基于非二次幂Curvelet变换的最小二乘匹配算法及其应用
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摘要
本文提出了基于非二次幂Curvelet变换的最小二乘匹配算法.首先,根据输入地震信号的频谱和方向等特征进行非二次幂Curvelet变换,根据其特征不同,最大程度地将有效信号和噪声分开;然后,在噪声能量集中的非二次幂Curvelet子记录上对输入数据和预测的噪声模型进行最小二乘匹配滤波处理.本方法提高了常规最小二乘匹配算法在时间空间域内进行信噪分离的稳定性和准确性.对含有面波的实际地震数据进行测试,其结果表明本方法可以有效地压制面波干扰,特别是当面波和有效信号有交叉或重叠等现象出现时,能较好地保护反射同相轴信息.本方法还可用于对含自由表面多次波和层间多次波等地震数据进行自适应信噪分离.
We propose a non-dyadic Curvelet transform based least-squares matching method.Firstly,in order to separate the signal and noise better,the input data is decomposed using non-dyadic Curvelet transform according to their spectral and directional characteristics.Secondly,the least-squares matching method is applied on non-dyadic Curvelet coefficients which contain noises most.Our approach improves the stability and accuracy of conventional time-spatial domain least-squares matching method.Results of field records show that the proposed approach performs well not only in suppressing energies of surface waves,but also in protecting effective reflection events,especially in case of overlapping events.The proposed approach can also be used to adaptively subtract predictable interferences such as free surface-related multiples and internal multiples.
We propose a non-dyadic Curvelet transform based least-squares matching method.Firstly,in order to separate the signal and noise better,the input data is decomposed using non-dyadic Curvelet transform according to their spectral and directional characteristics.Secondly,the least-squares matching method is applied on non-dyadic Curvelet coefficients which contain noises most.Our approach improves the stability and accuracy of conventional time-spatial domain least-squares matching method.Results of field records show that the proposed approach performs well not only in suppressing energies of surface waves,but also in protecting effective reflection events,especially in case of overlapping events.The proposed approach can also be used to adaptively subtract predictable interferences such as free surface-related multiples and internal multiples.
引文
[1]Candès E J,Donoho D L.Curvelets:A Surprisingly Effective Nonadaptive Representation for Objects with Edges,Curves and Surfaces.TN:Vanderbilt University Press,1999.
[2]Candès E J,Guo F.New multiscale transforms,minimum total variation synthesis:Applications to edge-preserving image reconstruction.Signal Processing,2002,82(11):1519-1543.
[3]Starck J,Murtagh F,Candes E,Donoho D.Gray and colorimage contrast enhancement by the Curvelet transform.IEEE Transactions on Image Processing,12:706-717.
[4]Candès E J,Donoho D L.Curvelets,multiresolution representation,and scaling laws.Wavelet Applications in Signal and Image Processing VIII,A.Aldroubi,A.F.Laine,M.A.Unser eds.,Proc.SPIE4119.
[5]Starck J L,Candès E J,Donoho D L.The Curvelet transform for image denoising.IEEE Trans.Image Processing,2002,11(6):670-684.
[6]Herrmann F J,Verschuur E.Curvelet-domain multiple elimination with sparseness constraints.Society of Exploration Geophysicists,Expanded Abstracts,2004,23(1):1333-1336.
[7]Hennenfent G,Herrmann F J.Three-term amplitude-versus-offset(AVO)inverse on revisited by Curvelet and wavelet transforms.Society of Exploration Geophysicists,Expanded Abstracts,2004,23:211-214.
[8]Chauris H,Nguyen T.Seismic demigration/migration in the Curvelet domain.Geophysics,2008,73(2):S35-S46.
[9]Douma H,de Hoop M.Leading-order seismic imaging using Curvelets.Geophysics,2007,72(6):S231-S248.
[10]Hermann F J,Wang D,Hennenfent G,et al.Curvelet-based seismic data processing:A multiscale and nonlinear approach.Geophysics,2008,73(1):706-716.
[11]Herrmann F G,Hennenfent G.Non-parametric seismic data recovery with Curvelet frames.Geophys.J.Int.,2008,173(1):233-248.
