基于小波分析技术的地震信号去噪方法研究
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摘要
地震勘探是一种重要的物探方法,野外采集的地震资料中包含着有关地下构造和岩性的信息,但这些信息与干扰背景相叠加,并且被外界因素所扭曲,不宜直接利用野外资料做地质解释,因此提高其信噪比是地震信号处理的重要任务。本论文着重研究了基于小波分析技术的地震勘探信号的去噪方法。
本文首先介绍地震勘探信号中噪声的特点及形成原因,然后详述小波分析理论;接着研究小波阈值去噪、小波变换模极大值去噪和小波包分析三种去噪方法。由于小波阈值去噪算法中阈值是通过经验公式选取的,对信噪比较低的地震信号去噪效果不好,有效信号损失较大,分辨率低,针对常用阈值选取的这些不足,提出了基于小波熵高分辨率阈值去噪方法,先经过相关性处理保留有效信号的高频信息,提高分辨率,再根据小波熵来选取阈值,小波熵是小波变换和信息熵的结合,通过对含噪的ricker子波、合成地震信号和实际地震信号去噪,验证了该改进算法具有很好的去噪效果。小波变换模极大值去噪算法中最大尺度上的阈值通常根据经验选取,并且在搜索由有效信号产生的模极大值的传播点时容易出现错选现象,针对小波变换模极大值去噪算法的这些不足,提出了小波熵和相关性结合的模极大值去噪方法,根据小波熵来选取最大尺度上的阈值,利用相关性来解决在搜索过程中出现的错选问题,通过对含噪的ricker子波、合成地震信号和实际地震信号去噪,验证了该改进算法具有很好的去噪效果。另外,还运用小波包分层阈值和全局阈值对含噪的ricker子波、合成地震信号和实际地震信号进行去噪处理,小波包分层阈值去噪也具有很好的去噪效果。
Seismic exploration is an important geophysical method, seismic data collected in the field includes the information about the subsurface structure and lithology, but the information is overlaid by background interference, and distorted by external factors. So field datas can not be used to do geological interpretation directly. Thereby, increasing signal to noise ratio is an important task of seismic signal processing. This paper focuses on research of seismic signal de-noising ways based on wavelet analysis.
This paper firstly introduces the characteristics and causes of the noise included in the seismic signal, and then describes wavelet analysis theory in detail; then studies wavelet threshold de-noising, wavelet transform modulus maxima de-noising and wavelet packet analysis. The threshold in the wavelet threshold de-noising algorithm is selected by empirical formula. The de-noising effect is not good for seismic signal of low signal to noise ratio, because the results lead to large effective signal loss and low resolution. For these deficiencies of common threshold selection, we propose a new de-noising method based on wavelet entropy high-resolution threshold. In order to reserving the high frequency information of the effective signal and improving resolution, the high-frequency wavelet coefficient is processed by the correlation. Then the threshold is selected by the wavelet entropy. The wavelet entropy is the combination of wavelet transform entropy and information entropy. Through the de-noising of noisy ricker wavelet, synthetic seismic signal and actual seismic signal, the good effect of this algorithm has been proved. The largest scale threshold in wavelet transforms modulus maxima de-noising algorithm is selected by Exp, and it is prone to be a wrong choice during the process of searching the modulus maximum points generated by valid signal. For these deficiencies of wavelet transform modulus maxima de-noising, we propose a wavelet entropy and correlation with the modulus maxima de-noising method. The threshold on the largest scale is selected by the wavelet entropy, and the wrong choice issue during the the process of searching is solved by the correlation. The improved algorithm has a good de-noising effect during the the process of de-noising the noisy ricker wavelet, the synthetic seismic signal and the actual seismic signal. In addition, we use the method of wavelet packet layered threshold and global threshold to process the noisy ricker wavelet, the synthetic seismic signal and the actual seismic signal. The wavelet packet layered threshold also has a good de-noising effect.
