高阶seislet变换及其在随机噪声消除中的应用
|
摘要
Seislet变换是一种小波类数学变换方法,主要根据不同小波级数上地震同相轴的局部倾角的不同来分析数据.一般意义上,测线方向上的离散小波变换(DWT)是一种特殊的零局部地震倾角的seislet变换.早期的工作基于低阶版本的离散小波变换来构建seislet变换,在本文中,通过使用Cohen-Daubechies-Feauveau(CDF)9/7双正交小波变换(常用于JPEG2000压缩标准)作为框架,扩展高阶seislet变换方法.通过分析理论模型和实际数据的处理结果,并对比傅里叶变换、离散小波变换和低阶seislet变换,高阶seislet变换可以为地震数据提供更好的压缩比.因此更加适用于地震数据去噪处理.
The seislet transform is a wavelet-like transform that analyzes seismic data by following variable slopes of seismic events across different scales.It generalizes the discrete wavelet transform(DWT)in the sense that DWT in the lateral direction is simply the seislet transform with zero slopes.An earlier work used low-order versions of DWT to construct the seislet transform.In this work,we extend this approach to a higher order,using the Cohen-Daubechies -Feauveau 9/7 biorthogonal wavelet transform(the basis for the JPEG2000 compression scheme)as a template.Using synthetic and field-data examples,we demonstrate that the new transform can provide a better compression rate for seismic events than the Fourier transform,DWT,or the low-order seislet transform.Therefore,the high-order seislet transform can be more suitable for data processing tasks such as data regularization and noise attenuation.
The seislet transform is a wavelet-like transform that analyzes seismic data by following variable slopes of seismic events across different scales.It generalizes the discrete wavelet transform(DWT)in the sense that DWT in the lateral direction is simply the seislet transform with zero slopes.An earlier work used low-order versions of DWT to construct the seislet transform.In this work,we extend this approach to a higher order,using the Cohen-Daubechies -Feauveau 9/7 biorthogonal wavelet transform(the basis for the JPEG2000 compression scheme)as a template.Using synthetic and field-data examples,we demonstrate that the new transform can provide a better compression rate for seismic events than the Fourier transform,DWT,or the low-order seislet transform.Therefore,the high-order seislet transform can be more suitable for data processing tasks such as data regularization and noise attenuation.
引文
[1] 王振国.陈小宏,王学军等.沙漠地区老地震资料的处理技术及效果分析.勘探地球物理进展,2007,30(2) :123～129Wang Z G,Cheng X H,Wang X J,et al.Processing of old seismic data from desert and its effect analysis.Progress in Exploration Geophysics(in Chinese),2007,30(2) :123～129
[2] 金龙,陈小宏,刘其成.基于奇异值分解的时移地震互均衡方法.勘探地球物理进展,2005,20(2) :294～297Jin L,Cheng X H,Liu Q C.New method for time-lapse seismic matching based on SVD.Progress in Exploration Geophysics(in Chinese),2005,20(2) :294～297
[3] 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.石油物探,1998,37(3) :29～33Zhao D B,Huang Z P,Wang C M.Random noise attenuation using predictive filtering in F-X domain by singular value decomposition.Geophysical Prospecting for Petroleum(in Chinese),1998,37(3) :29～33
[4] Gulunay N.Noncausal spatial prediction filtering for random noise reduction on 3-D poststack data.Geophysics,2000,65:1641～1653
[5] Ristau J P,Moon W M.Adaptive filtering of random noise in 2-D geophysical data.Geophysics,2001,66:342～349
[6] Liu C,Liu Y,Yang B,et al.A 2D multistage median filter to reduce random seismic noise.Geophysics,2006,71:105～110
[7] 邢贞贞,韩立国,王宇等.高阶统计量方法在地震信号分析中的应用.吉林大学学报(地球科学版),2007,37(增):139～142Xing Z Z,Han L G,Wang Y,et al.Application of high-order statistics in seismic signal analysis.Journal of Jilin University(Earth Science Edition)(in Chinese),2007,37(Suppl.):139～142
