基于递归高通滤波的经验模态分解及其在地震信号分析中的应用
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摘要
将地震信号分解成包含频谱互不重叠的单主周期的分量有利于地震信号的分析.分析了经验模态分解(EMD)中模态混叠的内在原因和已有的解决方法,梳理了解决模态混叠的思路框架,进而提出了一种新的基于输入递归高通滤波的EMD算法.首先用递归高通滤波器将信号预分解成频率由高到低的多个分量,实现信号的等价带通滤波,再用EMD对各带通分量按频率高低逐级递归筛分,获得完备的经验模态分量.通过合成信号和地震信号的仿真实验表明,该算法较好地克服了模态混叠,获得了频谱互不重叠的单主周期分量,并成功用于震相分离和分析,为地震信号分析提供了一种新思路.
Decomposing seismic signal into predominant-period components without frequency spectrum mixing is of help to seismic signal processing.The intrinsic cause of mode mixing in empirical model decomposition (EMD) and its traditional resolutions are studied,and the new ideas to solve the problem are analyzed,then a novel EMD algorithm based on the proposed recursive high-pass filter on the input signal is put forward.Firstly,the original signal is decomposed by recursive high-pass filters,which are as equal band-pass filters,into several components with the frequency decreasing,and then the components are sifted recursively by EMD with the frequency from high to low to obtain the complete intrinsic mode components. Experiments on artificial and natural seismic signals are designed for analysis and are made with a view to demonstrate the validity of the proposed method.The results of the experiments indicate that the proposed recursive high-pass filter algorithm can overcome mode mixing with the predominant-period components without frequency spectrum mixing,and is successfully applied to separate and analyze the seismic phases.The proposed method provides a novel approach for the seismic signal analysis.
Decomposing seismic signal into predominant-period components without frequency spectrum mixing is of help to seismic signal processing.The intrinsic cause of mode mixing in empirical model decomposition (EMD) and its traditional resolutions are studied,and the new ideas to solve the problem are analyzed,then a novel EMD algorithm based on the proposed recursive high-pass filter on the input signal is put forward.Firstly,the original signal is decomposed by recursive high-pass filters,which are as equal band-pass filters,into several components with the frequency decreasing,and then the components are sifted recursively by EMD with the frequency from high to low to obtain the complete intrinsic mode components. Experiments on artificial and natural seismic signals are designed for analysis and are made with a view to demonstrate the validity of the proposed method.The results of the experiments indicate that the proposed recursive high-pass filter algorithm can overcome mode mixing with the predominant-period components without frequency spectrum mixing,and is successfully applied to separate and analyze the seismic phases.The proposed method provides a novel approach for the seismic signal analysis.
引文
[1] M.巴特.地球物理学中的谱分析.郑治真等.北京:地震出版社,1978 Bath M.Spectral Analysis in Geophysics ( in Chinese),Translated by Zheng Z Z,et al.Beijing:Seismological Press,1978
[2] 赵鸿儒,孙进忠,唐文榜等.全波震相分析.北京:地震出版社,1991 Zhao H R,Shun J Z,Tang W B,et al.Wave Seismic Phase Analysis (in Chinese).Beijing:Seismological Press,1991
[3] Huang N E,Shen Z,Long S R,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis.Proc.R.Soc.Lond,1998,454:903 ～ 995
[4] Huang N E,Zheng S,Long S R.A new view of nonlinear water waves:the Hilbert spectrum.Annu.Rev.Fluid Mech,1999,31:417～457
[5] Boudraa A O.Cexus J C.EMD-Based Signal Filtering.IEEE Transactions on Instrumentation and Measurement,2007 ,56 (6) :2196 ～ 2202
