时频分析新方法研究及其在地震资料储层识别中的应用
|
摘要
时频谱分解技术是近年来发展起来的广泛用于油藏储层解释一种时频分析方法。随着对油气的发现与开采难度不断加大，需要对包括传统的时频谱分析方法在内的各种方法进行创新，以提高对地震资料储层预测的准确性。
在常规时频分析方法的基础上，先研究一些新型频谱分解技术的方法和理论；然后将其用于某地区三叠系（砂岩体）的3D地震数据。主要的研究内容和创新点有：
⑴.本文提出将盲信号处理中的独立分量分析算法与经验模态分解算法(EMD)融合形成的J-EMD算法.相比较EMD算法，论文研究的J-EMD算法具有一定优势，在一定程度上克服了EMD算法在应用中的缺陷。将EMD算法和J-EMD算法分别对于实际的3D地震资料应用效果进行对比，直接使用EMD算法分解的单个IMF分量不能有效识别油气信号频谱，证实了它的不足。而使用J-EMD算法，能够分离出独立的对油气敏感的IMF分量，提高对油气储层识别的可靠性。
⑵.本文提出将广义S变换和较为稳健的ICA算法（JADE算法）相结合的方法来对地震数据进行频谱分解。地震数据经过时频谱分解后可以得到许多的单频数据体，这给地震数据的分析和解释工作带来了极大不便。本文提出的方法可以将地震信号在时频域内的不同单频体中提取对油气敏感的独立的频谱。某些独立频谱是多个单频的共同频率信息表示，反映的某种地质体的信息。因而这种方法可以有效的对实际的3D地震资料储层进行识别和预测，减少多解性。
⑶.论文将S变换和分数阶Fourier变换结合，提出一种新的分数阶时频分析方法，即分数阶S变换，并推导出FRST的逆变换等性质。分数阶Fourier变换具有处理非平稳信号的能力，但由于仍然使用全局核函数，所得的分数阶Fourier谱没有时间信息，而分数阶S变换具有分数阶Fourier变换和ST的优点，可以对地震信号等非平稳、时变信号进行处理和分析，增强了S变换对信号时频分析的灵活性，具有广泛的应用前景。
⑷.论文从三个方面研究了分数阶S变换在地震资料储层识别中的应用。一方面，研究了对3D地震资料中最优分数阶参数的估计。相比普通S变换，在3D地震资料的储层FRST单频切片中，该方法具有较好的效果。另一方面，针对在3D地震数据中最优分数阶参数估计存在的不足，提出了将FRST和盲信号处理中的复数cFastICA算法进行结合。不需要对地震资料的最优分数阶参数进行估计，利用不同的分数阶参数挖掘更多有效的地质体信息频谱，提取识别有效地质特征信息的独立频谱，提高对地震数据的解释效率。最后，将FRST用于油气储层下方的低频阴影的检测。同时，本文利用了FRST的多分数阶参数多旋转角度的优势，提出了利用ICA算法从多个分数阶参数、多个低频处的单频中提取出“低频阴影”的方法，增加了对储层识别的可靠性，提高了识别的效率。
Spectral decomposition technology, which is a time-frequency analysis method,is widely used in reservoir interpretation in recent years. With the difficulty ofdiscovery and exploitation is growing, it is necessary to innovation a variety ofexisting methods including the traditional time-frequency spectral analysis methods,which can improve the accuracy of seismic data reservoir prediction. In this paper,based on the conventional time frequency analysis method, some new spectrumdecomposition technique methods are studied, which is used in a3D seismic data ofTriassic sand bodies in an area. The main contents and innovation points are asfollows.
⑴. In this paper, the Fusion algorithm, which combines to EMD and ICAalgorithm in blind signal processing, is proposed. Compared with EMD algorithm, theJ-EMD algorithm has some advantages in the certain extent, which overcomes thedefects of EMD algorithm in the application. The application effects of EMDalgorithm and J-EMD algorithm are compared in the actual3D seismic data. EMDalgorithm decomposes a single into IMF components that can not effectively identifysignal spectrum of oil and gas and its inadequacy is confirmed. However, the J-EMDalgorithm is able to obtain the independent IMF component that can improve thereliability for oil and gas reservoir identification.
⑵. This paper puts forward a method for spectral decomposition of seismic data,which combines the generalized S transformation and the JADE algorithm that is arobust ICA algorithm. The time-frequency spectrum decomposition of Seismic datacan obtain a lot of single frequency data that can give rise to the great inconveniencefor the seismic data analysis and interpretation work. The method can extract the oiland gas sensitive independent spectrum form the different single frequency data in thetime-frequency domain of seismic signals. Some of independent spectra are thecommon frequency information of some single-frequency data, which can reflectsome geological bodies’ information, respectively. So this method can effectivelyidentify and predict reservoir in the actual3D seismic data, and reduce ambiguity.
⑶. In this paper, we define a new fractional time-frequency method, thefractional Fourier S transform (FRST), based on the idea of the S transform(ST) and the FRFT, and study its inverse transform and others properties. The fractional Fouriertransform (FRFT) can process the non-stationary signals, but using a global kernel,the spectra of FRFT don’t show the time information. However, FRST has theadvantages of FRFT and ST, which can process the seismic signals and othertime-varying, non-stationary signals. Then the flexibility of time-frequency signalanalysis is increased, and then it has broad application prospect.
⑷. This paper study the application of FRST in seismic data reservoiridentification form three aspects as follows. First, the estimate of optimal fractionalparameter is studied in3D seismic data. Compared to ordinary ST, the method has agood effect in the FRST single-frequency slice of the3D seismic reservoir. Second,the optimal fractional parameter estimation method has some defects to apply in the3D seismic data. The combinative method of FRST and the complex cFastICAalgorithm is put forward, which can mine more effective spectra of geologicalinformation by using different fractional parameters, can extract the effectiveindependent spectrum of identifying geological characteristics information andimprove the efficiency of the interpretation of seismic data, while don’t need toestimate the optimal fractional parameter. Finally, the FRST is used to detect thelow-frequency shadows below oil and gas reservoir. At the same time, using theadvantages of the FRST fractional rotation parameters, this paper puts forward themethod that increases the reliability of reservoir identification and improve theefficiency of identification to exact the low-frequency shadows from multiplefractional parameters, low frequency single frequency data.
