S-变换时频分析技术及其在地震勘探中的应用研究
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摘要
傅立叶变换及其反变换建立了信号时域与频域的映射关系。虽然傅立叶变换可以分别从时域或频域的角度分析信号，但却无法直接将两者有机结合起来。对于非平稳的地震信号，了解不同时刻附近的频域特征是至关重要的，因此采用时间一频率联合表示描述时变信号，将一维时域信号映像到二维的时频平面，全面反映地震信号的时频联合特征。由于传统时频分析方法具有方法本身的缺陷(短时窗傅立叶变换的窗函数是固定的，而小波变换不是一种真正的时频谱)，本文引进了一种较新的时频分析方法—S-变换。
本文综述了传统的时频分析方法。对S-变换的定义、推导、特性进行了详细阐述，并介绍了二维S-变换和广义S-变换。S-变换可以分别由短时窗傅立叶变换和连续小波变换导出，它综合了两种变换的优点，而避免了它们的不足：它与傅立叶变换有着直接的联系，具有无损可逆性；与短时窗傅立叶变换和小波变换一样，是一种线性时频表示，因此不存在交义项的干扰；S-变换具有多种分辩率，克服了短时窗傅立叶变换固定分辩率的不足：另外，S-变换中含有相位因子，这是小波变换所不具备的特性。为了进一步理解S-变换的特性，我们设计一些理论模型，将S-变换与短时窗傅立叶变换和wigner-Ville分布进行比较分析。
基于上述基本理论，本文首次将S-变换应用到地震勘探的某些处理和解释中。
在地震处理方面：由于S-变换具有高时频分辩率，首先将S-变换应用于地震波的初至拾取，设置不同信噪比的理论地震记录，检测S-变换识别初至的容噪能力，并应用于信噪比低的山地资料层析静校正的初至拾取；其次，地震面波频率低，在时频面上具有区域性，并且S-变换具有无损可逆性，将S-变换压制面波技术应用于设置的理论记录和实际资料中。
在地震解释方面：首先将S-变换应用于地质旋回体识别。由于构造运动具有周期性，
Fourier transform and inverse Fourier transform build up mapping for signal between time domain and frequency domain. Although Fourier transform can analyze signals in terms of time-domain or frequency-domain respectively, can not integrate with both directly. For non-stationary seismic signal, it is very important to understand frequency characteristic of different time around, so time-variant signals can be described using time-frequency joint denotation, then 1D time-domain signals can be mapped into 2D time-frequency profile, time-frequency joint characteristic of seismic signals can be expressed entirely. Because of the limitation of traditional time-frequency analysis methods, a newer time-frequency analysis method, S-transform is introduced into this paper.
Traditional time-frequency analysis methods are summarized firstly in the paper, the definition, derivation and characteristic of S-transform are expatiated, 2D S-transform and generalized S-transform are introduced. S-tranform can be deduced from short-window Fourier transform or continuum wavelet transform and combine two kinds of time-frquency analysis methods advantage overcoming their disadvantage: S-transform has a direct relation with Fourier transform, the characteristics such as lossless invertibility, linearity, multi-resolution of wavelet. S-transform is a kind of linear time-frequency represent as short-time fourier transform and wavelet transform, so it has not cross-term ; S-transform has muti-resolution overcoming single resolution of short-time fourier transform. Otherwise, S-transform contains phase factor which wavelet transform has not. In order to understand the character of S-transform, theory models are designed, S-transform, short-time fouier transform and Wigner-Ville distributing are compared and analysised.
Based on above theory, S-transform is firstly applied to some processing and interpretation of seismic prospecting.
On the seismic processing, first-break picking is its first application due to high time-frequency resolution. different S/N ratios are added in theory seismic data, first-breaks are detected using S-transform, then which is applied to first-break picking of tomographic static in hilly data with lower S/N ratios; second, seismic surface wave has low frequency and regional property in time-frequency surface and S-transform has lossless invertibility. surface wave suppression technology based on S-transform is applied to theory data and practical data.
