基于频谱分解的碳酸盐岩储层识别
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摘要
频谱分解技术是将地震信号从时间域转换到频率域,分析频率对不同尺度地质体的振幅、相位响应特征的一项技术.频谱分解能够得到高于传统分辨率的解释结果,提高刻画储层分布的能力.本文详述了短时傅里叶变换、连续小波变换和S变换的数学原理及适用性:短时傅里叶变换使用固定时窗,不能根据信号的变化调整分辨率,只适合分析分段平稳或近似平稳的信号;连续小波变换使用移动的、尺度可变的小波作为时窗,具有多分辨率特点,但是实际中选择能反映信号特征的小波函数不易;S变换使用频率的倒数来调节时窗,具有多分辨率特征,对数据处理的适应性较强.将这三种方法分别应用于碳酸盐岩储层发育区,利用靠近地震主频的35Hz分频剖面,分析了不同时窗大小的短时傅里叶变换效果,不同类型小波的连续小波变换效果,并对比了不同频谱分解算法对储层的描述精度.通过分析得出分频剖面比常规地震剖面更有利于储层识别,且S变换效果最好.
Spectral decomposition technique is to convert seismic signals from the time domain to the frequency domain by mathematical transformation,and analyze amplitude and phase response characteristics of different scale geological bodies.Spectral decomposition technique could get higher interpretation resolution than the traditional technique by analyzing the amplitude of each frequency,which can improve the ability to describe the distribution of reservoirs.The lithology applicability fields of spectral decomposition technique are developed from clastic rock to carbonate rock,even volcanic rock.The application of spectral decomposition technique is developed from calculation of thin layer thickness to research of structure fracture system,reservoir boundary,reservoir prediction and fluid detection.There are three typical spectral decomposition methods: short time Fourier transform,continuous wavelet transform and S-transform.This paper analyzed algorithm and applicability of these three methods.STFT can not adjust the resolution according to the signal changes because it uses a fixed time window,which is only suitable for the analysis of piecewise smooth or approximate stationary signals.CWT is a muti-resolution method because it uses a move and variable wavelet as the time window.But it is not easy to select a wavelet function that can fully reflect the signal characteristics.ST is also a muti-resolution method because it uses the reciprocal of the frequency to adjust the time window,which is more convenient for data processing.This paper used these three methods for carbonate reservoir identification.It analyzed the effects of different time window size of STFT,and the effects of different wavelet type of CWT.It also compared reservoir description accuracy of different spectral decomposition algorithms,according to reservoir distribution of the three high-yield gas wells and 35Hz spectral decomposition sections.It proves that the frequency division section is more clearly than conventional seismic section in reservoir description.And ST gets the best result.
Spectral decomposition technique is to convert seismic signals from the time domain to the frequency domain by mathematical transformation,and analyze amplitude and phase response characteristics of different scale geological bodies.Spectral decomposition technique could get higher interpretation resolution than the traditional technique by analyzing the amplitude of each frequency,which can improve the ability to describe the distribution of reservoirs.The lithology applicability fields of spectral decomposition technique are developed from clastic rock to carbonate rock,even volcanic rock.The application of spectral decomposition technique is developed from calculation of thin layer thickness to research of structure fracture system,reservoir boundary,reservoir prediction and fluid detection.There are three typical spectral decomposition methods: short time Fourier transform,continuous wavelet transform and S-transform.This paper analyzed algorithm and applicability of these three methods.STFT can not adjust the resolution according to the signal changes because it uses a fixed time window,which is only suitable for the analysis of piecewise smooth or approximate stationary signals.CWT is a muti-resolution method because it uses a move and variable wavelet as the time window.But it is not easy to select a wavelet function that can fully reflect the signal characteristics.ST is also a muti-resolution method because it uses the reciprocal of the frequency to adjust the time window,which is more convenient for data processing.This paper used these three methods for carbonate reservoir identification.It analyzed the effects of different time window size of STFT,and the effects of different wavelet type of CWT.It also compared reservoir description accuracy of different spectral decomposition algorithms,according to reservoir distribution of the three high-yield gas wells and 35Hz spectral decomposition sections.It proves that the frequency division section is more clearly than conventional seismic section in reservoir description.And ST gets the best result.
引文
[1]蔡瑞.谱分解技术在储层预测中的应用[J].CT理论与应用研究,2003,12(2):22-25.Cai R.Applications of spectral decomposition technique toreservoir prediction[J].Computerized Tomography Theoryand Applications(in Chinese),2003,12(2):22-25.