在常规时频分析方法的基础上，先研究一些新型频谱分解技术的方法和理论；然后将其用于某地区三叠系（砂岩体）的3D地震数据。主要的研究内容和创新点有：
⑴.本文提出将盲信号处理中的独立分量分析算法与经验模态分解算法(EMD)融合形成的J-EMD算法.相比较EMD算法，论文研究的J-EMD算法具有一定优势，在一定程度上克服了EMD算法在应用中的缺陷。将EMD算法和J-EMD算法分别对于实际的3D地震资料应用效果进行对比，直接使用EMD算法分解的单个IMF分量不能有效识别油气信号频谱，证实了它的不足。而使用J-EMD算法，能够分离出独立的对油气敏感的IMF分量，提高对油气储层识别的可靠性。
⑵.本文提出将广义S变换和较为稳健的ICA算法（JADE算法）相结合的方法来对地震数据进行频谱分解。地震数据经过时频谱分解后可以得到许多的单频数据体，这给地震数据的分析和解释工作带来了极大不便。本文提出的方法可以将地震信号在时频域内的不同单频体中提取对油气敏感的独立的频谱。某些独立频谱是多个单频的共同频率信息表示，反映的某种地质体的信息。因而这种方法可以有效的对实际的3D地震资料储层进行识别和预测，减少多解性。
⑶.论文将S变换和分数阶Fourier变换结合，提出一种新的分数阶时频分析方法，即分数阶S变换，并推导出FRST的逆变换等性质。分数阶Fourier变换具有处理非平稳信号的能力，但由于仍然使用全局核函数，所得的分数阶Fourier谱没有时间信息，而分数阶S变换具有分数阶Fourier变换和ST的优点，可以对地震信号等非平稳、时变信号进行处理和分析，增强了S变换对信号时频分析的灵活性，具有广泛的应用前景。
⑷.论文从三个方面研究了分数阶S变换在地震资料储层识别中的应用。一方面，研究了对3D地震资料中最优分数阶参数的估计。相比普通S变换，在3D地震资料的储层FRST单频切片中，该方法具有较好的效果。另一方面，针对在3D地震数据中最优分数阶参数估计存在的不足，提出了将FRST和盲信号处理中的复数cFastICA算法进行结合。不需要对地震资料的最优分数阶参数进行估计，利用不同的分数阶参数挖掘更多有效的地质体信息频谱，提取识别有效地质特征信息的独立频谱，提高对地震数据的解释效率。最后，将FRST用于油气储层下方的低频阴影的检测。同时，本文利用了FRST的多分数阶参数多旋转角度的优势，提出了利用ICA算法从多个分数阶参数、多个低频处的单频中提取出“低频阴影”的方法，增加了对储层识别的可靠性，提高了识别的效率。
Spectral decomposition technology, which is a time-frequency analysis method,is widely used in reservoir interpretation in recent years. With the difficulty ofdiscovery and exploitation is growing, it is necessary to innovation a variety ofexisting methods including the traditional time-frequency spectral analysis methods,which can improve the accuracy of seismic data reservoir prediction. In this paper,based on the conventional time frequency analysis method, some new spectrumdecomposition technique methods are studied, which is used in a3D seismic data ofTriassic sand bodies in an area. The main contents and innovation points are asfollows.
⑴. In this paper, the Fusion algorithm, which combines to EMD and ICAalgorithm in blind signal processing, is proposed. Compared with EMD algorithm, theJ-EMD algorithm has some advantages in the certain extent, which overcomes thedefects of EMD algorithm in the application. The application effects of EMDalgorithm and J-EMD algorithm are compared in the actual3D seismic data. EMDalgorithm decomposes a single into IMF components that can not effectively identifysignal spectrum of oil and gas and its inadequacy is confirmed. However, the J-EMDalgorithm is able to obtain the independent IMF component that can improve thereliability for oil and gas reservoir identification.
⑵. This paper puts forward a method for spectral decomposition of seismic data,which combines the generalized S transformation and the JADE algorithm that is arobust ICA algorithm. The time-frequency spectrum decomposition of Seismic datacan obtain a lot of single frequency data that can give rise to the great inconveniencefor the seismic data analysis and interpretation work. The method can extract the oiland gas sensitive independent spectrum form the different single frequency data in thetime-frequency domain of seismic signals. Some of independent spectra are thecommon frequency information of some single-frequency data, which can reflectsome geological bodies’ information, respectively. So this method can effectivelyidentify and predict reservoir in the actual3D seismic data, and reduce ambiguity.
⑶. In this paper, we define a new fractional time-frequency method, thefractional Fourier S transform (FRST), based on the idea of the S transform(ST) and the FRFT, and study its inverse transform and others properties. The fractional Fouriertransform (FRFT) can process the non-stationary signals, but using a global kernel,the spectra of FRFT don’t show the time information. However, FRST has theadvantages of FRFT and ST, which can process the seismic signals and othertime-varying, non-stationary signals. Then the flexibility of time-frequency signalanalysis is increased, and then it has broad application prospect.
⑷. This paper study the application of FRST in seismic data reservoiridentification form three aspects as follows. First, the estimate of optimal fractionalparameter is studied in3D seismic data. Compared to ordinary ST, the method has agood effect in the FRST single-frequency slice of the3D seismic reservoir. Second,the optimal fractional parameter estimation method has some defects to apply in the3D seismic data. The combinative method of FRST and the complex cFastICAalgorithm is put forward, which can mine more effective spectra of geologicalinformation by using different fractional parameters, can extract the effectiveindependent spectrum of identifying geological characteristics information andimprove the efficiency of the interpretation of seismic data, while don’t need toestimate the optimal fractional parameter. Finally, the FRST is used to detect thelow-frequency shadows below oil and gas reservoir. At the same time, using theadvantages of the FRST fractional rotation parameters, this paper puts forward themethod that increases the reliability of reservoir identification and improve theefficiency of identification to exact the low-frequency shadows from multiplefractional parameters, low frequency single frequency data.
引文
[1]高军，凌云，周兴元等.时频域球面发散和吸收补偿[J].石油地球物理勘探，1996，31(6)856-866.
[2]白桦，李鳗鹏.基于时频分析的地层吸收补偿[J].石油地球物理勘探，1999，34(6):642-648.
