基于盲信号分离的多次波自适应相减技术
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摘要
多次波问题是地震勘探领域的一个突出问题,多次波压制算法的研究已经成为地震勘探领域必不可少的一项重要内容。本文将盲信号分离算法中的约束盲分离算法与多次波压制问题相结合,对基于约束盲分离方法的多次波自适应相减技术进行了比较深入的研究,针对现有的约束盲分离方法存在的问题提出了一些改进方法并取得了一定的成果。
约束盲信号分离方法是盲信号处理领域的一个研究热点,主要研究在对源信号有一定先验知识的基础上,如何将这些先验知识转化为约束条件进而利用相应的约束优化算法与盲源分离算法对盲信号分离问题进行求解。现有的用于解决多次波自适应相减问题的约束盲分离算法主要是基于地震信号的稀疏性的。本文对现有的稀疏盲分离算法提出了两种改进方法。
针对现有方法中分离出的一次波的同相轴产生畸变等问题,本文引入地震信号同相轴固有的连续性作为约束条件加入到算法当中,提出了一种连续性约束独立分量分析的算法。地震信号的横向连续性可以利用预测误差滤波器来表示。在算法的实现过程中,本文对多次波压制问题建模、子波差异消除方法、混合矩阵求解方法以及欠定情况下盲分离的求解方法等多方面都进行了一定的探讨。对合成数据与真实数据的实验结果表明该方法优于现有的约束盲分离算法。
对于欠定情况下的盲分离问题,文中提出了一种基于频域连续性的求解方法,利用频域预测误差滤波器转化的约束条件构建方程,将原有欠定问题的求解转化为超定方程的求解问题,对合成数据的初步实验结果表明该方法优于现有的约束盲分离算法。
It has been widely acknowledged that the research of multiple attenuation algorithms has become one of the most important subjects in the area of seismic exploration. This paper focuses on the research of adaptive multiple attenuation techonology based on constrained blind source separation method. The author presents some effective methods to improve current constrained blind source separation method and thus to solve some existing issues on multiple attenuation algorithms.
Constrained blind source separation method has received more and more attention in the area of blind source separation. The main focus of this subject is to convert priori knowledge on sources to constraints and solve blind source separation problem based on corresponding constrained optimization algorithms and blind source separation algorithms. Current constrained blind source separation algorithms which are designed for adaptive multiple attenuation is mainly based on sparsity of seismic data. This paper proposes two methods to improve existing constrained blind source separation algorithms.
In order to address the issues such as damages to primaries etc., this paper incorporates continuity of seismic data as constraints into algorithms and thus proposes a new algorithm of continuity constrained independent component analysis. During the realization phase of this algorithm, the author researched into many methods and issues such as multiple attenuation modeling, wavelet difference elimination method, mixed matrix and under-determined blind source separation etc. Experimental results on synthetic data and real data show that the algorithm this paper presents is better than current constrained blind source separation algorithms.
In addition to the research above, this paper proposes a method based on continuity in frequency domain to solve under-determined blind source separation problem. This method makes use of constraints provided by prediction error filter in frequency domain, and converts previous under-determined problem to determined problem. Experimental results on synthetic data prove that this method is more effective than current constrained blind source separation.
