时频分析在地震资料处理中的应用
摘要
傅里叶变换反映的是信号或函数的整体特征,其不具备时间分辨率,随着信号分析的深入,傅里叶变换难以满足分析要求,不适合处理非平稳信号；短时傅里叶变换具有一定的局部分析能力,但其时频窗口固定不变,意味着其在时间域和频率域的分辨率是固定的,不具备自适应性；小波变换具有可变的时间和频率分辨率,具有较好的自适应性,但小波基的选择是关键；Wigner-Ville变换是二次变换,时频聚焦性较强,但是会产生交叉干扰项；Cohen类函数通过加入核函数在一定程度上抑制了交叉干扰项,但这是以降低一定的时频分辨率为代价的。本文比较了传统时频分析方法的优缺点,介绍了高阶谱时频分析方法,以及提出了改进的FX域EMD去噪方法。
经验模态分解是比较新近提出的一种信号分解方法,它依据数据自身的时间尺度特征来进行信号分解,无需预先设定任何基函数。本文在Maiza Bekara的基础上,将FX域中的IMF1完全滤除,并滤除IMF2的高频噪声,这样可以达到更好的去噪目的。将其应用于井间地震数据去噪,提高了井间地震数据的信噪比。
高阶谱分析的最大特点是：(1)高阶累积量具有对高斯有色噪声恒为零的特点,因而可用于提取高斯有色噪声中的非高斯信号；(2)高阶累积量含有系统的相位信息,因而可用于非最小相位系统辨识：(3)高阶统计量可用于检测和描述系统的非线性。这些性质是的高阶谱分析迅速成为现代随机信号分析与处理的一个重要工具。所以,高阶统计量对于处理非平稳信号非常适合,而地震信号正是这样的非平稳信号,因此能够很好的应用在地震资料处理中。
Fourier Transformation, reflecting the unity features of the signals or functions, is not fit for processing the non-stationary signals. It doesn't have time domain resolution. Short Time Fourier Transformation (STFT), added by a fixed time-frequency window, has a limited time-frequency resolution. It means that the time-domain resolution and frequency-domain resolution are fixed in STFT, so it's not adaptive enough. Wavelet transformation, with a better adaptivity, has a flexible time-domain and frequency-domain resolution, but the wavelet basis is the key step. Wigner-Ville transform is a quadratic transformation, with a good time and frequency focusing, while it may generate crossing disturbances. Cohen class functions restrain the crossing disturbances to a certain extent by adding a kernel function while the resolution is decreased. The traditional time-frequency analysis methods are introduced in this paper. Their advantages and disadvantages will be summarized from the contrast of each other. Then high-order spectrum analysis method is introduced, and a method of improved EMD in the FX domain for noise attenuation is brought up.
EMD is a signal decompose method, which decomposes the signals by the time-scale feature of itself, with no prestablishing any base functions. Based on Maiza Bekara, all the IMF1 and the high frequency of the IMF2 are filtered out so as to denoising the noise and reserving the useful information. Then it is used into the cross well seismic data to increase the SNR of the data.
The evident features of high-order spectrum are:(1) the high-order cumulant is always be zero to Gauss colored noise, which can be used to pick up the non-Gauss signals from the Gauss colored noise; (2)the high-order cumulant contains the phase information, which can be used into the non-minimum phase system identification; (3) the high-order stastics can be used into detecting and describing the system's nonlinear. Above all, high-order spectrum analysis method becomes an important tool to analysis and processes the modern random signals. Therefore, high-order statistics is very fit for processing the non-stationary signals, while the seismic signals are the non-stationary signals, so it can be useful in the seismic data.