[6] Hadjileonliadis L J.A novel technique for denoising explosive lung sounds empirical mode decomposition and fractal dimension filter.Engineering in Medicine and Biology Magazine.IEEE,Jan.-Feb.2007 26(1) :130 ～ 39
[7] Nunes J C,Guyot S,Delechelle E.Texture analysis based on local analysis of the bidimensional empirical mode decomposition.Machine Vision and Applications ,2005,16:177 ～ 188
[8] Liu Z,Peng S.Boundary processing of bidimensional EMD using texture synthesis.IEEE Signal Process,Lett,2005,12(1) :33 ～ 36
[9] Linderhed A.Compression by image empirical mode decomposition,in proc.IEEE Int.Conf.Image Processing ,2006,1:553～556
[10] 张郁山.希尔伯特-黄变换(HHT)与地震动时程的希尔伯特谱-方法与应用研究研[博士论文].北京:中国地震局地球物理研究所,2003 Zhang Y S.HHT and Hilbert spectrum earthquake ground motion-Study of methods and applications [Ph.D.thesis] (in Chinese).Beijing:Institute of Geophysics,China Seismological Bureau,2003
[11] 张义平.爆破震动信号的HHT分析与应用研究[博士论文].长沙:中南大学资源与安全工程学院,2006 Zhang Y P.HHT Analysis of blasting vibration and its application [Ph.D.thesis] (in Chinese).Changsha:School of Resources and Safety Engineering,2006
[12] 曹晖,曹永红.HH变换在地震动信号分析中的应用.重庆大学学报,2008,31(8) :922～927 Cao H,Cao Y H.Application limitation of the HilbertHuang transform to earthquake ground motion analysis.Journal of Chongqing University (in Chinese),2008,31 (8) :922～927
[13] 段生全,贺振华,黄德济.HHT方法及其在地震信号处理中的应用.成都理工大学学报(自然科学版),2005,32(4) :396～400 Duan S Q,He Z H,Huang D J.Application of the HilbertHuang transform to the analysis of seismic signal.Journal of Cheng Du University of Technology (Science & Technology Edition) (in Chinese) 2005,32(4) :396 ～ 400
[14] Huang N E.A new spectral representation of earthquake data:Hilbert spectral analysis of station.Bulletin of the Seismological Society of America ,2001 ,5:1310～1338
[15] Zhan G R.Hilbert-Huang transform analysis of dynamic and earthquake motion recordings.ASCE,2003,8:861 ～ 875
[16] Rilling G,Flandrin P,Goncalves P.On empirical mode decomposition and its algorithms.EEE-EURASIP Workshop on Nonlinear Signal and Image Processing,NSIP-03,Grado (I).2003
[17] 钱昌松,刘代志,刘志刚等.间歇信号的经验模态筛选方法.第二炮兵工程学院学报,2009,1(23) :53～62 Qian C S,Liu D Z,Liu Z G,et al.A novel sifting method for empirical mode decomposition of intermittent signal.Journal of Second Artillery Enginering University ( in Chinese),2009 ,1(23) :53 ～62
[18] 禹丹江,任伟新.信号经验模式分解与间断频率.福州大学学报,2005,33(5) :638～642 Yu D J,Ren W X.Signal empirical mode decomposition and intermittency frequency.Journal of Fuzhou University (in Chinese),2005,33(5) ,638 ～ 642
[19] 宋立新,王祁,王玉静等.具有间断事件检测和分离的经验模态分解方法.哈尔滨工程大学学报,2007,28(2) :178～182 Song L X,Wang Q,Wang Y J,et al.Empirical mode decomposition method with intermittency test and separation.Journal of Harbin Engineering University ( in Chinese) ,2007,28(2) :178 ～182
[20] 赵进平.异常事件对EMD方法的影响及其解决方法研究.青岛海洋大学学报,2001,31(6) :805～814 Zhao J P.Study on the effects of abnormal events to empirical mode de-composition method and the removal method for abnormal signal.Journal of Ocean University of Qingdao (in Chinese),2001,31(6) :805～814
[21] Wu Z,Huang NE.Ensemble Empirical Mode Decomposition : a Noise-assisted Data Analysis Method.Centre for OceanLand-Atmosphere Studie,2004． 173
[22] Ryan D,James F K.The use of a masking signal to improve empirical mode decomposition.ICASSP 2005 ,2005,5:485～488
[23] Xuan B,Xie Q W,Peng S L.EMD sifting based on bandwidth.IEEE Signal Processing Letters ,2007,14(8) :537 ～ 540
[24] Huang Y P,Li X Y,Zhang R B.A research on local mean in empirical mode decomposition.Lecture Notes in Computer Science ,2007,44(89) :125 ～128
