):29~33.Zhao D B,Huang Z P,Wang C M.Random noise attenuation u-sing predictive filtering inF-Xdomain by singular value de-composition[J].Geophysical prospecting for petroleum,1998,37(3):29~33.
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[12]裴正林.小波理论及其在地震数据处理中的应用[J].地球物理学进展,2002,17(3):486~490.Pei Z L.Wavelet Theory and Its Application in Seismic DataProcessing[J].Progress in Geophysics,2002,17(3):486~490.
[13]郭刚明,时立彩,高生军,等.小波变换在地震资料处理中的应用效果分析[J].石油物探,2003,42(2):237~239.Guo G M,Shi L C,Gao S J,et al.Application of wavelet tr-arnsform in seismic data processing[J].Geophysical Prospec-ting for petroleum,2003,42(2):237~239.
[14]徐亚,郝天珧.提升小波:可用于重磁资料处理的新方法[J].地球物理学进展,2004,19(1):36~39.Xu Y,Hao T Y.Lifting scheme:a promising method in gravi-ty and magnetic data processing[J].Progress in Geophysics,2004,19(1):36~39.
[15]徐亚,郝天珧,周立宏等.位场小波变换研究进展[J].地球物理学进展,2006,21(4):1132~1138.Xu Y,Hao T Y,Zhou L H,et al.Review of wavelet transformin potential field[J].Progress in Geophysics,2006,21(4):1132~1138.
[16]李琪,林云芳,曾小苹.应用小波变换提取张北地震的震磁效应[J].地球物理学报,2006,49(3):855~863.Li Q,Liu Y F,Zeng X P.Wavelet analysis as a tool for revea-ling geomagnetic precursors of the Zhangbei earthquake[J].Chinese J.Geophys.,2006,49(3):855~863.
[17]马利华,韩延本,廖德春.小波变换应用于日长变化的研究进展[J].地球物理学进展,2007,22(4):1075~1079.Ma L H,Han Y B,Liao D C.Study progress of wavelet trans-form applying in length-of-day change[J].Progress in Geo-physics,2007,22(4):1075~1079.
[18]高静怀,毛剑,满蔚仕等.叠前地震资料噪声衰减的小波域方法研究[J].地球物理学报,2006,49(4):1155~1163.Gao J H,Mao J,Man W S,et al.On the denoising method ofprestack seismic data in wavelet domain[J].Chinese J.Geo-phys.,2006,49(4):1155~1163.
[19]柳建新,韩世礼,马捷.小波分析在地震资料去噪中的应用[J].地球物理学进展,2006,21(2):541~545.Liu J X,Han S L,Ma J.Application of wavelet analysis inseismic data denoising[J].Progress in Geophysics,2006,21(2):541~545.
[20]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 Z C,Liu T Y.Wavelet transform methods in seismic noiseattenuation[J].Progress in Geophysics,2008,23(2):493~499.
[21]张波,印兴耀,吴国忱,等.用小波分析和反演方法联合去除随机噪声的研究[J].石油地球物理勘探,1999,34(6):635~641.Zhang B,Yin X Y,Wu G C,et al.Random noise eliminationusing wavelet analysis and inversion[J].Oil geophysical pros-pecting,1999,34(6):635~641.
[22]吴爱弟,曹思远.用正交多小波压制地震信号的随机噪声[J].石油地球物理勘探,2002,37(5):473~476.Wu A D,Cao S Y.Random noise suppression of seismic signalusing orthogonal multi-wavelets[J].Oil Geophysical Prospec-ting,2002,37(5):473~476.
[23]杨立强,宋海斌,郝天珧,等.基于二维小波变换的随机噪声压制方法研究[J].石油物探,2005,44(1):4~6.Yang L Q,Song H B,Hao T Y,et al.Method of 2-D wavelettransform in attenuating random noise[J].Geophysical Pros-pecting For Petrole,2005,44(1):4~6.