[8] 王兆磊,周辉.在反演过程中利用不同范数准则压制噪声对反演结果的影响.地球物理学进展,2007,22(3) :919～923Wang Z L,Zhou H.Using different kinds of norms to suppress the effect of noise in the course of inversion.Progress in Geophysics(in Chinese),2007,22(3) :919～923
[9] Mallat S.A Wavelet Tour of Signal Processing.Academic Press,1999
[10] Foster D J,Mosher C C,Hassanzadeh S.Wavelet Transform Methods for Geophysical Applications.SEG Extended Abstract,1994:1465～1468
[11] Dessing F J.A wavelet transform approach to seismic processing[Ph.D.thesis].Delft:Delft University of Technology,1997
[12] 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.地球物理学进展,2003,18(4) :711～714Liu C,Wang D,Yang B J,et al.Apply of 2D wavelet transforms in surface wave eliminations of seismic exploration.Progress in Geophysics(in Chinese),2003,18(4) :711～714
[13] Wapenaar K,Ghose R,Toxopeus G,et al.The wavelet transform as a tool for geophysical data integration.Integrated Computer-Aided Engineering,2005,12:5～23
[14] 刘财,张海江,杨宝俊.小波变换及其在薄储层识别中的应用.石油物探,1995,34(3) :23～31Liu C,Zhang H J,Yang B J.Wavelet transform and its application in the recognition of thin-reservoir.Geophysical Prospecting for Petroleum(in Chinese),1995,34(3) :23～31
[15] 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.长春地质学院学报,1996,26(1) :78～82Liu C.Zhang H J,Yang B J,et al.Application of wavelet transform to digital processing in high resolution seismic prospecting.Journal of Changchun University of Earth Sciences(in Chinese),1996,26(1) :78～82
[16] 裴正林.小波理论及其在地震数据处理中的应用.地球物理学进展,2002,17(3) :486～490Pei Z L.Wavelet theory and its application in seismic data processing.Progress in Geophysics(in Chinese),2002,17(3) :486～490
[17] 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.石油物探,2003,42(2) :237～239Guo G M,Shi L C,Gao S J,et al.Application of wavelet transform in seismic data processing.Geophysical Prospecting for Petroleum(in Chinese),2003,42(2) :237～239
[18] 徐亚,郝天珧.提升小波:可用于重磁资料处理的新方法.地球物理学进展,2004,19(1) :36～39Xu Y,Hao T Y.Lifting scheme:a promising method in gravity and magnetic data processing.Progress in Geophysics(in Chinese),2004,19(1) :36～39
[19] 徐亚,郝天珧,周立宏等.位场小波变换研究进展.地球物理学进展,2006,21(4) :1132～1138Xu Y,Hao T Y,Zhou L H,et al.Review of wavelet transform in potential field.Progress in Geophysics(in Chinese),2006,21(4) :1132～1138
[20] 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.地球物理学报,2006,49(3) :855～863Li Q,Lin Y F,Zeng X P.Wavelet analysis as a tool for revealing geomagnetic precursors of the Zhangbei earthquake.Chinese J.Geophys.(in Chinese),2006,49(3) :855～863
[21] 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.地球物理学进展,2007,22(4) :1075～1079Ma L H,Han Y B,Liao D C.Study progress of wavelet transform applying in length-of-day change.Progress in Geophysics(in Chinese),2007,22(4) :1075～1079
[22] 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.地球物理学报,2006,49(4) :1155～1163Gao J H,Mao J,Man W S,et al.On the denoising method of prestack seismic data in wavelet domain.Chinese J.Geophys.(in Chinese),2006,49(4) :1155～1163
[23] 柳建新,韩世礼,马捷.小波分析在地震资料去噪中的应用.地球物理学进展,2006,21(2) :541～545Liu J X,Han S L,Ma J.Application of wavelet analysis in seismic data denoising.Progress in Geophysics(in Chinese),2006,21(2) :541～545
[24] 吴招才,刘天佑.地震数据去噪中的小波方法.地球物理学进展,2008,23(2) :493～499Wu Z C,Liu T Y.Wavelet transform methods in seismic noise attenuation.Progress in Geophysics(in Chinese),2008,23(2) :493～499