[25] 李雪耀,黄永平,张汝波.一种基于支持向量回归机的经验模态分解方法.哈尔滨工程大学学报,2007,28(7) :779～784 Li X Y,Huang Y P,Zhang R B.Empirical mode decomposition based on support vector regression machines.Journal of Harbin Engineering University (in Chinese),2007,28(7) :779～784
[26] 钱昌松,刘志刚,胡重庆等.一种新的经验模态分解及其应用初探.地球物理探测与应用.西安:西安地图出版社,2007． 201～205 Qian C S,Liu Z G,Hu C Q,et al.A novel empirical model decomposition and its primary application.Geophysics Detecting and Application (in Chinese),Xi'an:Xi'an Map Press,2007． 201～205
[27] 郭淑卿.EMD的频带滤波筛分方法.中国民航大学学报,2008,26(4) :20～34 Guo S Q.Improvement on EMD method of Hilbert-Huang transform.Journal of Civil Aviation University of China (in Chinese),2008,26(4) :20 ～ 34
[28] 高云超,桑恩方,许继友.分离EMD中混叠模态的新方法.哈尔滨工程大学学报,2008,29(9) :468～451 Gao Y C,Sang E F,Xu J Y.A new method for separating mixed modes in empirical mode decomposition.Journal of Harbin Engineering University (in Chinese),2008,29(9) :468～451
[29] Park-McClellan,Parks T W,Burrus C S.Digital Filter Design.John Wiley & Sons,1987． 54 ～ 83
[30] 刘代志,钱昌松,刘志刚等.基于EMD的联合模态单元滤波及其在高斯消噪中的应用[OL].中国科技论文在线, (http://www.paper3． edu.en).2008． 7． 22 Liu D Z,Qian C S,Liu Z G,et al.Joint mode cell filter based on EMD and its application on Gaussian denoising,[OL] (in Chinese).Chinese Science paper online (http://www.paper.edu.cn).2008． 7． 22
[31] Flandrin P,Rilling G,Goncalves P.Empirical mode decomposition as a filter bank.IEEE Signal Processing Letters,2004,11(11) :112 ～114
[2] 赵鸿儒,孙进忠,唐文榜等.全波震相分析.北京:地震出版社,1991 Zhao H R,Shun J Z,Tang W B,et al.Wave Seismic Phase Analysis (in Chinese).Beijing:Seismological Press,1991
[3] Huang N E,Shen Z,Long S R,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis.Proc.R.Soc.Lond,1998,454:903 ～ 995
[4] Huang N E,Zheng S,Long S R.A new view of nonlinear water waves:the Hilbert spectrum.Annu.Rev.Fluid Mech,1999,31:417～457
[5] Boudraa A O.Cexus J C.EMD-Based Signal Filtering.IEEE Transactions on Instrumentation and Measurement,2007 ,56 (6) :2196 ～ 2202
[6] Hadjileonliadis L J.A novel technique for denoising explosive lung sounds empirical mode decomposition and fractal dimension filter.Engineering in Medicine and Biology Magazine.IEEE,Jan.-Feb.2007 26(1) :130 ～ 39
[7] Nunes J C,Guyot S,Delechelle E.Texture analysis based on local analysis of the bidimensional empirical mode decomposition.Machine Vision and Applications ,2005,16:177 ～ 188
[8] Liu Z,Peng S.Boundary processing of bidimensional EMD using texture synthesis.IEEE Signal Process,Lett,2005,12(1) :33 ～ 36
[9] Linderhed A.Compression by image empirical mode decomposition,in proc.IEEE Int.Conf.Image Processing ,2006,1:553～556
[10] 张郁山.希尔伯特-黄变换(HHT)与地震动时程的希尔伯特谱-方法与应用研究研[博士论文].北京:中国地震局地球物理研究所,2003 Zhang Y S.HHT and Hilbert spectrum earthquake ground motion-Study of methods and applications [Ph.D.thesis] (in Chinese).Beijing:Institute of Geophysics,China Seismological Bureau,2003
[11] 张义平.爆破震动信号的HHT分析与应用研究[博士论文].长沙:中南大学资源与安全工程学院,2006 Zhang Y P.HHT Analysis of blasting vibration and its application [Ph.D.thesis] (in Chinese).Changsha:School of Resources and Safety Engineering,2006
[12] 曹晖,曹永红.HH变换在地震动信号分析中的应用.重庆大学学报,2008,31(8) :922～927 Cao H,Cao Y H.Application limitation of the HilbertHuang transform to earthquake ground motion analysis.Journal of Chongqing University (in Chinese),2008,31 (8) :922～927
[13] 段生全,贺振华,黄德济.HHT方法及其在地震信号处理中的应用.成都理工大学学报(自然科学版),2005,32(4) :396～400 Duan S Q,He Z H,Huang D J.Application of the HilbertHuang transform to the analysis of seismic signal.Journal of Cheng Du University of Technology (Science & Technology Edition) (in Chinese) 2005,32(4) :396 ～ 400