On the seismic interpretation, the geological cyclothem bodies identification is its first
本文综述了传统的时频分析方法。对S-变换的定义、推导、特性进行了详细阐述，并介绍了二维S-变换和广义S-变换。S-变换可以分别由短时窗傅立叶变换和连续小波变换导出，它综合了两种变换的优点，而避免了它们的不足：它与傅立叶变换有着直接的联系，具有无损可逆性；与短时窗傅立叶变换和小波变换一样，是一种线性时频表示，因此不存在交义项的干扰；S-变换具有多种分辩率，克服了短时窗傅立叶变换固定分辩率的不足：另外，S-变换中含有相位因子，这是小波变换所不具备的特性。为了进一步理解S-变换的特性，我们设计一些理论模型，将S-变换与短时窗傅立叶变换和wigner-Ville分布进行比较分析。
基于上述基本理论，本文首次将S-变换应用到地震勘探的某些处理和解释中。
在地震处理方面：由于S-变换具有高时频分辩率，首先将S-变换应用于地震波的初至拾取，设置不同信噪比的理论地震记录，检测S-变换识别初至的容噪能力，并应用于信噪比低的山地资料层析静校正的初至拾取；其次，地震面波频率低，在时频面上具有区域性，并且S-变换具有无损可逆性，将S-变换压制面波技术应用于设置的理论记录和实际资料中。
在地震解释方面：首先将S-变换应用于地质旋回体识别。由于构造运动具有周期性，
Fourier transform and inverse Fourier transform build up mapping for signal between time domain and frequency domain. Although Fourier transform can analyze signals in terms of time-domain or frequency-domain respectively, can not integrate with both directly. For non-stationary seismic signal, it is very important to understand frequency characteristic of different time around, so time-variant signals can be described using time-frequency joint denotation, then 1D time-domain signals can be mapped into 2D time-frequency profile, time-frequency joint characteristic of seismic signals can be expressed entirely. Because of the limitation of traditional time-frequency analysis methods, a newer time-frequency analysis method, S-transform is introduced into this paper.
Traditional time-frequency analysis methods are summarized firstly in the paper, the definition, derivation and characteristic of S-transform are expatiated, 2D S-transform and generalized S-transform are introduced. S-tranform can be deduced from short-window Fourier transform or continuum wavelet transform and combine two kinds of time-frquency analysis methods advantage overcoming their disadvantage: S-transform has a direct relation with Fourier transform, the characteristics such as lossless invertibility, linearity, multi-resolution of wavelet. S-transform is a kind of linear time-frequency represent as short-time fourier transform and wavelet transform, so it has not cross-term ; S-transform has muti-resolution overcoming single resolution of short-time fourier transform. Otherwise, S-transform contains phase factor which wavelet transform has not. In order to understand the character of S-transform, theory models are designed, S-transform, short-time fouier transform and Wigner-Ville distributing are compared and analysised.
Based on above theory, S-transform is firstly applied to some processing and interpretation of seismic prospecting.
On the seismic processing, first-break picking is its first application due to high time-frequency resolution. different S/N ratios are added in theory seismic data, first-breaks are detected using S-transform, then which is applied to first-break picking of tomographic static in hilly data with lower S/N ratios; second, seismic surface wave has low frequency and regional property in time-frequency surface and S-transform has lossless invertibility. surface wave suppression technology based on S-transform is applied to theory data and practical data.
On the seismic interpretation, the geological cyclothem bodies identification is its first
引文
[1] Gabor, D. Theory of Communication. Journal of the IEEE. 1946, Vol 93: 429-497.
[2] Cohen L. Generalized phase-space distribution functions. Jour. Math. Phys., 1966,7: 781-786
[3] Morlet J, Arens G, Fourgeau E, Giard D. Wave progagation and sampling theory-Part Ⅰ: Complex signal and scattering in multilayered media. Geophysics, 1982,47: 203-221.
[4] Metier J, Arens G, Fourgeau E, Giard D. Wave propagation and sampling theory-Part Ⅱ: Sampling theory and complex waves. Geophysics, 1982,47(2): 222-236.
[5] 张玉芬等，时频分析方法在储集层横向预测中的应用．地质科技情报，1995，14(1)：83-88．
[6] 刘传虎，刘福贵，李卫忠．时频分析方法及在储层预测中的应用．石油地球物理勘探，1996，31(增1)：11-20．
[7] 高军等，时频域球面发散和吸收补偿．石油地球物理勘探，1996，31(6)：856-866、905
[8] 白桦，李鳗鹏．基于时频分析的地层吸收补偿．石油地球物理勘探．1999，34(6)：642-648．
[9] 章珂等．二进小波变换方法的地震信号分时．分频去噪处理．地球物理学报．1996．39(2)：265-270．
[10] Satish K.Sinha, Partha S.Routh, Phil D.Anno et al. Time-Frequency attribute of seismic data using continuous wavelet transform. In: Proc.73th SEG Annual Meeting, Houston, Texas, USA,2003: 1481-1484.