约束盲信号分离方法是盲信号处理领域的一个研究热点,主要研究在对源信号有一定先验知识的基础上,如何将这些先验知识转化为约束条件进而利用相应的约束优化算法与盲源分离算法对盲信号分离问题进行求解。现有的用于解决多次波自适应相减问题的约束盲分离算法主要是基于地震信号的稀疏性的。本文对现有的稀疏盲分离算法提出了两种改进方法。
针对现有方法中分离出的一次波的同相轴产生畸变等问题,本文引入地震信号同相轴固有的连续性作为约束条件加入到算法当中,提出了一种连续性约束独立分量分析的算法。地震信号的横向连续性可以利用预测误差滤波器来表示。在算法的实现过程中,本文对多次波压制问题建模、子波差异消除方法、混合矩阵求解方法以及欠定情况下盲分离的求解方法等多方面都进行了一定的探讨。对合成数据与真实数据的实验结果表明该方法优于现有的约束盲分离算法。
对于欠定情况下的盲分离问题,文中提出了一种基于频域连续性的求解方法,利用频域预测误差滤波器转化的约束条件构建方程,将原有欠定问题的求解转化为超定方程的求解问题,对合成数据的初步实验结果表明该方法优于现有的约束盲分离算法。
It has been widely acknowledged that the research of multiple attenuation algorithms has become one of the most important subjects in the area of seismic exploration. This paper focuses on the research of adaptive multiple attenuation techonology based on constrained blind source separation method. The author presents some effective methods to improve current constrained blind source separation method and thus to solve some existing issues on multiple attenuation algorithms.
Constrained blind source separation method has received more and more attention in the area of blind source separation. The main focus of this subject is to convert priori knowledge on sources to constraints and solve blind source separation problem based on corresponding constrained optimization algorithms and blind source separation algorithms. Current constrained blind source separation algorithms which are designed for adaptive multiple attenuation is mainly based on sparsity of seismic data. This paper proposes two methods to improve existing constrained blind source separation algorithms.
In order to address the issues such as damages to primaries etc., this paper incorporates continuity of seismic data as constraints into algorithms and thus proposes a new algorithm of continuity constrained independent component analysis. During the realization phase of this algorithm, the author researched into many methods and issues such as multiple attenuation modeling, wavelet difference elimination method, mixed matrix and under-determined blind source separation etc. Experimental results on synthetic data and real data show that the algorithm this paper presents is better than current constrained blind source separation algorithms.
In addition to the research above, this paper proposes a method based on continuity in frequency domain to solve under-determined blind source separation problem. This method makes use of constraints provided by prediction error filter in frequency domain, and converts previous under-determined problem to determined problem. Experimental results on synthetic data prove that this method is more effective than current constrained blind source separation.
引文
[1]牛滨华,沈操,黄新武.波动方程多次波压制技术的进展.地球物理学进展. 2002. 17(3):480-485
[2] Jutten C and Herault J. 1986. Space or time adaptive signal processing by neural network models. International Conference on Neural Networks for Computing. 206-211
[3] Giannakis G B, Swami A. New results on state-space and input-output indentification of non-Gaussian processing using cumulants. In: Proc. SPIE’87, San Diego, CA, 1987, 826:199-205
[4] Linsker R. Self-organization in a perceptual network. Computer, 1988, 21: 105-117
[5] Linsker R. An application of the principle of maximum information preservation to linear systems. Adv. Neural Inform. Processing Systems, 1989
[6] Jutten C and Herault J. 1991. Blind separation of sources. Part I: an adaptive algorithm based on neuromimetic architecture. Signal Processing. 24:1-10
[7] Comon P, Jutten C and Herault J. 1991. Blind separation of sources, Part II: problems statements. Signal Processing. 24:11-20
[8] Sorouchyari E. 1991. Blind separation of sources. Part III: stability analysis. Signal Processing. 24:21-29
[9] Tong L, Liu R W, Soon V C, et al. 1991. Indeterminacy and identifiability of blind identification. IEEE Transactions on Circuits and Systems. 38(5):499-509
[10] Comon P. 1994. Independent component analysis—a new concept? Signal Processing. 36:287-314
[11] Cichocki A,Unbehauen R,Moszczynski L,et al. A new on-line adaptive learning algorithm for blind separation of source signals. In: ISANN94,Taiwan,1994: 406-411