[3]章坷，刘贵忠，周大文等，二进小波变换方法的地震信号分时分频去噪处理[J].地球物理学报，1996，39(2):265-270.
[4] Satish K Sinha，Partha S Routh，PhilD. Anno，et al.Time-Frequency attribute of seismic datausing continuous wavelet transform[J].In:Proe.73th SEG Annual Meeting，Houston，Texas，USA，2003:1481-1484.
[5] Stockwell R G, Mansinha L, Lowe R P. Localization of the complex spectrum: the Stransform[J]. IEEE trans. on signal processing,1996,44(4):998-1001.
[6]高静怀,陈文超,李幼铭等.广义S变换与薄互层地震响应[J].地球物理学报，2003，46(4):526-532.
[7] Pinnegar C R, Mansinha L. The S-transform with windows of arbitrary and varyingshape[J].Geophysics,2003,68(1):381-385.
[8] McFadden P D, Cook J G, Forster L M. Decomposition of Gear vibration signals bygeneralized S transform[J]. Mechanical Systems and Signal Processing，1999,13(5):691-707.
[9]邹文，陈爱萍，贺振华等.基于S变换的地震相分析技术[J].石油物探，2006，45(1):48－51.
[10] Pinnegar C R, Eaton D W. Application of the S transform to prestack noise attenuationfiltering [J]. Journal of Geophysical Research,2003,108(B9):1-10.
[11]刘喜武，刘洪，李幼铭，等.基于广义S变换研究地震地层特征[J].地球物理学进展，2006，21（2）：440-451.
[12]陈学华，贺振华，黄德济.基于广义S变换的信号提取与抑噪[J].成都理工大学学报（自然科学版），2006,33（4）：331-335.
[13]陈学华，贺振华，黄德济.时频域高分辨地震层序识别[J].吉林大学学报（地球科学版），2008，38(1)：152-155.
[14] Gabor D. Theory of communication [J]. Journal of Institute for Electrical Engineering, SPIE,1946,93:429-457.
[15] Wigner E P. On the quantum correction for thermodynamic equilibrium[J]. Phys. Rev.,1932,40:749-759.
[16] Ville J. Theorie et application de la notion de signal analytique[J]. Cables etTransmission,1948,2A:61-74.
[17] Morlet J, Arens G, Fourgeau E, et al. Wave propagation and sampling theory-Part I: Complexsignal and scattering in multilayered media[J]. Geophysics,1982,47(2):203-221.
[18] Goupillaud P, Grossmann A, Morlet J. Cycle-octave and related transforms in seismic signalanalysis[J]. Geoexploration，1984,85(23):85-102.
[19] Peyton L, Bottjer R, Partyka G. Interpretation of incised valleys using new3D seismictechniques: A case history using spectral decomposition and coherency[J]. The leading Edge,1998,17(10):1294-1298.
[20] Partyka G, Gridley J, Lopez J. Interpretational applications of spectral decom-position inreservoir characterization[J]. The Leading Edge,1999,18(3):353-360.
[21] Castagna J P, Sun S, Siegfried R W. Instantaneous spectral analysis: Detection oflow-frequency shadows associated with hydrocarbons[J]. The Leading Edge,2003,22(2):120-127.
[22]陈学华，贺振华，黄德济.基于广义S变换的地震资料高效时频谱分解[J].石油地球物理勘探，2008，43（5）530-534.
[23]黄饶,陈小宏,李景叶.基于谱分解的气藏识别技术与应用[J].石油地球物理勘探，2010,45(1):35-65.
[24] Li Y D, and Zheng X D. Spectral decomposition using Wigner-Ville distribution withapplications to carbonate reservoir characterization[J]. The Leading Edge,2008,27(8),1050-1057.
[25] Wang Y H. Seismic time-frequency spectral decomposition by matching pursuit[J].Geophysics,2007,72(1):13-20.
[26] Liu J and Marfurt K J. Instantaneous spectral attributes to detect channels[J]. Geophysics,2007,72(2):23-31.
[27] Castagna J P, Sun S, Siegfried R W. Instantaneous spectral analysis: Detection oflow-frequency shadows associated with hydrocarbons[J]. The leading edge,2003,22(2):120-127.
[28] Goloshubin G M, Schuyver C V, Korneev V A, et al. Reservoir imaging using lowfrequencies of seismic reflections[J]. The leading edge,2006,25(5):527-531.
[29] Taner M T, Koehler F, Sheriff R E. Complex seismic trace analysis[J]. Geophysics,1979,44(6):1041-1063.
[30] Goloshubin G M, Korneev V A, Vingalov V M. Seismic low-frequency effects fromoil-saturated reservoir zones[J].Expanded Abstracts of SEG Int'l Exposition and72nd AnnualMeeting,2002.
[31] Ebrom D. The low-frequency gas shadow on seismic sections[J].The Leading Edge,2004,23(8):772.
[32] Korneev V A, Goloshubin G M, Daley T M, et al. Seismic low-frequency effects inmonitoring fluid-saturated reservoirs[J].Geophysics,2004,69(2):522-532.
[33] He Zhen-hua, Xiong Xiao-jun, Bian Li-en. Numerical simulation of seismic low-frequencyshadows and its application[J].Applied Geophysics,2008,5(4):301-306.
[34] Tai S H, Puryear C and Castagna J P. Local frequency as a direct hydrocarbon indicator[C].79th Annual International Meeting SEG, Expanded Abstracts,2009,2160–2164.
[35]陈学华，贺振华，黄德济等.时频域油气储层低频阴影检测[J].地球物理学报，2009，52(1):215-221.
[36] Huang N E. Computer implicated empirical mode decomposition method, apparatus, andarticale of manufacture[P].U.S.Patent Pending,1996.
[37] Huang N E，et al．The empirical mode decomposition and the Hilbert spectrum for nonlinearand non-stationary time series analyses[J]. Proc.R Soc.Lond.(1998)454,903-995.
[38] Jeng Yih, Lin Ming-Juin, Chen Chih-Sung，et al．Noise reduction and data recovery for aVLF-EM survey using a nonlinear decomposition method[J]. GEOPHYSICS,2007,72(5):223-235.
[39]陈子雄，吴琛，周瑞忠.希尔伯特一黄变换谱及其在地震信号分析中的应用[J].福州大学学报（自然科学版），2006,34(2):260-264.
