基于地震信号波形形态差异的面波噪声稀疏优化分离方法
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摘要
实际地震信号通常可表示为具有波形特征差异的多种基本波形信号的线性组合,如叠前道集中的工频干扰噪声与有效波信号、面波噪声与体波信号等.选择单一数学变换方法,往往不易实现地震信号的稀疏表示.近年来发展的形态成分分析理论,通过联合多种数学变换,可实现对复杂信号的稀疏表示.本文根据单道地震记录中面波与体波信号波形结构特征的差异性,提出一种基于形态成分分析的面波噪声衰减方法.针对面波的低频、窄带以及频散特性选择一维平稳小波变换作为其稀疏表示字典,而针对体波波形的局部相关特性选择局部离散余弦变换作为其稀疏表示字典,建立基于双波形字典的形态成分分析模型,通过求解该稀疏优化问题获得最终的信噪分离结果.理论模型和实际地震资料处理证实该方法不仅能够衰减单炮地震记录中的强面波干扰噪声,同时能够更好地保护有效信号的波形特征与频谱带宽,为地震资料的后续处理和分析提供良好的数据基础.
Real seismic signals can usually be represented as a linear combination of multiple basic waveforms of different morphological characteristics,such as powerline single frequency interference noise and effective seismic signal,ground roll and body wave signals.By selecting a single mathematical transformation method,it will hard to achieve sparse representations of seismic signals.Morphological component analysis(MCA) theory has been developed in recent years,which can sparsely decompose complex signals through the augmented dictionary of basic mathematical transformations.According to the waveform divergence of ground-roll and body wave signals,this paper proposes a ground-roll attenuation method based on the morphological component analysis theory.To match with the requirements of the MCA,the 1D stationary wavelet transform(SWT) is chosen as the sparse representation dictionary of ground-roll due to its low frequency and narrow spectral bandwidth nature.Meanwhile,the local discrete cosine transform(LDCT) is chosen as the sparse representation dictionary of body waves due to its local interdependency characteristics.The optimization model on basis of the MCA is then built on the two amalgamated dictionaries and properly solved to obtain the final signal-noise separation results.The theoretical and real data processing results confirm that the method can not only attenuate strong ground-roll noise in seismic records but also preserves the waveform characteristics and spectral bandwidth of effective signal well.The method can provide high quality data for subsequent processing and analysis.
Real seismic signals can usually be represented as a linear combination of multiple basic waveforms of different morphological characteristics,such as powerline single frequency interference noise and effective seismic signal,ground roll and body wave signals.By selecting a single mathematical transformation method,it will hard to achieve sparse representations of seismic signals.Morphological component analysis(MCA) theory has been developed in recent years,which can sparsely decompose complex signals through the augmented dictionary of basic mathematical transformations.According to the waveform divergence of ground-roll and body wave signals,this paper proposes a ground-roll attenuation method based on the morphological component analysis theory.To match with the requirements of the MCA,the 1D stationary wavelet transform(SWT) is chosen as the sparse representation dictionary of ground-roll due to its low frequency and narrow spectral bandwidth nature.Meanwhile,the local discrete cosine transform(LDCT) is chosen as the sparse representation dictionary of body waves due to its local interdependency characteristics.The optimization model on basis of the MCA is then built on the two amalgamated dictionaries and properly solved to obtain the final signal-noise separation results.The theoretical and real data processing results confirm that the method can not only attenuate strong ground-roll noise in seismic records but also preserves the waveform characteristics and spectral bandwidth of effective signal well.The method can provide high quality data for subsequent processing and analysis.
引文
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[2]Embree P,Burg J P,Backus M M.Wide-band velocity filtering-the pie-slice process.Geophysics,1963,28(6):948-974.
[3]Gelisli K,Karsli H.F-k filtering using the Hartley transform.Journal of Seismic Exploration,1988,7(2):101-108.
[4]Treitel S,Shanks J L,Frasier C W.Some aspects of fan filtering.Geophysics,1967,32(5):789-800.
[5]刘法启,张关泉.小波变换与F-K算法在滤波中的应用.石油地球物理勘探,1996,31(6):782-791.Liu F Q,Zhang G Q.Application of wavelet transform andF-K algorithm in filtering.Oil Geophysical Prospecting(in Chinese),1996,31(6):782-791.