[12] Bell A J and Sejnowski T J. 1995. An information maximization approach to blind separation and blind deconvolution. Neural Computation. 7:1129-1159
[13]李艳东.约束盲信号分离算法及应用研究[博士学位论文].北京:清华大学,2006
[14] Cardoso J F and Laheld B. 1996. Equivariant adaptive source separation. IEEE Transactions on Signal Processing. 44(12): 3017-3030
[15] Amari S, Cichocki A and Yang H H. 1996. A new learning algorithm for blind signal separation. Advances in Neural Information Processing Systems (NIPS’96). 757-763
[16] Hyv?rinen A. 1999a. Fast and robust fixed-point algorithms for independent component analysis. IEEE Transactions on Neural Networks. 10(3):626-634
[17] Karhunen J, Pajunen P and Oja E. 1998. The nonlinear PCA criterion in blind source separation: Relations with other approaches. Neurocomputing. 22:5-20
[18] Pham D, Garrat P and Jutten C. 1992. Separation of a mixture of independent sources through a maximum likelihood approach. European Signal Processing Conference. 771-774
[19] Cardoso J F. 1997. Infomax and maximum likelihood for source separation. IEEE Signal Processing Letters. 4:112-114
[20] Cardoso J F. 1998a. Blind signal separation: statistical principles. Proceedings of the IEEE. 86(10):2009-2025
[21] Pearlmutter B A and Parra L C. 1996. A context-sensitive generalization of ICA. Proc. of the International Conference on Neural Information Processing (ICONIP’96). 151-157
[22] Lee T W, Girolami M and Sejnowski T. 2000. A unifying framework for independent component analysis. International Journal on Mathematical and Computer Modelling 39(11):1-21
[23] Karhunen J, Pajunen P and Oja E. 1998. The nonlinear PCA criterion in blind source separation: Relations with other approaches. Neurocomputing. 22:5-20
[24] Cichocki A, Karhunen J, Kasprzak W, et al. 1999. Neural networks for blind separation with unknown number of sources. Neurocomputing. 24:55-93
[25] Amari S T, Chen and Cichocki A. 2000. Nonholonomic orthogonal constraints in blind source separation. Neural Computatation. 12(6): 1463-1484
[26] Yuan Z, Oja E.A FastICA Algorithm for Non-negative Independent Component Analysis.In: Proc. ICA2004,Granada,Spain,2004:1-8
[27] Zibulevsky M and Pearlmutter B A. 2001. Blind source separation by sparse decomposition in a signal dictionary. Neural Computation 13(4): 863-882
[28] Gharbi A and Salam F. 1997. Algorithm for blind signal separation and recovery in static and dynamic environments. Proc. of the IEEE Symposium on Circuits and Systems. 713-719
[29] Salam F and Erten G.1999. The state space framework for blind dynamic signal extraction and recovery. IEEE International Symposium on. Circuits and Systems. 5:66-69
[30] Zhang L Q and Cichocki A. 2000. Blind deconvolution of dynamical systems: a state space approach. Journal of Signal Processing. 4(2):111-130
[31] Weglein A B. 1999. Multiple attenuation: an overview of recent advance and the road ahead. The Leading Edge. 18:40-44
[32] Backus M M. Water reverberations - their nature and elimination. Geophysics,1959,24 (2):233-261
[33] Robinson E A. Principles of digital Wiener filtering. Geophysical Prospecting,1967,15 (3):311-333
[34] Foster D J. Suppression of multiple reflections using the Radon transform. Geophysics,1992, 57 (3):386-395
[35] Yilmaz O. Velocity stack processing. Geophysical Prospecting,1989,37 (4):357-382
[36] Anstey N A, Newman P. Part I-The sectional autocorrelogram; Part II-The sectional retro-correlogram[J]. Geophysical Prospecting, 1966, 14:389-426
[37] Riley D C. Multiple reflections. Geophysics,1976,41 (4):592-620
[38] Morley L. Predictive deconvolution in short-receiver space. Geophysics, 1983, 48 (5):515-531
[39] Wiggins J W. Attenuation of complex water-bottom multiples by wave equation based prediction and sub-traction. Geophysics,1988,53 (12):1527-1539
[40] Verschurr D J. Adaptive surface related multiple elimination. Geophysics,1992,57 (9):1166-1177
[41] Berkhout A J, Verschuur D J. Estimation of multiple scattering by iterative inversion, part I-Theoretical considerations[J]. Geophysics, 1997, 62:1586-1596
[42] Kelamis P G,Verschuur D J. Surface-related multiple elimination on land seismic data—Strategies via case studies[J].Geophysics,2000,65:719-734.
