稀疏时频分解方法的研究与运用（英文）
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摘要
Gabor变换和S变换是常用的时频分析工具。根据测不准原理,它们的时频分解结果无法在时间域和频率域同时具有很高的分辨率。为了提高非平稳信号时频分解结果的分辨率,本文提出瞬时频率分布函数(IFDF)并利用它表达非平稳信号。当非平稳信号时频成分的分布满足测不准原理对信号可分辨的要求时,瞬时频率分布函数的支集和短时Fourier变换的小波脊支集是同一个集合。利用IFDF的该特征,本文提出一种迭代算法(Sparse-STFT)实现了信号的稀疏时频分解。该算法在每次迭代过程中利用残留信号的短时Fourier变换结果的脊支集更新信号的时频成分,每次迭代得到的时频成分的叠加结果即为最终的稀疏时频分解结果。文中的数值实验证明了Sparse-STFT可以有效地提高非平稳信号时频分解结果的分辨率。最后,本文将该方法应用于地震数据面波的压制中,取得了理想的处理结果。
The Gabor and S transforms are frequently used in time-frequency decomposition methods. Constrained by the uncertainty principle, both transforms produce low-resolution time-frequency decomposition results in the time and frequency domains. To improve the resolution of the time-frequency decomposition results, we use the instantaneous frequency distribution function(IFDF) to express the seismic signal. When the instantaneous frequencies of the nonstationary signal satisfy the requirements of the uncertainty principle, the support of IFDF is just the support of the amplitude ridges in the signal obtained using the short-time Fourier transform. Based on this feature, we propose a new iteration algorithm to achieve the sparse time-frequency decomposition of the signal. The iteration algorithm uses the support of the amplitude ridges of the residual signal obtained with the short-time Fourier transform to update the time-frequency components of the signal. The summation of the updated time-frequency components in each iteration is the result of the sparse timefrequency decomposition. Numerical examples show that the proposed method improves the resolution of the time-frequency decomposition results and the accuracy of the analysis of the nonstationary signal. We also use the proposed method to attenuate the ground roll of field seismic data with good results.
The Gabor and S transforms are frequently used in time-frequency decomposition methods. Constrained by the uncertainty principle, both transforms produce low-resolution time-frequency decomposition results in the time and frequency domains. To improve the resolution of the time-frequency decomposition results, we use the instantaneous frequency distribution function(IFDF) to express the seismic signal. When the instantaneous frequencies of the nonstationary signal satisfy the requirements of the uncertainty principle, the support of IFDF is just the support of the amplitude ridges in the signal obtained using the short-time Fourier transform. Based on this feature, we propose a new iteration algorithm to achieve the sparse time-frequency decomposition of the signal. The iteration algorithm uses the support of the amplitude ridges of the residual signal obtained with the short-time Fourier transform to update the time-frequency components of the signal. The summation of the updated time-frequency components in each iteration is the result of the sparse timefrequency decomposition. Numerical examples show that the proposed method improves the resolution of the time-frequency decomposition results and the accuracy of the analysis of the nonstationary signal. We also use the proposed method to attenuate the ground roll of field seismic data with good results.
引文
Askari,R.,and Siahkoohi,H.R.,2008,Ground roll attenuation using the S and x-f-k transforms:Geophysical Prospecting,56,105–114.
Bonar,D.C.,and Sacchi,M.D.,2010,Complex spectral decomposition via inversion strategies:80th SEG Annual International Meeting,Expanded Abstracts,1408–1412.
Castagna,J.,Sun,S.,and Siegfried,R.,2003,Instantaneouss pectral analysis:Detection of low-frequency shadows associated with hydrocarbons:The Leading Edge,22,120–127C.
Castagna,J.,and Sun,S.,2006,Comparison of spectral decomposition methods:First Break,24,75–79.
Chuang,H.,and Lawton,D.C.,1991,Some propertiesof thin beds:61st Annual International Meeting,SEG,Expanded Abstracts,224–227.
Ebrom,D.,2004,The low-frequency gas shadow onseismic sections:The Leading Edge,23,772,
Gao,J.H.,2003,Generalized S transform and seismicresponse analysis of thin interbeds:Chinese J.ofGeophysics,46(4),526–532.
Gabor,D.,1946,Theory of communication:Journal of the Institute of Electrical Engineers,93,429–457.
Gholami,2012,Sparse time–frequency decomposition and some applications:IEEE Transactions on Geoscience and Remote Sensing,51,3598–3604,
Huang,N.E.,Shen,Z.,Long,S.R.,Wu,M.C.,Shih,H.H.,Zheng,Q.,Yen,N.C.,Tung,C.C.,and Liu,H.H.,1998.The empirical mode decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis:Proceedings of the Royal Society of London A,454,903–995.
Huang,N.E.,and Shen,S.S.P.,2005,Hilbert-Huang transform and its applications:World Scientific,.ondon.
Li,X.Y.,Chen,S.M.,Wang,J.M.,Pei,J.Y.,and Wang,Y.B.,2012,Forward modeling studies on the time frequency characteristics of thin layers:Chinese J.of Geophysics,55(10),3410–3419.
Liu,G.,Fomel,S.,and Chen,X.,2009,Time-frequency characterization of seismic data using local attributes:79th SEG Annual International Meeting,Expanded Abstracts,1825–1829.
Liu,J.,and Marfurt,K.J.,2006,Thin bed thickness prediction using peak instantaneous frequency:76th SEG Annual International Meeting,Expanded Abstracts,968–972.