经验模态分解是比较新近提出的一种信号分解方法,它依据数据自身的时间尺度特征来进行信号分解,无需预先设定任何基函数。本文在Maiza Bekara的基础上,将FX域中的IMF1完全滤除,并滤除IMF2的高频噪声,这样可以达到更好的去噪目的。将其应用于井间地震数据去噪,提高了井间地震数据的信噪比。
高阶谱分析的最大特点是：(1)高阶累积量具有对高斯有色噪声恒为零的特点,因而可用于提取高斯有色噪声中的非高斯信号；(2)高阶累积量含有系统的相位信息,因而可用于非最小相位系统辨识：(3)高阶统计量可用于检测和描述系统的非线性。这些性质是的高阶谱分析迅速成为现代随机信号分析与处理的一个重要工具。所以,高阶统计量对于处理非平稳信号非常适合,而地震信号正是这样的非平稳信号,因此能够很好的应用在地震资料处理中。
Fourier Transformation, reflecting the unity features of the signals or functions, is not fit for processing the non-stationary signals. It doesn't have time domain resolution. Short Time Fourier Transformation (STFT), added by a fixed time-frequency window, has a limited time-frequency resolution. It means that the time-domain resolution and frequency-domain resolution are fixed in STFT, so it's not adaptive enough. Wavelet transformation, with a better adaptivity, has a flexible time-domain and frequency-domain resolution, but the wavelet basis is the key step. Wigner-Ville transform is a quadratic transformation, with a good time and frequency focusing, while it may generate crossing disturbances. Cohen class functions restrain the crossing disturbances to a certain extent by adding a kernel function while the resolution is decreased. The traditional time-frequency analysis methods are introduced in this paper. Their advantages and disadvantages will be summarized from the contrast of each other. Then high-order spectrum analysis method is introduced, and a method of improved EMD in the FX domain for noise attenuation is brought up.
EMD is a signal decompose method, which decomposes the signals by the time-scale feature of itself, with no prestablishing any base functions. Based on Maiza Bekara, all the IMF1 and the high frequency of the IMF2 are filtered out so as to denoising the noise and reserving the useful information. Then it is used into the cross well seismic data to increase the SNR of the data.
The evident features of high-order spectrum are:(1) the high-order cumulant is always be zero to Gauss colored noise, which can be used to pick up the non-Gauss signals from the Gauss colored noise; (2)the high-order cumulant contains the phase information, which can be used into the non-minimum phase system identification; (3) the high-order stastics can be used into detecting and describing the system's nonlinear. Above all, high-order spectrum analysis method becomes an important tool to analysis and processes the modern random signals. Therefore, high-order statistics is very fit for processing the non-stationary signals, while the seismic signals are the non-stationary signals, so it can be useful in the seismic data.
引文
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[4]唐向宏,李齐良.时频分析与小波变换[M].北京：科学出版社,2008：128.
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[11]Hongbing Li, Wenzhi Zhao. Measures of scale based on the wavelet scalogram with applications to seismic attenuation[J]. Geophysics,2006,71(5):111～118.
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[25]Colas M., Gelle G., Delaunay G.. Time varying higher order statistics for FM signals analysis and decision[J]. Digital Signal Processing,2004,14(1):72～92.
[26]李志农,何永勇,诸福磊.基于Wigner高阶谱的机械故障诊断的研究[J].机械工程学报,2005,41(4)：119～122.
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[29]SwarIli A., Medal J.M.. Higher-order spectral analysis toolbox users guide[J]. The Math Works Inc.,1998,11(2):67～128.
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[31]Huang N.E.. The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis[J]. Proceedings of the Royal Society,1996,7(11):903～952.
[32]杨世锡,胡劲松,吴昭同.旋转机械振动信号基于EMD的希尔伯特变换和小波变换时频分析比较[J].中国电机工程学报,2003,23(6)：102～107.
[33]钟佑明,秦树人,汤宝平.一种振动信号新变换法的研究[J].振动工程学报,2002,15(2)：233～238.
[34]Maiza Bekara, Mirkovander Ban. Random and coherent noise attenuation by empirical mode decomposition[J]. Geophysics,2009,74(5):89～98.
[35]杨晓萍,刘普森,钟彦儒.基于经验模式分解的有源滤波器谐波检测[J].电工技术学报,2009,23(5)：197～202.
