天然气储层多极子声波测井响应特征数值模拟研究
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摘要
对天然气储层的准确识别、评价是天然气储集层勘探开发的重要环节。本文通过建立双相介质孔隙地层多极子井孔声场数值模型,系统研究气层多极子阵列声波测井响应特征,提取对气层敏感的参数,以进行气层的识别和评价,据此形成一套迅速、准确识别天然气储层的多极子阵列声波识别方法。
根据井孔声场理论建立双相介质孔隙地层多极子井孔声场数值模型,模拟各种地质条件下多极源激发的阵列声波。分析全波各组分波纵波、横波、模式波对气层的测井响应特征;利用时频分析技术来提取声波全波中的信息,将时间域和频率域有效地结合起来,通过时频分析对信号开窗,可以得到各个谱分量的时间局域化的信息。采用时间-频率谱图,可以清晰、直观显示不同含气饱和度下全波各组分波在一定的时间、频率下能量的变化,以提取气层的敏感响应。
声波的速度信息是识别气层的有效手段。纵横波速度比识别气层存在一定的适用范围,通过模拟不同孔隙度、渗透率及含气饱和度条件下的阵列声波测井响应,提取纵横波速度比的响应特征,以确定其在不同环境下的适用性。通过与油层的对比,确定其在气层响应的特殊性,为快速直观的多极子阵列声波识别气层和定量计算打下基础。
偶极子弯曲波的频谱信息也可作为识别气层的着手点。通过数值模拟的阵列声波偶极子弯曲波频谱的提取,分析不同孔渗条件,不同含气条件下,偶极子弯曲波各组参数对气层的响应特征,寻找其中对气层有特殊响应的敏感参数,确定各个参数在不同环境下的适用性,并以此作为定性识别气层的标准。
本文的研究和探索为定性识别天然气储层提供了新的思路和方法。
The accurate identification and evaluation of natural gas reservoir is the key to the exploration and development of gas bearing reservoir. By establish two-phase porous formation’s multipole borehole acoustic field numerical model, Systematic study of the logging response characteristics on the multipole array acoustic in the gas reservoir. Extract the sensitive parameters to identify and evaluate the gas bearing reservoir. Accordingly, form a rapid and accurate multipole array acoustic method to identify the natural gas reservoir.
Based on the theory of borehole acoustic field,we build the two-phase porous formation’s multipole acoustic field numerical model. To simulate the array acoustic wave in different geological conditions which are stimulated by multipole source. Analysis compressional wave, shear wave and mode wave that different component waveform of full wave’s logging response characteristics of the gas. Using time-frequency analysis technology to extract information from acoustic full wave, and it makes time domain and frequency domain to effectively integrate. Opening a window to the signal by time-frequency analysis technology, we can get the time local domain information from various spectrum components. By using time-frequency spectrum figure, we can clearly and directly observe the energy of full wave’s various components change with different gas saturation. Find out the special response of the gas layer.
The velocity information of acoustic is an effective mean to identify gas layer. Ratio of compressional and shear wave velocity presence some applicable scope. Simulate the array acoustic logging response in different porosity, permeability and gas saturation. Extracting characteristics response of ratio of compressional and shear wave velocity. And decide its application in different environment. By comparing with the oil layer, determine its special response in gas layer, and lay the foundation for fast and intuitive multipole array acoustic identification and quantitative calculation.
Spectrum information of dipole flexural wave can also be used to identify gas layer. By extracting the spectrum of dipole flexural wave from array acoustic, analysis the various sets of parameters of dipole flexural wave’s response characteristic for gas layer in different porosity, permeability and gas saturation. And find out the sensitive parameters from them that have the special response for gas layer. Determine the different parameters’application in different environment, and to be as a standard of qualitative identification of gas reservoir.
All these researches provide a completely new method for fully using well logging information to identify gas reservoir.
根据井孔声场理论建立双相介质孔隙地层多极子井孔声场数值模型,模拟各种地质条件下多极源激发的阵列声波。分析全波各组分波纵波、横波、模式波对气层的测井响应特征;利用时频分析技术来提取声波全波中的信息,将时间域和频率域有效地结合起来,通过时频分析对信号开窗,可以得到各个谱分量的时间局域化的信息。采用时间-频率谱图,可以清晰、直观显示不同含气饱和度下全波各组分波在一定的时间、频率下能量的变化,以提取气层的敏感响应。
声波的速度信息是识别气层的有效手段。纵横波速度比识别气层存在一定的适用范围,通过模拟不同孔隙度、渗透率及含气饱和度条件下的阵列声波测井响应,提取纵横波速度比的响应特征,以确定其在不同环境下的适用性。通过与油层的对比,确定其在气层响应的特殊性,为快速直观的多极子阵列声波识别气层和定量计算打下基础。
偶极子弯曲波的频谱信息也可作为识别气层的着手点。通过数值模拟的阵列声波偶极子弯曲波频谱的提取,分析不同孔渗条件,不同含气条件下,偶极子弯曲波各组参数对气层的响应特征,寻找其中对气层有特殊响应的敏感参数,确定各个参数在不同环境下的适用性,并以此作为定性识别气层的标准。
本文的研究和探索为定性识别天然气储层提供了新的思路和方法。
The accurate identification and evaluation of natural gas reservoir is the key to the exploration and development of gas bearing reservoir. By establish two-phase porous formation’s multipole borehole acoustic field numerical model, Systematic study of the logging response characteristics on the multipole array acoustic in the gas reservoir. Extract the sensitive parameters to identify and evaluate the gas bearing reservoir. Accordingly, form a rapid and accurate multipole array acoustic method to identify the natural gas reservoir.