[40] Battista Bradley Matthew, Knapp Camelia, McGee Tom, Vaughn Goebel. Application of theempirical mode decomposition and Hilbert-Huang transform to seismic reflection data[J].Geophysics,2007,72(2):29-37.
[41]陈林，宋海斌.基于经验模态分解的地震瞬时属性提取[J].地球物理学进展，2008,23(4):1179-1185.
[42]何峰,代金芝,郑旭. Hilbert-Huang变换在油气检测和工程物探中的应用[J].石油天然气学报，2010,32(3):243-247.
[43]宋海斌，拜阳等.南海东北部内波特征——经验模态分解方法应用初探[J].地球物理学报，2010，53(2):393-400.
[44]钱昌松,刘代志等.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[J].地球物理学报，2010,53(5):1215-1225.
[45] Huang N E, Chen C C, Huang K, et al. A New Spectral Representation of Earthquake Data:Hilbert Spectral Analysis of Station TCU129, Chi-Chi, Taiwan,21September1999[J].Bulletin of the Seismological Society of America,2001,91(5):1310-1338.
[46]杨培杰,印兴耀,张广智.希尔伯特—黄变换地震信号时频分析与属性提取[J].地球物理学进展，2007,22(5):1585-1590.
[47]钱昌松,刘代志等.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[J].地球物理学报，2010,53(5):1215-1225.
[48]皮红梅,刘财,王典.利用Hilbert—Huang变换提取地震信号瞬时参数[J].石油地球物理勘探,2007,42(4):418-424.
[49] Wen Xiaotao, He Zhenhua, and Huang Deji. Reservoir detection based on EMD andcorrelation dimension [J]. Applied Geophysics,2009,6(1):70-76.
[50] Herault J and Jutten C. Space or time adaptive signal processing by Neural Network Models
[C]. Nural Network for computing: AIP Conference Proceedings151,1986:206-211.
[51] Comon P. Independent component analysis, a new concept[J]. Signal Processing,1994,36(3):287-314.
[52] Bell A J and Sejnowski T J. An information-maximization approach to blind separation andblind deconvolution[J]. Neural Computation,1995,7(6)：1129-1159.
[53] Girolami M,et al.. An extended exploratory projection pursuit network with linear andnonlinear anti-Hebbian lateral connection applied to the cocktail party problem[J]. NeuralNetwork,1997,10(9):1607-1618.
[54] Fyfe C. A comparative study of two neural methods of exploratory projection pursuit[J].Neural Network,1997,10(2):257-262.
[55] Hyv rinen A, Oja E. A fast fixed-point algorithm for independent component analysis[J].Neural Computation,1997,9(7),1483-1492.
[56] Hyv rinen A. Fast and robust fixed-point algorithm for independent component analysis[J].IEEE Trans. on Neural Network,1999,10(3),626-634.
[57] Cardoso J F, at al.. Blind beamforming for non-Gaussian signals [J].1993,140(6):362-370.
[58] Cardoso J F. Higher order contrasts for independent component analysis [J].NeuralComputation,1999,11(1):157-192.
[59] Cardoso J F, Delabrouille J, Patanchon G. Independent component analysis of the cosmicmicrowave background[C]. In: Proc. ICA2003, Nara, Japan,2003:1111-1116.
[60] Yuan Z, Oja E. A FastICA Algorithm for Non-negative Independent Component Analysis[C].In: Proc. ICA2004, Granada, Spain,2004:1-8.
[61] Cardoso J F.Informax and maximum likelihood for blind source separation[J].IEEE SigalProcessing Letter.1997,4(4):112-114.
[62] Lee T W,et al. A unifying information-theoretic framework for independent componentanalysis.International Journal of Computer and Mathmatics with Application.2000,31(11):1-12.
[63] Cardoso J F. Blind sigal processing: statistical principles [J].Proc.IEEE.1998,86(10):2009-2025.
[64] Yang H H,et al.Adaptive on-line learning algorithms for blind separation: Maximum entropyand minimum mutual information[J].Neural Networks.1997,9(67):1457-1481.
[65]何振亚，刘据，杨绿溪等.盲均衡和信道参数估计的一种ICA和进化计算方法[J].中国科学(E辑)，2000，30(l):l-7.
[66]张贤达,保铮.盲源分离[J].电子学报,2001,29(12A):1766-1771.
[67]马建仓等.盲信号处理[M].国防工业出版社,2006.
[68]刘喜武，刘洪，李幼铭.独立分量分析及其在地震信息处理中的应用初探[J].地球物理学进展，2003，18(1):90-96.
[69]吕文彪，尹成，张白林等.利用独立分量分析方法消除地震噪声[J].石油地球物理勘探，2007，42(2):132-136.
[70]陆文凯，骆毅，赵波等.基于独立分量分析的多次波自适应相减技术[J].地球物理学报，2004，47(5):886-891.
[71]陆斌等.独立成分分析在随钻地震信号处理中的应用[J].石油地球物理勘探，2010,45(1):15-22.
[72]王任一，梅廉夫.利用独立分量分析技术对油气富集区进行地震识别[J].石油学报，2008,29(4):544-548.
[73]吕文彪,尹成等.基于独立分量分析的地震属性优化[J].天然气工业，2008,,28(9):44-46
[74]刘喜武,高伟等.基于带状混合矩阵ICA实现地震盲反褶积[J].地球物理学进展，2007，22(4):1153-1163.
[75]印兴耀,刘杰,杨培杰.一种基于负熵的Bussgang地震盲反褶积方法[J].石油地球物理勘探，2007,42(5):499-505.
[76] Bingham E and Hyv rinen A. A fast fixed-point algorithm for independent componentanalysis of complex-valued signals [J], Int. J. Neural Systems,2000,10(1):1-8.
[77] Wiener N. Hermitian Polynomials and Fourier Analysis[J]. Journal of Mathematics PhysicsMIT,1929,18:70-73.
[78] Condon E U. Immersion of Fourier Transform in a Continuous Group of FunctionalTransformations[J]. Proc. National Academy of Sciences,1937,23:158-164.
[79] Bargmann V. On a Hilbert Space of Analytic Functions and Associated Integral Transform,Part I[J]. Comm.. Pure. Appl.Math.1961,14:187-214.
[80] Namias V. The fractional order Fourier transform and its application to quantummechanics[J]. J. Inst Math Appl,1980,25:241-265.