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[8]Porsani M J,Silva M G,Melo P E M,et al.SVD filtering applied to ground-roll attenuation.Journal of Geophysics and Engineering,2010,7(3):284-289.
[9]Karsli H,Bayrak Y.Using the Wiener-Levinson algorithm to suppress ground-roll.Journal of Applied Geophysics,2004,55(3-4):187-197.
[10]罗国安,杜世通.小波变换及信号重建在压制面波中的应用.石油地球物理勘探,1996,31(3):337-349.Luo G A,Du S T.Application of wavelet transform and signal reconstruction in surface wave elimination.Oil Geophysical Prospecting(in Chinese),1996,31(3):337-349.
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[13]陈文超,高静怀,包乾宗等.基于连续小波变换的自适应面波压制方法.地球物理学报,2009,52(11):2854-2861.Chen W C,Gao J H,Bao Q Z,et al.Adaptive attenuation of ground roll via continuous wavelet transform.Chinese Journal of Geophysics(in Chinese),2009,52(11):2854-2861.
[14]Nguyen M Q,Mars N J I.Filtering surface waves using2D Discrete Wavelet Transform.∥69 th Annual International Meeting,SEG.Expanded Abstract,1999:1228-1231.
[15]Abdul-Jauwad S H,Khène M F.Two-dimensional wavelet-based ground roll filtering.∥70th Annual International Meeting,SEG.Expanded Abstract,2000.
[16]刘财,王典,杨宝俊.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):711-714.Liu C,Wang D,Yang B J.Apply of2-D wavelet transforms in surface wave eliminations of seismic exploration.Progress in Geophysics(in Chinese),2003,18(4):711-714.
[17]Zhang R F,Ulrych T J.Physical wavelet frame denoising.Geophysics,2003,68(1):225-231.
[18]Zhang R F,Trad D,Ulrych T J.Hybrid,wavelet transform based,noise attenuation.Integrated Computer-Aided Engineering,2005,12(1):91-98.
[19]Askari R,Siahkoohi H R.Ground roll attenuation using the S and x-f-k transforms.Geophysical Prospecting,2008,56(1):105-114.
[20]包乾宗,高静怀,陈文超.面波压制的Ridgelet域方法.地球物理学报,2007,50(4):1210-1215.Bao Q Z,Gao J H,Chen W C.Ridgelet domain method of ground-roll suppression.Chinese Journal of Geophysics(in Chinese),2007,50(4):1210-1215.
[21]Zheng J J,Yin X Y,Zhang G Z,et al.The surface wave suppression using the second generation curvelet transform.AppliedGeophysics,2010,7(4):325-335.
[22]Trad D,Sacchi M D,Ulrych T J.A hybrid linear-hyperbolic Radon transform.Journal of Seismic Exploration,2001,9(4):303-318.
[23]Trad D,Ulrych T J,Sacchi M.Latest views of the sparse radon transform.Geophysics,2003,68(1):386-399.
[24]Yarham C,Boeniger U,Herrmann F J,et al.Curvelet-based ground roll removal.∥76th Annual International Meeting,SEG.Expanded Abstract,2006:2777-2781.
[25]Sardy S,Bruce A G,Tseng P.Block coordinate relaxationmethods for nonparametric wavelet denoising.∥Proceedings of the SPIE-The International Society for Optical Engineering,1998:75-86.
[26]Wang W,Chen W C,Lei J L,et al.Ground-roll separation by sparsity and morphological diversity promotion.∥80th Annual International Meeting,SEG.Expanded Abstract,2010:3705-3710.
[27]Wang W,Gao J H,Chen W C,et al.Data adaptive ground-roll attenuation via sparsity promotion.Journal of Applied Geophysics,2012,83:19-28.
[28]Mallat S.A Wavelet Tour of Signal Processing,3rd ed.Boston:Academic Press,2009.
[29]Starck J L,Elad M,Donoho D L.Image decomposition via the combination of sparse representations and a variational approach.IEEE Transactions on Image Processing,2005,14(10):1570-1582.