本文首先介绍地震勘探信号中噪声的特点及形成原因,然后详述小波分析理论;接着研究小波阈值去噪、小波变换模极大值去噪和小波包分析三种去噪方法。由于小波阈值去噪算法中阈值是通过经验公式选取的,对信噪比较低的地震信号去噪效果不好,有效信号损失较大,分辨率低,针对常用阈值选取的这些不足,提出了基于小波熵高分辨率阈值去噪方法,先经过相关性处理保留有效信号的高频信息,提高分辨率,再根据小波熵来选取阈值,小波熵是小波变换和信息熵的结合,通过对含噪的ricker子波、合成地震信号和实际地震信号去噪,验证了该改进算法具有很好的去噪效果。小波变换模极大值去噪算法中最大尺度上的阈值通常根据经验选取,并且在搜索由有效信号产生的模极大值的传播点时容易出现错选现象,针对小波变换模极大值去噪算法的这些不足,提出了小波熵和相关性结合的模极大值去噪方法,根据小波熵来选取最大尺度上的阈值,利用相关性来解决在搜索过程中出现的错选问题,通过对含噪的ricker子波、合成地震信号和实际地震信号去噪,验证了该改进算法具有很好的去噪效果。另外,还运用小波包分层阈值和全局阈值对含噪的ricker子波、合成地震信号和实际地震信号进行去噪处理,小波包分层阈值去噪也具有很好的去噪效果。
Seismic exploration is an important geophysical method, seismic data collected in the field includes the information about the subsurface structure and lithology, but the information is overlaid by background interference, and distorted by external factors. So field datas can not be used to do geological interpretation directly. Thereby, increasing signal to noise ratio is an important task of seismic signal processing. This paper focuses on research of seismic signal de-noising ways based on wavelet analysis.
This paper firstly introduces the characteristics and causes of the noise included in the seismic signal, and then describes wavelet analysis theory in detail; then studies wavelet threshold de-noising, wavelet transform modulus maxima de-noising and wavelet packet analysis. The threshold in the wavelet threshold de-noising algorithm is selected by empirical formula. The de-noising effect is not good for seismic signal of low signal to noise ratio, because the results lead to large effective signal loss and low resolution. For these deficiencies of common threshold selection, we propose a new de-noising method based on wavelet entropy high-resolution threshold. In order to reserving the high frequency information of the effective signal and improving resolution, the high-frequency wavelet coefficient is processed by the correlation. Then the threshold is selected by the wavelet entropy. The wavelet entropy is the combination of wavelet transform entropy and information entropy. Through the de-noising of noisy ricker wavelet, synthetic seismic signal and actual seismic signal, the good effect of this algorithm has been proved. The largest scale threshold in wavelet transforms modulus maxima de-noising algorithm is selected by Exp, and it is prone to be a wrong choice during the process of searching the modulus maximum points generated by valid signal. For these deficiencies of wavelet transform modulus maxima de-noising, we propose a wavelet entropy and correlation with the modulus maxima de-noising method. The threshold on the largest scale is selected by the wavelet entropy, and the wrong choice issue during the the process of searching is solved by the correlation. The improved algorithm has a good de-noising effect during the the process of de-noising the noisy ricker wavelet, the synthetic seismic signal and the actual seismic signal. In addition, we use the method of wavelet packet layered threshold and global threshold to process the noisy ricker wavelet, the synthetic seismic signal and the actual seismic signal. The wavelet packet layered threshold also has a good de-noising effect.
引文
[1]王玉英.地震勘探信号降噪处理技术研究[D].大庆石油学院,2006,1~8.
[2]朱晓明.工程地震信号去噪技术研究[D].中国海洋大学,2007,1~14.
[3]王秀明.应用地球物理方法原理[M].北京:石油工业出版社,2000,8:23~25.
[4] L.L.Cales,“Random noise reduction”[J].The 54 th meeting of SEG, 1984, 21:35-40.
