地震数据去噪中的小波方法
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摘要
地震资料去噪是地震数据处理中是必不可少的步骤,随着地震勘探的进步和勘探目的层加深,对地震资料的信噪比和分辨率提出了越来越高的要求.小波分析作为一个新兴的数学方法在地震资料去噪中也有巨大的潜力.本文从小波去噪的特点出发,介绍了小波分频和小波域阈值去噪的特点,并详细总结了地震资料去噪中的小波方法,主要有面波的压制和随机噪声的衰减.最后简要叙述了地震资料小波去噪的一些问题和发展.
Noise attenuation is an essential step for seismic data processing.With the seismic exploration progress and the increase of objective stratum depth,it is forward demanded to enhance the seismic data S/N rate and resolution.As a new mathematical method,wavelet transform have more advantage in seismic noise elimination.In this paper,we firstly introduce the characteristics of wavelet transform used for noise elimination,and then detailedly summarize the wavelet method in seismic noise elimination,mainly included surfer wave suppression and random noise attenuation;lastly,we talk briefly about the problem and development trend of wavelet de-noising in seismic data.
Noise attenuation is an essential step for seismic data processing.With the seismic exploration progress and the increase of objective stratum depth,it is forward demanded to enhance the seismic data S/N rate and resolution.As a new mathematical method,wavelet transform have more advantage in seismic noise elimination.In this paper,we firstly introduce the characteristics of wavelet transform used for noise elimination,and then detailedly summarize the wavelet method in seismic noise elimination,mainly included surfer wave suppression and random noise attenuation;lastly,we talk briefly about the problem and development trend of wavelet de-noising in seismic data.
引文
[1]张华军,吕宁,田连玉,等.地震资料去噪方法、技术综合评述[J].地球物理学进展,2005,20(4):1083～1091.
[2]陆文凯,丁文龙,张善文,等.基于信号子空间分解的三维地震资料高分辨率处理方法[J].地球物理学报,2005,48(4):896～901
[3]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
[4]Mallat S,Zhong S.Characterization of signals from multiscale edges[J].IEEE Trans.PAMI,1992,14:710～732.
[5]Xu Y,Weaver J B,Healy D M,Ln J.Wavelet transformdo-main filters:A spatially selective noise filtration technique[J],IEEE Trans.Image Processing,1994,3:747～758.
[6]Donoho D L,Johnstone I M.Ideal time-frequency denoising.Technical Report[R].Dept.of Statistics,Standford Universi-ty,1994.
[7]Donoho D L,Johnstone L M.Ideal spatial adaptation via wavelet shrinkage[J].Biometrika,1994,81:425～455.
[8]Donoho D L.De-noising by soft-thresholding[J].IEEE Trans.Information Theory,1995,41:613～627.
[9]张磊,潘泉,张洪才,等.小波域滤波阈值参数c的选取[J].电子学报,2001,29(3):400～402.
[10]Zhang L,Bao P,Pan Q.Threshold analysisin wavelet-based de-noising[J].IEE Electronics Letters.2001,37(24):1485～1486.
[11]Donoho D L,Johnstone L M.Adapting to unknown wavelet shrinkage[J].J.Arner:Statist,1995,90:1200～1224.
[12]Nason G P.Wavelet shrinkage using cross-validation[J].Journal of the Royal Statistical Society Series B,1996,58:463～479.
[13]Jansen M,et al.Generalized cross-validation for wavelet thresholding[J].Signal processing,1997,56(1):33～44.
[14]Jansen M,Bultheel A.Multiple wavelet threshold estimation by generalized cross validation for data with correlated noise[J].IEEE Trans.Image Processing,1999,8(7):947～953.
[15]Moulin P,Liu Juan.Analysis of multiresolution image de-noising schemes using generalized-Gaussian and complexity priors[J].IEEE Trans.Inform,Theory,1999,45(3):909～919.
[16]Bruce A G,Gao Hong Ye.Understanding Waveshrink:Va-riance and bias estimation[J].Biometrika,1996,83(4):727～745.