[25] 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.石油地球物理勘探,1999,34(6) :635～641Zhang B,Yin X Y,Wu G C,et al.Random noise elimination using wavelet analysis and inversion.Oil Geophysical Prospecting(in Chinese),1999,34(6) :635～641
[26] 吴爱弟,曹思远.用正交多小波压制地震信号的随机噪声.石油地球物理勘探,2002,37(5) :473～476Wu A D,Cao S Y.Random noise suppression of seismic signal using orthogonal multi-wavelets.Oil Geophysical Prospecting(in Chinese),2002,37(5) :473～476
[27] 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.石油物探,2006,44(1) :4～6 Yang L Q,Song H B,Hao T Y,et al.Method of 2-D wavelet transform in attenuating random noise.Geophysical Prospecting for Petroleum(in Chinese),2005,44(1) :4～6
[28] 王典,刘财,刘洋等.基于提升算法和百分位数软阈值的小波去噪技术.地球物理学进展,2008,23(4) :1124～1130Wang D,Liu C,Liu Y,et al.The application of wavelet transform based on lifting scheme and percentiles soft-threshold in seismic random noise elimination.Progress in Geophysics(in Chinese),2008,23(4) :1124～1130
[29] Douma H,de Hoop M V.Leading-order seismic imaging using curvelets.Geophysics,2007,72(6) :S231～S248
[30] Chauris H,Nguyen T.Seismic demigration/migration in the curvelet domain.Geophysics,2008,73(2) :S35～S46
[31] Herrmann F J,Wang D,Hennenfent G,et al.Curvelet-based seismic data processing:a multiscale and nonlinear approach.Geophysics,2008,73(1) :1～5
[32] Pennec E L,Mallat S.Sparse geometric image representation with bandelets.IEEE Trans.Image Process,2005,14(4) :423～438
[33] Do M N,Vetterli M.The contourlet transform:an efficient directional multiresolution image representation.IEEE Trans.Image Process,2005,14(12) :2091～2106
[34] Starck J L,Candés E J,Donoho D L.The Curvelet transform for image denoising.IEEE Trans.Image Process,2002,11(6) :670～684
[35] Velisavljevic V.Directionlets:anisotropic multi-directional representation with separable filtering[Ph.D.thesis]. Lausanne,Switzerland:Ecole Polytechnique Fédérale de Lausanne,2005
[36] Fomel S.Towards the seislet transform.SEG Extended Abstract,2006:2847～2851
[37] Cohen A,Daubechies I,Feauveau J.Biorthogonal bases of compactly supported wavelets.Comm.Pure Appl.Math,2006,45(5) :485～560
[38] Acharya T,Tsai P-S.JPEG2000 Standard for Image Compression:Concepts,Algorithms and VLSI Architectures.Wiley-Interscience,2004
[39] Sweldens W.The lifting scheme:a new philosophy in biorthogonal wavelet constructions.Wavelet Applications in Signal and Image Processing Ⅲ,Proc.SPIE 2569,1995:68～79
[40] Sweldens W,Schroder P.Building Your Own Wavelets at Home,in Wavelets in Computer Graphics.ACM SIGGRAPH Course Notes,1996:15～87
[41] Fomel S.Applications of plane-wave destruction filters.Geophysics,2002,67(6) :1946～1960
[42] Lian C,Chen K,Chen H,et al.Lifting based discrete wavelet transform architecture for JPEG2000． IEEE International Symposium on Circuits and Systems,2001:Ⅱ445～Ⅱ448
[43] Donoho D L.De-noising by soft-thresholding.IEEE Trans.on Inform.Theory,1995,41(3) :613～627
[44] Fomel S.Shaping regularization in geophysical estimation problems.Geophysics,2007,72(2) :R29～R36
[2] 金龙,陈小宏,刘其成.基于奇异值分解的时移地震互均衡方法.勘探地球物理进展,2005,20(2) :294～297Jin L,Cheng X H,Liu Q C.New method for time-lapse seismic matching based on SVD.Progress in Exploration Geophysics(in Chinese),2005,20(2) :294～297
[3] 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.石油物探,1998,37(3) :29～33Zhao D B,Huang Z P,Wang C M.Random noise attenuation using predictive filtering in F-X domain by singular value decomposition.Geophysical Prospecting for Petroleum(in Chinese),1998,37(3) :29～33
[4] Gulunay N.Noncausal spatial prediction filtering for random noise reduction on 3-D poststack data.Geophysics,2000,65:1641～1653
