S变换的时频分析特性及其改进
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摘要
地震信号具有非线性、非平稳的特性,用时频分析的方法处理地震信号,可以最大限度的保留原始信息,也可以较为精确地分析数据的时间、频率特征.现阶段应用于地震数据处理的时频分析方法主要有:短时傅里叶变换,小波变换和匹配追踪算法等等.S变换是近几年发展起来的一种新的时频分析方法.S变换结合了短时傅里叶变换和小波变换的优点,具有相位信息,同时该变换与小波变换一样,其时频窗可以调节大小以适应非平稳信号的特点.S变换的这些优点,使得它在地球物理方面得到广泛的应用.但是针对于S变换窗函数特性定量分析及其改进的文章较少,本文首先通过具体的实验说明了S变换的不足之处,然后通过理论分析,剖析了S变换的时频特性.指出了导致该变换不足之处的根源.最后指出了相应的改进办法,并且通过实验验证了改进后的S变换确实是对原来S变换的一种提高.
Seismic signals have nonlinear,non-stationary properties.Using time frequency method to process seismic signals could reserve the primary information of the data in maximal extend,and accurately analyze the properties of the data in the time frequency domain.Until now,there are many time frequency methods,such as the short time Fourier transform(STFT),the wavelet transform(WT) and the matching pursuit method(MP),and so on.The S transform is a new time-frequency method developed in recent years.The transform takes both the advantages of short time Fourier transform and the wavelet transform,that is to say the transform has phase information just as the STFT and its time frequency windows adjust adaptively according to the non-stationary signal just as the WT.These advantages make it is used widely in geophysics area.However,there are few papers quantitatively discussing the lime frequency properties of the S transform.This paper points out the shortages of the S transform through experiments,finds the root of the shortages by theories analysis and points out the ways to improve the S transform. Furthermore,experiments conducted validate that the remedy ways are indeed effective.
Seismic signals have nonlinear,non-stationary properties.Using time frequency method to process seismic signals could reserve the primary information of the data in maximal extend,and accurately analyze the properties of the data in the time frequency domain.Until now,there are many time frequency methods,such as the short time Fourier transform(STFT),the wavelet transform(WT) and the matching pursuit method(MP),and so on.The S transform is a new time-frequency method developed in recent years.The transform takes both the advantages of short time Fourier transform and the wavelet transform,that is to say the transform has phase information just as the STFT and its time frequency windows adjust adaptively according to the non-stationary signal just as the WT.These advantages make it is used widely in geophysics area.However,there are few papers quantitatively discussing the lime frequency properties of the S transform.This paper points out the shortages of the S transform through experiments,finds the root of the shortages by theories analysis and points out the ways to improve the S transform. Furthermore,experiments conducted validate that the remedy ways are indeed effective.
引文
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[8]Mallat S.A Wavelet Tour of Signal Processing[M].2~(nd) ed. Academic Press,1999,86-132.
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[13]高静怀,汪文秉,朱光明,等.地震资料处理中小波函数的选取研究[J].地球物理学报,1996,39(3):389-397. Gao J H,Wang W B,Zhu G M,et al.On the Choice of wavelet functions for seismic data processing[J].Chinese J. Geophys.(in Chinese),1996,39(3):389-397.
[14]Stockwell R G,Mansmha L,Lowe R P.Localization of the complex spectrum:the S transform[J].IEEE Trans.Signal Process,1996,44(4):998-1001.
[15]Mansinha L,Stockwell R G,Lowe R P.Pattern analysis with two-dimensional spectral localisation:Applications of two-dimensional S transforms[J].Physica,1997,239(1-3): 286-295.
[16]Pinnegar C R,Mansinha L.The S-transform with windows of arbitrary and varying shape[J].Geophysics,2003,68(1): 381-385.
[17]高静怀,陈文超,李幼铭,等.广义S变换与薄互层地震响应分析[J].地球物理学报,2003,7,46(4):526-532. Gao J H,Chen W C,Li Y M,et al.Generalized S transform and seismic response analysis of thin interbeds[J].Chinese J. Geophys.(in Chinese),2003,7,46(4):526-532.
[18]赵淑红,朱光明.S变换时频滤波去噪方法[J].石油地球物理勘探,2007,8,42(4):402-406. Zhao S H,Zhu G M.Time-frequency filtering to denoise by S transform[J].OGP(in Chinese),2007,8,42(4):402- 406.
