结合曲波变换的焦点变换在地震数据去噪和插值中的应用
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摘要
为了更好地衰减地震数据中的随机噪声,以及更加精确地对缺失地震数据进行重构,在自由表面多次波的反馈迭代方法中,用多维加权互相关替换多维加权褶积,即焦点变换方法。该方法为全数据驱动过程,不需要任何地下信息,尤其当地下地质体比较复杂并且需要考虑的各种信息较多时。为了改善传统基于最小平方计算的焦点变换有效信号聚焦不够集中地效果,笔者提出将三维曲波变换与焦点变换结合,并采用L1范数最优化求解。模型及实测资料试验证明,联合三维曲波变换与焦点变换在地震数据随机噪声衰减中聚焦点有效信号更加集中,切除噪声后有效信号保存更完整;对缺失地震数据的重构更加完整和精细,并且有效保存了高频信息。
In order to better attenuate random noise of seismic data and get more accurate seismic data reconstruction,the authors,based on the free surface multiples feedback iteration method,employed multidimensional weighted cross-correlation to replace multidimensional weighted convolution,also known as " the focal transformation method".This method is a whole data driven process in which underground information is not required,especially when the local underground geological bodies are complicated and the information that should be considered is large.In order to improve the traditional effective signal based on the focus of the least square calculation transform whose focus is not centrally concentrated,the authors combined 3D curvelet transform and focal transform and used the L1 norm optimization algorithm to get the solution.The combination of 3D curvelet transform with focal transform random noise attenuation of seismic data can make effective signal more concentrated,and the preservation of effective signal becomes more complete after the removal of the noise signal.In comparison with the interpolation method that only uses curvelet transform or focal transform means,the interpolation experiment used in this paper can reconstruct seismic data more completely and sophistically,and the high frequency information can be preserved effectively.
In order to better attenuate random noise of seismic data and get more accurate seismic data reconstruction,the authors,based on the free surface multiples feedback iteration method,employed multidimensional weighted cross-correlation to replace multidimensional weighted convolution,also known as " the focal transformation method".This method is a whole data driven process in which underground information is not required,especially when the local underground geological bodies are complicated and the information that should be considered is large.In order to improve the traditional effective signal based on the focus of the least square calculation transform whose focus is not centrally concentrated,the authors combined 3D curvelet transform and focal transform and used the L1 norm optimization algorithm to get the solution.The combination of 3D curvelet transform with focal transform random noise attenuation of seismic data can make effective signal more concentrated,and the preservation of effective signal becomes more complete after the removal of the noise signal.In comparison with the interpolation method that only uses curvelet transform or focal transform means,the interpolation experiment used in this paper can reconstruct seismic data more completely and sophistically,and the high frequency information can be preserved effectively.
引文
[1]刘洋,王典,刘财.数学变换方法在地震勘探中的应用[J].吉林大学学报:地球科学版,2005,35(S1):1-8.
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[5]Berkhout A J,Verschuur D J,Romijn R.Reconstruction of seismicdata using the focal transformation[C]//The 74th Annual Interna-tional Meeting of SEG Expanded Abstracts,2004:1993-1996.
[6]Berkhout A J,Verschuur D J.Focal transformation,an imaging con-cept for signal restoration and noise remova[J].Geophysics,2006,71(6):A55-A59.
[7]Elad M,Starck J L,Querre P,et al.Simulataneous Cartoon andTextureImage Inpainting using Morphological Component Analysis(MCA)[C]//Appl.Comput.Harmon.Anal,2005,19:340-358.
[8]Daubechies I,Defrise M,Mol C D.An iterative thresholding algo-rithm for linear inverse problems with a sparsity constraint[J].Communications on Pure and Applied Mathematics,2004,57:1413-1457.
[9]Daubechies,Teschke G,Vese L.Iteratively Solving Linear InverseProblems under General Convex Constraints:ZIB-Report[J].2006:1-20.
[2]Candès E,Donoho D.Curvelets:A surprisingly effective nonadap-tive representation of objects with edges[M].TN:Vanderbilt Uni-versity Press,1999.
[3]Herrmann F,Hennenfent G,Moghaddam P.Seismic imaging andprocessing with curvelets[C]//The 69th Annual InternationalMeeting of SEG Expanded Abstracts.
[4]Lexing Ying,Laurent Demanet,Emmanuel Candès.3D DiscreteCurvelet Transform[M].Applied and Computational Mathematics,2006.
[5]Berkhout A J,Verschuur D J,Romijn R.Reconstruction of seismicdata using the focal transformation[C]//The 74th Annual Interna-tional Meeting of SEG Expanded Abstracts,2004:1993-1996.
[6]Berkhout A J,Verschuur D J.Focal transformation,an imaging con-cept for signal restoration and noise remova[J].Geophysics,2006,71(6):A55-A59.
[7]Elad M,Starck J L,Querre P,et al.Simulataneous Cartoon andTextureImage Inpainting using Morphological Component Analysis(MCA)[C]//Appl.Comput.Harmon.Anal,2005,19:340-358.
[8]Daubechies I,Defrise M,Mol C D.An iterative thresholding algo-rithm for linear inverse problems with a sparsity constraint[J].Communications on Pure and Applied Mathematics,2004,57:1413-1457.
[9]Daubechies,Teschke G,Vese L.Iteratively Solving Linear InverseProblems under General Convex Constraints:ZIB-Report[J].2006:1-20.
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