基于二维希尔伯特变换的地震倾角求取方法及其在构造导向滤波中的应用（英文）
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摘要
在地震勘探数据采集中,随机噪声严重影响地震资料质量,给后期解释工作带来很大困难。如何在不损失剖面有效信息的前提下压制随机噪声,有效地提高地震资料的信噪比和保真度,是本文的研究目标。构造导向滤波技术的核心是构造方向表征的求取以及如何实现非平稳滤波,来达到提高地震数据信噪比和保真度的目的。本文首先通过分析函数二维导数与希尔伯特变换的频率响应关系,推导出了基于二维希尔伯特变换的非迭代地震同相轴倾角求取算子,进而达到了构造方向表征的求取;其次选取多项式拟合作为构造导向滤波中的非平稳滤波方法,扩展了非平稳多项式拟合的应用范围;最后沿构造倾角方向进行变振幅同相轴的非平稳多项式拟合,实现和构建了新的自适应构造导向滤波方法。理论模型和实际地震资料处理的结果表明,所提出的方法实现了既保护构造信息又有效地压制了随机噪声的目的。
In seismic data processing, random noise seriously affects the seismic data quality and subsequently the interpretation. This study aims to increase the signal-to-noise ratio by suppressing random noise and improve the accuracy of seismic data interpretation without losing useful information. Hence, we propose a structure-oriented polynomial fitting filter. At the core of structure-oriented filtering is the characterization of the structural trend and the realization of nonstationary filtering. First, we analyze the relation of the frequency response between two-dimensional(2D) derivatives and the 2D Hilbert transform. Then, we derive the noniterative seismic local dip operator using the 2D Hilbert transform to obtain the structural trend. Second, we select polynomial fitting as the nonstationary filtering method and expand the application range of the nonstationary polynomial fitting. Finally, we apply variableamplitude polynomial fitting along the direction of the dip to improve the adaptive structureoriented filtering. Model and field seismic data show that the proposed method suppresses the seismic noise while protecting structural information.
In seismic data processing, random noise seriously affects the seismic data quality and subsequently the interpretation. This study aims to increase the signal-to-noise ratio by suppressing random noise and improve the accuracy of seismic data interpretation without losing useful information. Hence, we propose a structure-oriented polynomial fitting filter. At the core of structure-oriented filtering is the characterization of the structural trend and the realization of nonstationary filtering. First, we analyze the relation of the frequency response between two-dimensional(2D) derivatives and the 2D Hilbert transform. Then, we derive the noniterative seismic local dip operator using the 2D Hilbert transform to obtain the structural trend. Second, we select polynomial fitting as the nonstationary filtering method and expand the application range of the nonstationary polynomial fitting. Finally, we apply variableamplitude polynomial fitting along the direction of the dip to improve the adaptive structureoriented filtering. Model and field seismic data show that the proposed method suppresses the seismic noise while protecting structural information.
引文
Bekara,M.,and van der Baan,M.,2009,Random and coherent noise attenuation by empirical mode decomposition:Geophysics,74(5),V89-V98.
Fehmers,G.C,and Hocker,C.F.W.,2003,Fast structural interpretation with structure-oriented filtering:Geophysics,68(4),1286-1293.
Fomel,S.,and Guitton,A.,2006,Regularizing seismic inverse problems by model reparameterization using plane-wave construction:Geophysics,71(5),A43-A47.
Fomel,S.,2009,Adaptive multiple subtraction using regularized nonstationary regression:Geophysics,74(1),V25-V33.
Fomel,S.,2002,Applications of plane-wave destruction filters:Geophysics,67(6),1946-1960.
Fomel,S.,2007,Shaping regularization in geophysicalestimation problems:Geophysics,72(2),R29-R36.
Hoeber,H.C,Brandwood,S.,and Whitcombe,D.N.,2006,Structurally consistent filtering:In 68th EAGE Conference Exhibition.
Lehmer,D.H.,1985,Interesting series involving the central binomial coefficient:American Mathematical Monthly,449-457.
