Focal变换及其在地震数据去噪和插值中的应用研究
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摘要
Berkhout等人提出的SRME方法通过时空域褶积来预测多次波,在这个理论基础上将褶积过程用互相关过程来代替,引出了本文多用的Focal变换法。应用Focal变换法进行地震数据随机噪声衰减和地震缺失道的插值,是本文的研究重点。
本文除利用常规的聚焦变换法做处理外,还在前人的工作基础上,将Curvelet阈值迭代法与聚焦变换结合,将去噪和插值的问题转换为解优化反演问题。其中在做随机噪声去除时,通过FX反褶积法和Curvelet阈值迭代法与其作对比,数学模型实验表明,将常规聚焦变换方法与Curvelet阈值迭代法结合,能够更好的提高资料的信噪比。
另外通过实验得知,无论是常规方法还是新聚焦变换法在做地震缺失道插值时,都可以达到良好的效果,结合方法的效果更优,尤其是在大比例缺失的情况下,几乎可以达到完好插值。结合三维Curvelet变换的新Focal变换方法,避免了二维插值情况下对大比例缺失不能很好插值的缺陷。
Oil and gas resources are important energy for human survival and development. Nowadays, with the increasing levels of exploration and the continuous extension of the exploration area, seismic exploration is becoming much more difficult than ever before. Complex surface and geological conditions led to variety of deep seismic signal distortion,as a result, the signal to noise ratio of seismic record is lower.Also complex noise type and weak effective signals severely restricted the high-resolution seismic data processing.Seismic data.We continuous search for more efficient signal processing method,in order to deal with various problems in seismic data processing. Focus transformation is a new data processing method recently been proposed,which is based on SRME method.This transformation is a adaptive process, regardless of medium effect on the wave propagation characteristics. Applying this method in seismic data processing helps us open new ideas in signal to noise ratio improvement.
This paper systematicly studied the new Focal transformation which is based on conventional Focal and combined with the Curvelet iteration threshold method. For the purpose of dealing with noise attenuation of seismic data and seismic interpolation deletion trace. We focused on the problem of random noise attenuation of seismic data processing and seismic deficiency trace interpolation based on the high signal energy concentration of Focal transformation and good sparsity of Curvelet transformation.
Focus transformation was first introduced in 2003 by Berkhout, applied on anti-aliasing noise in 2004. The method was originated in the removal of free surface multiples (SRME) method.However, The process is exactly the opposite. Instead of using original weighted convolution, cross-correlation process was applied.It has been found that through focused transformation, the surface effect on the wave propagation was removed, and the purpose of multiple wave reduction can be achieved.According to this feature, focus transformation can be applied to seismic data processing as a process tool. The focus is how to build a appropriate focusing operator according to obtained seismic data, and then remove random noise. Similarly, if processing coherent noise, we build the corresponding operator under different circumstances.
In this paper, we combined Curvelet iteration threshold with conventional Focal transformation based on the work of predecessors, and applied this method on the random noise attenuation and seismic deficiency trace interpolation. Known from previous work in two-dimensional case, Curvelet threshold iterative method can achieve good results in denoising.However, when the percentage of trace loss is greater than 40%, the interpolation result is getting poorer and poorer with the increasing percentage of loss ratio, Pseudo-frequency noise can not be removed too. Three-dimensional Curvelet transform was applied in processing in this paper. Three-dimensional transformation is an extension of two-dimensional transform, the mathematical theory is same with two-dimensional transform. Two-dimensional transform has given the best description for two-dimensional objects which has singular points along smooth curves. Similarly, three-dimensional Curvelet transform has given the best optimized description of three-dimensional objects which has singular point along a smooth two-dimensional surface. The algorithm can be obtained from two-dimensional transformation.
After the combination with Curvelet iteration threshold, the new focal transformation converted the processing problem to the solving sparse optimization Inversion problem. Based on the work of predecessors known, Curvelet transform has better sparse nature than Fourier transform and wavelet transform,which has laid a theoretical foundation for the better processing results of this new method. Thus, new denoising and interpolation method can be described as one-norm optimization inverse problem.