[81] McBride A C, Kerr F H. On Namia’s fractional Fourier transform. IMA J Appl Math,1987,39:159-175.
[82] Almeida L B. The fractional Fourier transform and time-frequency representations [J].IEEE Tran Signal Processing,1994,42(11):3084-3091.
[83] Ozaktas H M, Arikan O, et al. Digital Computation of the Fractional Fourier Transform[J].IEEE Trans. Signal Processing,1996,44(9):2141-2150.
[84] Stankovi L J, Alieva T, Bastiaans M J. Time-frequency signal analysis based on thewindowed fractional Fourier transform[J] Signal Processing.83(11)(2003)2459-2468.
[85] Capus C and Brown K. Short-time fractional Fourier methods for the time-frequencyrepresentation of chirp signals[J]. J. Acoust. Soc. Amer.,2003,113(6):3253–3263.
[86] Durak L. Shift-invariance of short-time Fourier transform in fractional Fourier domains[J].Journal of the Franklin Institute,2009,346:136-146.
[87] Capus C, Brown K. Short-time fractional Fourier methods for the time-frequencyrepresentation of chirp signals[J]. J. Acoust. Soc. Am.2003,113(6)3253-3263.
[88] Mendlovic D, Zalevsky Z, Mas D, Garcia J, Ferreira C, Fractional wavelet transform[J].APPLIED OPTICS,1997,36(20):4801-4806.
[89] Huang Y, Suter B. The Fractional Wave Packet Transform[J]. Multidimensional Systems andSignal Processing,1998,9:399-402.
[90] Tao R, Li YL, Wang Y. Short-Time Fractional Fourier Transform and Its Applications[J].IEEE Trans. Signal Process,2010,58(5):2568-2580.
[91] C. A．Montana，G. F．Margrave．Spatial prediction filtering in fractional Fourier domains[C].72th Ann. Internat．Mtg．Soc．Exp l．Geophys, Expanded Abstracts,2004.
[92]耿春,尹成,张白林.分数Fourier变换在可控震源信号处理中的应用[J].工程地球物理学报,2006,3(6):427～436.
[93]刘喜武,刘婉莹等.地震信号广义时频分析及其数值实现[J].物探化探计算技术,2007,29(5):386～390.
[94]陈红，彭真明，王峻等.地震信号分数阶Gabor变换谱分解方法及应用[J].地球物理学报，2011，54(3):867～873.
[95]陶然，邓兵，王越.分数阶Fourier变换在信号处理领域的研究进展[J].中国科学E辑信息科学,2006,36(2):113-136.
[96] Deco G, Obradovic D. An information-Theoretic Approach to Neural Computing[M].Springer Verlag,1996.
[97]杨福生，洪波.独立分量分析的原理与应用[M].清华大学出版社，2006.
[98]史习智.盲信号处理——理论与实践[M].上海交通大学出版社，2008.
[99]杜爱民等.Hilbert-Huang变换中的一种端点处理方法[J].地震研究，2007,30(1):54-58.
[100]熊学军等.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.
[101]张贤达.现代信号处理[M].北京：清华大学出版社，2002:1-528.
[102] Zayed A I. A convolution and product theorem for the fractional Fourier Transform[J]. IEEESignal Process. Lett.,1998,5(4):101–103.
[103] Erden M F, Kutay M A and Ozaktas H M. Repeated filtering in consecutive fractional Fourierdomains and its application to signal restoration[J]. IEEE Trans. Signal Process.,1999,47(5):1458–1462.
[104] Tao R, Deng B, and Wang Y. Research progress of the fractional Fourier Transform in signalprocessing[J].Sci. China: Series F Inf. Sci.,2006,491–25.
[105] Tao R, Li B Z, and Wang Y. Spectral analysis and reconstruction for periodic non-uniformlysampled signals in fractional Fourier domain[J]. IEEE Trans. Signal Process,2007,55(7):3541–3547.
[106] Alieva T, Lopez V, et al. The fractional Fourier Transform in optical propagation problems[J]. J. Mod. Opt.,1994,41:1037–1040.
[107] Zhang Feng, Bi Guoan, Chen Yan Qiu. Tomography Time-frequency Transform[J]. IEEEtrans. Signal Processing,2002,50(6):1398-1801.
[108] Ozaktas H M, Erkaya N, Kutay M A. Effect of Fractional Fourier Transformation onTime-Frequency Distributions Belonging to the Cohen Class[J]. IEEE Signal ProcessingLetters,1996,3(2):40-41.
[109] Lee S Y, Szu HH. Fractional Fourier Transform, Wavelet Transforms, and Adaptive NeuralNetworks[J]. Opt. Engineering,1994,33:2326-2330.
[110]陶然等.分数阶傅里叶变换及其应用[M].北京：清华大学出版社，2009.
[111] Akan A, eki Y. A fractional Gabor expansion. Journal of the Franklin Institute,2003,340(5):391～397.
[112] Akan A, nen E. A discrete fractional Gabor expansion for multi-component signals[J].AEU-International Journal of Electronics and Communications,2007,61(5):279～185.
[113] Wexler J, Raz S. Discrete Gabor expansions[J]. Signal Processing,1990,21(3),207-221.
[114]吴媚，符力耘等.高分辨率非线性储层物性参数反演方法和应用[J].地球物理学报，2008,51(2):546-557.
[115]钱绍新.应用模式识别方法预测油气储集层[J].地球物理学报，1992,35(5):630-636.
[116]王瑞飞,陈明强.特低渗透砂岩储层可动流体赋存特征及影响因素[J].石油学报，2008,29(4):558-561.
[117]李景叶,陈小宏.基于地震资料的储层流体识别[J].石油学报，2008,29（2）:235-238.
[118] Li Zishun, Guo Xuebin. Predicting the distribution of thin bed reservoirs by broad frequencyband seismic[J]. APPLIED GEOPHYSICS,2008,4(2):118-126.
[119] Bastiaans M J. Gabor's Expansion of a Signal into Gaussian Elementary Signals[J]. Pro.IEEE,1980,68:538-539.
[120] Guo Hao, Marfurt K J, and Liu Jianlei. Principal component spectral analysis[J]. Geophysics,2009,74(4):35-43.
[2]白桦，李鳗鹏.基于时频分析的地层吸收补偿[J].石油地球物理勘探，1999，34(6):642-648.