[24]陈香朋,曹思远.第二代小波变换及其在地震信号去噪中的应用[J].石油物探,2004,43(6):547~550.Chen X P,Cao S Y.Second-generation wavelet transform andits application in the de-noising of seismic data[J].Geophysi-cal Prospecting For Petrole,2004,43(6):547~550.
[25]Sweldens W.The lifting scheme:A new philosophy inbiorthogonal wavelet constructions[M].Wavelet Applicationsin Signal and Image Processing III,Proc.SPIE 2569,1995:68~79.
[26]Sweldens W,Schroder P.Building your own wavelets athome,in Wavelets in Computer Graphics[M].ACM SIG-GRAPH Course notes,1996:15~87.
[27]Cohen A,Daubechies I,Feauveau J.Bi-orthogonal bases ofcompactly supported wavelets[J].Comm.Pure Appl.Math.,1992,45:485~560.
[28]Claerbout J F.Basic Earth imaging:Stanford Exploration Pro-ject[OL],2006,http://sepwww.stanford.edu/sep/prof/.
[2]Ristau J P,Moon W M.Adaptive filtering of random noise in 2-D geophysical data[J].Geophysics,2001,66:342~349.
[3]Liu C,Liu Y,Yang B,Wang D,Sun J.A 2D multistage medianfilter to reduce random seismic noise[J].Geophysics,2006,71:V105~V110.
[4]赵德斌,黄真萍,王春梅.F-X域奇异值分解预测滤波法随机噪声衰减[J].石油物探,1998,37(3):29~33.Zhao D B,Huang Z P,Wang C M.Random noise attenuation u-sing predictive filtering inF-Xdomain by singular value de-composition[J].Geophysical prospecting for petroleum,1998,37(3):29~33.
[5]Mallat S.A wavelet tour of signal processing[M].AcademicPress,1999.
[6]Foster D J,Mosher C C,Hassanzadeh S.Wavelet transformmethods for geophysical applications[J].64th SEG ExpandAbstract,1994:1465~1468.
[7]Dessing F J.A wavelet transform approach to seismic process-ing[D].PhD thesis,Delft University of Technology,1997.
[8]刘财,王典,杨宝俊,刘洋.二维小波变换在地震勘探面波消除中的应用[J].地球物理学进展,2003,18(4):711~714.Liu C,Wang D,Yang B J,Liu Y.Apply of 2D wavelet trans-forms in surface wave eliminations of seismic exploration[J].Progress in Geophysics,2003,18(4):711~714.
[9]Wapenaar K,Ghose R,Toxopeus G,Fokkema J.The wavelettransform as a tool for geophysical data integration[J].Inte-grated Computer-Aided Engineering,2005,12:5~23.
[10]刘财,张海江,杨宝俊.小波变换及其在薄储层识别中的应用[J].石油物探,1995,34(3):23~31.Liu C,Zhang H J,Yang B J.Wavelet transform and its appli-cation in the recognition of thin-reservoir[J].GeophysicalProspecting for Petroleum,1995,34(3):23~31.
[11]刘财,张海江,杨宝俊,等.小波变换在高分辨率地震勘探数据处理中的应用[J].长春地质学院学报,1996,26(1):78~82.Liu C,Zhang H J,Yang B J,et al.Application of wavelettransform to digital processing in high resolution seismicprospecting[J].Journal of Changchun University of EarthSciences,1996,26(1):78~82.
[12]裴正林.小波理论及其在地震数据处理中的应用[J].地球物理学进展,2002,17(3):486~490.Pei Z L.Wavelet Theory and Its Application in Seismic DataProcessing[J].Progress in Geophysics,2002,17(3):486~490.
[13]郭刚明,时立彩,高生军,等.小波变换在地震资料处理中的应用效果分析[J].石油物探,2003,42(2):237~239.Guo G M,Shi L C,Gao S J,et al.Application of wavelet tr-arnsform in seismic data processing[J].Geophysical Prospec-ting for petroleum,2003,42(2):237~239.