[17]Gao Hong Ye,Bruce A G.Waveshrink and semi soft shrink-age[J].StaSci Research Report No.39,1995
[18]Bruce A G,Gao Hong Ye.Waveshrink with firmshrinkage[J].Statistica Sinica,1997,7(4):855～874.
[19]谢杰成,张大力,徐文立.小波图像去噪综述[J].中国图像图形学报,2002,77(3):209～217.
[20]夏洪瑞,朱勇,周开明.小波变换及其在去噪中的应用[J].石油地球物理勘探,1994,29(3):274～285.
[21]罗国安,杜世通.小波变换及信号重建在压制面波中的应用[J].石油地球物理勘探,1996,31(3):337～350.
[22]刘法启,张关泉.小波变换与f-k算法在滤波中的应用[J].石油地球物理勘探,1996,31(6):782～792.
[23]AndrewJ.Deighan and Doyle R.Watts.Ground-roll suppres-sion using wavelet transforms.Geophysics,1997,62(6):1896～1903.
[24]李卫忠,张明振,王成礼,等.压制面波的波场分离方法[J].石油地球物理勘探,1998,33(5):679～691.
[25]Miao X,Cheadle S P.Noise attenuation with wavelet trans-forms.68th Ann.Internat.Mtg.,Soc.Expl.Geophysics,Ex-panded Abstracts,1998,1072～1075.
[26]Nguyen M Q,Mars J.Filtering surface waves using2-Ddis-crete wavelet transform.69th,Ann.Internat.mtg[J].Soc.Expl.Geophys,Expanded Abstracts,1999,1228～1230.
[27]刘财,王典,杨宝俊,等.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.
[28]张华,潘冬明,红兴岩.二维小波变换在去除面波干扰中的应用[J].石油物探,2007,46(2):147～150.
[29]王振国,周熙襄,钟本善.小波包对叠前地震面波的分离与信号重建[J].石油地球物理勘探,2002,37(5):460～462,472
[30]詹毅,周熙襄.小波包分析与奇异值分解(SVD)叠前去噪方法[J].石油地球物理勘探.2004,39(4):394～397.
[31]章珂,刘贵忠,邹大文,等.二进小波变换方法的地震信号分时分频去噪处理[J].地球物理学报,1996,39(2):225～271.
[32]宗涛,孟鸿鹰,贾玉兰,刘贵忠.小波包域前后向预测去噪[J].地球物理学报,1998,41(增刊):337～346.
[33]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.
[34]王振国,周熙襄,李晶.基于小波变换的最小光滑滤波去噪[J].石油地球物理勘探,2002,37(6):594～600.
[35]彭才,朱仕军,孙建库,等.小波变换域K-L变换及其去噪效果分析[J].石油物探,2007,46(2):112～114.
[36]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.
[37]张宇,张关泉.小波变换用于去除高频随机噪声[J].石油地球物理勘探,1997,32(3):327～337.
[38]付燕,赵荣椿,王刚.小波变换在地震信号噪声处理中的应用[J].西北工业大学学报,2004,22(6),774～777.
[39]付燕.基于二次小波变换的地震信号去噪方法[J].石油地球物理勘探,2005,40(2):154～157.
[40]王振国,汪恩华.小波包相关阀值去噪[J].石油物探,2002,41(4):400～405.
[41]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.
[42]Daniel O T,Jandyr MT.Wavelet filtering of magnetotelluric data[J].Geophysics,2000,65(2):482～491.
[43]Welford J K,Zhang R F.Ground-roll suppression fromdeep crustal seismic reflection data using a wavelet-based ap-proach:Acase study from western Canada[J].Geophysics,2004,69(4):877～884.
[44]Zhang R,Trad D.Noise attenuation:a hybrid approach based on wavelet transform:Presented at Annual Meeting,Canadian Society of Exploration Geophysics,2002.
[45]吴爱第,牟永光.地震信号的小波包分解压噪方法[J].石油地球物理勘探,1998,33(4):588～562.
[46]Zhang R F,Tadeusz J U.Physical wavelet frame denoising[J].Geophysics,2003,68(1):225～231.