[3]章坷，刘贵忠，周大文等，二进小波变换方法的地震信号分时分频去噪处理[J].地球物理学报，1996，39(2):265-270.
[4] Satish K Sinha，Partha S Routh，PhilD. Anno，et al.Time-Frequency attribute of seismic datausing continuous wavelet transform[J].In:Proe.73th SEG Annual Meeting，Houston，Texas，USA，2003:1481-1484.
[5] Stockwell R G, Mansinha L, Lowe R P. Localization of the complex spectrum: the Stransform[J]. IEEE trans. on signal processing,1996,44(4):998-1001.
[6]高静怀,陈文超,李幼铭等.广义S变换与薄互层地震响应[J].地球物理学报，2003，46(4):526-532.
[7] Pinnegar C R, Mansinha L. The S-transform with windows of arbitrary and varyingshape[J].Geophysics,2003,68(1):381-385.
[8] McFadden P D, Cook J G, Forster L M. Decomposition of Gear vibration signals bygeneralized S transform[J]. Mechanical Systems and Signal Processing，1999,13(5):691-707.
[9]邹文，陈爱萍，贺振华等.基于S变换的地震相分析技术[J].石油物探，2006，45(1):48－51.
[10] Pinnegar C R, Eaton D W. Application of the S transform to prestack noise attenuationfiltering [J]. Journal of Geophysical Research,2003,108(B9):1-10.
[11]刘喜武，刘洪，李幼铭，等.基于广义S变换研究地震地层特征[J].地球物理学进展，2006，21（2）：440-451.
[12]陈学华，贺振华，黄德济.基于广义S变换的信号提取与抑噪[J].成都理工大学学报（自然科学版），2006,33（4）：331-335.
[13]陈学华，贺振华，黄德济.时频域高分辨地震层序识别[J].吉林大学学报（地球科学版），2008，38(1)：152-155.
[14] Gabor D. Theory of communication [J]. Journal of Institute for Electrical Engineering, SPIE,1946,93:429-457.
[15] Wigner E P. On the quantum correction for thermodynamic equilibrium[J]. Phys. Rev.,1932,40:749-759.
[16] Ville J. Theorie et application de la notion de signal analytique[J]. Cables etTransmission,1948,2A:61-74.
[17] Morlet J, Arens G, Fourgeau E, et al. Wave propagation and sampling theory-Part I: Complexsignal and scattering in multilayered media[J]. Geophysics,1982,47(2):203-221.
[18] Goupillaud P, Grossmann A, Morlet J. Cycle-octave and related transforms in seismic signalanalysis[J]. Geoexploration，1984,85(23):85-102.
[19] Peyton L, Bottjer R, Partyka G. Interpretation of incised valleys using new3D seismictechniques: A case history using spectral decomposition and coherency[J]. The leading Edge,1998,17(10):1294-1298.
[20] Partyka G, Gridley J, Lopez J. Interpretational applications of spectral decom-position inreservoir characterization[J]. The Leading Edge,1999,18(3):353-360.
[21] Castagna J P, Sun S, Siegfried R W. Instantaneous spectral analysis: Detection oflow-frequency shadows associated with hydrocarbons[J]. The Leading Edge,2003,22(2):120-127.
[22]陈学华，贺振华，黄德济.基于广义S变换的地震资料高效时频谱分解[J].石油地球物理勘探，2008，43（5）530-534.
[23]黄饶,陈小宏,李景叶.基于谱分解的气藏识别技术与应用[J].石油地球物理勘探，2010,45(1):35-65.
[24] Li Y D, and Zheng X D. Spectral decomposition using Wigner-Ville distribution withapplications to carbonate reservoir characterization[J]. The Leading Edge,2008,27(8),1050-1057.
[25] Wang Y H. Seismic time-frequency spectral decomposition by matching pursuit[J].Geophysics,2007,72(1):13-20.
[26] Liu J and Marfurt K J. Instantaneous spectral attributes to detect channels[J]. Geophysics,2007,72(2):23-31.
[27] Castagna J P, Sun S, Siegfried R W. Instantaneous spectral analysis: Detection oflow-frequency shadows associated with hydrocarbons[J]. The leading edge,2003,22(2):120-127.
[28] Goloshubin G M, Schuyver C V, Korneev V A, et al. Reservoir imaging using lowfrequencies of seismic reflections[J]. The leading edge,2006,25(5):527-531.
[29] Taner M T, Koehler F, Sheriff R E. Complex seismic trace analysis[J]. Geophysics,1979,44(6):1041-1063.
[30] Goloshubin G M, Korneev V A, Vingalov V M. Seismic low-frequency effects fromoil-saturated reservoir zones[J].Expanded Abstracts of SEG Int'l Exposition and72nd AnnualMeeting,2002.
[31] Ebrom D. The low-frequency gas shadow on seismic sections[J].The Leading Edge,2004,23(8):772.
[32] Korneev V A, Goloshubin G M, Daley T M, et al. Seismic low-frequency effects inmonitoring fluid-saturated reservoirs[J].Geophysics,2004,69(2):522-532.
[33] He Zhen-hua, Xiong Xiao-jun, Bian Li-en. Numerical simulation of seismic low-frequencyshadows and its application[J].Applied Geophysics,2008,5(4):301-306.
[34] Tai S H, Puryear C and Castagna J P. Local frequency as a direct hydrocarbon indicator[C].79th Annual International Meeting SEG, Expanded Abstracts,2009,2160–2164.
[35]陈学华，贺振华，黄德济等.时频域油气储层低频阴影检测[J].地球物理学报，2009，52(1):215-221.
[36] Huang N E. Computer implicated empirical mode decomposition method, apparatus, andarticale of manufacture[P].U.S.Patent Pending,1996.
[37] Huang N E，et al．The empirical mode decomposition and the Hilbert spectrum for nonlinearand non-stationary time series analyses[J]. Proc.R Soc.Lond.(1998)454,903-995.
[38] Jeng Yih, Lin Ming-Juin, Chen Chih-Sung，et al．Noise reduction and data recovery for aVLF-EM survey using a nonlinear decomposition method[J]. GEOPHYSICS,2007,72(5):223-235.
[39]陈子雄，吴琛，周瑞忠.希尔伯特一黄变换谱及其在地震信号分析中的应用[J].福州大学学报（自然科学版），2006,34(2):260-264.