[43] Wang Y. Multiple prediction through inversion: a fully data driven concept for surface-related multiple attenuation[J].Geophysics,2004,69:547-553
[44] Zibulevsky M and Pearlmutter B A. 2001. Blind source separation by sparse decomposition in a signal dictionary. Neural Computation 13(4): 863-882
[45] Bofill P and Zibulevsky M. 2001. Underdetermined blind source separation using sparse representations. Signal Processing. 81:2353-2362
[46] Hyv?rinen A and Oja E. 1998. Independent component analysis by general non-linear Hebbian-like learning rules. Sginal Processing. 64(3):301-313
[47] Cardoso J F. 1999b. Higher-order contrasts for independent component analysis. Neural Computation. 11:157-192
[48]陈祖传,多次波的剩余时差分析法.北京:石油工业出版社,1997.
[49] Haykin S. 1998.自适应滤波器原理.北京:电子工业出版社
[50] Abma R and Claerbout J. 1997a. Application of 2D deconvolution. Stanford Exploration Project. Report 77: 289-303
[51] Abma R and Claerbout J. 1997b. Lateral prediction for noise attenuation by t-x and f-x techniques. Stanford Exploration Project. Report 70:15-35
[52] Claerbout J. 1998. Multidimensional recursive filters via a helix. Geophysics. 63:1532-1541
[53] Dragoset W H and Jericevic Z. 1998. Some remarks on surface multiple attenuation. Geophysics. 63:772-789
[54] Guo J. 2003. Adaptive multiple subtraction with a pattern-based technique. SEG Expanded Abstracts. 21:1953-1956
[55] Spitz S. 1999. Pattern recognition, spatial predictivity, and subtraction of multiple events. The Leading Edge. 18:55-59
[56] Luo Y, Kelamis P G and Wang Y. 2003. Simultaneous inversion of multiples and primaries: inversion versus subtraction. The Leading Edge. 22:814-819
[57] Lu W K, Luo Y, Zhao B, et al. 2003. Adaptive multiple subtraction using independent component analysis. SEG Expanded Abstract. 22:2048-2051
[58] Lu W K, Luo Y, Zhao B, et al. 2004. Adaptive multiple wave subtraction using independent component analysis. Chinese Journal of Geophysics. 47:886-891
[59] Lu W K and Mao F. 2005. Adaptive multiple subtraction using independent component analysis. The Leading Edge. 24:282-284
[60] Guitton A. 2005. Multiple attenuation in complex geology with a pattern-based approach. Geophysics. 70:V97-V107
[61] Chen S B, Donoho D L and Saunders M A. 1998. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing. 20(1):33-61
[62] Ray Abma and Jon Claerbout. Lateral prediction for noise attenuation by t-x and f-x techniques. GEOPHYSICS 60 (6): 1887-1896 NOV-DEC 1995
[2] Jutten C and Herault J. 1986. Space or time adaptive signal processing by neural network models. International Conference on Neural Networks for Computing. 206-211
[3] Giannakis G B, Swami A. New results on state-space and input-output indentification of non-Gaussian processing using cumulants. In: Proc. SPIE’87, San Diego, CA, 1987, 826:199-205
[4] Linsker R. Self-organization in a perceptual network. Computer, 1988, 21: 105-117
[5] Linsker R. An application of the principle of maximum information preservation to linear systems. Adv. Neural Inform. Processing Systems, 1989
[6] Jutten C and Herault J. 1991. Blind separation of sources. Part I: an adaptive algorithm based on neuromimetic architecture. Signal Processing. 24:1-10
[7] Comon P, Jutten C and Herault J. 1991. Blind separation of sources, Part II: problems statements. Signal Processing. 24:11-20
[8] Sorouchyari E. 1991. Blind separation of sources. Part III: stability analysis. Signal Processing. 24:21-29
[9] Tong L, Liu R W, Soon V C, et al. 1991. Indeterminacy and identifiability of blind identification. IEEE Transactions on Circuits and Systems. 38(5):499-509
[10] Comon P. 1994. Independent component analysis—a new concept? Signal Processing. 36:287-314
[11] Cichocki A,Unbehauen R,Moszczynski L,et al. A new on-line adaptive learning algorithm for blind separation of source signals. In: ISANN94,Taiwan,1994: 406-411
[12] Bell A J and Sejnowski T J. 1995. An information maximization approach to blind separation and blind deconvolution. Neural Computation. 7:1129-1159