[47]S.P.Kozaitis,A.A.Basuhail Adaptive wavelet threshold se-lection using higher-order statistics for signal denoising[J].SPIE,1998,3391:68～74.
[48]Kozaitis S P,Ingun A.Speckle denoising using wavelet trans-forms and higher-order statistics[J].SPIE,2004,5438:222～228.
[49]Wu Z C,Liu T Y,Hua C H.Wavelet Threshold De-noising Based on Higher-Order Statistics in Attenuating Random Noise[A].in76th SEG Technical Program Expanded Ab-stracts[C].2006,2857～2861.
[50]张三宗,徐义贤.地震记录小波域高阶相关叠加技术[J].地球物理学报,2006,49(2):554～560.
[51]Liu J,Moulin P.Image denoising based on scale-space mix-ture modeling of wavelet coefficients.In Proceedings of IEEE international conference on image processing[J].Kobe Ja-pan,1999,286～390.
[2]陆文凯,丁文龙,张善文,等.基于信号子空间分解的三维地震资料高分辨率处理方法[J].地球物理学报,2005,48(4):896～901
[3]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
[4]Mallat S,Zhong S.Characterization of signals from multiscale edges[J].IEEE Trans.PAMI,1992,14:710～732.
[5]Xu Y,Weaver J B,Healy D M,Ln J.Wavelet transformdo-main filters:A spatially selective noise filtration technique[J],IEEE Trans.Image Processing,1994,3:747～758.
[6]Donoho D L,Johnstone I M.Ideal time-frequency denoising.Technical Report[R].Dept.of Statistics,Standford Universi-ty,1994.
[7]Donoho D L,Johnstone L M.Ideal spatial adaptation via wavelet shrinkage[J].Biometrika,1994,81:425～455.
[8]Donoho D L.De-noising by soft-thresholding[J].IEEE Trans.Information Theory,1995,41:613～627.
[9]张磊,潘泉,张洪才,等.小波域滤波阈值参数c的选取[J].电子学报,2001,29(3):400～402.
[10]Zhang L,Bao P,Pan Q.Threshold analysisin wavelet-based de-noising[J].IEE Electronics Letters.2001,37(24):1485～1486.
[11]Donoho D L,Johnstone L M.Adapting to unknown wavelet shrinkage[J].J.Arner:Statist,1995,90:1200～1224.
[12]Nason G P.Wavelet shrinkage using cross-validation[J].Journal of the Royal Statistical Society Series B,1996,58:463～479.
[13]Jansen M,et al.Generalized cross-validation for wavelet thresholding[J].Signal processing,1997,56(1):33～44.
[14]Jansen M,Bultheel A.Multiple wavelet threshold estimation by generalized cross validation for data with correlated noise[J].IEEE Trans.Image Processing,1999,8(7):947～953.
[15]Moulin P,Liu Juan.Analysis of multiresolution image de-noising schemes using generalized-Gaussian and complexity priors[J].IEEE Trans.Inform,Theory,1999,45(3):909～919.
[16]Bruce A G,Gao Hong Ye.Understanding Waveshrink:Va-riance and bias estimation[J].Biometrika,1996,83(4):727～745.
[17]Gao Hong Ye,Bruce A G.Waveshrink and semi soft shrink-age[J].StaSci Research Report No.39,1995
[18]Bruce A G,Gao Hong Ye.Waveshrink with firmshrinkage[J].Statistica Sinica,1997,7(4):855～874.
[19]谢杰成,张大力,徐文立.小波图像去噪综述[J].中国图像图形学报,2002,77(3):209～217.
[20]夏洪瑞,朱勇,周开明.小波变换及其在去噪中的应用[J].石油地球物理勘探,1994,29(3):274～285.
[21]罗国安,杜世通.小波变换及信号重建在压制面波中的应用[J].石油地球物理勘探,1996,31(3):337～350.
[22]刘法启,张关泉.小波变换与f-k算法在滤波中的应用[J].石油地球物理勘探,1996,31(6):782～792.
[23]AndrewJ.Deighan and Doyle R.Watts.Ground-roll suppres-sion using wavelet transforms.Geophysics,1997,62(6):1896～1903.
