局域波分解及其在地震信号时频分析中的应用
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摘要
讨论非平稳、非线性局域波信号分解方法的物理意义和自适应性,数值实现三种局域波分解算法,研究局域波分解在地震信号时频分析中的应用方法和实践.通过Hilbert变换得到地震信号时频分布特征,与Fourier变换谱物理意义不同.采用一定的计算策略,改善瞬时频率计算精度,突出瞬时频率属性的物理意义;将局域波分解同Wigner分布结合,计算地震信号基于局域波分解的Wigner分布,抑制交叉项.模型和实际地震数据试算结果表明实现算法的正确性和有效性.研究表明:在地震信号时频分析中采用局域波分解求Hilbert谱具有自适应性,时域和频域的分辨率也较高;而基于局域波分解的地震信号Wigner分布,保留Wigner分布优良特性,抑制交叉项方法简单易实现;局域波分解方法适合处理地震信号,值得进一步研究和推广.
The local waves decomposition method is suitbale for processing nonstaionanry and nonlinear signals,because the Intrinsic Mode Functions are of determined physical meanings and adaptive.In this papers,the local waves decomposition algorithms and their applications to seismic signals time-frequency analysis are studied.By the Hilbert ttransform,the distributions in the amplititude-time-frequency dimensions can be computed,and the computed instantaneous frequency not only is of determined physical meanings,but also more accurate with some tricks.Combining the local waves decomposition with Wigner distribution,the crossing iterms effects can be reduced very well.The numerical experiments of model and real seismic data show the method is adaptive,the time-frequency resolution is better and the local decomposition Wigner distribution is feasible.On base of the results,it can be concluded that the local wave decomposition is advantagous for seismic signal processing and worth doing more researchs.
The local waves decomposition method is suitbale for processing nonstaionanry and nonlinear signals,because the Intrinsic Mode Functions are of determined physical meanings and adaptive.In this papers,the local waves decomposition algorithms and their applications to seismic signals time-frequency analysis are studied.By the Hilbert ttransform,the distributions in the amplititude-time-frequency dimensions can be computed,and the computed instantaneous frequency not only is of determined physical meanings,but also more accurate with some tricks.Combining the local waves decomposition with Wigner distribution,the crossing iterms effects can be reduced very well.The numerical experiments of model and real seismic data show the method is adaptive,the time-frequency resolution is better and the local decomposition Wigner distribution is feasible.On base of the results,it can be concluded that the local wave decomposition is advantagous for seismic signal processing and worth doing more researchs.
引文
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[27]武安绪,吴培稚,兰从欣,等Hilbert-Huang变换与地震信号的时频分析[J].中国地震,2005,21(2):207~215.
[28]罗其峰,石春香.Hilbert-Huang变换理论及其计算中的问题[J].同济大学学报,2003,31(6):637~640.
[29]石春香,罗其峰.时程信号的Hilbert-Huang变换与小波分析[J].地震学报,2003,25(4):398~405.
[30]石春香,罗其峰.Hilbert-Huang变换在地震信号纠偏中的应用[J].同济大学学报,2005,33(7):895~899.
[31]段生全,等.HHT方法及其在地震信号处理中的应用[J].成都理工大学学报(自然科学版),2005,32(4):396~400.
[32]张凤旭,孟令顺,张凤琴,刘财,王世煜.利用Hilbert变换计算重力归一化总梯度[J].地球物理学报,2005,48(3):704~709.
[33]陈赟,张中杰,田小波.基于加窗Hilbert变换的复偏振分析方法及其应用[J].地球物理学报,2005,48(4):889~895.
[34]陆文凯,丁文龙,张善文,肖焕钦,赵铭海.基于信号子空间分解的三维地震资料高分辨率处理方法[J].地球物理学报,2005,48(4):896~901
[35]陈雨红,杨长春,曹齐放,等.几种时频分析方法比较[J].地球物理学进展,2006,21(4):1180~1185.
[2]Ronald N B.The Fourier Transform and Its Applications[M].McGraw-Hilll,2000.
[3]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.
[4]王宏禹.信号处理相关理论综合与统一法[M].北京:国防工业出版社,2005.
[5]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.
[6]Qian S,Chen D.Joint time-frequency analysis:Method andapplication[M].New Jersey Prentice Hall PTR,1996.
[7]刘喜武,刘洪,李幼铭.基于广义S变换的研究地震地层特征[J].地球物理学进展,2006,21(2):440~451.