[13]李艳东.约束盲信号分离算法及应用研究[博士学位论文].北京:清华大学,2006
[14] Cardoso J F and Laheld B. 1996. Equivariant adaptive source separation. IEEE Transactions on Signal Processing. 44(12): 3017-3030
[15] Amari S, Cichocki A and Yang H H. 1996. A new learning algorithm for blind signal separation. Advances in Neural Information Processing Systems (NIPS’96). 757-763
[16] Hyv?rinen A. 1999a. Fast and robust fixed-point algorithms for independent component analysis. IEEE Transactions on Neural Networks. 10(3):626-634
[17] Karhunen J, Pajunen P and Oja E. 1998. The nonlinear PCA criterion in blind source separation: Relations with other approaches. Neurocomputing. 22:5-20
[18] Pham D, Garrat P and Jutten C. 1992. Separation of a mixture of independent sources through a maximum likelihood approach. European Signal Processing Conference. 771-774
[19] Cardoso J F. 1997. Infomax and maximum likelihood for source separation. IEEE Signal Processing Letters. 4:112-114
[20] Cardoso J F. 1998a. Blind signal separation: statistical principles. Proceedings of the IEEE. 86(10):2009-2025
[21] Pearlmutter B A and Parra L C. 1996. A context-sensitive generalization of ICA. Proc. of the International Conference on Neural Information Processing (ICONIP’96). 151-157
[22] Lee T W, Girolami M and Sejnowski T. 2000. A unifying framework for independent component analysis. International Journal on Mathematical and Computer Modelling 39(11):1-21
[23] Karhunen J, Pajunen P and Oja E. 1998. The nonlinear PCA criterion in blind source separation: Relations with other approaches. Neurocomputing. 22:5-20
[24] Cichocki A, Karhunen J, Kasprzak W, et al. 1999. Neural networks for blind separation with unknown number of sources. Neurocomputing. 24:55-93
[25] Amari S T, Chen and Cichocki A. 2000. Nonholonomic orthogonal constraints in blind source separation. Neural Computatation. 12(6): 1463-1484
[26] Yuan Z, Oja E.A FastICA Algorithm for Non-negative Independent Component Analysis.In: Proc. ICA2004,Granada,Spain,2004:1-8
[27] Zibulevsky M and Pearlmutter B A. 2001. Blind source separation by sparse decomposition in a signal dictionary. Neural Computation 13(4): 863-882
[28] Gharbi A and Salam F. 1997. Algorithm for blind signal separation and recovery in static and dynamic environments. Proc. of the IEEE Symposium on Circuits and Systems. 713-719
[29] Salam F and Erten G.1999. The state space framework for blind dynamic signal extraction and recovery. IEEE International Symposium on. Circuits and Systems. 5:66-69
[30] Zhang L Q and Cichocki A. 2000. Blind deconvolution of dynamical systems: a state space approach. Journal of Signal Processing. 4(2):111-130
[31] Weglein A B. 1999. Multiple attenuation: an overview of recent advance and the road ahead. The Leading Edge. 18:40-44
[32] Backus M M. Water reverberations - their nature and elimination. Geophysics,1959,24 (2):233-261
[33] Robinson E A. Principles of digital Wiener filtering. Geophysical Prospecting,1967,15 (3):311-333
[34] Foster D J. Suppression of multiple reflections using the Radon transform. Geophysics,1992, 57 (3):386-395
[35] Yilmaz O. Velocity stack processing. Geophysical Prospecting,1989,37 (4):357-382
[36] Anstey N A, Newman P. Part I-The sectional autocorrelogram; Part II-The sectional retro-correlogram[J]. Geophysical Prospecting, 1966, 14:389-426
[37] Riley D C. Multiple reflections. Geophysics,1976,41 (4):592-620
[38] Morley L. Predictive deconvolution in short-receiver space. Geophysics, 1983, 48 (5):515-531
[39] Wiggins J W. Attenuation of complex water-bottom multiples by wave equation based prediction and sub-traction. Geophysics,1988,53 (12):1527-1539
[40] Verschurr D J. Adaptive surface related multiple elimination. Geophysics,1992,57 (9):1166-1177
[41] Berkhout A J, Verschuur D J. Estimation of multiple scattering by iterative inversion, part I-Theoretical considerations[J]. Geophysics, 1997, 62:1586-1596
[42] Kelamis P G,Verschuur D J. Surface-related multiple elimination on land seismic data—Strategies via case studies[J].Geophysics,2000,65:719-734.