[40] Battista Bradley Matthew, Knapp Camelia, McGee Tom, Vaughn Goebel. Application of theempirical mode decomposition and Hilbert-Huang transform to seismic reflection data[J].Geophysics,2007,72(2):29-37.
[41]陈林，宋海斌.基于经验模态分解的地震瞬时属性提取[J].地球物理学进展，2008,23(4):1179-1185.
[42]何峰,代金芝,郑旭. Hilbert-Huang变换在油气检测和工程物探中的应用[J].石油天然气学报，2010,32(3):243-247.
[43]宋海斌，拜阳等.南海东北部内波特征——经验模态分解方法应用初探[J].地球物理学报，2010，53(2):393-400.
[44]钱昌松,刘代志等.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[J].地球物理学报，2010,53(5):1215-1225.
[45] Huang N E, Chen C C, Huang K, et al. A New Spectral Representation of Earthquake Data:Hilbert Spectral Analysis of Station TCU129, Chi-Chi, Taiwan,21September1999[J].Bulletin of the Seismological Society of America,2001,91(5):1310-1338.
[46]杨培杰,印兴耀,张广智.希尔伯特—黄变换地震信号时频分析与属性提取[J].地球物理学进展，2007,22(5):1585-1590.
[47]钱昌松,刘代志等.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[J].地球物理学报，2010,53(5):1215-1225.
[48]皮红梅,刘财,王典.利用Hilbert—Huang变换提取地震信号瞬时参数[J].石油地球物理勘探,2007,42(4):418-424.
[49] Wen Xiaotao, He Zhenhua, and Huang Deji. Reservoir detection based on EMD andcorrelation dimension [J]. Applied Geophysics,2009,6(1):70-76.
[50] Herault J and Jutten C. Space or time adaptive signal processing by Neural Network Models
[C]. Nural Network for computing: AIP Conference Proceedings151,1986:206-211.
[51] Comon P. Independent component analysis, a new concept[J]. Signal Processing,1994,36(3):287-314.
[52] Bell A J and Sejnowski T J. An information-maximization approach to blind separation andblind deconvolution[J]. Neural Computation,1995,7(6)：1129-1159.
[53] Girolami M,et al.. An extended exploratory projection pursuit network with linear andnonlinear anti-Hebbian lateral connection applied to the cocktail party problem[J]. NeuralNetwork,1997,10(9):1607-1618.
[54] Fyfe C. A comparative study of two neural methods of exploratory projection pursuit[J].Neural Network,1997,10(2):257-262.
[55] Hyv rinen A, Oja E. A fast fixed-point algorithm for independent component analysis[J].Neural Computation,1997,9(7),1483-1492.
[56] Hyv rinen A. Fast and robust fixed-point algorithm for independent component analysis[J].IEEE Trans. on Neural Network,1999,10(3),626-634.
[57] Cardoso J F, at al.. Blind beamforming for non-Gaussian signals [J].1993,140(6):362-370.
[58] Cardoso J F. Higher order contrasts for independent component analysis [J].NeuralComputation,1999,11(1):157-192.
[59] Cardoso J F, Delabrouille J, Patanchon G. Independent component analysis of the cosmicmicrowave background[C]. In: Proc. ICA2003, Nara, Japan,2003:1111-1116.
[60] Yuan Z, Oja E. A FastICA Algorithm for Non-negative Independent Component Analysis[C].In: Proc. ICA2004, Granada, Spain,2004:1-8.
[61] Cardoso J F.Informax and maximum likelihood for blind source separation[J].IEEE SigalProcessing Letter.1997,4(4):112-114.
[62] Lee T W,et al. A unifying information-theoretic framework for independent componentanalysis.International Journal of Computer and Mathmatics with Application.2000,31(11):1-12.
[63] Cardoso J F. Blind sigal processing: statistical principles [J].Proc.IEEE.1998,86(10):2009-2025.
[64] Yang H H,et al.Adaptive on-line learning algorithms for blind separation: Maximum entropyand minimum mutual information[J].Neural Networks.1997,9(67):1457-1481.
[65]何振亚，刘据，杨绿溪等.盲均衡和信道参数估计的一种ICA和进化计算方法[J].中国科学(E辑)，2000，30(l):l-7.
[66]张贤达,保铮.盲源分离[J].电子学报,2001,29(12A):1766-1771.
[67]马建仓等.盲信号处理[M].国防工业出版社,2006.
[68]刘喜武，刘洪，李幼铭.独立分量分析及其在地震信息处理中的应用初探[J].地球物理学进展，2003，18(1):90-96.
[69]吕文彪，尹成，张白林等.利用独立分量分析方法消除地震噪声[J].石油地球物理勘探，2007，42(2):132-136.
[70]陆文凯，骆毅，赵波等.基于独立分量分析的多次波自适应相减技术[J].地球物理学报，2004，47(5):886-891.
[71]陆斌等.独立成分分析在随钻地震信号处理中的应用[J].石油地球物理勘探，2010,45(1):15-22.
[72]王任一，梅廉夫.利用独立分量分析技术对油气富集区进行地震识别[J].石油学报，2008,29(4):544-548.
[73]吕文彪,尹成等.基于独立分量分析的地震属性优化[J].天然气工业，2008,,28(9):44-46
[74]刘喜武,高伟等.基于带状混合矩阵ICA实现地震盲反褶积[J].地球物理学进展，2007，22(4):1153-1163.
[75]印兴耀,刘杰,杨培杰.一种基于负熵的Bussgang地震盲反褶积方法[J].石油地球物理勘探，2007,42(5):499-505.
[76] Bingham E and Hyv rinen A. A fast fixed-point algorithm for independent componentanalysis of complex-valued signals [J], Int. J. Neural Systems,2000,10(1):1-8.
[77] Wiener N. Hermitian Polynomials and Fourier Analysis[J]. Journal of Mathematics PhysicsMIT,1929,18:70-73.
[78] Condon E U. Immersion of Fourier Transform in a Continuous Group of FunctionalTransformations[J]. Proc. National Academy of Sciences,1937,23:158-164.
[79] Bargmann V. On a Hilbert Space of Analytic Functions and Associated Integral Transform,Part I[J]. Comm.. Pure. Appl.Math.1961,14:187-214.