Li,H.S.,Wu,G.C,and Yin,X.Y.,2012,Application of Morphological Component Analysis to Remove of Random Noise in Seismic Data:Journal of Jilin University(Earth Science Edition),42(2),554-561.
Li,Y,Yang,B.I,Lin,and H.B.,et al.2013,Suppression of strong random noise in seismic data by using timefrequency peak filtering:Science China Earth Sciences,56(7),1200-1208.
Liu,C,Liu,Y,and Yang,B.J.,et al.2006,A 2D multistage median filter to reduce random seismic noise:Geophysics,71(5),V105-V110.
Liu,G.,Chen,X.,2013,Noncausal f-x-y regularized nonstationary prediction filtering for random noise attenuation on 3D seismic data:Journal of Applied Geophysics,93,60-66.
Liu,G.C,Chen,X.H.,and Li,J.Y,et al.2011,Seismic noise attenuation using nonstationary polynomial fitting:Applied Geophysics,8(1),18-26.
Liu,G.,Chen,X.,and Du,J.,et al.2012,Random noise attenuation using f-x regularized nonstationary autoregression:Geophysics,77(2),V61-V69.
Liu,Y,Fomel,S.,and Liu,G.,2010,Nonlinear structureenhancing filtering using plane-wave prediction:Geophysical Prospecting,58(3),415-427.
Liu,Y,Fomel,S.,and Liu,C,et al.2009,High-order seislet transform and its application of random noise attenuation:Chinese Journal of Geophysics,52(8),2142-2151.
Liu,Y,Liu,C,and Wang,D,2008,A 1D time-varying median filter for seismic random,spike-like noise elimination:Geophysics,74(1),V17-V24.
Liu,Y,Wang,D.,and Liu,C,et al.2011,Weighted median filter based on local correlation and its application to poststack random noise attenuation:Chinese Journal of Geophysics,54(2),358-367.
Liu,Z.,Zhao,W.,and Chen,X.,et al 2012,Local SVD for random noise suppression of seismic data in frequency domain:Oil Geophysical Prospecting,47(2),202-206.
Lu,W.,Zhang,W.,and Liu,D.,2006,Local linear coherent noise attenuation based on local polynomial approximation:Geophysics,71(6),V163-V169.
Lu,Y H.,and Lu,W.K.,2009,Edge-preserving polynomial fitting method to suppress random seismic noise:Geophysics,74(4),V69-V73.
Maraschini,M.,Neill Turton,C.G.G.,2013,Assessing the impact of a Non-Local-Means random noise attenuator on coherency:SEG Technical Program Expanded Abstracts,4294-4298.
Ottolini,R.,1983,Signal/noise separation in dip space:SEP Report,37,143-149.
Pei,S.C,and Wang,P.H.,2001,Closed-form design of maximally flat FIR Hilbert transformers,differentiators,and fractional delayers by power series expansion:IEEE Transactions on,Circuits and Systems I:Fundamental Theory and Applications,48(4),389-398.
Schleicher,I,Costa,J.C,and Santos,L.T.,et al.2009,On the estimation of local slopes:Geophysics,74(4),P25-P33.
Tikhonov,A.,1963,Solution of incorrectly formulated problems and the regularization method:In Soviet Math.Dokl,pp.,1035-1038.
Zhang,C,Lin,H.B.,and Li,Y.,et al.2013,Seismic random noise attenuation by time-frequency peak filtering based on joint time-frequency distribution:Comptes Rendus Geoscience,345(9),383-391.
Fehmers,G.C,and Hocker,C.F.W.,2003,Fast structural interpretation with structure-oriented filtering:Geophysics,68(4),1286-1293.
Fomel,S.,and Guitton,A.,2006,Regularizing seismic inverse problems by model reparameterization using plane-wave construction:Geophysics,71(5),A43-A47.
Fomel,S.,2009,Adaptive multiple subtraction using regularized nonstationary regression:Geophysics,74(1),V25-V33.