[11] 吴国忱，三维时频分析方法在地震层序分析中的应用，石油大学学报(自然科学版)，2000，24(1)：81-84．
[12] 董臣强等，时频分析技术在三角洲层序分析中的应用，断块油气田．2002，9(2)：18-20．
[13] 崔凤林，管叶君．时频分析-薄互层结构研究的新途径．石油物探，1992，31(2)：1-15．
[14] Hirokazu Modya and Hiroaki Niitsuma. Precise detection of a P-wave in low S/N signal by using Time-Frequency representations of a triaxial hodogram. Geophysics, 1996, 61(5): 1453-1466.
[15] Theophanis, S., and Queen, J., Color display of the localized spectrum: Geophysics. 2000, 65: 1330-1340.
[16] Strockwell R G, Mansinha L, Lowe R P. Localization of the Complex Spectrum: The S-Transform. IEEE Transactions on Signal Processing, 1996, 44(4): 998-1001.
[17] Livanos G, Ranganathan N, Jiang J.Heart sound analysis using the S Transform.Computers in Cardiology, 2000,27: 587-590.
[18] Robert Pinnegar. C and lalu Mansinha. The S-transform with windows of arbitrary and varying shape.Geophysis, 2003, 68(1): 381-385.
[19] Mansinha, L., R.G. Stockwell, R.P. Lowe, M. Eramian, and R.A. Schincariol.Local-spectrum analysis of 1-D and 2-D data. Physics of the Earth and Planetary Interiors 1997, 103: 29-336.
[20] 张贤达，保铮．《非平稳信号的分析与处理》．国防工业出版社．1998．
[21] 沈民奋，孙莉萨．《现代随机信号与系统分析》．科学出版社1998．
[22] Portnoff MR. Time-frequency representation of digital signals and systems based on short-time fourier analysis. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1980, ASSP-28(1).
[23] Morlet J, Arens G, Fourgeau E, Giard D. Wave progagation and sampling theory-Part Ⅰ: Complex signal and scattering in multilayered media. Geophysics, 1982, 47: 203-221.
[24] Morlet J, Arens G, Fourgeau E, Giard D. Wave propagation and sampling theory-Part Ⅱ: Sampling theory and complex waves. Geophysics,, 1982, 47(2): 222-236.
[25] Wigner E. On the quantum correction for thermodynamic equilibrium. Phys.Rev s., 1932, 40: 749-759.
[26] Ville.Theorie et applications de la notion de signal analytique. Cables et Transmission, 2, 1948
[27] Janssen A. Optimality property of the Gaussian window spectrogram. IEEE Transactions on Acoustics, Speech and Signal Processing, 1991, ASSP-39(1).
[28] Wilson R., Calway A.D., andPearson E.R.S. A generalized wavelet transform for fourier analysis: the multiresolution fourier transform and its application to image and audio signal analysis. IEEE Trans.Info.Theory, 1992,38: 674-690.
[29] Farge M. Wavelet transforms and their application to turbulence. Annual Review of Fluid Mechanics,1992, 24: 395-457.
[30] Brigham E.O. The fast fourier transform. Prentics-Hall Inc., 1974.
[31] Mansinha L, Stockwell R G, Lowe R P. Pattern analysis with two-dimensional spectral localization: Applications of two-dimensional S transforms. Physics A, 1997, 239: 286-295.
[32] Mansinha L., Stockwell R. G., Lowe R. P., et al. Local S Spectrum Analysis of 1-D and 2-D Data,Physics of the Earth and Planetary Interiors, 1997, 103: 329-336.
[33] Stockwell R.G, PhD. S-Transform Analysis of Gravity Wave Activity from a Small Scale Network of Airglow Imagers, 1999, The University of Western Ontario.
[34] 高静怀等．广义S变换与薄互层地震响应分析．地球物理学报．2003，46(4)526-532．
[35] McFadden, P.D., Cook, J.G., and Forster, L.M., .Decomposition of gear vibration signals by the generalized S-transform:Mech.Syst Signal Process, 1999, 13: 691-707.
[36] 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．勘探地球物理进展，2004，27(4)：246-250，259．
[37] 蔡希玲．地震数据时频分析方法研究及应用．2000，成都理工学院．
[38] 何樵登，等．地震勘探原理和方法．北京：地质出版社，1985．
[39] 孙明，林君．t-p变换去除金属矿地震资料中的线性干扰．物探与化探，2001，25(6)：432-436．
[40] Turnet G. Aliasing in the tau-p transform and the removal of spatially aliased coherent noise.Geophysics, 1990, 55(11): 1496-1503.