[14] Huang N E.A new spectral representation of earthquake data:Hilbert spectral analysis of station.Bulletin of the Seismological Society of America ,2001 ,5:1310～1338
[15] Zhan G R.Hilbert-Huang transform analysis of dynamic and earthquake motion recordings.ASCE,2003,8:861 ～ 875
[16] Rilling G,Flandrin P,Goncalves P.On empirical mode decomposition and its algorithms.EEE-EURASIP Workshop on Nonlinear Signal and Image Processing,NSIP-03,Grado (I).2003
[17] 钱昌松,刘代志,刘志刚等.间歇信号的经验模态筛选方法.第二炮兵工程学院学报,2009,1(23) :53～62 Qian C S,Liu D Z,Liu Z G,et al.A novel sifting method for empirical mode decomposition of intermittent signal.Journal of Second Artillery Enginering University ( in Chinese),2009 ,1(23) :53 ～62
[18] 禹丹江,任伟新.信号经验模式分解与间断频率.福州大学学报,2005,33(5) :638～642 Yu D J,Ren W X.Signal empirical mode decomposition and intermittency frequency.Journal of Fuzhou University (in Chinese),2005,33(5) ,638 ～ 642
[19] 宋立新,王祁,王玉静等.具有间断事件检测和分离的经验模态分解方法.哈尔滨工程大学学报,2007,28(2) :178～182 Song L X,Wang Q,Wang Y J,et al.Empirical mode decomposition method with intermittency test and separation.Journal of Harbin Engineering University ( in Chinese) ,2007,28(2) :178 ～182
[20] 赵进平.异常事件对EMD方法的影响及其解决方法研究.青岛海洋大学学报,2001,31(6) :805～814 Zhao J P.Study on the effects of abnormal events to empirical mode de-composition method and the removal method for abnormal signal.Journal of Ocean University of Qingdao (in Chinese),2001,31(6) :805～814
[21] Wu Z,Huang NE.Ensemble Empirical Mode Decomposition : a Noise-assisted Data Analysis Method.Centre for OceanLand-Atmosphere Studie,2004． 173
[22] Ryan D,James F K.The use of a masking signal to improve empirical mode decomposition.ICASSP 2005 ,2005,5:485～488
[23] Xuan B,Xie Q W,Peng S L.EMD sifting based on bandwidth.IEEE Signal Processing Letters ,2007,14(8) :537 ～ 540
[24] Huang Y P,Li X Y,Zhang R B.A research on local mean in empirical mode decomposition.Lecture Notes in Computer Science ,2007,44(89) :125 ～128
[25] 李雪耀,黄永平,张汝波.一种基于支持向量回归机的经验模态分解方法.哈尔滨工程大学学报,2007,28(7) :779～784 Li X Y,Huang Y P,Zhang R B.Empirical mode decomposition based on support vector regression machines.Journal of Harbin Engineering University (in Chinese),2007,28(7) :779～784
[26] 钱昌松,刘志刚,胡重庆等.一种新的经验模态分解及其应用初探.地球物理探测与应用.西安:西安地图出版社,2007． 201～205 Qian C S,Liu Z G,Hu C Q,et al.A novel empirical model decomposition and its primary application.Geophysics Detecting and Application (in Chinese),Xi'an:Xi'an Map Press,2007． 201～205
[27] 郭淑卿.EMD的频带滤波筛分方法.中国民航大学学报,2008,26(4) :20～34 Guo S Q.Improvement on EMD method of Hilbert-Huang transform.Journal of Civil Aviation University of China (in Chinese),2008,26(4) :20 ～ 34
[28] 高云超,桑恩方,许继友.分离EMD中混叠模态的新方法.哈尔滨工程大学学报,2008,29(9) :468～451 Gao Y C,Sang E F,Xu J Y.A new method for separating mixed modes in empirical mode decomposition.Journal of Harbin Engineering University (in Chinese),2008,29(9) :468～451
[29] Park-McClellan,Parks T W,Burrus C S.Digital Filter Design.John Wiley & Sons,1987． 54 ～ 83
[30] 刘代志,钱昌松,刘志刚等.基于EMD的联合模态单元滤波及其在高斯消噪中的应用[OL].中国科技论文在线, (http://www.paper3． edu.en).2008． 7． 22 Liu D Z,Qian C S,Liu Z G,et al.Joint mode cell filter based on EMD and its application on Gaussian denoising,[OL] (in Chinese).Chinese Science paper online (http://www.paper.edu.cn).2008． 7． 22
[31] Flandrin P,Rilling G,Goncalves P.Empirical mode decomposition as a filter bank.IEEE Signal Processing Letters,2004,11(11) :112 ～114
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