Liu,Y.,and Fomel,S.,2010,Local time-frequency transform and its application to ground-roll noiseattenuation:80th SEG Annual International Meeting,Expanded Abstracts,3711–3716.
Mallat,S.,2009,A wavelet tour of signal processing–Thesparse way(Third Edition).
Marfurt,K.J.,and Kirlin,R.L.,2001,Narrow-band spectral analysis and thin-bed tuning:Geophysics,66,1274–1283
Partyka,G.,Gridley,A.J.,and Lope z,J.,1999,Interpretational applications of spectral decomposition inreservoir characterization:The Leading Edge,18,353–360,
Ren,H.,Goloshubin,G.,and Hilterman,F.,2007,Spectracross plot:77th Annual International Meeting,SEG,Expanded Abstracts,199–203.
Rioul,O.,and Vetterli,M.,1991,Wavelets and signal processing:IEEE Signal Processing Magazine,8(4),14–38,
Sinha,S.,Routh,P.S.,Anno,P.D.,and Castagna,J.P.,2005,Spectral decomposition of seismic data with continuous-wavelet transform:Geophysics,70(6),19–25,
Steeghs,P.,and Drijkoningen,G.,2001,Seismic sequence analysis and attribute extraction using quadratic time frequency representations:Geophysics,66,1947–1959,
Stockwell,R.G.,Mansinha,L.,and Lowe,R.P.,1996,Localization of the complex spectrum:the S transform:IEEE Transactions on Signal Processing,44(4),998–1001.
Wang,Y.,2007,Seismictime-frequency spectral decomposition by matching pursuit:Geophysics,72(1),V13–V20
Wigner,E.,1932,On the quantum correction for thermo dynamic equilibrium:Physical Review,40(5),749.
Bonar,D.C.,and Sacchi,M.D.,2010,Complex spectral decomposition via inversion strategies:80th SEG Annual International Meeting,Expanded Abstracts,1408–1412.
Castagna,J.,Sun,S.,and Siegfried,R.,2003,Instantaneouss pectral analysis:Detection of low-frequency shadows associated with hydrocarbons:The Leading Edge,22,120–127C.
Castagna,J.,and Sun,S.,2006,Comparison of spectral decomposition methods:First Break,24,75–79.
Chuang,H.,and Lawton,D.C.,1991,Some propertiesof thin beds:61st Annual International Meeting,SEG,Expanded Abstracts,224–227.
Ebrom,D.,2004,The low-frequency gas shadow onseismic sections:The Leading Edge,23,772,
Gao,J.H.,2003,Generalized S transform and seismicresponse analysis of thin interbeds:Chinese J.ofGeophysics,46(4),526–532.
Gabor,D.,1946,Theory of communication:Journal of the Institute of Electrical Engineers,93,429–457.
Gholami,2012,Sparse time–frequency decomposition and some applications:IEEE Transactions on Geoscience and Remote Sensing,51,3598–3604,
Huang,N.E.,Shen,Z.,Long,S.R.,Wu,M.C.,Shih,H.H.,Zheng,Q.,Yen,N.C.,Tung,C.C.,and Liu,H.H.,1998.The empirical mode decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis:Proceedings of the Royal Society of London A,454,903–995.
Huang,N.E.,and Shen,S.S.P.,2005,Hilbert-Huang transform and its applications:World Scientific,.ondon.
Li,X.Y.,Chen,S.M.,Wang,J.M.,Pei,J.Y.,and Wang,Y.B.,2012,Forward modeling studies on the time frequency characteristics of thin layers:Chinese J.of Geophysics,55(10),3410–3419.
Liu,G.,Fomel,S.,and Chen,X.,2009,Time-frequency characterization of seismic data using local attributes:79th SEG Annual International Meeting,Expanded Abstracts,1825–1829.
Liu,J.,and Marfurt,K.J.,2006,Thin bed thickness prediction using peak instantaneous frequency:76th SEG Annual International Meeting,Expanded Abstracts,968–972.
Liu,Y.,and Fomel,S.,2010,Local time-frequency transform and its application to ground-roll noiseattenuation:80th SEG Annual International Meeting,Expanded Abstracts,3711–3716.
Mallat,S.,2009,A wavelet tour of signal processing–Thesparse way(Third Edition).
Marfurt,K.J.,and Kirlin,R.L.,2001,Narrow-band spectral analysis and thin-bed tuning:Geophysics,66,1274–1283
Partyka,G.,Gridley,A.J.,and Lope z,J.,1999,Interpretational applications of spectral decomposition inreservoir characterization:The Leading Edge,18,353–360,
Ren,H.,Goloshubin,G.,and Hilterman,F.,2007,Spectracross plot:77th Annual International Meeting,SEG,Expanded Abstracts,199–203.
Rioul,O.,and Vetterli,M.,1991,Wavelets and signal processing:IEEE Signal Processing Magazine,8(4),14–38,
Sinha,S.,Routh,P.S.,Anno,P.D.,and Castagna,J.P.,2005,Spectral decomposition of seismic data with continuous-wavelet transform:Geophysics,70(6),19–25,
Steeghs,P.,and Drijkoningen,G.,2001,Seismic sequence analysis and attribute extraction using quadratic time frequency representations:Geophysics,66,1947–1959,
Stockwell,R.G.,Mansinha,L.,and Lowe,R.P.,1996,Localization of the complex spectrum:the S transform:IEEE Transactions on Signal Processing,44(4),998–1001.
Wang,Y.,2007,Seismictime-frequency spectral decomposition by matching pursuit:Geophysics,72(1),V13–V20
Wigner,E.,1932,On the quantum correction for thermo dynamic equilibrium:Physical Review,40(5),749.
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