[30]Mallat S G,Zhang Z F.Matching Pursuits with Time-Frequency Dictionaries.IEEE Transactions on Signal Processing,1993,41(12):3397-3415.
[31]Chen S S,Donoho D L,Saunders M A.Atomic decomposition by basis pursuit.Siam Journal on Scientific Computing,1998,20(1):33-61.
[32]Elad M,Bruckstein A M.A generalized uncertainty principle and sparse representation in pairs of bases.IEEE Transactions on Information Theory,2002,48(9):2558-2567.
[33]Rubinstein R,Bruckstein A M,Elad M.Dictionaries for sparse representation modeling.Proceedings of the IEEE,2010,98(6):1045-1057.
[34]Daubechies I.Orthonormal bases of compactly supported wavelets II:Variations on a theme.Siam Journal on Mathematical Analysis,1993,24(2):499-519.
[35]Wang Y Z,Wu R S.Seismic data compression by an adaptive local cosine/sine transform and its effects on migration.Geophysical Prospecting,2000,48(6):1009-1031.
[36]陆文凯.基于离散余弦变换的地震随机噪声压制技术.石油地球物理勘探,2011,46(2):202-206.Lu W K.Seismic random noise suppression based on the discrete cosine transform.Oil Geophysical Prospecting(in Chinese),2011,46(2):202-206.
[37]Mao J A,Wu R S,Gao J H.Directional illumination analysis using the local exponential frame.Geophysics,2010,75(4):S163-S174.
[2]Embree P,Burg J P,Backus M M.Wide-band velocity filtering-the pie-slice process.Geophysics,1963,28(6):948-974.
[3]Gelisli K,Karsli H.F-k filtering using the Hartley transform.Journal of Seismic Exploration,1988,7(2):101-108.
[4]Treitel S,Shanks J L,Frasier C W.Some aspects of fan filtering.Geophysics,1967,32(5):789-800.
[5]刘法启,张关泉.小波变换与F-K算法在滤波中的应用.石油地球物理勘探,1996,31(6):782-791.Liu F Q,Zhang G Q.Application of wavelet transform andF-K algorithm in filtering.Oil Geophysical Prospecting(in Chinese),1996,31(6):782-791.
[6]Liu X W.Ground roll supression using the Karhunen-Loeve transform.Geophysics,1999,64(2):564-566.
[7]Montagne R,Vasconcelos G L.Optimized suppression of coherent noise from seismic data using the Karhunen-Loeve transform.Physical Review E,2006,74(1Pt2):16213.
[8]Porsani M J,Silva M G,Melo P E M,et al.SVD filtering applied to ground-roll attenuation.Journal of Geophysics and Engineering,2010,7(3):284-289.
[9]Karsli H,Bayrak Y.Using the Wiener-Levinson algorithm to suppress ground-roll.Journal of Applied Geophysics,2004,55(3-4):187-197.
[10]罗国安,杜世通.小波变换及信号重建在压制面波中的应用.石油地球物理勘探,1996,31(3):337-349.Luo G A,Du S T.Application of wavelet transform and signal reconstruction in surface wave elimination.Oil Geophysical Prospecting(in Chinese),1996,31(3):337-349.
[11]Deighan A J,Watts D R.Ground-roll suppression using the wavelet transform.Geophysics,1997,62(6):1896-1903.
[12]孙学文,陈文超,高静怀等.小波域强面波衰减方法研究.石油地球物理勘探,2008,43(1):22-28.Sun X W,Chen W C,Gao J H,et al.Study on attenuation of strong surface wave in wavelet domain.OilGeophysical Prospecting(in Chinese),2008,43(1):22-28.
[13]陈文超,高静怀,包乾宗等.基于连续小波变换的自适应面波压制方法.地球物理学报,2009,52(11):2854-2861.Chen W C,Gao J H,Bao Q Z,et al.Adaptive attenuation of ground roll via continuous wavelet transform.Chinese Journal of Geophysics(in Chinese),2009,52(11):2854-2861.
[14]Nguyen M Q,Mars N J I.Filtering surface waves using2D Discrete Wavelet Transform.∥69 th Annual International Meeting,SEG.Expanded Abstract,1999:1228-1231.