[19]Daubechies I.The wavelet transform,Time frequency localization and signal analysis[J],IEEE Trans.Infor. Theory,1990,36(5):961-1005.
[20]Chui C K.An Introduction to Wavelets.Volume 1.Wavelet Analysis and Its Applications[M].Academic Press,1992,66 -100.
[2]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,1998,101-120. Zhang X D.Bao Z.Nonstationary Signals Analysis and Procesing[M].Beijing:National Defense Industry Press. 1998,101-120.
[3]Hlawatsch F,Boudreaux-Bartels G F.Linear and quadratic time-frequency signal representations[J].IEEE Signal Processing Magazine,1992,9(2):21-67.
[4]Barnes A E.The calculation of instantaneous frequency and instantaneous bandwidth[J].Geophysics.1992.57(11): 1520-1524.
[5]程乾生.希尔伯特变换与信号的包络、瞬时相位和瞬时频率[J].石油地球物理勘探,1979,(3):1-14. Cheng Q S.Hilbert transform and the envelopes, instantaneous phases and instantaneous frequencies of signals [J].OGP(in Chinese),1979,(3):1-14.
[6]Gabor D.Theory of communication[J].Journal of Institute for Electrical Engineering.SP1E,1946,93:429-457.
[7]Daubechies I.Where do wavelets come from? a personal point of view.IEEE Proc.,1996,84(5):510-513.
[8]Mallat S.A Wavelet Tour of Signal Processing[M].2~(nd) ed. Academic Press,1999,86-132.
[9]Mallat S G.A theory for multiresolution signal decomposition:the wavelet representation[J].IEEE Trans. PAMI,1989,11(7):674-693.
[10]王西文,杨孔庆,周立宏,等.基于小波变换的地震相干体算法研究[J].地球物理学报,2002,45(6):847-853. Wang X W,Yang K Q,Zhou L H,et al.Methods of calculating coherence cube on the basis of wavelet transform[J].Chinese J. Geophys.(in Chinese),2002,45(6):847-853.
[11]高静怀,汪文秉,朱光明.小波变换与信号瞬时特征分析[J].地球物理学报,1997,40(6):821-832. Gao J H,Wang W B,Zhu G M.Wavelet transform and its instantaneous attributes analysis[J].Chinese J.Geophys. (in Chinese),1997,40(6):821-832.
[12]Sarkar T K,Su C.A tutorial on wavelets from an electrical engineering perspective,Part 2:the continuous case[J]. IEEE Antennas & Propagation Magazine,1988,40(6):36～49.
[13]高静怀,汪文秉,朱光明,等.地震资料处理中小波函数的选取研究[J].地球物理学报,1996,39(3):389-397. Gao J H,Wang W B,Zhu G M,et al.On the Choice of wavelet functions for seismic data processing[J].Chinese J. Geophys.(in Chinese),1996,39(3):389-397.
[14]Stockwell R G,Mansmha L,Lowe R P.Localization of the complex spectrum:the S transform[J].IEEE Trans.Signal Process,1996,44(4):998-1001.
[15]Mansinha L,Stockwell R G,Lowe R P.Pattern analysis with two-dimensional spectral localisation:Applications of two-dimensional S transforms[J].Physica,1997,239(1-3): 286-295.
[16]Pinnegar C R,Mansinha L.The S-transform with windows of arbitrary and varying shape[J].Geophysics,2003,68(1): 381-385.
[17]高静怀,陈文超,李幼铭,等.广义S变换与薄互层地震响应分析[J].地球物理学报,2003,7,46(4):526-532. Gao J H,Chen W C,Li Y M,et al.Generalized S transform and seismic response analysis of thin interbeds[J].Chinese J. Geophys.(in Chinese),2003,7,46(4):526-532.
[18]赵淑红,朱光明.S变换时频滤波去噪方法[J].石油地球物理勘探,2007,8,42(4):402-406. Zhao S H,Zhu G M.Time-frequency filtering to denoise by S transform[J].OGP(in Chinese),2007,8,42(4):402- 406.
[19]Daubechies I.The wavelet transform,Time frequency localization and signal analysis[J],IEEE Trans.Infor. Theory,1990,36(5):961-1005.
[20]Chui C K.An Introduction to Wavelets.Volume 1.Wavelet Analysis and Its Applications[M].Academic Press,1992,66 -100.
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