时频分析在地震信号处理中的研究及应用
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摘要
时频分析方法作为分析非平稳信号的有力工具,成为了现代信号处理研究的一个热点。本论文系统地介绍时频分析的基本概念,给出几种常用的时频分析方法的公式,详细分析了短时傅立叶变换、小波变换、S变换、广义S变换、Wigner-Ville分布几种方法的性质特征；并在Mansinha提出的广义S变换的基础上,发展了一种新的时频分析方法——含可变因子的广义S变换。通过对相同的非平稳信号的分析处理,对比研究了几种时频分析方法的应用效果。结果表明,相比其它方法,含可变因子的广义S变换更能细致地反映非平稳信号的局部特征,也更具目的性和实用性。
地震信号是一种非平稳信号,时频分析方法提供了时间域与频率域的联合分布信息,清楚地描述了地震信号频率随时间变化的关系。本文把时频分析方法应用到地震资料的处理过程中,通过对模型数据的分析处理,对比研究了短时傅立叶变换、连续小波变换、含可变因子的广义s变换在探测薄层分界中的应用效果；同时,把含可变因子的广义S变换应用到地震剖面的分频处理和时频滤波过程中,也达到了预期的效果。本论文还分析了薄层的层厚、品质因子、波速、震源主频等因素对地震波峰值频率的影响情况。在实际的地震资料处理过程中,结合谱分解与时频分析技术,利用低频率异常探测油气藏储层的位置,取得了理想的效果。
Time-frequency analysis is a powerful tool for non-stationary signals, and it becomes a hot spot in the modern signal processing study. In this paper, it introduces the basic concept of time-frequency analysis systematically, and gives the formulas of several commonly used methods and their nature in details, including short time Fourier transform, continuous wavelet transform, S transform and generalized S transform. Based on the generalized S transform developed by Mansinha, a new method is developed, and it's named as generalized S-transform with variable-factor. By processing the same non-stationary signal, I study the application effect of the several time-frequency analysis methods comparatively, and the results shows that, compared with other methods, the generalized S-transform with variable-factor can describe the local characteristics of non-stationary signals more detailedly, and it's much more objective and practical.
Seismic signals are non-stationary signals, the time-frequency analysis method provides us joint distribution information in time-frequency domain of the signals, which describes the relationship clearly as the frequency of the seismic signals changing over time. In this paper, the time-frequency analysis methods are applied to seismic data processing. By processing the model data, I study the application effect of the short time Fourier transform, continuous wavelet transform and the generalized s transform with variable-factor comparatively in detecting the thin bed's boundary. At the same time, the generalized s transform with variable-factor is applied to the sub-frequency processing and the time-frequency filtering, and some desired results are achieved. The influences of the some factors on the peak frequency of the seismic wave are analyzed, such as the thickness, quality factor and wave velocity of the thin layer and the peak frequency of the source seismic wave. In the field seismic data processing, by combining the time-frequency analysis methods with spectral decomposition technique, I utilize the low frequency anomalies to detect the location of oil and gas reservoirs, and some desired results are also achieved.
地震信号是一种非平稳信号,时频分析方法提供了时间域与频率域的联合分布信息,清楚地描述了地震信号频率随时间变化的关系。本文把时频分析方法应用到地震资料的处理过程中,通过对模型数据的分析处理,对比研究了短时傅立叶变换、连续小波变换、含可变因子的广义s变换在探测薄层分界中的应用效果；同时,把含可变因子的广义S变换应用到地震剖面的分频处理和时频滤波过程中,也达到了预期的效果。本论文还分析了薄层的层厚、品质因子、波速、震源主频等因素对地震波峰值频率的影响情况。在实际的地震资料处理过程中,结合谱分解与时频分析技术,利用低频率异常探测油气藏储层的位置,取得了理想的效果。
Time-frequency analysis is a powerful tool for non-stationary signals, and it becomes a hot spot in the modern signal processing study. In this paper, it introduces the basic concept of time-frequency analysis systematically, and gives the formulas of several commonly used methods and their nature in details, including short time Fourier transform, continuous wavelet transform, S transform and generalized S transform. Based on the generalized S transform developed by Mansinha, a new method is developed, and it's named as generalized S-transform with variable-factor. By processing the same non-stationary signal, I study the application effect of the several time-frequency analysis methods comparatively, and the results shows that, compared with other methods, the generalized S-transform with variable-factor can describe the local characteristics of non-stationary signals more detailedly, and it's much more objective and practical.