[15]Abdul-Jauwad S H,Khène M F.Two-dimensional wavelet-based ground roll filtering.∥70th Annual International Meeting,SEG.Expanded Abstract,2000.
[16]刘财,王典,杨宝俊.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):711-714.Liu C,Wang D,Yang B J.Apply of2-D wavelet transforms in surface wave eliminations of seismic exploration.Progress in Geophysics(in Chinese),2003,18(4):711-714.
[17]Zhang R F,Ulrych T J.Physical wavelet frame denoising.Geophysics,2003,68(1):225-231.
[18]Zhang R F,Trad D,Ulrych T J.Hybrid,wavelet transform based,noise attenuation.Integrated Computer-Aided Engineering,2005,12(1):91-98.
[19]Askari R,Siahkoohi H R.Ground roll attenuation using the S and x-f-k transforms.Geophysical Prospecting,2008,56(1):105-114.
[20]包乾宗,高静怀,陈文超.面波压制的Ridgelet域方法.地球物理学报,2007,50(4):1210-1215.Bao Q Z,Gao J H,Chen W C.Ridgelet domain method of ground-roll suppression.Chinese Journal of Geophysics(in Chinese),2007,50(4):1210-1215.
[21]Zheng J J,Yin X Y,Zhang G Z,et al.The surface wave suppression using the second generation curvelet transform.AppliedGeophysics,2010,7(4):325-335.
[22]Trad D,Sacchi M D,Ulrych T J.A hybrid linear-hyperbolic Radon transform.Journal of Seismic Exploration,2001,9(4):303-318.
[23]Trad D,Ulrych T J,Sacchi M.Latest views of the sparse radon transform.Geophysics,2003,68(1):386-399.
[24]Yarham C,Boeniger U,Herrmann F J,et al.Curvelet-based ground roll removal.∥76th Annual International Meeting,SEG.Expanded Abstract,2006:2777-2781.
[25]Sardy S,Bruce A G,Tseng P.Block coordinate relaxationmethods for nonparametric wavelet denoising.∥Proceedings of the SPIE-The International Society for Optical Engineering,1998:75-86.
[26]Wang W,Chen W C,Lei J L,et al.Ground-roll separation by sparsity and morphological diversity promotion.∥80th Annual International Meeting,SEG.Expanded Abstract,2010:3705-3710.
[27]Wang W,Gao J H,Chen W C,et al.Data adaptive ground-roll attenuation via sparsity promotion.Journal of Applied Geophysics,2012,83:19-28.
[28]Mallat S.A Wavelet Tour of Signal Processing,3rd ed.Boston:Academic Press,2009.
[29]Starck J L,Elad M,Donoho D L.Image decomposition via the combination of sparse representations and a variational approach.IEEE Transactions on Image Processing,2005,14(10):1570-1582.
[30]Mallat S G,Zhang Z F.Matching Pursuits with Time-Frequency Dictionaries.IEEE Transactions on Signal Processing,1993,41(12):3397-3415.
[31]Chen S S,Donoho D L,Saunders M A.Atomic decomposition by basis pursuit.Siam Journal on Scientific Computing,1998,20(1):33-61.
[32]Elad M,Bruckstein A M.A generalized uncertainty principle and sparse representation in pairs of bases.IEEE Transactions on Information Theory,2002,48(9):2558-2567.
[33]Rubinstein R,Bruckstein A M,Elad M.Dictionaries for sparse representation modeling.Proceedings of the IEEE,2010,98(6):1045-1057.
[34]Daubechies I.Orthonormal bases of compactly supported wavelets II:Variations on a theme.Siam Journal on Mathematical Analysis,1993,24(2):499-519.
[35]Wang Y Z,Wu R S.Seismic data compression by an adaptive local cosine/sine transform and its effects on migration.Geophysical Prospecting,2000,48(6):1009-1031.
[36]陆文凯.基于离散余弦变换的地震随机噪声压制技术.石油地球物理勘探,2011,46(2):202-206.Lu W K.Seismic random noise suppression based on the discrete cosine transform.Oil Geophysical Prospecting(in Chinese),2011,46(2):202-206.
[37]Mao J A,Wu R S,Gao J H.Directional illumination analysis using the local exponential frame.Geophysics,2010,75(4):S163-S174.
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