[12]Naghizadeh M,Sacchi M D.Beyond alias hierarchical scale Curvelet interpolation of regularly and irregularly sampled seismic data.Geophysics,2010,75(6):WB189-WB202.
[13]Neelamani R,Baumstein A I,Gillard D G,et al.Coherent and random noise attenuation using the Curvelet transform.The Leading Edge,2008,27(2):240-248.
[14]袁艳华,王一博,刘伊克,常旭.非二次幂Curvelet变换及其在地震噪声压制中的应用.地球物理学报,2013,56(3):1023-1032.Yuan Y H,Wang Y B,Liu Y K,Chang X.Non-dyadic Curvelet transform and its application in seismic noise elimination.Chinese J.Geophys.(in Chinese),2013,56(3):1023-1032.
[15]Wang Y B,Yuan Y H,Liu Y K,Chang X.Geophysical data oriented Curvelet-like transform.SEG Abstract,2011:3663-3667.
[16]Yuan Y H,Wang Y B,Liu Y K,Chang X.Curvelet domain adaptive least-squares subtraction of internal multiple.Journal of Seismic Exploration,2011,20(3):273-288.
[17]包乾宗,高静怀,陈文超.Curvelet域垂直地震剖面波场分离.西安交通大学学报,2007,41(6):650-654.Bao Q Z,Gao J H,Chen W C.Wave field separation of vertical seismic profiling in Curvelet domain.Journal of Xi′an Jiaotong University(in Chinese),2007,41(6):650-654.
[18]Wang Y B,Xue Y W,Dong S Q.Surface waves suppression using interferometric prediction and Curvelet domain hybrid L1/L2norm subtraction.SEG Expanded Abstracts,2009,28:3292.
[19]Verschuur D J,Berkhout A J,Wapenaar C P A.Adaptive surface-related multiple elimination.Geophysics,1992,57(9):1166-1177.
[20]Spitz S.Pattern recognition,spatial predictability and subtraction of multiple events.The Leading Edge,1999,18(1):55-58.
[21]Guitton A.Multiple attenuation with multidimensional prediction-error filter.73th Ann.Internat.Mtg.,Soc.Expl.Geophys.,Expanded Abstracts,2003:57-74.
[22]金德刚,常旭,刘伊克.逆散射级数法预测层间多次波的算法改进及其策略.地球物理学报,2008,51(4):1209-1217.Jin D G,Chang X,Liu Y K.Algorithm improvement and strategy of internal multiples prediction based on inverse scattering series method.Chinese J.Geophys.(in Chinese),2008,51(4):1209-1217.
[23]Lin D,Young D,Huang Y,et al.3-D SRME application in the Gulf of Mexico.74th Ann.Internat.Mtg.,Soc.Expl.Geophys.,Expanded abstracts,2004,23:1257-1260.
[24]Berkhout A J,Verschuur D J.Estimation of multiple scattering by iterative inversion,part I:theoretical considerations.Geophysics,1997,62(5):1586-1595.
[25]Weglein A B,Carvalho F A,Stolt P M.An inverse scattering series method for attenuating multiples in seismic reflection data.Geophysics,1997,62(6):1975-1989.
[2]Candès E J,Guo F.New multiscale transforms,minimum total variation synthesis:Applications to edge-preserving image reconstruction.Signal Processing,2002,82(11):1519-1543.
[3]Starck J,Murtagh F,Candes E,Donoho D.Gray and colorimage contrast enhancement by the Curvelet transform.IEEE Transactions on Image Processing,12:706-717.
[4]Candès E J,Donoho D L.Curvelets,multiresolution representation,and scaling laws.Wavelet Applications in Signal and Image Processing VIII,A.Aldroubi,A.F.Laine,M.A.Unser eds.,Proc.SPIE4119.
[5]Starck J L,Candès E J,Donoho D L.The Curvelet transform for image denoising.IEEE Trans.Image Processing,2002,11(6):670-684.
[6]Herrmann F J,Verschuur E.Curvelet-domain multiple elimination with sparseness constraints.Society of Exploration Geophysicists,Expanded Abstracts,2004,23(1):1333-1336.