[24]李卫忠,张明振,王成礼,等.压制面波的波场分离方法[J].石油地球物理勘探,1998,33(5):679～691.
[25]Miao X,Cheadle S P.Noise attenuation with wavelet trans-forms.68th Ann.Internat.Mtg.,Soc.Expl.Geophysics,Ex-panded Abstracts,1998,1072～1075.
[26]Nguyen M Q,Mars J.Filtering surface waves using2-Ddis-crete wavelet transform.69th,Ann.Internat.mtg[J].Soc.Expl.Geophys,Expanded Abstracts,1999,1228～1230.
[27]刘财,王典,杨宝俊,等.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.
[28]张华,潘冬明,红兴岩.二维小波变换在去除面波干扰中的应用[J].石油物探,2007,46(2):147～150.
[29]王振国,周熙襄,钟本善.小波包对叠前地震面波的分离与信号重建[J].石油地球物理勘探,2002,37(5):460～462,472
[30]詹毅,周熙襄.小波包分析与奇异值分解(SVD)叠前去噪方法[J].石油地球物理勘探.2004,39(4):394～397.
[31]章珂,刘贵忠,邹大文,等.二进小波变换方法的地震信号分时分频去噪处理[J].地球物理学报,1996,39(2):225～271.
[32]宗涛,孟鸿鹰,贾玉兰,刘贵忠.小波包域前后向预测去噪[J].地球物理学报,1998,41(增刊):337～346.
[33]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.
[34]王振国,周熙襄,李晶.基于小波变换的最小光滑滤波去噪[J].石油地球物理勘探,2002,37(6):594～600.
[35]彭才,朱仕军,孙建库,等.小波变换域K-L变换及其去噪效果分析[J].石油物探,2007,46(2):112～114.
[36]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.
[37]张宇,张关泉.小波变换用于去除高频随机噪声[J].石油地球物理勘探,1997,32(3):327～337.
[38]付燕,赵荣椿,王刚.小波变换在地震信号噪声处理中的应用[J].西北工业大学学报,2004,22(6),774～777.
[39]付燕.基于二次小波变换的地震信号去噪方法[J].石油地球物理勘探,2005,40(2):154～157.
[40]王振国,汪恩华.小波包相关阀值去噪[J].石油物探,2002,41(4):400～405.
[41]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.
[42]Daniel O T,Jandyr MT.Wavelet filtering of magnetotelluric data[J].Geophysics,2000,65(2):482～491.
[43]Welford J K,Zhang R F.Ground-roll suppression fromdeep crustal seismic reflection data using a wavelet-based ap-proach:Acase study from western Canada[J].Geophysics,2004,69(4):877～884.
[44]Zhang R,Trad D.Noise attenuation:a hybrid approach based on wavelet transform:Presented at Annual Meeting,Canadian Society of Exploration Geophysics,2002.
[45]吴爱第,牟永光.地震信号的小波包分解压噪方法[J].石油地球物理勘探,1998,33(4):588～562.
[46]Zhang R F,Tadeusz J U.Physical wavelet frame denoising[J].Geophysics,2003,68(1):225～231.
[47]S.P.Kozaitis,A.A.Basuhail Adaptive wavelet threshold se-lection using higher-order statistics for signal denoising[J].SPIE,1998,3391:68～74.
[48]Kozaitis S P,Ingun A.Speckle denoising using wavelet trans-forms and higher-order statistics[J].SPIE,2004,5438:222～228.
[49]Wu Z C,Liu T Y,Hua C H.Wavelet Threshold De-noising Based on Higher-Order Statistics in Attenuating Random Noise[A].in76th SEG Technical Program Expanded Ab-stracts[C].2006,2857～2861.
[50]张三宗,徐义贤.地震记录小波域高阶相关叠加技术[J].地球物理学报,2006,49(2):554～560.
[51]Liu J,Moulin P.Image denoising based on scale-space mix-ture modeling of wavelet coefficients.In Proceedings of IEEE international conference on image processing[J].Kobe Ja-pan,1999,286～390.
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