Seismic signals are non-stationary signals, the time-frequency analysis method provides us joint distribution information in time-frequency domain of the signals, which describes the relationship clearly as the frequency of the seismic signals changing over time. In this paper, the time-frequency analysis methods are applied to seismic data processing. By processing the model data, I study the application effect of the short time Fourier transform, continuous wavelet transform and the generalized s transform with variable-factor comparatively in detecting the thin bed's boundary. At the same time, the generalized s transform with variable-factor is applied to the sub-frequency processing and the time-frequency filtering, and some desired results are achieved. The influences of the some factors on the peak frequency of the seismic wave are analyzed, such as the thickness, quality factor and wave velocity of the thin layer and the peak frequency of the source seismic wave. In the field seismic data processing, by combining the time-frequency analysis methods with spectral decomposition technique, I utilize the low frequency anomalies to detect the location of oil and gas reservoirs, and some desired results are also achieved.
引文
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[2]邹文,陈爱萍,顾汉明.联合时频分析技术在地震勘探中的应用闭[J].勘探地球物理进展,2004,27(4),246-250
[3]刘葵,刘招君,朱建伟等.时频分析在石油地球物理勘探中的应用[J].世界地质,2000,19(3),282-285
[4]刘庆云,李志舜,刘朝晖.时频分析技术及研究现状[J].计算机工程,2004,30(1)：171-173
[5]何继善,温佩琳,肖兵等.小波分析在地球物理勘探中的应用明[J].中国有色金属学报,1997,7(4),14-19
[6]王衍文,王海滨,程敬之.心音信号的时频分析[J].生物医学工程学杂志,1998,15(1),41-46
[7]柯熙政,吴振森.太阳黑子数的时-频域模型[J].中国科学院研究生院学报,1998,15(1),68-73
[8]李天云,赵妍,李楠等.基于HHT的电能质量检测新方法闭[J].中国电机工程学报,2005,25(17),52-56
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[20]Koenig R., Dunn H. K. and Lacy L. Y The sound spectrograph. Acoust, Vol.18,1946, pp 19-49
[21]Potter R K, Kopp G, Green H C. Visible speech. New York:Van Nostrand, 1947
[22]Grossmann A., Morlet J. Decomposion of Hardy function into square integrable wavelets of constant shape. SIAM J. Math,1984,15(4):pp723-736
[23]Mallat S. G. Multifrequency channel decomposition of image and wavelet model[J]. IEEE trans. ASSP,1989,37(12):pp2091-2110
[24]Daubechies I. The wavelet transform, time-frequency localization and signal analysis[J]. IEEE trans. Information Theory,1990, (36):pp961-1005
[25]Vetterli M. Herley C. Wavelet and filter banks:theory and design [J]. IEEE traps. Signal Processing,1992,40(9):pp2207-2232
[26]杨忠民,黄大云.小波变换在提高地震资料的信噪比和分辨率中的应用[J].石油地球物理勘探,1994,29(5)：623-629
[27]吴国忱,印兴耀,张广智等.小波分析方法在提高地震分辨率及地震层序分析中的应用[J].石油物探,1997.36(增刊)：45-51
[28]陈香朋,曹思远.第二代小波变换及其在地震信号去噪中的应用[J].石油物探,2004,43(6)：547-550
[29]Cao Siyuan, Chen Xiangpeng . The Second-generation Wavelet Transform and its Applicationin Denoising of Seismic Data [J]. APPLIED GEOPHYSICS, 2005,2(2):70-74
[30]冯林,程璐,吴振宇.基于提升算法的测井信号去噪处理[J].石油物探,2004.43(3)：238-241
[31]赵俊猛,汤吉,张海江等.小波变换在地震宽角反折射资料处理中的应用[J].地球物理学报,2000,43(s)：666-676
[32]陈传仁,周熙襄.小波谱白化方法提高地震资料的分辨率[J].石油地球物理勘探,2000.35(6)：703-709
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[34]李组鹏,李衍达,张学工.基于小波包分解的地层吸收补偿[J].地球物理学报,2000.43(4)：542~549
[35]罗国安,杜世通.小波变换及信号重建在压制面波中的应用[J].石油地球物理勘探,1996.31(2)：337-349
[36]STOCKWELL R G, MANSINHA L, LOWE R P. Localization of the complex spectrum the S transform[J]. IEEE Transactions on Signal Processing, 1996; 44(4):998-1001.