[14]徐亚,郝天珧.提升小波:可用于重磁资料处理的新方法[J].地球物理学进展,2004,19(1):36~39.Xu Y,Hao T Y.Lifting scheme:a promising method in gravi-ty and magnetic data processing[J].Progress in Geophysics,2004,19(1):36~39.
[15]徐亚,郝天珧,周立宏等.位场小波变换研究进展[J].地球物理学进展,2006,21(4):1132~1138.Xu Y,Hao T Y,Zhou L H,et al.Review of wavelet transformin potential field[J].Progress in Geophysics,2006,21(4):1132~1138.
[16]李琪,林云芳,曾小苹.应用小波变换提取张北地震的震磁效应[J].地球物理学报,2006,49(3):855~863.Li Q,Liu Y F,Zeng X P.Wavelet analysis as a tool for revea-ling geomagnetic precursors of the Zhangbei earthquake[J].Chinese J.Geophys.,2006,49(3):855~863.
[17]马利华,韩延本,廖德春.小波变换应用于日长变化的研究进展[J].地球物理学进展,2007,22(4):1075~1079.Ma L H,Han Y B,Liao D C.Study progress of wavelet trans-form applying in length-of-day change[J].Progress in Geo-physics,2007,22(4):1075~1079.
[18]高静怀,毛剑,满蔚仕等.叠前地震资料噪声衰减的小波域方法研究[J].地球物理学报,2006,49(4):1155~1163.Gao J H,Mao J,Man W S,et al.On the denoising method ofprestack seismic data in wavelet domain[J].Chinese J.Geo-phys.,2006,49(4):1155~1163.
[19]柳建新,韩世礼,马捷.小波分析在地震资料去噪中的应用[J].地球物理学进展,2006,21(2):541~545.Liu J X,Han S L,Ma J.Application of wavelet analysis inseismic data denoising[J].Progress in Geophysics,2006,21(2):541~545.
[20]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 Z C,Liu T Y.Wavelet transform methods in seismic noiseattenuation[J].Progress in Geophysics,2008,23(2):493~499.
[21]张波,印兴耀,吴国忱,等.用小波分析和反演方法联合去除随机噪声的研究[J].石油地球物理勘探,1999,34(6):635~641.Zhang B,Yin X Y,Wu G C,et al.Random noise eliminationusing wavelet analysis and inversion[J].Oil geophysical pros-pecting,1999,34(6):635~641.
[22]吴爱弟,曹思远.用正交多小波压制地震信号的随机噪声[J].石油地球物理勘探,2002,37(5):473~476.Wu A D,Cao S Y.Random noise suppression of seismic signalusing orthogonal multi-wavelets[J].Oil Geophysical Prospec-ting,2002,37(5):473~476.
[23]杨立强,宋海斌,郝天珧,等.基于二维小波变换的随机噪声压制方法研究[J].石油物探,2005,44(1):4~6.Yang L Q,Song H B,Hao T Y,et al.Method of 2-D wavelettransform in attenuating random noise[J].Geophysical Pros-pecting For Petrole,2005,44(1):4~6.
[24]陈香朋,曹思远.第二代小波变换及其在地震信号去噪中的应用[J].石油物探,2004,43(6):547~550.Chen X P,Cao S Y.Second-generation wavelet transform andits application in the de-noising of seismic data[J].Geophysi-cal Prospecting For Petrole,2004,43(6):547~550.
[25]Sweldens W.The lifting scheme:A new philosophy inbiorthogonal wavelet constructions[M].Wavelet Applicationsin Signal and Image Processing III,Proc.SPIE 2569,1995:68~79.
[26]Sweldens W,Schroder P.Building your own wavelets athome,in Wavelets in Computer Graphics[M].ACM SIG-GRAPH Course notes,1996:15~87.
[27]Cohen A,Daubechies I,Feauveau J.Bi-orthogonal bases ofcompactly supported wavelets[J].Comm.Pure Appl.Math.,1992,45:485~560.
[28]Claerbout J F.Basic Earth imaging:Stanford Exploration Pro-ject[OL],2006,http://sepwww.stanford.edu/sep/prof/.
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