[5] Ristau J P,Moon W M.Adaptive filtering of random noise in 2-D geophysical data.Geophysics,2001,66:342～349
[6] Liu C,Liu Y,Yang B,et al.A 2D multistage median filter to reduce random seismic noise.Geophysics,2006,71:105～110
[7] 邢贞贞,韩立国,王宇等.高阶统计量方法在地震信号分析中的应用.吉林大学学报(地球科学版),2007,37(增):139～142Xing Z Z,Han L G,Wang Y,et al.Application of high-order statistics in seismic signal analysis.Journal of Jilin University(Earth Science Edition)(in Chinese),2007,37(Suppl.):139～142
[8] 王兆磊,周辉.在反演过程中利用不同范数准则压制噪声对反演结果的影响.地球物理学进展,2007,22(3) :919～923Wang Z L,Zhou H.Using different kinds of norms to suppress the effect of noise in the course of inversion.Progress in Geophysics(in Chinese),2007,22(3) :919～923
[9] Mallat S.A Wavelet Tour of Signal Processing.Academic Press,1999
[10] Foster D J,Mosher C C,Hassanzadeh S.Wavelet Transform Methods for Geophysical Applications.SEG Extended Abstract,1994:1465～1468
[11] Dessing F J.A wavelet transform approach to seismic processing[Ph.D.thesis].Delft:Delft University of Technology,1997
[12] 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.地球物理学进展,2003,18(4) :711～714Liu C,Wang D,Yang B J,et al.Apply of 2D wavelet transforms in surface wave eliminations of seismic exploration.Progress in Geophysics(in Chinese),2003,18(4) :711～714
[13] Wapenaar K,Ghose R,Toxopeus G,et al.The wavelet transform as a tool for geophysical data integration.Integrated Computer-Aided Engineering,2005,12:5～23
[14] 刘财,张海江,杨宝俊.小波变换及其在薄储层识别中的应用.石油物探,1995,34(3) :23～31Liu C,Zhang H J,Yang B J.Wavelet transform and its application in the recognition of thin-reservoir.Geophysical Prospecting for Petroleum(in Chinese),1995,34(3) :23～31
[15] 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.长春地质学院学报,1996,26(1) :78～82Liu C.Zhang H J,Yang B J,et al.Application of wavelet transform to digital processing in high resolution seismic prospecting.Journal of Changchun University of Earth Sciences(in Chinese),1996,26(1) :78～82
[16] 裴正林.小波理论及其在地震数据处理中的应用.地球物理学进展,2002,17(3) :486～490Pei Z L.Wavelet theory and its application in seismic data processing.Progress in Geophysics(in Chinese),2002,17(3) :486～490
[17] 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.石油物探,2003,42(2) :237～239Guo G M,Shi L C,Gao S J,et al.Application of wavelet transform in seismic data processing.Geophysical Prospecting for Petroleum(in Chinese),2003,42(2) :237～239
[18] 徐亚,郝天珧.提升小波:可用于重磁资料处理的新方法.地球物理学进展,2004,19(1) :36～39Xu Y,Hao T Y.Lifting scheme:a promising method in gravity and magnetic data processing.Progress in Geophysics(in Chinese),2004,19(1) :36～39
[19] 徐亚,郝天珧,周立宏等.位场小波变换研究进展.地球物理学进展,2006,21(4) :1132～1138Xu Y,Hao T Y,Zhou L H,et al.Review of wavelet transform in potential field.Progress in Geophysics(in Chinese),2006,21(4) :1132～1138
[20] 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.地球物理学报,2006,49(3) :855～863Li Q,Lin Y F,Zeng X P.Wavelet analysis as a tool for revealing geomagnetic precursors of the Zhangbei earthquake.Chinese J.Geophys.(in Chinese),2006,49(3) :855～863
[21] 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.地球物理学进展,2007,22(4) :1075～1079Ma L H,Han Y B,Liao D C.Study progress of wavelet transform applying in length-of-day change.Progress in Geophysics(in Chinese),2007,22(4) :1075～1079
[22] 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.地球物理学报,2006,49(4) :1155～1163Gao J H,Mao J,Man W S,et al.On the denoising method of prestack seismic data in wavelet domain.Chinese J.Geophys.(in Chinese),2006,49(4) :1155～1163
