利用改进希尔伯特—黄变换进行地震资料时频分析
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摘要
为了克服常规希尔伯特—黄变换(HHT)的缺陷,消除常规经验模态分解(EMD)产生的本征模态函数分量(IMF)中混叠的振荡模式,本文运用改进HHT,即通过引进小波包变换,首先将信号分解成一系列窄带信号,然后对这些窄带信号进行EMD获得一些IMF分量,再根据相关系数法,保留需要的IMF分量,去除虚假的IMF分量,最后进行HHT求取瞬时频率,得到改进HHT谱。改进HHT摆脱了小波变换中的海森堡测不准原理的限制,以及常规HHT模态混叠对分析的干扰。虽然改进HHT谱高频成分存在跳跃现象,但都围绕在真实频率值周围,并且较小波时频图的频带窄很多,能够反映信号的真实频率特性。数值模拟与实际地震记录处理结果证明了改进HHT的可行性。
As deficiencies of the conventional Hilbert-Huang transform(HHT),the oscillation mode mixing interference in the intrinsic mode function(IMF) components is generated by the conventional empirical mode decomposition(EMD).In order to eliminate this mode,this paper proposes an improved Hilbert-Huang transform method.Firstly,the wavelet packet transform(WPT) is used to decompose a signal into a few narrow band signals.Then EMD decompose these narrow band signals into intrinsic mode functions(IMFs).After that,the true IMFs are kept and unrelated IMFs are removed from the result according to the correlation coefficient method.Finally Hilbert transform instantaneous frequency and improved HHT amplitude are obtained.The improved HHT method gets rid of the Heisenberg uncertainty principle limits of wavelet transform,and the oscillation mode mixing interference of the conventional HHT.Although improved HHT amplitude have jump phenomenon in high frequency parts,they are all around the real frequency value and have narrow frequency band.This new method can reflect the real characteristics of frequency.The numerical and real data examples show that the improved method has feasibility in seismic data analysis.
As deficiencies of the conventional Hilbert-Huang transform(HHT),the oscillation mode mixing interference in the intrinsic mode function(IMF) components is generated by the conventional empirical mode decomposition(EMD).In order to eliminate this mode,this paper proposes an improved Hilbert-Huang transform method.Firstly,the wavelet packet transform(WPT) is used to decompose a signal into a few narrow band signals.Then EMD decompose these narrow band signals into intrinsic mode functions(IMFs).After that,the true IMFs are kept and unrelated IMFs are removed from the result according to the correlation coefficient method.Finally Hilbert transform instantaneous frequency and improved HHT amplitude are obtained.The improved HHT method gets rid of the Heisenberg uncertainty principle limits of wavelet transform,and the oscillation mode mixing interference of the conventional HHT.Although improved HHT amplitude have jump phenomenon in high frequency parts,they are all around the real frequency value and have narrow frequency band.This new method can reflect the real characteristics of frequency.The numerical and real data examples show that the improved method has feasibility in seismic data analysis.
引文
[1]刘喜武,张宁,勾永峰等.地震勘探信号时频分析方法对比与应用分析.地球物理学进展,2008,23(3):743～753Liu Xiwu,Zhang Ning,Gou Yongfeng et al.Thecomparison and application of time-frequency analysismethods to seismic signal.Progress in Geophysics,2008,23(3):743～753
[2]刘葵,刘招君,朱建伟等.时频分析在石油地球物理勘探中的应用.世界地质,2000,19(3):282～284Liu Kui,Liu Zhaojun,Zhu Jianwei et al.Applicationof time-frequency analysis in geology.World Geolo-gy,2000,19(3):282～284
[3]Philippe S,Guy D.Seismic sequence analysis and at-tribute extraction using quadratic time-frequency rep-resentations.Geophysics,2001,66(6):1947～1959
[4]汪小将,陈宝书,曹思远.HHT振幅频率恢复处理技术研究与应用.中国海上油气,2009,21(1):20～22Wang Xiaojiang,Chen Baoshu,Cao Siyuan.A re-search on HHT amplitude and frequency restorationtechnique and its application.China Offshore Oiland Gas,2009,21(1):20～22