[5] I.F.Jones and S.levy,“Signal-to-noise ratio enhancement in multichannel seismic data via the Karhunen-Loeve transform”[J].Geophysical prospecting, 1987, 35:12-32.
[6] D.Donoho,“De-noising by soft-Thresholding”[C].IEEE.Trans.on IT, 1995, 3: 613 -627.
[7]周怀来.基于小波变换的地震信号去噪方法研究与应用[D].成都理工大学,2006:1~7.
[8]付燕.人工地震信号去噪方法研究[D].西北工业大学,2002:1~5.
[9]胡昌华,李国华,刘涛,周志杰.基于MATLAB 6.x的系统分析与设计——小波分析[M].西安:西安电子科技大学出版社,2004,1:1~27
[10] Young R. An introduction to nolinear Fourier series [M].New York Academic, 1980:210-225.
[11] BattleA. Ablocbspin construction of ondelettes [J].Comm. Math. Phys. 1982, 110: 601-615.
[12] Morlet Jetal. Wave propagation and sampling theory and complex waves [J].Geophysics, 1982, 47(2):801-813.
[13] Grossman A and Morlet J. Decomposition of hardy functions into square integrable wavelets of constant shape [J].SIMA J.Math.Anal, 1984, 15:723-736.
[14] Meyer Y. Wavelets: algorithms&applications. Translated by R.D. Ryan, 1993.
[15] Mallat S. Multifrequency channel decomposition of images and wavelet models [J]. IEEE trans.On ASSP, 1989, 37(12):2091-2110.
[16] Mallat S. Multiresolution approximations and wavelet orthonornal bases of L2 (R)[J]. Trans, Amer.Math.Soc, 1989,315 (1):67-87.
[17] Vetlerli M. Wavelet and filter banks: theory and design [J].IEEE trans.On signal Processing, 1991, 40(9):2207-2232.
[18] Daubechies I. Orthonomal bases of compactly supported wavelets [J].Comm. On Pure and Applly Math, 1988, XLI: 909-996.
[19] Cohen A. Daubechies I. Feauveau J C. Biorthogonal bases of compactly supported wavelets [J].Comm. On Pure Appl. Math, 1992, XLV: 485-560
[20] Soman AK. Vaidynanathan PP. Paraunitary filters banks and wavelet packets [M]. ICASSP, 1992: 387-400.
[21]马军海,小波变换在斜拉桥结构检测分析中的应用研究[D].合肥工业大学,2004,6~13.
[22]魏童,小波变换在探地雷达信号中的应用[D].长安大学,2009,14~18.
[23]梁学章,何甲兴,王新民,李强.小波分析[M].北京:国防工业出版社,2005,1:1~40.
[24] P.Burt and E.Adelson,“The Laplacian Pyramid as a compact image code”[J].IEEE Trans. on communications, 1983, 31(4):532-540.
[25] S.Mallat,“A Theory for Multiresolution Signal Decomposition: The Wavelet Representation”[J].IEEE Tran. On pattern Analysis and Machine Intelligence, 1989, 11 (7):874-893.
[26]孙志新.小波分析在地震数据噪声处理中的应用研究[D].中国地震局工程力学研究所,2008,12:51~56.
[27]倪豪.小波消噪与分解对结构地震反应得影响研究[D].大庆石油学院,2004,2:24~29.
[28]兰芸.基于小波变换的振动信号去噪方法研究[D].五邑大学,2008,4:29-40.
[29]陶红艳,秦华峰,余成波.基于改进阈值函数的小波域去噪算法的研究[J].压电与声光,2008,30(1):93-95.
[30] LIU Wei-dong, LIU Shang-he. A New Modified Method Based on Wavelet Threshold De-Noising Functions [J].Chinese Journal of Electron Devices.2007, 30:58-62.
[31]杜继永,黄国荣,程洪炳,刘华伟.基于改进小波阈值法处理MEMS陀螺信号噪声[J].电光与控制,2009,16(12):61-64.