[2]李世雄.一维波动方程的奇性反演与小波[J].地球物理学报,1995,38(1):93-104.Li S X.Analysis and inversion of singularities of one-dimensional wave equations and wavelets[J].Chinese J.Geophys.(in Chinese),1995,38(1):93-104.
[3]章珂,刘贵忠,邹大文,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.Zhang K,Liu G Z,Zou D W,et al.Seismic data time-frequency domain denoising based on dyadic wavelet transform[J].Chinese J.Geophys.(in Chinese),1996,39(2):265-270.
[4]宗涛,孟鸿鹰,贾玉兰,等.小波包F-X域前后向预测去噪[J].地球物理学报,1998,41(增刊):337-346.Zong T,Meng H Y,Jia Y L,et al.Denoising method basedon wavelet packet and forward-backward prediction in F-Xdomain[J].Chinese J.Geophys.(in Chinese),1998,41(S1):337-346.
[5]孟鸿鹰,刘贵忠.小波变换多尺度地震波形反演[J].地球物理学报,1999,42(2):241-248.Meng H Y,Liu G Z.Multiscale seismic waveform inversionby wavelet transforms[J].Chinese J.Geophys.(in Chinese),1999,42(2):241-248.
[6]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(5):666-676.Zhao J M,Tang J,Zhang H J,et al.Wavelet transform andits application in data processing and interpretation of seismicreflection/refraction profile[J].Chinese J.Geophys.(inChinese),2000,43(5):666-676.
[7]王西文,杨孔庆,周立宏,等.基于小波变换的地震相干体算法研究[J].地球物理学报,2002,45(6):847-852.Wang X W,Yang K Q,Zhou L H,et al.Methods ofcalculating coherence cube on the basis of wavelet transform[J].Chinese J.Geophys.(in Chinese),2002,45(6):847-852.
[8]张延章,尹寿鹏,张巧玲,等.地震分频技术的地质内涵及其效果分析[J].石油勘探与开发,2006,33(1):64-66.Zhang Y Z,Yin S P,Zhang Q L,et al.Geologic significanceof the seismic spectral decomposition technology and itsapplication analysis[J].Petroleum Exploration andDevelopment(in Chinese),2006,33(1):64-66.
[9]杨艳,卢黎霞,龚志祥,等.谱分解技术在断层识别上的应用[J].复杂油气藏,2009,2(1):26-31.Yang Y,Lu L X,Gong Z X,et al.Application of spectraldecomposition technique in fault identification[J].ComplexHydrocarbon Reservoirs(in Chinese),2009,2(1):26-31.
[10]岳文正,陶果.小波变换在识别储层流体性质中的应用[J].地球物理学报,2003,46(6):863-869.Yue W Z,Tao G.A method for recognition of fluid propertyin reservoirs using wavelet transformation[J].Chinese J.Geophys.(in Chinese),2003,46(6):863-869.
[11]李鲤鹏,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.Li L P,Li Y D,Zhang X G.A method to compensate earthfiltering based on wavelet packet[J].Chinese J.Geophys.(in Chinese),2003,43(4):542-549.
[12]Koenig W,Dunn H K,Lacy L Y.The sound spectrograph[J].Journal of the Acoustical Society of America,1946,18(1):19-49.
[13]Potter R K,Kopp G,Green H C.Visible Speech[M].NewYork:D.Van Nostrand Co.,1947.
[14]Wigner E P.On the quantum correction for thermodynamicequilibrium[J].Physical Review,1932,40(5):749-759.
[15]Ville J.Theorie et applications de la notion de signal analytique[J].Cables et Transmissions,1948,20A:61-74.
[16]Cohen L.Time-frequency distributions-A review[J].Proceedingsof the IEEE,1989,77(7):941-981.
[17]Morlet J,Arens G,Fourgeau E,et al.Wave propagationand sampling theory-part I:Complex signal and scattering inmultilayered media[J].Geophysics,1982,47(2):203-221.
[18]Meyer Y.Wavelets:Algorithms and Applications[M].Philadelphia:Society for Industrial and AppliedMathematics,1993:11-196.
[19]Grossmann A,Morlet J,Paul T.Transforms associated tosquare integrable group representations.I.General results[J].Journal of Mathematical Physics,1985,26(10):2473-2479.
[20]Stockwell R G,Mansinha L,Lowe R P.Localization of thecomplex spectrum:the S transform[J].IEEE Transactionson Signal Processing,1996,44(4):998-1001.