[7]Hennenfent G,Herrmann F J.Three-term amplitude-versus-offset(AVO)inverse on revisited by Curvelet and wavelet transforms.Society of Exploration Geophysicists,Expanded Abstracts,2004,23:211-214.
[8]Chauris H,Nguyen T.Seismic demigration/migration in the Curvelet domain.Geophysics,2008,73(2):S35-S46.
[9]Douma H,de Hoop M.Leading-order seismic imaging using Curvelets.Geophysics,2007,72(6):S231-S248.
[10]Hermann F J,Wang D,Hennenfent G,et al.Curvelet-based seismic data processing:A multiscale and nonlinear approach.Geophysics,2008,73(1):706-716.
[11]Herrmann F G,Hennenfent G.Non-parametric seismic data recovery with Curvelet frames.Geophys.J.Int.,2008,173(1):233-248.
[12]Naghizadeh M,Sacchi M D.Beyond alias hierarchical scale Curvelet interpolation of regularly and irregularly sampled seismic data.Geophysics,2010,75(6):WB189-WB202.
[13]Neelamani R,Baumstein A I,Gillard D G,et al.Coherent and random noise attenuation using the Curvelet transform.The Leading Edge,2008,27(2):240-248.
[14]袁艳华,王一博,刘伊克,常旭.非二次幂Curvelet变换及其在地震噪声压制中的应用.地球物理学报,2013,56(3):1023-1032.Yuan Y H,Wang Y B,Liu Y K,Chang X.Non-dyadic Curvelet transform and its application in seismic noise elimination.Chinese J.Geophys.(in Chinese),2013,56(3):1023-1032.
[15]Wang Y B,Yuan Y H,Liu Y K,Chang X.Geophysical data oriented Curvelet-like transform.SEG Abstract,2011:3663-3667.
[16]Yuan Y H,Wang Y B,Liu Y K,Chang X.Curvelet domain adaptive least-squares subtraction of internal multiple.Journal of Seismic Exploration,2011,20(3):273-288.
[17]包乾宗,高静怀,陈文超.Curvelet域垂直地震剖面波场分离.西安交通大学学报,2007,41(6):650-654.Bao Q Z,Gao J H,Chen W C.Wave field separation of vertical seismic profiling in Curvelet domain.Journal of Xi′an Jiaotong University(in Chinese),2007,41(6):650-654.
[18]Wang Y B,Xue Y W,Dong S Q.Surface waves suppression using interferometric prediction and Curvelet domain hybrid L1/L2norm subtraction.SEG Expanded Abstracts,2009,28:3292.
[19]Verschuur D J,Berkhout A J,Wapenaar C P A.Adaptive surface-related multiple elimination.Geophysics,1992,57(9):1166-1177.
[20]Spitz S.Pattern recognition,spatial predictability and subtraction of multiple events.The Leading Edge,1999,18(1):55-58.
[21]Guitton A.Multiple attenuation with multidimensional prediction-error filter.73th Ann.Internat.Mtg.,Soc.Expl.Geophys.,Expanded Abstracts,2003:57-74.
[22]金德刚,常旭,刘伊克.逆散射级数法预测层间多次波的算法改进及其策略.地球物理学报,2008,51(4):1209-1217.Jin D G,Chang X,Liu Y K.Algorithm improvement and strategy of internal multiples prediction based on inverse scattering series method.Chinese J.Geophys.(in Chinese),2008,51(4):1209-1217.
[23]Lin D,Young D,Huang Y,et al.3-D SRME application in the Gulf of Mexico.74th Ann.Internat.Mtg.,Soc.Expl.Geophys.,Expanded abstracts,2004,23:1257-1260.
[24]Berkhout A J,Verschuur D J.Estimation of multiple scattering by iterative inversion,part I:theoretical considerations.Geophysics,1997,62(5):1586-1595.
[25]Weglein A B,Carvalho F A,Stolt P M.An inverse scattering series method for attenuating multiples in seismic reflection data.Geophysics,1997,62(6):1975-1989.
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