[41] Spitzer R, Nitsche F, Green A G. Reducing source-generated noise in shallow seismic data using linear and hyperbolicτ-p transformations. Geophysics, 2001, 66(5): 1612-1621.
[42] 罗国安，杜世通．小波变涣及信号重建在压制面波中的应用．石油地球物理勘探，1996，31(3)：337—349．
[43] 王振国，周熙襄，钟本善．小波包对叠前地震面波的分离与信号重建．石油地球物理勘探，2002，37(5)：460-462，472．
[44] 李晶，王振国，陈裕明，等．小波包变换叠前地震资料去噪方法研究．成都理工大学学报：自然科学版，2003，30(5)：541-546．
[45] 陈爱萍，邹文．基于S-变换的面波压制技术．世界地质，2005，24(1)，82-86．
[46] 张军华，王永刚，杨国权等．地震旋回体的概念及应用．石油地球物理勘探，2003，38(3)：281-284．
[47] 王永刚，宋若微．层序地震学在地层内部结构分析中的应用．石油物探，1997，36(增刊)：36-39．
[48] 董波．时频分析在地层旋回性分析中的应用．华北地震科学，2004，22(4)：16-19．
[49] 牛毓荃等译．地震地层学(在油气勘探中的应用)．石油工业出版社，1980．
[50] Steeghs, PH.D .Local Power Spectra and Seismic Interpretation. 1997, 100-120.
[51] 顾汉明．塔河油田南部岩溶缝洞型储层地震正演模拟及储层预测研究，中国地质大学(武汉)，2005．3．
[2] Cohen L. Generalized phase-space distribution functions. Jour. Math. Phys., 1966,7: 781-786
[3] Morlet J, Arens G, Fourgeau E, Giard D. Wave progagation and sampling theory-Part Ⅰ: Complex signal and scattering in multilayered media. Geophysics, 1982,47: 203-221.
[4] Metier J, Arens G, Fourgeau E, Giard D. Wave propagation and sampling theory-Part Ⅱ: Sampling theory and complex waves. Geophysics, 1982,47(2): 222-236.
[5] 张玉芬等，时频分析方法在储集层横向预测中的应用．地质科技情报，1995，14(1)：83-88．
[6] 刘传虎，刘福贵，李卫忠．时频分析方法及在储层预测中的应用．石油地球物理勘探，1996，31(增1)：11-20．
[7] 高军等，时频域球面发散和吸收补偿．石油地球物理勘探，1996，31(6)：856-866、905
[8] 白桦，李鳗鹏．基于时频分析的地层吸收补偿．石油地球物理勘探．1999，34(6)：642-648．
[9] 章珂等．二进小波变换方法的地震信号分时．分频去噪处理．地球物理学报．1996．39(2)：265-270．
[10] Satish K.Sinha, Partha S.Routh, Phil D.Anno et al. Time-Frequency attribute of seismic data using continuous wavelet transform. In: Proc.73th SEG Annual Meeting, Houston, Texas, USA,2003: 1481-1484.
[11] 吴国忱，三维时频分析方法在地震层序分析中的应用，石油大学学报(自然科学版)，2000，24(1)：81-84．
[12] 董臣强等，时频分析技术在三角洲层序分析中的应用，断块油气田．2002，9(2)：18-20．
[13] 崔凤林，管叶君．时频分析-薄互层结构研究的新途径．石油物探，1992，31(2)：1-15．
[14] Hirokazu Modya and Hiroaki Niitsuma. Precise detection of a P-wave in low S/N signal by using Time-Frequency representations of a triaxial hodogram. Geophysics, 1996, 61(5): 1453-1466.
[15] Theophanis, S., and Queen, J., Color display of the localized spectrum: Geophysics. 2000, 65: 1330-1340.
[16] Strockwell R G, Mansinha L, Lowe R P. Localization of the Complex Spectrum: The S-Transform. IEEE Transactions on Signal Processing, 1996, 44(4): 998-1001.
[17] Livanos G, Ranganathan N, Jiang J.Heart sound analysis using the S Transform.Computers in Cardiology, 2000,27: 587-590.
[18] Robert Pinnegar. C and lalu Mansinha. The S-transform with windows of arbitrary and varying shape.Geophysis, 2003, 68(1): 381-385.
[19] Mansinha, L., R.G. Stockwell, R.P. Lowe, M. Eramian, and R.A. Schincariol.Local-spectrum analysis of 1-D and 2-D data. Physics of the Earth and Planetary Interiors 1997, 103: 29-336.