[43] Wang Y. Multiple prediction through inversion: a fully data driven concept for surface-related multiple attenuation[J].Geophysics,2004,69:547-553
[44] Zibulevsky M and Pearlmutter B A. 2001. Blind source separation by sparse decomposition in a signal dictionary. Neural Computation 13(4): 863-882
[45] Bofill P and Zibulevsky M. 2001. Underdetermined blind source separation using sparse representations. Signal Processing. 81:2353-2362
[46] Hyv?rinen A and Oja E. 1998. Independent component analysis by general non-linear Hebbian-like learning rules. Sginal Processing. 64(3):301-313
[47] Cardoso J F. 1999b. Higher-order contrasts for independent component analysis. Neural Computation. 11:157-192
[48]陈祖传,多次波的剩余时差分析法.北京:石油工业出版社,1997.
[49] Haykin S. 1998.自适应滤波器原理.北京:电子工业出版社
[50] Abma R and Claerbout J. 1997a. Application of 2D deconvolution. Stanford Exploration Project. Report 77: 289-303
[51] Abma R and Claerbout J. 1997b. Lateral prediction for noise attenuation by t-x and f-x techniques. Stanford Exploration Project. Report 70:15-35
[52] Claerbout J. 1998. Multidimensional recursive filters via a helix. Geophysics. 63:1532-1541
[53] Dragoset W H and Jericevic Z. 1998. Some remarks on surface multiple attenuation. Geophysics. 63:772-789
[54] Guo J. 2003. Adaptive multiple subtraction with a pattern-based technique. SEG Expanded Abstracts. 21:1953-1956
[55] Spitz S. 1999. Pattern recognition, spatial predictivity, and subtraction of multiple events. The Leading Edge. 18:55-59
[56] Luo Y, Kelamis P G and Wang Y. 2003. Simultaneous inversion of multiples and primaries: inversion versus subtraction. The Leading Edge. 22:814-819
[57] Lu W K, Luo Y, Zhao B, et al. 2003. Adaptive multiple subtraction using independent component analysis. SEG Expanded Abstract. 22:2048-2051
[58] Lu W K, Luo Y, Zhao B, et al. 2004. Adaptive multiple wave subtraction using independent component analysis. Chinese Journal of Geophysics. 47:886-891
[59] Lu W K and Mao F. 2005. Adaptive multiple subtraction using independent component analysis. The Leading Edge. 24:282-284
[60] Guitton A. 2005. Multiple attenuation in complex geology with a pattern-based approach. Geophysics. 70:V97-V107
[61] Chen S B, Donoho D L and Saunders M A. 1998. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing. 20(1):33-61
[62] Ray Abma and Jon Claerbout. Lateral prediction for noise attenuation by t-x and f-x techniques. GEOPHYSICS 60 (6): 1887-1896 NOV-DEC 1995