Seismic data noise (random noise reduction and aliasing noise reduction) is the main contents of this paper. Based on previous work,I make a systematic analysis on the subject and relevant issues,which is focus on the application research of Focal transformation in seismic data processing. Mainly completed the following work: (1)Through inspection and collection of relevant information,I make in-depth understanding and analysis in Focal transformation and relevant content:
①Berkhout data matrix representation, and the derivation of WRW model forward seismic data principle.
②Start by the removal of free surface multiples, introduced the principle of Focal transformation.
③Dscourse of Focusing operator constructing
(2)Systematically understand the principle of Curvelet transform, focused on the 3D Curvelet transform developed on the second-generation discrete Curvelet transform.
①Develop process of Curvelet transform
②2D transform theory,and the extended 3D transformation principle
③Discussed the inverse demand optimization problem from the combination of Curvelet transform and Iteration threshold. (3)The core of this paper is the Formation of Sparse inverse optimization problem form the combination of Curvelet transform and Iteration threshold. (4)Processing model data spreadsheet under the guidance of the above theory, which verifies the correctness and effectiveness of this approach. (5)Summarizing my work.
本文除利用常规的聚焦变换法做处理外,还在前人的工作基础上,将Curvelet阈值迭代法与聚焦变换结合,将去噪和插值的问题转换为解优化反演问题。其中在做随机噪声去除时,通过FX反褶积法和Curvelet阈值迭代法与其作对比,数学模型实验表明,将常规聚焦变换方法与Curvelet阈值迭代法结合,能够更好的提高资料的信噪比。
另外通过实验得知,无论是常规方法还是新聚焦变换法在做地震缺失道插值时,都可以达到良好的效果,结合方法的效果更优,尤其是在大比例缺失的情况下,几乎可以达到完好插值。结合三维Curvelet变换的新Focal变换方法,避免了二维插值情况下对大比例缺失不能很好插值的缺陷。
Oil and gas resources are important energy for human survival and development. Nowadays, with the increasing levels of exploration and the continuous extension of the exploration area, seismic exploration is becoming much more difficult than ever before. Complex surface and geological conditions led to variety of deep seismic signal distortion,as a result, the signal to noise ratio of seismic record is lower.Also complex noise type and weak effective signals severely restricted the high-resolution seismic data processing.Seismic data.We continuous search for more efficient signal processing method,in order to deal with various problems in seismic data processing. Focus transformation is a new data processing method recently been proposed,which is based on SRME method.This transformation is a adaptive process, regardless of medium effect on the wave propagation characteristics. Applying this method in seismic data processing helps us open new ideas in signal to noise ratio improvement.
This paper systematicly studied the new Focal transformation which is based on conventional Focal and combined with the Curvelet iteration threshold method. For the purpose of dealing with noise attenuation of seismic data and seismic interpolation deletion trace. We focused on the problem of random noise attenuation of seismic data processing and seismic deficiency trace interpolation based on the high signal energy concentration of Focal transformation and good sparsity of Curvelet transformation.
Focus transformation was first introduced in 2003 by Berkhout, applied on anti-aliasing noise in 2004. The method was originated in the removal of free surface multiples (SRME) method.However, The process is exactly the opposite. Instead of using original weighted convolution, cross-correlation process was applied.It has been found that through focused transformation, the surface effect on the wave propagation was removed, and the purpose of multiple wave reduction can be achieved.According to this feature, focus transformation can be applied to seismic data processing as a process tool. The focus is how to build a appropriate focusing operator according to obtained seismic data, and then remove random noise. Similarly, if processing coherent noise, we build the corresponding operator under different circumstances.
In this paper, we combined Curvelet iteration threshold with conventional Focal transformation based on the work of predecessors, and applied this method on the random noise attenuation and seismic deficiency trace interpolation. Known from previous work in two-dimensional case, Curvelet threshold iterative method can achieve good results in denoising.However, when the percentage of trace loss is greater than 40%, the interpolation result is getting poorer and poorer with the increasing percentage of loss ratio, Pseudo-frequency noise can not be removed too. Three-dimensional Curvelet transform was applied in processing in this paper. Three-dimensional transformation is an extension of two-dimensional transform, the mathematical theory is same with two-dimensional transform. Two-dimensional transform has given the best description for two-dimensional objects which has singular points along smooth curves. Similarly, three-dimensional Curvelet transform has given the best optimized description of three-dimensional objects which has singular point along a smooth two-dimensional surface. The algorithm can be obtained from two-dimensional transformation.