[36]刘洋,FOMEL Sergey,刘财.高阶seislet变换及其在随机噪声消除中的应用[J].地球物理学报,2009,52(8)：2142～2151.
[37]隋淑玲.井间地震资料的属性分析及应用[J].石油勘探与开发,2005,32(3)：76～77.
[38]陆孟基等,地震勘探原理及资料解释[M].北京：石油工业出版社,1991：178.
[39]钱绍瑚,地震勘探[M].北京：中国地质大学出版社,1989：134.
[40]何惺华,井间地震中的反射波分析[J].油气地球物理,2005,3(4)：1～8.
[41]韩瑞民.井间地震技术简介[J].石油仪器,1994，8(2)：63～66.
[42]何继善,温佩玲.小波分析在地球物理勘探中的应用[J].地球科学与环境学报,2005,7(4)：14～19.
[43]郝云虎,王福明.小波变换在信号处理中的应用[J].机械管理开发,2008,23(6)：78～79.
[44]文进爱,彭仲,欧瑜枫.小波分析及其应用研究[J].大众科技,2009,(8)：30～31.
[45]李宏伟,程乾生.高阶统计量与随机信号分析[M].武汉：中国地质大学出版社,2002：78.
[46]张贤达.时间序列分析—高阶统计量方法[M].北京：清华大学出版社,1996：127.
[47]姚天任,孙洪.现代信号处理[M].武汉：华中理工大学出版社,1999：137.
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[2]董建华,顾汉明,张星.几种时频分析方法的比较及应用[J].工程地球物理学报,2007,4(4)：312～316.
[3]张贤达,保铮.几种时频分析技术的性能研究及在河道砂体预测中的应用[J].天然气工业,2007,27(12)：451～453.
[4]唐向宏,李齐良.时频分析与小波变换[M].北京：科学出版社,2008：128.
[5]夏洪瑞,朱勇,周开明.小波变换及其在去噪中的应用[J].石油地球物理勘探,1994,29(3)：274～285.
[6]O. Rioul, and M. Vetterli. Wavelet and signal processing [J]. IEEE Signal Processing,1991,12(4):14～38.
[7]Avijit Chakraborty, David Okaya. Frequency-time decomposition of seismic data using wavelet based methods[J]. Geophysics,1995,60(6):1906～1916.
[8]胡昌华,李国华,刘涛.基于MATLAB 6. X的系统分析与设计-小波分析(第二版)[M].西安：电子科技大学出版社,2000：34.
[9]徐长发,李国宽.实用小波方法(第二版)[M].武汉：华中科技大学出版社,2004：137.
[10]Satish Sinha, Partha S. Routh. Spectral decomposition of seismic data with continuous wavelet transform[J]. Geophysics,2005,70(6):19～25.
[11]Hongbing Li, Wenzhi Zhao. Measures of scale based on the wavelet scalogram with applications to seismic attenuation[J]. Geophysics,2006,71(5):111～118.
[12]张德丰.MATLAB小波分析[M].北京：机械工业出版社,2009： 6.
[13]张贤达,保铮.非平稳信号分析与处理[M].北京：国防工业出版社,1998：167.
[14]葛哲学,陈仲生.Matlab时频分析技术及其应用[M].北京：人民邮电出版社,2006：145.
[15]纪跃波,秦树人,汤宝平.Wigner分不干扰项抑制及其算法[J].重庆大学学报,2001,24(4)：26～30.
[16]包勇,杨世超,诸葛起.Wigner谱及其在心好时频两维分布中的应用[J].振动、测试与诊断,1992,12(2)：6～12.
[17]耿遵敏,郑效忠,种方.Wigner分布的改进及其在非平稳振动分析及诊断中的应用[J].信号处理,1995,11(2)：116～123.
[18]刘开培,马秉伟,周莉等.基于改进的Cohen类时频分布的简谐波检测[J].高电压技术,2008,34(9)：1949～1953.
[19]H.L. Choi, Williams. Improved time-frequency representation of multi component signals using exponential kernels[J]. IEEE Transactions on Acoustics,1989,37(6):862～871.