Fomel,S.,2002,Applications of plane-wave destruction filters:Geophysics,67(6),1946-1960.
Fomel,S.,2007,Shaping regularization in geophysicalestimation problems:Geophysics,72(2),R29-R36.
Hoeber,H.C,Brandwood,S.,and Whitcombe,D.N.,2006,Structurally consistent filtering:In 68th EAGE Conference Exhibition.
Lehmer,D.H.,1985,Interesting series involving the central binomial coefficient:American Mathematical Monthly,449-457.
Li,H.S.,Wu,G.C,and Yin,X.Y.,2012,Application of Morphological Component Analysis to Remove of Random Noise in Seismic Data:Journal of Jilin University(Earth Science Edition),42(2),554-561.
Li,Y,Yang,B.I,Lin,and H.B.,et al.2013,Suppression of strong random noise in seismic data by using timefrequency peak filtering:Science China Earth Sciences,56(7),1200-1208.
Liu,C,Liu,Y,and Yang,B.J.,et al.2006,A 2D multistage median filter to reduce random seismic noise:Geophysics,71(5),V105-V110.
Liu,G.,Chen,X.,2013,Noncausal f-x-y regularized nonstationary prediction filtering for random noise attenuation on 3D seismic data:Journal of Applied Geophysics,93,60-66.
Liu,G.C,Chen,X.H.,and Li,J.Y,et al.2011,Seismic noise attenuation using nonstationary polynomial fitting:Applied Geophysics,8(1),18-26.
Liu,G.,Chen,X.,and Du,J.,et al.2012,Random noise attenuation using f-x regularized nonstationary autoregression:Geophysics,77(2),V61-V69.
Liu,Y,Fomel,S.,and Liu,G.,2010,Nonlinear structureenhancing filtering using plane-wave prediction:Geophysical Prospecting,58(3),415-427.
Liu,Y,Fomel,S.,and Liu,C,et al.2009,High-order seislet transform and its application of random noise attenuation:Chinese Journal of Geophysics,52(8),2142-2151.
Liu,Y,Liu,C,and Wang,D,2008,A 1D time-varying median filter for seismic random,spike-like noise elimination:Geophysics,74(1),V17-V24.
Liu,Y,Wang,D.,and Liu,C,et al.2011,Weighted median filter based on local correlation and its application to poststack random noise attenuation:Chinese Journal of Geophysics,54(2),358-367.
Liu,Z.,Zhao,W.,and Chen,X.,et al 2012,Local SVD for random noise suppression of seismic data in frequency domain:Oil Geophysical Prospecting,47(2),202-206.
Lu,W.,Zhang,W.,and Liu,D.,2006,Local linear coherent noise attenuation based on local polynomial approximation:Geophysics,71(6),V163-V169.
Lu,Y H.,and Lu,W.K.,2009,Edge-preserving polynomial fitting method to suppress random seismic noise:Geophysics,74(4),V69-V73.
Maraschini,M.,Neill Turton,C.G.G.,2013,Assessing the impact of a Non-Local-Means random noise attenuator on coherency:SEG Technical Program Expanded Abstracts,4294-4298.
Ottolini,R.,1983,Signal/noise separation in dip space:SEP Report,37,143-149.
Pei,S.C,and Wang,P.H.,2001,Closed-form design of maximally flat FIR Hilbert transformers,differentiators,and fractional delayers by power series expansion:IEEE Transactions on,Circuits and Systems I:Fundamental Theory and Applications,48(4),389-398.
Schleicher,I,Costa,J.C,and Santos,L.T.,et al.2009,On the estimation of local slopes:Geophysics,74(4),P25-P33.
Tikhonov,A.,1963,Solution of incorrectly formulated problems and the regularization method:In Soviet Math.Dokl,pp.,1035-1038.
Zhang,C,Lin,H.B.,and Li,Y.,et al.2013,Seismic random noise attenuation by time-frequency peak filtering based on joint time-frequency distribution:Comptes Rendus Geoscience,345(9),383-391.
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