After the combination with Curvelet iteration threshold, the new focal transformation converted the processing problem to the solving sparse optimization Inversion problem. Based on the work of predecessors known, Curvelet transform has better sparse nature than Fourier transform and wavelet transform,which has laid a theoretical foundation for the better processing results of this new method. Thus, new denoising and interpolation method can be described as one-norm optimization inverse problem.
Seismic data noise (random noise reduction and aliasing noise reduction) is the main contents of this paper. Based on previous work,I make a systematic analysis on the subject and relevant issues,which is focus on the application research of Focal transformation in seismic data processing. Mainly completed the following work: (1)Through inspection and collection of relevant information,I make in-depth understanding and analysis in Focal transformation and relevant content:
①Berkhout data matrix representation, and the derivation of WRW model forward seismic data principle.
②Start by the removal of free surface multiples, introduced the principle of Focal transformation.
③Dscourse of Focusing operator constructing
(2)Systematically understand the principle of Curvelet transform, focused on the 3D Curvelet transform developed on the second-generation discrete Curvelet transform.
①Develop process of Curvelet transform
②2D transform theory,and the extended 3D transformation principle
③Discussed the inverse demand optimization problem from the combination of Curvelet transform and Iteration threshold. (3)The core of this paper is the Formation of Sparse inverse optimization problem form the combination of Curvelet transform and Iteration threshold. (4)Processing model data spreadsheet under the guidance of the above theory, which verifies the correctness and effectiveness of this approach. (5)Summarizing my work.
引文
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[5]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,2005(35): 1-8.
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[7] Kabir, M.M.N., Verschuur, D.J. Restoration of missing offsets by parabolic radon transform[J]. Geophysical Prospecting, 1995, 43(3): 347-368.
[8] A.J. Berkhout. Seismic Migration:Imaging of acoustic energy by wave field extrapolation[M]. Elsevier Scientific Pub.Com., 1982.
[9] Verschuur, D.J., A.J. Berkhout, C.P.A. Wapenaar. Adaptive surface-related multiple elimination[J]. Geophysics, 1992, 57, 1166-1177.
[10] A.J. Berkhout, D.J. Verschuur. Imaging of multiple reflections[J]. Geophysics, 2006, 71(4): S1209-S1220.
[11] A.J. Berkhout, D.J. Verschuur. Focal transformation, an imaging concept for signal restoration and noise removal[J]. Geophysics, 2006, 71(6): A55-A59.
[12] Harlan, W.S., J.F. Claerbout, F. Rocca. Signal/noise separation and velocity estimation[J]. Geophysics, 1984, 49, 1169-1180.
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[22] Herrmann F, Hennenfent G, Moghaddam P. Seismic imaging and processing with curvelets[J].the 69th Annual Meeting,Extended Abstracts,EAGE.
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[34]巩向博,韩立国,王恩利,杜立志.压制噪声的高分辨率Radon变换法[J].吉林大学学报,2009, 39(1): 152-157.
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[2]滕吉文. 21世纪地球物理学的机遇与挑战[J].地球物理学进展,2004(02): 208-215.
[3]何樵登,熊维纲.应用地球物理教程—地震勘探[M].北京:科学出版社,2005.
[4]张军华,吕宁,田连玉,陆文志,钟磊.地震资料去噪方法技术综合评价[J].地球物理学进展,2006, 21 (2):546-553.
[5]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,2005(35): 1-8.
[6]李信富,李小凡.地震数据重建方法原理及运用[J].物探化探计算技术,2008,30(5): 357-362.
[7] Kabir, M.M.N., Verschuur, D.J. Restoration of missing offsets by parabolic radon transform[J]. Geophysical Prospecting, 1995, 43(3): 347-368.
[8] A.J. Berkhout. Seismic Migration:Imaging of acoustic energy by wave field extrapolation[M]. Elsevier Scientific Pub.Com., 1982.
[9] Verschuur, D.J., A.J. Berkhout, C.P.A. Wapenaar. Adaptive surface-related multiple elimination[J]. Geophysics, 1992, 57, 1166-1177.
[10] A.J. Berkhout, D.J. Verschuur. Imaging of multiple reflections[J]. Geophysics, 2006, 71(4): S1209-S1220.