[21]Mansinha L,Stockwell R G,Lowe R P.Pattern analysiswith two-dimensional spectral localisation:applications oftwo-dimensional S transforms[J].Physic A,1997,239(1-3):286-295.
[22]Pinnegar C R,Mansinha L.Time-local spectral analysis fornon-stationary time series:the S-transform for noisy signals[J].Fluctuation and Noise Letters,2003,3(3):357-364.
[23]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.Gao J H,Chen W C,Li Y M,et al.Generalized S transformand seismic response analysis of thin interbeds[J].Chinese J.Geophys.(in Chinese),2003,46(4):526-532.
[24]Partyka G A,Gridley J M,Lopez J.Interpretational applicationsof spectral decomposition in reservoir characterization[J].The Leading Edge,1999,18(3):353-360.
[25]袁志云,孔令洪,王成林,等.频谱分解技术在储层预测中的应用[J].石油地球物理勘探,2006,41(增刊):l1-15.Yuan Z F,Kong L H,Wang C L,et al.Application ofspectrum decomposition in reservoir prediction[J].OGP(inChinese),2006,41(S1):11-15.
[26]胥良君,李录明,党录瑞,等.频谱分解在生物礁储层油气检测中的应用[J].物探化探计算技术,2011,33(5):544-548.Xu L X,Li L M,Dang L R,et al.Application of spectraldecomposition technology to prediction of hydrocarbonpotential in reef reservoirs[J].Computing Techniques forGeophysical and Geochemical Exploration(in Chinese),2011,33(5):544-548.
[27]李宏兵,赵文智,曹宏,等.小波尺度域含气储层地震波衰减特征[J].地球物理学报,2004,47(5):892-898.Li H B,Zhao W Z,Cao H,et al.Characteristics of seismicattenuation of gas reservoirs in wavelet domain[J].ChineseJ.Geophys.(in Chinese),2004,47(5):892-898.
[28]刘振明,顾汉明,詹凤林.S变换时频分析在隧道岩溶地震勘探解释中的应用[J].工程地球物理学报,2010,7(1):50-54.Liu Z M,Gu H M,Zhan F L.Application of S-Transformtime-frequency analysis in seismic prospection interpretationfor karst caves under tunnel[J].Chinese Journal ofEngineering Geophysics(in Chinese),2010,7(1):50-54.
[2]李世雄.一维波动方程的奇性反演与小波[J].地球物理学报,1995,38(1):93-104.Li S X.Analysis and inversion of singularities of one-dimensional wave equations and wavelets[J].Chinese J.Geophys.(in Chinese),1995,38(1):93-104.
[3]章珂,刘贵忠,邹大文,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.Zhang K,Liu G Z,Zou D W,et al.Seismic data time-frequency domain denoising based on dyadic wavelet transform[J].Chinese J.Geophys.(in Chinese),1996,39(2):265-270.
[4]宗涛,孟鸿鹰,贾玉兰,等.小波包F-X域前后向预测去噪[J].地球物理学报,1998,41(增刊):337-346.Zong T,Meng H Y,Jia Y L,et al.Denoising method basedon wavelet packet and forward-backward prediction in F-Xdomain[J].Chinese J.Geophys.(in Chinese),1998,41(S1):337-346.
[5]孟鸿鹰,刘贵忠.小波变换多尺度地震波形反演[J].地球物理学报,1999,42(2):241-248.Meng H Y,Liu G Z.Multiscale seismic waveform inversionby wavelet transforms[J].Chinese J.Geophys.(in Chinese),1999,42(2):241-248.
[6]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(5):666-676.Zhao J M,Tang J,Zhang H J,et al.Wavelet transform andits application in data processing and interpretation of seismicreflection/refraction profile[J].Chinese J.Geophys.(inChinese),2000,43(5):666-676.
[7]王西文,杨孔庆,周立宏,等.基于小波变换的地震相干体算法研究[J].地球物理学报,2002,45(6):847-852.Wang X W,Yang K Q,Zhou L H,et al.Methods ofcalculating coherence cube on the basis of wavelet transform[J].Chinese J.Geophys.(in Chinese),2002,45(6):847-852.
[8]张延章,尹寿鹏,张巧玲,等.地震分频技术的地质内涵及其效果分析[J].石油勘探与开发,2006,33(1):64-66.Zhang Y Z,Yin S P,Zhang Q L,et al.Geologic significanceof the seismic spectral decomposition technology and itsapplication analysis[J].Petroleum Exploration andDevelopment(in Chinese),2006,33(1):64-66.