[8]刘喜武,年静波,刘洪.基于广义S变换的地震波能量衰减分析[J].勘探地球物理进展,2006,29(1):20~24.
[9]刘喜武,年静波,刘洪.基于广义S变换的地层吸收地震波衰减补偿[J].石油物探,2006,45(1):9~14.
[10]刘喜武,年静波,黄文松.利用广义S变换提取地震旋回的方法[J],石油物探,2006,45(2):129~133.
[11]Huang N E,Shen Z,Long S R,et al.The empirical modedecomposition and Hilbert spectrum for nonlinear and non-stationary time series analysis[J].Pro.R.Soc.Lond.A,1998,454:903~995.
[12]Huang N E,Zheng S,Steven R L.A new view of nonlinearwater waves:the Hilbert spectrum[J].Annu.Rev.FluidMech,1999,31:417~457.
[13]Huang N E,et al.A new spectral representation of earth-quake data:Hilbert spectral analysis of station TCU129,Chi-Chi,Taiwan,21 September 1999[J].BSSA,2001,91(5):1310~1338.
[14]Loh C H,Wu T C,Huang N E.Application of the empiricalmode decomposition-Hilbert spectrum method to identifynear-fault ground motion characteristics and structural re-sponses[J].BSSA,2001,91(5):1339~1357.
[15]Vincent H T,Hu S L J,Hou Z.Damage detection using em-pirical mode decomposition method and a comparison withwavelet analysis[A].Structural Health Monitoring,SignalProcessing and Diagnostic Method[C].2000,891~890.
[16]Nikoiaos P P.Advanced time-frequency analysis applicationsin earthquake engineering[J].Seismic Design and Analysis ofStructures,2004,23~24.
[17]杨世锡,胡劲松,吴昭同,等.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.
[18]陈健林.旋转机械振动信号时频分析及软件系统[D].汕头:汕头大学硕士学位论文,2004年6月.
[19]程军圣,基于Hilbert-Huang变换的旋转机械故障诊断方法研究[D].长沙:湖南大学博士学位论文,2005.
[20]张郁山,梁建文.应用自回归模型处理EMD方法中的边界问题[J].自然科学进展,2003,22(4):388~390
[21]熊学军,郭炳火,胡筱敏,刘建军.EMD方法和Hilbert谱分析法的应用与探讨[J].黄渤海海洋,2002,20(2):12~21.
[22]Albenna D V.Wave and group transformation by a Hilbertspectrum[J].Coastal Engineering Journal,2002,44(4):283~300.
[23]覃善文.多分辨希尔伯特—黄(Hilbert-Huang)变换[D].重庆:重庆大学博士学位论文,2001.
[24]覃善文,秦树人,汤宝平.Hilbert-Huang变换的滤波特性及其应用[J].重庆大学学报2004,27(2):9~12.
[25]张海勇,马孝江,盖强.一种新的时频分析算法[J].火力与指挥控制,2000,25(3):39~42.
[26]公茂盛,谢礼立.HHT方法在地震工程中的应用之初步探讨[J].世界地震工程2003,19(3):39~43.
[27]武安绪,吴培稚,兰从欣,等Hilbert-Huang变换与地震信号的时频分析[J].中国地震,2005,21(2):207~215.
[28]罗其峰,石春香.Hilbert-Huang变换理论及其计算中的问题[J].同济大学学报,2003,31(6):637~640.
[29]石春香,罗其峰.时程信号的Hilbert-Huang变换与小波分析[J].地震学报,2003,25(4):398~405.
[30]石春香,罗其峰.Hilbert-Huang变换在地震信号纠偏中的应用[J].同济大学学报,2005,33(7):895~899.
[31]段生全,等.HHT方法及其在地震信号处理中的应用[J].成都理工大学学报(自然科学版),2005,32(4):396~400.
[32]张凤旭,孟令顺,张凤琴,刘财,王世煜.利用Hilbert变换计算重力归一化总梯度[J].地球物理学报,2005,48(3):704~709.
[33]陈赟,张中杰,田小波.基于加窗Hilbert变换的复偏振分析方法及其应用[J].地球物理学报,2005,48(4):889~895.
[34]陆文凯,丁文龙,张善文,肖焕钦,赵铭海.基于信号子空间分解的三维地震资料高分辨率处理方法[J].地球物理学报,2005,48(4):896~901
[35]陈雨红,杨长春,曹齐放,等.几种时频分析方法比较[J].地球物理学进展,2006,21(4):1180~1185.
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