[23] 柳建新,韩世礼,马捷.小波分析在地震资料去噪中的应用.地球物理学进展,2006,21(2) :541～545Liu J X,Han S L,Ma J.Application of wavelet analysis in seismic data denoising.Progress in Geophysics(in Chinese),2006,21(2) :541～545
[24] 吴招才,刘天佑.地震数据去噪中的小波方法.地球物理学进展,2008,23(2) :493～499Wu Z C,Liu T Y.Wavelet transform methods in seismic noise attenuation.Progress in Geophysics(in Chinese),2008,23(2) :493～499
[25] 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.石油地球物理勘探,1999,34(6) :635～641Zhang B,Yin X Y,Wu G C,et al.Random noise elimination using wavelet analysis and inversion.Oil Geophysical Prospecting(in Chinese),1999,34(6) :635～641
[26] 吴爱弟,曹思远.用正交多小波压制地震信号的随机噪声.石油地球物理勘探,2002,37(5) :473～476Wu A D,Cao S Y.Random noise suppression of seismic signal using orthogonal multi-wavelets.Oil Geophysical Prospecting(in Chinese),2002,37(5) :473～476
[27] 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.石油物探,2006,44(1) :4～6 Yang L Q,Song H B,Hao T Y,et al.Method of 2-D wavelet transform in attenuating random noise.Geophysical Prospecting for Petroleum(in Chinese),2005,44(1) :4～6
[28] 王典,刘财,刘洋等.基于提升算法和百分位数软阈值的小波去噪技术.地球物理学进展,2008,23(4) :1124～1130Wang D,Liu C,Liu Y,et al.The application of wavelet transform based on lifting scheme and percentiles soft-threshold in seismic random noise elimination.Progress in Geophysics(in Chinese),2008,23(4) :1124～1130
[29] Douma H,de Hoop M V.Leading-order seismic imaging using curvelets.Geophysics,2007,72(6) :S231～S248
[30] Chauris H,Nguyen T.Seismic demigration/migration in the curvelet domain.Geophysics,2008,73(2) :S35～S46
[31] Herrmann F J,Wang D,Hennenfent G,et al.Curvelet-based seismic data processing:a multiscale and nonlinear approach.Geophysics,2008,73(1) :1～5
[32] Pennec E L,Mallat S.Sparse geometric image representation with bandelets.IEEE Trans.Image Process,2005,14(4) :423～438
[33] Do M N,Vetterli M.The contourlet transform:an efficient directional multiresolution image representation.IEEE Trans.Image Process,2005,14(12) :2091～2106
[34] Starck J L,Candés E J,Donoho D L.The Curvelet transform for image denoising.IEEE Trans.Image Process,2002,11(6) :670～684
[35] Velisavljevic V.Directionlets:anisotropic multi-directional representation with separable filtering[Ph.D.thesis]. Lausanne,Switzerland:Ecole Polytechnique Fédérale de Lausanne,2005
[36] Fomel S.Towards the seislet transform.SEG Extended Abstract,2006:2847～2851
[37] Cohen A,Daubechies I,Feauveau J.Biorthogonal bases of compactly supported wavelets.Comm.Pure Appl.Math,2006,45(5) :485～560
[38] Acharya T,Tsai P-S.JPEG2000 Standard for Image Compression:Concepts,Algorithms and VLSI Architectures.Wiley-Interscience,2004
[39] Sweldens W.The lifting scheme:a new philosophy in biorthogonal wavelet constructions.Wavelet Applications in Signal and Image Processing Ⅲ,Proc.SPIE 2569,1995:68～79
[40] Sweldens W,Schroder P.Building Your Own Wavelets at Home,in Wavelets in Computer Graphics.ACM SIGGRAPH Course Notes,1996:15～87
[41] Fomel S.Applications of plane-wave destruction filters.Geophysics,2002,67(6) :1946～1960
[42] Lian C,Chen K,Chen H,et al.Lifting based discrete wavelet transform architecture for JPEG2000． IEEE International Symposium on Circuits and Systems,2001:Ⅱ445～Ⅱ448
[43] Donoho D L.De-noising by soft-thresholding.IEEE Trans.on Inform.Theory,1995,41(3) :613～627
[44] Fomel S.Shaping regularization in geophysical estimation problems.Geophysics,2007,72(2) :R29～R36
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心