[32]姜绍辉.小波变换及在提高地震资料信噪比中的应用[D].中国海洋大学,2005,6:24~35.
[33]吕瑞兰.小波阈值去噪的性能分析及基于能量元的小波阈值去噪方法研究[D].浙江大学,2003,2:28-29.
[34]张斌,王彤,谷传纲,戴正元.改进的小波阈值消噪法在湍流信号处理中的应用[J].工程热物理学报,2009,30(30):407~410.
[35]刘洋,李承楚.地震资料信噪比估计的几种方法[J].石油地球物理勘探,1997,4:257~262.
[36]孙延奎.小波分析及其应用[M].北京:机械工业出版社,2005,3:224-236.
[37]印欣运,何永勇,彭志科,褚福磊.小波熵及其在状态趋势分析中的应用[J].振动工程学报,2004,17(2):165~169.
[38]陈小勤.基于小波熵测度的电力暂态信号检测与分类方法研究[D].西南交通大学,2006,5:7~15.
[39]何正友,刘志刚,钱清泉.小波熵理论及其在电力系统中应用的可行性探讨[J].电网技术,2004,28(21):17~21.
[40]张荣标,胡海燕,冯友兵.基于小波熵的微弱信号检测方法研究[J].仪器仪表学报,2007,28(11):2078-2083.
[41]何凯,王树勋,戴逸松.基于Shannon熵的1/f类分形信号去噪方法[J].吉林大学学报(信息科学版),2003,21(1):21~26.
[42]李晓飞.小波分析在光谱数据去噪处理中的应用[D].上海交通大学,2009,1:28~32.
[43]田金文,高谦,杜拥军.基于小波变换模极大值的地震信号去噪处理方法[J].江汉石油学院学报,2001,23(1):22~25.
[44]徐长发,李国宽.实用小波方法[M].武汉:华中科技大学出版社,2004,1:107~119.
[45]蒋鹏.小波理论在信号去噪和数据压缩的应用研究[D].浙江大学,2004,5:47~59.
[46]段炜.基于小波变换的探地雷达信号去噪方法研究[D].中南大学,2008,6:43~54.
[47]胡广书.现代信号处理教程[M].北京:清华大学出版社,2001,3:124~146.
[48]姚胜利.地震信号的小波去噪方法研究[D].中南大学,2007,22~37.
[49] Mallat S.G,Zhong S. Characterization of signals from multiscale edges [J].IEEE Trans. Pattern Anal and Machine Intell, 1992, 14(7):710-732,
[50]赵玉宝.小波变换在地震信号去噪中的应用研究[D].中南大学,2005,4:36~45.
[51]陈德智,唐磊,盛剑霓,王恒利.由小波变换的模极大值快速重构信号[J].电子学报,1998,26(9):82-85.
[52]孙丰荣,翟广涛,李艳玲等.由小波变换模极大值重构信号的快速算法[J].小型微型计算机系统,2005,26(12):2147-2149.
[53]刘齐芬.小波包去噪方法研究及其在GPS数据处理中的应用[D].河北师范大学,2008,3:25~30.
[54]吴勇.基于小波的信号去噪方法研究[D].武汉理工大学,2007,5:44~56.
[55]丛丽丽.基于小波包和全变差的图像去噪算法[D].吉林大学,2010,4:24-34.
[56] Wang Sheng-qian, Zou Yuan-hua, Zou Dao-wen.Adaptive shrinkage denosing using the neighborhood characteristic [J].ElectronicsLetters, 2002, 38(11):23-29.
[57]邓承志,汪胜前,刘祝华等.基于层间特性的多级小波收缩去噪算法[J].江西师范大学学报(自然科学版),2004,28(4):334~336.
[2]朱晓明.工程地震信号去噪技术研究[D].中国海洋大学,2007,1~14.
[3]王秀明.应用地球物理方法原理[M].北京:石油工业出版社,2000,8:23~25.