[20]姜鸣,陈进,汪慰军.几种Cohen类时频分布的比较及应用[J].机械工程学报,2003,39(8)：129～134.
[21]王军,李亚安.多分量信号时频分布的交叉抑制研究[J].探测与控制学报,2004,26(4)：13～17.
[22]王书明,李宏伟,朱培明.地球物理学中的高阶统计量方法[M].北京：科学出版社,2006：69.
[23]D.M. Yang, A.F. Stronach, P. Macconnell. Third order spectral techniques for the diagnosis of motor bearing condition using artificial neural networks[J]. Mechanical Systems and Signal Processing,2006,16(2):391～411.
[24]Peter J. Schreier. Louis L. Reeharf. Higher—order spectral analysis of complex signals[J]. Signal Processing,2006,86(11):3321～3333.
[25]Colas M., Gelle G., Delaunay G.. Time varying higher order statistics for FM signals analysis and decision[J]. Digital Signal Processing,2004,14(1):72～92.
[26]李志农,何永勇,诸福磊.基于Wigner高阶谱的机械故障诊断的研究[J].机械工程学报,2005,41(4)：119～122.
[27]Fonollosa J.R., Nikias C.L.. Wigner higher-order moment spectra:definitions, properties, computation and applications to transient signal detection. IEEE Transaction on Signal Processing,1993,42(1):245～266.
[28]Gerr N.L.. Introducing a third-order Wigner distribution. In:Proceedings of the IEEE,1988,76(3):290～292.
[29]SwarIli A., Medal J.M.. Higher-order spectral analysis toolbox users guide[J]. The Math Works Inc.,1998,11(2):67～128.
[30]董建华.分数谱与高阶谱估计技术在地震储层预测中的应用研究[D].武汉：中国地质大学硕士学位论文,2008：
[31]Huang N.E.. The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis[J]. Proceedings of the Royal Society,1996,7(11):903～952.
[32]杨世锡,胡劲松,吴昭同.旋转机械振动信号基于EMD的希尔伯特变换和小波变换时频分析比较[J].中国电机工程学报,2003,23(6)：102～107.
[33]钟佑明,秦树人,汤宝平.一种振动信号新变换法的研究[J].振动工程学报,2002,15(2)：233～238.
[34]Maiza Bekara, Mirkovander Ban. Random and coherent noise attenuation by empirical mode decomposition[J]. Geophysics,2009,74(5):89～98.
[35]杨晓萍,刘普森,钟彦儒.基于经验模式分解的有源滤波器谐波检测[J].电工技术学报,2009,23(5)：197～202.
[36]刘洋,FOMEL Sergey,刘财.高阶seislet变换及其在随机噪声消除中的应用[J].地球物理学报,2009,52(8)：2142～2151.
[37]隋淑玲.井间地震资料的属性分析及应用[J].石油勘探与开发,2005,32(3)：76～77.
[38]陆孟基等,地震勘探原理及资料解释[M].北京：石油工业出版社,1991：178.
[39]钱绍瑚,地震勘探[M].北京：中国地质大学出版社,1989：134.
[40]何惺华,井间地震中的反射波分析[J].油气地球物理,2005,3(4)：1～8.
[41]韩瑞民.井间地震技术简介[J].石油仪器,1994，8(2)：63～66.
[42]何继善,温佩玲.小波分析在地球物理勘探中的应用[J].地球科学与环境学报,2005,7(4)：14～19.
[43]郝云虎,王福明.小波变换在信号处理中的应用[J].机械管理开发,2008,23(6)：78～79.
[44]文进爱,彭仲,欧瑜枫.小波分析及其应用研究[J].大众科技,2009,(8)：30～31.
[45]李宏伟,程乾生.高阶统计量与随机信号分析[M].武汉：中国地质大学出版社,2002：78.
[46]张贤达.时间序列分析—高阶统计量方法[M].北京：清华大学出版社,1996：127.
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