[20] 张贤达，保铮．《非平稳信号的分析与处理》．国防工业出版社．1998．
[21] 沈民奋，孙莉萨．《现代随机信号与系统分析》．科学出版社1998．
[22] Portnoff MR. Time-frequency representation of digital signals and systems based on short-time fourier analysis. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1980, ASSP-28(1).
[23] Morlet J, Arens G, Fourgeau E, Giard D. Wave progagation and sampling theory-Part Ⅰ: Complex signal and scattering in multilayered media. Geophysics, 1982, 47: 203-221.
[24] Morlet J, Arens G, Fourgeau E, Giard D. Wave propagation and sampling theory-Part Ⅱ: Sampling theory and complex waves. Geophysics,, 1982, 47(2): 222-236.
[25] Wigner E. On the quantum correction for thermodynamic equilibrium. Phys.Rev s., 1932, 40: 749-759.
[26] Ville.Theorie et applications de la notion de signal analytique. Cables et Transmission, 2, 1948
[27] Janssen A. Optimality property of the Gaussian window spectrogram. IEEE Transactions on Acoustics, Speech and Signal Processing, 1991, ASSP-39(1).
[28] Wilson R., Calway A.D., andPearson E.R.S. A generalized wavelet transform for fourier analysis: the multiresolution fourier transform and its application to image and audio signal analysis. IEEE Trans.Info.Theory, 1992,38: 674-690.
[29] Farge M. Wavelet transforms and their application to turbulence. Annual Review of Fluid Mechanics,1992, 24: 395-457.
[30] Brigham E.O. The fast fourier transform. Prentics-Hall Inc., 1974.
[31] Mansinha L, Stockwell R G, Lowe R P. Pattern analysis with two-dimensional spectral localization: Applications of two-dimensional S transforms. Physics A, 1997, 239: 286-295.
[32] Mansinha L., Stockwell R. G., Lowe R. P., et al. Local S Spectrum Analysis of 1-D and 2-D Data,Physics of the Earth and Planetary Interiors, 1997, 103: 329-336.
[33] Stockwell R.G, PhD. S-Transform Analysis of Gravity Wave Activity from a Small Scale Network of Airglow Imagers, 1999, The University of Western Ontario.
[34] 高静怀等．广义S变换与薄互层地震响应分析．地球物理学报．2003，46(4)526-532．
[35] McFadden, P.D., Cook, J.G., and Forster, L.M., .Decomposition of gear vibration signals by the generalized S-transform:Mech.Syst Signal Process, 1999, 13: 691-707.
[36] 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．勘探地球物理进展，2004，27(4)：246-250，259．
[37] 蔡希玲．地震数据时频分析方法研究及应用．2000，成都理工学院．
[38] 何樵登，等．地震勘探原理和方法．北京：地质出版社，1985．
[39] 孙明，林君．t-p变换去除金属矿地震资料中的线性干扰．物探与化探，2001，25(6)：432-436．
[40] Turnet G. Aliasing in the tau-p transform and the removal of spatially aliased coherent noise.Geophysics, 1990, 55(11): 1496-1503.
[41] Spitzer R, Nitsche F, Green A G. Reducing source-generated noise in shallow seismic data using linear and hyperbolicτ-p transformations. Geophysics, 2001, 66(5): 1612-1621.
[42] 罗国安，杜世通．小波变涣及信号重建在压制面波中的应用．石油地球物理勘探，1996，31(3)：337—349．
[43] 王振国，周熙襄，钟本善．小波包对叠前地震面波的分离与信号重建．石油地球物理勘探，2002，37(5)：460-462，472．
[44] 李晶，王振国，陈裕明，等．小波包变换叠前地震资料去噪方法研究．成都理工大学学报：自然科学版，2003，30(5)：541-546．
[45] 陈爱萍，邹文．基于S-变换的面波压制技术．世界地质，2005，24(1)，82-86．
[46] 张军华，王永刚，杨国权等．地震旋回体的概念及应用．石油地球物理勘探，2003，38(3)：281-284．
[47] 王永刚，宋若微．层序地震学在地层内部结构分析中的应用．石油物探，1997，36(增刊)：36-39．
[48] 董波．时频分析在地层旋回性分析中的应用．华北地震科学，2004，22(4)：16-19．
[49] 牛毓荃等译．地震地层学(在油气勘探中的应用)．石油工业出版社，1980．
[50] Steeghs, PH.D .Local Power Spectra and Seismic Interpretation. 1997, 100-120.
[51] 顾汉明．塔河油田南部岩溶缝洞型储层地震正演模拟及储层预测研究，中国地质大学(武汉)，2005．3．