[4] L.L.Cales,“Random noise reduction”[J].The 54 th meeting of SEG, 1984, 21:35-40.
[5] I.F.Jones and S.levy,“Signal-to-noise ratio enhancement in multichannel seismic data via the Karhunen-Loeve transform”[J].Geophysical prospecting, 1987, 35:12-32.
[6] D.Donoho,“De-noising by soft-Thresholding”[C].IEEE.Trans.on IT, 1995, 3: 613 -627.
[7]周怀来.基于小波变换的地震信号去噪方法研究与应用[D].成都理工大学,2006:1~7.
[8]付燕.人工地震信号去噪方法研究[D].西北工业大学,2002:1~5.
[9]胡昌华,李国华,刘涛,周志杰.基于MATLAB 6.x的系统分析与设计——小波分析[M].西安:西安电子科技大学出版社,2004,1:1~27
[10] Young R. An introduction to nolinear Fourier series [M].New York Academic, 1980:210-225.
[11] BattleA. Ablocbspin construction of ondelettes [J].Comm. Math. Phys. 1982, 110: 601-615.
[12] Morlet Jetal. Wave propagation and sampling theory and complex waves [J].Geophysics, 1982, 47(2):801-813.
[13] Grossman A and Morlet J. Decomposition of hardy functions into square integrable wavelets of constant shape [J].SIMA J.Math.Anal, 1984, 15:723-736.
[14] Meyer Y. Wavelets: algorithms&applications. Translated by R.D. Ryan, 1993.
[15] Mallat S. Multifrequency channel decomposition of images and wavelet models [J]. IEEE trans.On ASSP, 1989, 37(12):2091-2110.
[16] Mallat S. Multiresolution approximations and wavelet orthonornal bases of L2 (R)[J]. Trans, Amer.Math.Soc, 1989,315 (1):67-87.
[17] Vetlerli M. Wavelet and filter banks: theory and design [J].IEEE trans.On signal Processing, 1991, 40(9):2207-2232.
[18] Daubechies I. Orthonomal bases of compactly supported wavelets [J].Comm. On Pure and Applly Math, 1988, XLI: 909-996.
[19] Cohen A. Daubechies I. Feauveau J C. Biorthogonal bases of compactly supported wavelets [J].Comm. On Pure Appl. Math, 1992, XLV: 485-560
[20] Soman AK. Vaidynanathan PP. Paraunitary filters banks and wavelet packets [M]. ICASSP, 1992: 387-400.
[21]马军海,小波变换在斜拉桥结构检测分析中的应用研究[D].合肥工业大学,2004,6~13.
[22]魏童,小波变换在探地雷达信号中的应用[D].长安大学,2009,14~18.
[23]梁学章,何甲兴,王新民,李强.小波分析[M].北京:国防工业出版社,2005,1:1~40.
[24] P.Burt and E.Adelson,“The Laplacian Pyramid as a compact image code”[J].IEEE Trans. on communications, 1983, 31(4):532-540.
[25] S.Mallat,“A Theory for Multiresolution Signal Decomposition: The Wavelet Representation”[J].IEEE Tran. On pattern Analysis and Machine Intelligence, 1989, 11 (7):874-893.
[26]孙志新.小波分析在地震数据噪声处理中的应用研究[D].中国地震局工程力学研究所,2008,12:51~56.
[27]倪豪.小波消噪与分解对结构地震反应得影响研究[D].大庆石油学院,2004,2:24~29.
[28]兰芸.基于小波变换的振动信号去噪方法研究[D].五邑大学,2008,4:29-40.
[29]陶红艳,秦华峰,余成波.基于改进阈值函数的小波域去噪算法的研究[J].压电与声光,2008,30(1):93-95.
[30] LIU Wei-dong, LIU Shang-he. A New Modified Method Based on Wavelet Threshold De-Noising Functions [J].Chinese Journal of Electron Devices.2007, 30:58-62.