[37]MANSINHA L, STOCKWELL R G. Local S-spectrum analysis of 1-D and 2-D data[J]. Physics of the Earth and Plantetary Interiors,1997; 103 (3): 329-336.
[38]PINNEGAR C R, MANSINHA L. The s transform with windows of arbitrary and varying shape[J]. Geophysics,2003; 68(1):381-385.
[39]PINNEGAR C R, MANSINHA L . Time-local spectral analysis for non-stationary time series:the S-transform for noisy signals[J]. Fluctuation and Noise Letters,2003; 3(3):357-364.
[40]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.2003,46(4)：526-532.
[41]邹红星,周小波,李衍达.时频分析：回溯与前瞻[J].电子学报,2000.28(9),78-84
[42]Sun, S., J. P. Castagna, and R. W. Seigfried, 2002, Examples of wavelet transform time frequency analysis in direct hydrocarbon detection:72nd Annual International Meeting, SEG Expanded Abstracts,457-460.
[43]Castagna, J., S. Sun, and R. Siegfried, 2003, Instantaneous spectral analysis:detection of low frequency shadows associated with hydrocarbons:The Leading Edge, 22,120-127.
[44]Liu, J., Wu, Y, Han, D. and Li, X.,2004, Time-Frequency decomposition based on Ricker wavelet:74thAnn. Intl.Mtg., Soc. Expl. Geophys. ExpandedAbstracts,1937-1940.
[45]J Liu, KJ Marfurt,2005, Matching pursuit decomposition using Morlet wavelets: 75thAnn. Intl.Mtg., Soc. Expl. Geophys. Expanded Abstracts,786-789
[46]Li Chun-Feng,2003, Rescaled-range and power spectrum analyses on well-logging data. Geophys. J.Int.,153:201-212
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[48]Li Chun-Feng. Information passage from acoustic impedance to seismograms:perspective from wavelet-based multi scale analysis:J. Geophys. Res.,2004,109, B07301, doi:10.1029/2003JB002882
[49]高静怀,万涛,陈文超等.三参数小波及其在地震资料分析中的应用[J].地球物理学报,2006,49(6)：1802-1812
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[2]邹文,陈爱萍,顾汉明.联合时频分析技术在地震勘探中的应用闭[J].勘探地球物理进展,2004,27(4),246-250
[3]刘葵,刘招君,朱建伟等.时频分析在石油地球物理勘探中的应用[J].世界地质,2000,19(3),282-285
[4]刘庆云,李志舜,刘朝晖.时频分析技术及研究现状[J].计算机工程,2004,30(1)：171-173
[5]何继善,温佩琳,肖兵等.小波分析在地球物理勘探中的应用明[J].中国有色金属学报,1997,7(4),14-19
[6]王衍文,王海滨,程敬之.心音信号的时频分析[J].生物医学工程学杂志,1998,15(1),41-46
[7]柯熙政,吴振森.太阳黑子数的时-频域模型[J].中国科学院研究生院学报,1998,15(1),68-73
[8]李天云,赵妍,李楠等.基于HHT的电能质量检测新方法闭[J].中国电机工程学报,2005,25(17),52-56
[9]李崛鹏,刘业新,李衍达等.小波变换的过零点特性与地震勘探信号的信噪比和分辨率[J].地球物理学报,1997,40(4)：561-569
[10]崔风林、管叶君.时频分析一薄互层结构研究的新途径[J].石油地球物理勘探,No.2,1992
[11]崔风林等.松辽盆地茂8井三维地震区薄互层储层预测方法及效果[J].石油物探,No.4,1993
[12]康仁华等.三维时频分析方法在地震层序分析中的应用[J].石油大学学报,No.1,1998
[13]刘传虎等.时频分析方法及在储层预测中的应用[J].石油地球物理勘探,增刊1,1996
[14]雷克辉等.在小波时频域中研究沉积旋回[J].石油地球物理勘探,增刊1,1998
[15]Marfurt, K. J., and R. L. Kirlin, 2001, Narrow-band spectral analysis and thin-bed tuning[J]:Geophysics, 66, 1274-1283.
[16]Widess, M. B.,1973, How thin is a thin bed? [J]:Geophysics,38, 1176-1180.
[17]Partyka, G, J. Gridley, and J. Lopez, 1999, Interpretational applications of spectral decomposition in reservoir characterization: The Leading Edge, 18, 353-360.