[5]Stéphane Mallat.A Wavelet Tour of Signal Process-ing(Second Edition).Academic Press,1999
[6]Huang Norden E,Samuel S P.Hilbert-Huang Trans-form and its Applications.World Scientific Publish-ing,2008
[7]Huang Norden E,Shen Z,Steven R L et al.The em-pirical mode decomposition and the Hilbert spectrumfor nonlinear and non-stationary time series analysis.Proc R Soc Lond,1998,454:903～995
[8]Huang Norden E,Wu M L,Qu W D et al.Applica-tions of Hilbert-Huang transform to non-stationaryfinancial time series analysis.Appl Stochastic ModelsBus Ind,2003,19:245～268
[9]Huang Norden E,Wu M L,Steven R L et al.A confi-dence limit for the empirical mode decomposition andHilbert spectral analysis.Proc R Soc Lond,2003,459:2317～2345
[10]Peng Z K,Peter W T,Chu F L.A comparison studyof improved Hilbert-Huang transform and wavelettransform:application to fault diagnosis for rollingbearing.Mechnical Systems and Signal Processing,2005,19:974～988
[11]Peng Z K,Peter W T,Chu F L.An improved Hilbert-Huang transform and its application in vibration sig-nal analysis.Journal of Sound and Vibration,2005,286:187～205
[12]Leon Cohen.Time-Frequency Analysis.Prentice HallSignal Processing,1995
[13]Coifman R R,Meyer Y,Quake S et al.Signal pro-cessing and compression with wavelet packets.Wavelets and Their Applications,1994,442:363～379
[14]杨建国.小波分析及其工程应用.北京:机械工业出版社,2005
[15]王大凯,彭进业.小波分析及其在信号处理中的应用.北京:电子工业出版社,2006
[2]刘葵,刘招君,朱建伟等.时频分析在石油地球物理勘探中的应用.世界地质,2000,19(3):282～284Liu Kui,Liu Zhaojun,Zhu Jianwei et al.Applicationof time-frequency analysis in geology.World Geolo-gy,2000,19(3):282～284
[3]Philippe S,Guy D.Seismic sequence analysis and at-tribute extraction using quadratic time-frequency rep-resentations.Geophysics,2001,66(6):1947～1959
[4]汪小将,陈宝书,曹思远.HHT振幅频率恢复处理技术研究与应用.中国海上油气,2009,21(1):20～22Wang Xiaojiang,Chen Baoshu,Cao Siyuan.A re-search on HHT amplitude and frequency restorationtechnique and its application.China Offshore Oiland Gas,2009,21(1):20～22
[5]Stéphane Mallat.A Wavelet Tour of Signal Process-ing(Second Edition).Academic Press,1999
[6]Huang Norden E,Samuel S P.Hilbert-Huang Trans-form and its Applications.World Scientific Publish-ing,2008
[7]Huang Norden E,Shen Z,Steven R L et al.The em-pirical mode decomposition and the Hilbert spectrumfor nonlinear and non-stationary time series analysis.Proc R Soc Lond,1998,454:903～995
[8]Huang Norden E,Wu M L,Qu W D et al.Applica-tions of Hilbert-Huang transform to non-stationaryfinancial time series analysis.Appl Stochastic ModelsBus Ind,2003,19:245～268
[9]Huang Norden E,Wu M L,Steven R L et al.A confi-dence limit for the empirical mode decomposition andHilbert spectral analysis.Proc R Soc Lond,2003,459:2317～2345
[10]Peng Z K,Peter W T,Chu F L.A comparison studyof improved Hilbert-Huang transform and wavelettransform:application to fault diagnosis for rollingbearing.Mechnical Systems and Signal Processing,2005,19:974～988
[11]Peng Z K,Peter W T,Chu F L.An improved Hilbert-Huang transform and its application in vibration sig-nal analysis.Journal of Sound and Vibration,2005,286:187～205
[12]Leon Cohen.Time-Frequency Analysis.Prentice HallSignal Processing,1995
[13]Coifman R R,Meyer Y,Quake S et al.Signal pro-cessing and compression with wavelet packets.Wavelets and Their Applications,1994,442:363～379
[14]杨建国.小波分析及其工程应用.北京:机械工业出版社,2005
[15]王大凯,彭进业.小波分析及其在信号处理中的应用.北京:电子工业出版社,2006
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