[11] A.J. Berkhout, D.J. Verschuur. Focal transformation, an imaging concept for signal restoration and noise removal[J]. Geophysics, 2006, 71(6): A55-A59.
[12] Harlan, W.S., J.F. Claerbout, F. Rocca. Signal/noise separation and velocity estimation[J]. Geophysics, 1984, 49, 1169-1180.
[13] D.O. Trad. Interpolation and multiple attenuation with migration operators[J]. Geophysics, 2003, 68, 2043-2054.
[14] A.J. Berkhout, D.J. Verschuur. Transformation of multiples into primary reflections[C]. 73rd Annual International Meeting, SEG, Expanded Abstracts, 2003, p1925-1928.
[15] A.J. Berkhout, D.J. Verschuur, R.Romijn. Reconstruction of seismic data using the focal transformation[C]. 74th Annual International Meeting, SEG, ExpandedAbstracts, 2004, p1993-1996.
[16] G.J.A. van Groenestijn, D.J. Verschuur, Reconstruction of missing data from multiples using the focal transform[C]. SEG, 2006, 2737-2741.
[17] A.Dutt and V.Rokhlin. Fast Fourier transforms for nonequispaced data[J] SIAM J.Sci.Stat.Comput, 1993, 14(6):1368-1393.
[18] Candès EJ. Ridgelets: a key to higher-dimensional intermittency[J]. Philosophical Transactions: Mathematical, Physical and Engineering Sciences, 1999, 357(1760):2495-2509.
[19]侯彪,刘芳,焦李成.基于脊波变换的直线特征检测[J].中国科学(E辑),2003,33(1):65-73.
[20] Candès E, Donoho D. Curvelets:A surprisingly effective nonadaptive representation of objects with edges[M].TN:Vanderbilt University Press,1999.
[21] Herrmann FJ, Verschuur E. Curvelet-domain multiple elimination with sparseness constraints[C]. Society of Exploration Geophysicists, Expanded Abstracts, 2004, p1333-1336.
[22] Herrmann F, Hennenfent G, Moghaddam P. Seismic imaging and processing with curvelets[J].the 69th Annual Meeting,Extended Abstracts,EAGE.
[23] Herrmann FJ, Moghaddam P, Stolk C. Sparsity-and continuity-promoting seismic image recovery with curvelets frames[J]. Applied and Computational Harmonic Analysis, 2007.
[24]张素芳,徐义贤,雷栋.基于Curvelet变换的多次波去除技术[J].石油地球物理勘探,2006,41(3):262-265.
[25]刘冰.基于Curvelet变换的地震数据去噪方法研究[D].长春:吉林大学,2008.
[26]仝中飞. Curvelet阈值迭代法在地震数据去噪和插值中的应用研究[D].长春:吉林大学,2009.
[27] Lexing Ying, Laurent Demanet, Emmanuel Candès. 3D Discrete Curvelet Transform[R]. Applied and Computational Mathematics.
[28]李庆忠.走向精确勘探的道路——高分辨率勘探系统工程分析[M]石油工业出版社,1994.
[29]郝雪.地震勘探资料中的随机噪声消除方法[D].长春:吉林大学,2007.
[30] Huang J, Milkereit B. Wave equation based separation of P- and S-wave modes[J]. 75th Annual International Meeting, Society of Exploration Geophysicists,Expanded Abstracts,2007:2135-2139.
[31]刘喜武,刘洪,李幼铭.独立分量分析及其在地震信息处理中应用初探[J].地球物理学进展,2003,18(1):90-96.
[32]陆文凯,骆毅,赵波等人.基于独立分量分析的多次波自适应相减技术[J].地球物理学报,2004,47(5):886-891.
[33]张山. F-x域内提高地震资料信噪比[J].石油地球物理勘探, 1992, 27(5):648-653.
[34]巩向博,韩立国,王恩利,杜立志.压制噪声的高分辨率Radon变换法[J].吉林大学学报,2009, 39(1): 152-157.
[35] Brian Russell, Dan Hampson, Joong Chun. Noise elimination and the radon transform, Part1[J]. The Leading Edge, 1990,9(11):18-23.
[36] Brian Russell, Dan Hampson, Joong Chun. Noise elimination and the radon transform, Part2[J]. The Leading Edge, 1990,9(11):31-37.
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