[80] Namias V. The fractional order Fourier transform and its application to quantummechanics[J]. J. Inst Math Appl,1980,25:241-265.
[81] McBride A C, Kerr F H. On Namia’s fractional Fourier transform. IMA J Appl Math,1987,39:159-175.
[82] Almeida L B. The fractional Fourier transform and time-frequency representations [J].IEEE Tran Signal Processing,1994,42(11):3084-3091.
[83] Ozaktas H M, Arikan O, et al. Digital Computation of the Fractional Fourier Transform[J].IEEE Trans. Signal Processing,1996,44(9):2141-2150.
[84] Stankovi L J, Alieva T, Bastiaans M J. Time-frequency signal analysis based on thewindowed fractional Fourier transform[J] Signal Processing.83(11)(2003)2459-2468.
[85] Capus C and Brown K. Short-time fractional Fourier methods for the time-frequencyrepresentation of chirp signals[J]. J. Acoust. Soc. Amer.,2003,113(6):3253–3263.
[86] Durak L. Shift-invariance of short-time Fourier transform in fractional Fourier domains[J].Journal of the Franklin Institute,2009,346:136-146.
[87] Capus C, Brown K. Short-time fractional Fourier methods for the time-frequencyrepresentation of chirp signals[J]. J. Acoust. Soc. Am.2003,113(6)3253-3263.
[88] Mendlovic D, Zalevsky Z, Mas D, Garcia J, Ferreira C, Fractional wavelet transform[J].APPLIED OPTICS,1997,36(20):4801-4806.
[89] Huang Y, Suter B. The Fractional Wave Packet Transform[J]. Multidimensional Systems andSignal Processing,1998,9:399-402.
[90] Tao R, Li YL, Wang Y. Short-Time Fractional Fourier Transform and Its Applications[J].IEEE Trans. Signal Process,2010,58(5):2568-2580.
[91] C. A．Montana，G. F．Margrave．Spatial prediction filtering in fractional Fourier domains[C].72th Ann. Internat．Mtg．Soc．Exp l．Geophys, Expanded Abstracts,2004.
[92]耿春,尹成,张白林.分数Fourier变换在可控震源信号处理中的应用[J].工程地球物理学报,2006,3(6):427～436.
[93]刘喜武,刘婉莹等.地震信号广义时频分析及其数值实现[J].物探化探计算技术,2007,29(5):386～390.
[94]陈红，彭真明，王峻等.地震信号分数阶Gabor变换谱分解方法及应用[J].地球物理学报，2011，54(3):867～873.
[95]陶然，邓兵，王越.分数阶Fourier变换在信号处理领域的研究进展[J].中国科学E辑信息科学,2006,36(2):113-136.
[96] Deco G, Obradovic D. An information-Theoretic Approach to Neural Computing[M].Springer Verlag,1996.
[97]杨福生，洪波.独立分量分析的原理与应用[M].清华大学出版社，2006.
[98]史习智.盲信号处理——理论与实践[M].上海交通大学出版社，2008.
[99]杜爱民等.Hilbert-Huang变换中的一种端点处理方法[J].地震研究，2007,30(1):54-58.
[100]熊学军等.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.
[101]张贤达.现代信号处理[M].北京：清华大学出版社，2002:1-528.
[102] Zayed A I. A convolution and product theorem for the fractional Fourier Transform[J]. IEEESignal Process. Lett.,1998,5(4):101–103.
[103] Erden M F, Kutay M A and Ozaktas H M. Repeated filtering in consecutive fractional Fourierdomains and its application to signal restoration[J]. IEEE Trans. Signal Process.,1999,47(5):1458–1462.
[104] Tao R, Deng B, and Wang Y. Research progress of the fractional Fourier Transform in signalprocessing[J].Sci. China: Series F Inf. Sci.,2006,491–25.
[105] Tao R, Li B Z, and Wang Y. Spectral analysis and reconstruction for periodic non-uniformlysampled signals in fractional Fourier domain[J]. IEEE Trans. Signal Process,2007,55(7):3541–3547.
[106] Alieva T, Lopez V, et al. The fractional Fourier Transform in optical propagation problems[J]. J. Mod. Opt.,1994,41:1037–1040.
[107] Zhang Feng, Bi Guoan, Chen Yan Qiu. Tomography Time-frequency Transform[J]. IEEEtrans. Signal Processing,2002,50(6):1398-1801.
[108] Ozaktas H M, Erkaya N, Kutay M A. Effect of Fractional Fourier Transformation onTime-Frequency Distributions Belonging to the Cohen Class[J]. IEEE Signal ProcessingLetters,1996,3(2):40-41.
[109] Lee S Y, Szu HH. Fractional Fourier Transform, Wavelet Transforms, and Adaptive NeuralNetworks[J]. Opt. Engineering,1994,33:2326-2330.
[110]陶然等.分数阶傅里叶变换及其应用[M].北京：清华大学出版社，2009.
[111] Akan A, eki Y. A fractional Gabor expansion. Journal of the Franklin Institute,2003,340(5):391～397.
[112] Akan A, nen E. A discrete fractional Gabor expansion for multi-component signals[J].AEU-International Journal of Electronics and Communications,2007,61(5):279～185.
[113] Wexler J, Raz S. Discrete Gabor expansions[J]. Signal Processing,1990,21(3),207-221.
[114]吴媚，符力耘等.高分辨率非线性储层物性参数反演方法和应用[J].地球物理学报，2008,51(2):546-557.
[115]钱绍新.应用模式识别方法预测油气储集层[J].地球物理学报，1992,35(5):630-636.
[116]王瑞飞,陈明强.特低渗透砂岩储层可动流体赋存特征及影响因素[J].石油学报，2008,29(4):558-561.
[117]李景叶,陈小宏.基于地震资料的储层流体识别[J].石油学报，2008,29（2）:235-238.
[118] Li Zishun, Guo Xuebin. Predicting the distribution of thin bed reservoirs by broad frequencyband seismic[J]. APPLIED GEOPHYSICS,2008,4(2):118-126.
[119] Bastiaans M J. Gabor's Expansion of a Signal into Gaussian Elementary Signals[J]. Pro.IEEE,1980,68:538-539.
[120] Guo Hao, Marfurt K J, and Liu Jianlei. Principal component spectral analysis[J]. Geophysics,2009,74(4):35-43.