[9]杨艳,卢黎霞,龚志祥,等.谱分解技术在断层识别上的应用[J].复杂油气藏,2009,2(1):26-31.Yang Y,Lu L X,Gong Z X,et al.Application of spectraldecomposition technique in fault identification[J].ComplexHydrocarbon Reservoirs(in Chinese),2009,2(1):26-31.
[10]岳文正,陶果.小波变换在识别储层流体性质中的应用[J].地球物理学报,2003,46(6):863-869.Yue W Z,Tao G.A method for recognition of fluid propertyin reservoirs using wavelet transformation[J].Chinese J.Geophys.(in Chinese),2003,46(6):863-869.
[11]李鲤鹏,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.Li L P,Li Y D,Zhang X G.A method to compensate earthfiltering based on wavelet packet[J].Chinese J.Geophys.(in Chinese),2003,43(4):542-549.
[12]Koenig W,Dunn H K,Lacy L Y.The sound spectrograph[J].Journal of the Acoustical Society of America,1946,18(1):19-49.
[13]Potter R K,Kopp G,Green H C.Visible Speech[M].NewYork:D.Van Nostrand Co.,1947.
[14]Wigner E P.On the quantum correction for thermodynamicequilibrium[J].Physical Review,1932,40(5):749-759.
[15]Ville J.Theorie et applications de la notion de signal analytique[J].Cables et Transmissions,1948,20A:61-74.
[16]Cohen L.Time-frequency distributions-A review[J].Proceedingsof the IEEE,1989,77(7):941-981.
[17]Morlet J,Arens G,Fourgeau E,et al.Wave propagationand sampling theory-part I:Complex signal and scattering inmultilayered media[J].Geophysics,1982,47(2):203-221.
[18]Meyer Y.Wavelets:Algorithms and Applications[M].Philadelphia:Society for Industrial and AppliedMathematics,1993:11-196.
[19]Grossmann A,Morlet J,Paul T.Transforms associated tosquare integrable group representations.I.General results[J].Journal of Mathematical Physics,1985,26(10):2473-2479.
[20]Stockwell R G,Mansinha L,Lowe R P.Localization of thecomplex spectrum:the S transform[J].IEEE Transactionson Signal Processing,1996,44(4):998-1001.
[21]Mansinha L,Stockwell R G,Lowe R P.Pattern analysiswith two-dimensional spectral localisation:applications oftwo-dimensional S transforms[J].Physic A,1997,239(1-3):286-295.
[22]Pinnegar C R,Mansinha L.Time-local spectral analysis fornon-stationary time series:the S-transform for noisy signals[J].Fluctuation and Noise Letters,2003,3(3):357-364.
[23]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.Gao J H,Chen W C,Li Y M,et al.Generalized S transformand seismic response analysis of thin interbeds[J].Chinese J.Geophys.(in Chinese),2003,46(4):526-532.
[24]Partyka G A,Gridley J M,Lopez J.Interpretational applicationsof spectral decomposition in reservoir characterization[J].The Leading Edge,1999,18(3):353-360.
[25]袁志云,孔令洪,王成林,等.频谱分解技术在储层预测中的应用[J].石油地球物理勘探,2006,41(增刊):l1-15.Yuan Z F,Kong L H,Wang C L,et al.Application ofspectrum decomposition in reservoir prediction[J].OGP(inChinese),2006,41(S1):11-15.
[26]胥良君,李录明,党录瑞,等.频谱分解在生物礁储层油气检测中的应用[J].物探化探计算技术,2011,33(5):544-548.Xu L X,Li L M,Dang L R,et al.Application of spectraldecomposition technology to prediction of hydrocarbonpotential in reef reservoirs[J].Computing Techniques forGeophysical and Geochemical Exploration(in Chinese),2011,33(5):544-548.
[27]李宏兵,赵文智,曹宏,等.小波尺度域含气储层地震波衰减特征[J].地球物理学报,2004,47(5):892-898.Li H B,Zhao W Z,Cao H,et al.Characteristics of seismicattenuation of gas reservoirs in wavelet domain[J].ChineseJ.Geophys.(in Chinese),2004,47(5):892-898.
[28]刘振明,顾汉明,詹凤林.S变换时频分析在隧道岩溶地震勘探解释中的应用[J].工程地球物理学报,2010,7(1):50-54.Liu Z M,Gu H M,Zhan F L.Application of S-Transformtime-frequency analysis in seismic prospection interpretationfor karst caves under tunnel[J].Chinese Journal ofEngineering Geophysics(in Chinese),2010,7(1):50-54.
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