基于自适应窗函数的最优分数域Gabor变换及其应用(英文)
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摘要
本文利用分数阶傅里叶变换(FrFT)的时频旋转性,设计基于广义时间带宽积准则的最优窗函数,从而实现自适应分数域最优Gabor变换,达到提高时频聚集性的目的。该算法首先找到最优旋转因子,然后对信号做该阶次下的FrFT,将经过FrFT后的信号做频谱成像,最后反方向旋转到原时频位置,从而解决了时频轴在旋转中失去物理意义的问题,这将推进FrFT在高精度储层预测领域的应用。另外,本文从分数域Parseval定理角度提出一种自适应搜索最优旋转因子的方法,降低了算法整体运算复杂度。地震信号谱分解结果表明本文算法获得的谱分解瞬时频率切片显著优于传统Gabor变换。这种自适应时频分析对于复杂地震信号处理具有重大意义。
We designed the window function of the optimal Gabor transform based on the time–frequency rotation property of the fractional Fourier transform. Thus, we obtained the adaptive optimal Gabor transform in the fractional domain and improved the time–frequency concentration of the Gabor transform. The algorithm first searches for the optimal rotation factor, then performs the p-th FrFT of the signal and, finally, performs time and frequency analysis of the FrFT result. Finally, the algorithm rotates the plane in the fractional domain back to the normal time–frequency plane. This promotes the application of FrFT in the field of high-resolution reservoir prediction. Additionally, we proposed an adaptive search method for the optimal rotation factor using the Parseval principle in the fractional domain, which simplifies the algorithm. We carried out spectrum decomposition of the seismic signal, which showed that the instantaneous frequency slices obtained by the proposed algorithm are superior to the ones obtained by the traditional Gabor transform. The adaptive time frequency analysis is of great significance to seismic signal processing.
We designed the window function of the optimal Gabor transform based on the time–frequency rotation property of the fractional Fourier transform. Thus, we obtained the adaptive optimal Gabor transform in the fractional domain and improved the time–frequency concentration of the Gabor transform. The algorithm first searches for the optimal rotation factor, then performs the p-th FrFT of the signal and, finally, performs time and frequency analysis of the FrFT result. Finally, the algorithm rotates the plane in the fractional domain back to the normal time–frequency plane. This promotes the application of FrFT in the field of high-resolution reservoir prediction. Additionally, we proposed an adaptive search method for the optimal rotation factor using the Parseval principle in the fractional domain, which simplifies the algorithm. We carried out spectrum decomposition of the seismic signal, which showed that the instantaneous frequency slices obtained by the proposed algorithm are superior to the ones obtained by the traditional Gabor transform. The adaptive time frequency analysis is of great significance to seismic signal processing.
引文
Almeida,L.B.,1994,The fractional Fourier transform and time-frequency representations:IEEE Transactions on Signal Processing,42(11),3084–3091.
Chen,Y.P.,Peng,Z.M.,2012,A novel optimal STFrFT and its application in seismic signal processing:The third International Conference on Computational ProblemSolving,Leshan,China,328–331.
Durak,L.,and Ankan,O.,2002,Generalized time bandwidth product optimal short time Fourier transformation:IEEE conference publications,2,1465–1468.
Liu,J.,and Marfurt,K.J.,2007,Instantaneous spectral attributes to detect channels:Geophysics,72(2),23–31.
Liu,X.W.,Liu,W.Y.,Liu,H.,and Li,Y.M.,2007,Generalized seismic signal time-frequency analysisand numerical algorithms:Computing techniques forgeophysical and geochemical exploration(in Chinese),29 (5),386–390.
Montana,C.A.,and Margrave,G.F.,2004,Spatial prediction filtering in fractional Fourier domains:SEG Annual,41(2),241–244.
Ozaktas,H.M.,Ankan,O.,Kutay,M.A.,and Bozdagt,G.,1996,Digital Computation of the Fractional FourierTransform:IEEE Transactions on signal processing,44 (9),2141–2150.
Ozaktas,H.M.,and Kutay,M.A.,1999,Introduction tothe fractional Fourier transform and its applications:Advances in imaging and electron,volume 106,239–291.
Sinha,S.,Routh,P.S.,Anno,P.D.,and Castagna,J.P.C.,2005,Spectral decomposition of seismic data with continuous-wavelet transform:Geophysics,70(6),19–25.
Xu,D.P.and Guo,K.,2012,Fractional S transform–Part 1:Theory:Applied geophysics,9(1),73–79.
Wang,Z.W.,Wang,X.L.,Xiang,W.,Liu,Q.H.,Zhang,X.A.,and Yang,C.,2012,Reservoir information extraction using a fractional Fourier transform and a smooth pseudo Wigner-Ville distribution:Applied geophysics,9(4),391–400.
Wexler,J.,and Raz,S.,1990,Discrete Gabor expansions:Signal Processing,21(3),207–221.
Chen,Y.P.,Peng,Z.M.,2012,A novel optimal STFrFT and its application in seismic signal processing:The third International Conference on Computational ProblemSolving,Leshan,China,328–331.
Durak,L.,and Ankan,O.,2002,Generalized time bandwidth product optimal short time Fourier transformation:IEEE conference publications,2,1465–1468.
Liu,J.,and Marfurt,K.J.,2007,Instantaneous spectral attributes to detect channels:Geophysics,72(2),23–31.
Liu,X.W.,Liu,W.Y.,Liu,H.,and Li,Y.M.,2007,Generalized seismic signal time-frequency analysisand numerical algorithms:Computing techniques forgeophysical and geochemical exploration(in Chinese),29 (5),386–390.
Montana,C.A.,and Margrave,G.F.,2004,Spatial prediction filtering in fractional Fourier domains:SEG Annual,41(2),241–244.
Ozaktas,H.M.,Ankan,O.,Kutay,M.A.,and Bozdagt,G.,1996,Digital Computation of the Fractional FourierTransform:IEEE Transactions on signal processing,44 (9),2141–2150.
Ozaktas,H.M.,and Kutay,M.A.,1999,Introduction tothe fractional Fourier transform and its applications:Advances in imaging and electron,volume 106,239–291.
Sinha,S.,Routh,P.S.,Anno,P.D.,and Castagna,J.P.C.,2005,Spectral decomposition of seismic data with continuous-wavelet transform:Geophysics,70(6),19–25.
Xu,D.P.and Guo,K.,2012,Fractional S transform–Part 1:Theory:Applied geophysics,9(1),73–79.
Wang,Z.W.,Wang,X.L.,Xiang,W.,Liu,Q.H.,Zhang,X.A.,and Yang,C.,2012,Reservoir information extraction using a fractional Fourier transform and a smooth pseudo Wigner-Ville distribution:Applied geophysics,9(4),391–400.
Wexler,J.,and Raz,S.,1990,Discrete Gabor expansions:Signal Processing,21(3),207–221.
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