[18]张贤达.现代信号处理[M].北京：清华大学出版社,2002
[19]Gabor D. Theory of communication. J. IEEE, Vol.93, No.3, 1946, pp429-457
[20]Koenig R., Dunn H. K. and Lacy L. Y The sound spectrograph. Acoust, Vol.18,1946, pp 19-49
[21]Potter R K, Kopp G, Green H C. Visible speech. New York:Van Nostrand, 1947
[22]Grossmann A., Morlet J. Decomposion of Hardy function into square integrable wavelets of constant shape. SIAM J. Math,1984,15(4):pp723-736
[23]Mallat S. G. Multifrequency channel decomposition of image and wavelet model[J]. IEEE trans. ASSP,1989,37(12):pp2091-2110
[24]Daubechies I. The wavelet transform, time-frequency localization and signal analysis[J]. IEEE trans. Information Theory,1990, (36):pp961-1005
[25]Vetterli M. Herley C. Wavelet and filter banks:theory and design [J]. IEEE traps. Signal Processing,1992,40(9):pp2207-2232
[26]杨忠民,黄大云.小波变换在提高地震资料的信噪比和分辨率中的应用[J].石油地球物理勘探,1994,29(5)：623-629
[27]吴国忱,印兴耀,张广智等.小波分析方法在提高地震分辨率及地震层序分析中的应用[J].石油物探,1997.36(增刊)：45-51
[28]陈香朋,曹思远.第二代小波变换及其在地震信号去噪中的应用[J].石油物探,2004,43(6)：547-550
[29]Cao Siyuan, Chen Xiangpeng . The Second-generation Wavelet Transform and its Applicationin Denoising of Seismic Data [J]. APPLIED GEOPHYSICS, 2005,2(2):70-74
[30]冯林,程璐,吴振宇.基于提升算法的测井信号去噪处理[J].石油物探,2004.43(3)：238-241
[31]赵俊猛,汤吉,张海江等.小波变换在地震宽角反折射资料处理中的应用[J].地球物理学报,2000,43(s)：666-676
[32]陈传仁,周熙襄.小波谱白化方法提高地震资料的分辨率[J].石油地球物理勘探,2000.35(6)：703-709
[33]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
[34]李组鹏,李衍达,张学工.基于小波包分解的地层吸收补偿[J].地球物理学报,2000.43(4)：542~549
[35]罗国安,杜世通.小波变换及信号重建在压制面波中的应用[J].石油地球物理勘探,1996.31(2)：337-349
[36]STOCKWELL R G, MANSINHA L, LOWE R P. Localization of the complex spectrum the S transform[J]. IEEE Transactions on Signal Processing, 1996; 44(4):998-1001.
[37]MANSINHA L, STOCKWELL R G. Local S-spectrum analysis of 1-D and 2-D data[J]. Physics of the Earth and Plantetary Interiors,1997; 103 (3): 329-336.
[38]PINNEGAR C R, MANSINHA L. The s transform with windows of arbitrary and varying shape[J]. Geophysics,2003; 68(1):381-385.
[39]PINNEGAR C R, MANSINHA L . Time-local spectral analysis for non-stationary time series:the S-transform for noisy signals[J]. Fluctuation and Noise Letters,2003; 3(3):357-364.
[40]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.2003,46(4)：526-532.
[41]邹红星,周小波,李衍达.时频分析：回溯与前瞻[J].电子学报,2000.28(9),78-84
[42]Sun, S., J. P. Castagna, and R. W. Seigfried, 2002, Examples of wavelet transform time frequency analysis in direct hydrocarbon detection:72nd Annual International Meeting, SEG Expanded Abstracts,457-460.
[43]Castagna, J., S. Sun, and R. Siegfried, 2003, Instantaneous spectral analysis:detection of low frequency shadows associated with hydrocarbons:The Leading Edge, 22,120-127.
[44]Liu, J., Wu, Y, Han, D. and Li, X.,2004, Time-Frequency decomposition based on Ricker wavelet:74thAnn. Intl.Mtg., Soc. Expl. Geophys. ExpandedAbstracts,1937-1940.
[45]J Liu, KJ Marfurt,2005, Matching pursuit decomposition using Morlet wavelets: 75thAnn. Intl.Mtg., Soc. Expl. Geophys. Expanded Abstracts,786-789
[46]Li Chun-Feng,2003, Rescaled-range and power spectrum analyses on well-logging data. Geophys. J.Int.,153:201-212
[47]Li Chun-Feng.Scaling and wavelet-based singularity analyses for geological and Geophysical interpretation [Ph. D dissertation]. Tulsa:Univ. of Tulsa, 2002
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