[31]杜继永,黄国荣,程洪炳,刘华伟.基于改进小波阈值法处理MEMS陀螺信号噪声[J].电光与控制,2009,16(12):61-64.
[32]姜绍辉.小波变换及在提高地震资料信噪比中的应用[D].中国海洋大学,2005,6:24~35.
[33]吕瑞兰.小波阈值去噪的性能分析及基于能量元的小波阈值去噪方法研究[D].浙江大学,2003,2:28-29.
[34]张斌,王彤,谷传纲,戴正元.改进的小波阈值消噪法在湍流信号处理中的应用[J].工程热物理学报,2009,30(30):407~410.
[35]刘洋,李承楚.地震资料信噪比估计的几种方法[J].石油地球物理勘探,1997,4:257~262.
[36]孙延奎.小波分析及其应用[M].北京:机械工业出版社,2005,3:224-236.
[37]印欣运,何永勇,彭志科,褚福磊.小波熵及其在状态趋势分析中的应用[J].振动工程学报,2004,17(2):165~169.
[38]陈小勤.基于小波熵测度的电力暂态信号检测与分类方法研究[D].西南交通大学,2006,5:7~15.
[39]何正友,刘志刚,钱清泉.小波熵理论及其在电力系统中应用的可行性探讨[J].电网技术,2004,28(21):17~21.
[40]张荣标,胡海燕,冯友兵.基于小波熵的微弱信号检测方法研究[J].仪器仪表学报,2007,28(11):2078-2083.
[41]何凯,王树勋,戴逸松.基于Shannon熵的1/f类分形信号去噪方法[J].吉林大学学报(信息科学版),2003,21(1):21~26.
[42]李晓飞.小波分析在光谱数据去噪处理中的应用[D].上海交通大学,2009,1:28~32.
[43]田金文,高谦,杜拥军.基于小波变换模极大值的地震信号去噪处理方法[J].江汉石油学院学报,2001,23(1):22~25.
[44]徐长发,李国宽.实用小波方法[M].武汉:华中科技大学出版社,2004,1:107~119.
[45]蒋鹏.小波理论在信号去噪和数据压缩的应用研究[D].浙江大学,2004,5:47~59.
[46]段炜.基于小波变换的探地雷达信号去噪方法研究[D].中南大学,2008,6:43~54.
[47]胡广书.现代信号处理教程[M].北京:清华大学出版社,2001,3:124~146.
[48]姚胜利.地震信号的小波去噪方法研究[D].中南大学,2007,22~37.
[49] Mallat S.G,Zhong S. Characterization of signals from multiscale edges [J].IEEE Trans. Pattern Anal and Machine Intell, 1992, 14(7):710-732,
[50]赵玉宝.小波变换在地震信号去噪中的应用研究[D].中南大学,2005,4:36~45.
[51]陈德智,唐磊,盛剑霓,王恒利.由小波变换的模极大值快速重构信号[J].电子学报,1998,26(9):82-85.
[52]孙丰荣,翟广涛,李艳玲等.由小波变换模极大值重构信号的快速算法[J].小型微型计算机系统,2005,26(12):2147-2149.
[53]刘齐芬.小波包去噪方法研究及其在GPS数据处理中的应用[D].河北师范大学,2008,3:25~30.
[54]吴勇.基于小波的信号去噪方法研究[D].武汉理工大学,2007,5:44~56.
[55]丛丽丽.基于小波包和全变差的图像去噪算法[D].吉林大学,2010,4:24-34.
[56] Wang Sheng-qian, Zou Yuan-hua, Zou Dao-wen.Adaptive shrinkage denosing using the neighborhood characteristic [J].ElectronicsLetters, 2002, 38(11):23-29.
[57]邓承志,汪胜前,刘祝华等.基于层间特性的多级小波收缩去噪算法[J].江西师范大学学报(自然科学版),2004,28(4):334~336.