Based on the theory of borehole acoustic field,we build the two-phase porous formation’s multipole acoustic field numerical model. To simulate the array acoustic wave in different geological conditions which are stimulated by multipole source. Analysis compressional wave, shear wave and mode wave that different component waveform of full wave’s logging response characteristics of the gas. Using time-frequency analysis technology to extract information from acoustic full wave, and it makes time domain and frequency domain to effectively integrate. Opening a window to the signal by time-frequency analysis technology, we can get the time local domain information from various spectrum components. By using time-frequency spectrum figure, we can clearly and directly observe the energy of full wave’s various components change with different gas saturation. Find out the special response of the gas layer.
The velocity information of acoustic is an effective mean to identify gas layer. Ratio of compressional and shear wave velocity presence some applicable scope. Simulate the array acoustic logging response in different porosity, permeability and gas saturation. Extracting characteristics response of ratio of compressional and shear wave velocity. And decide its application in different environment. By comparing with the oil layer, determine its special response in gas layer, and lay the foundation for fast and intuitive multipole array acoustic identification and quantitative calculation.
Spectrum information of dipole flexural wave can also be used to identify gas layer. By extracting the spectrum of dipole flexural wave from array acoustic, analysis the various sets of parameters of dipole flexural wave’s response characteristic for gas layer in different porosity, permeability and gas saturation. And find out the sensitive parameters from them that have the special response for gas layer. Determine the different parameters’application in different environment, and to be as a standard of qualitative identification of gas reservoir.
All these researches provide a completely new method for fully using well logging information to identify gas reservoir.
引文
[1]李长文.阵列声波测井资料的分波处理及应用[D].测井技术.1997,21(1):1-7
[2]张碧星,王克协.各向异性介质地层中多极源声波测井的现状与发展[J].地球物理学进展,1998,13(2):1-8
[3]李维彦.利用偶极横波成像测井资料评价地层的各向异性[J].江汉石油学院学报,1999,21(4):36-38
[4]陶果,邹辉.现代阵列声波测井数据处理和解释方法研究[J].石油勘探与开发,2000,27(2):76-78
[5]陈必孝,张筠.声波全波列测井资料分析处理技术及应用[J].测井技术,2002,26(5):369-372
[6]谭廷栋.天然气勘探中的测井技术[M].北京:石油工业出版社,1994
[7]杨雷,高秋涛.利用XMAC测井资料识别油气层段[J].新疆石油地质,2002,23(5):402-404
[8]赵军,李进福.测井新技术在塔里木油田气藏描术中的应用[J].天然气地球科学,2004,15(3):285-289
[9]江明,李兆阳.声波全波列测井资料的处理方法及应用[J].石油仪器,2005,19(5):53-58
[10]肖亮,初玉林.测井资料识别气层方法研究[J].工程地球物理学报,2006,3(6):470-472
[11]燕继承,刘李春.基于测井资料识别气层及适用性分析研究[J].国外测井技术, 2009,6,171:16-18
[12]章成广,江万哲,肖承文,等.声波全波资料识别气层方法研究[J].测井技术,2004,28(5):397-401
[13]令狐松,王敬农.利用偶极横波资料进行疑难气层评价[J].测井技术,2006,30(3):230-232
[14]刘有霞,裴鹏.偶极声波测井在YU地区的气层识别[J].测井技,2007,31(5):445-447
[15]高楚桥,钟兴水.测井信息识别低电阻率气层[J].江汉石油学院学,1999,21(4):15-17
[16]赵辉.阵列声波测井资料判别储层流体性质方法及应用,测井技术信息[J],2004,17(5):42-46
[17]陈雪莲,王瑞甲.多极子声波测井在低孔低渗气层中的数值研究[J].地球物理学进展,2007,12,22(6):1836~1840
[18]邵才瑞,张福明.井筒声场研究回顾与展望[J].地球物理学进展,2004,9,19(3):524-532
[19] Biot M A.Theory of elasticity and consolidation for a porous anisotropic solid [J]. Appl Phys, 1955, 26:182-185.
[20] Biot MA.Theory of propagation of elastic waves in a fluid-saturated porous solid, I: Low-frequency range[J]. Acoust Soc Amer, 1956a,28:68-178.
[21] Biot MA.Theory of propagation of elastic waves in a fluid-saturated porous solid, II: Higher-frequency range[J]. Acoust Soc Amer,1956b, 28:179-191.
[22] Amos Nur著,许云译.双相介质中波的传播[M].北京:石油工业出版社,1986
[23] Schmitt D P.Acoustic multipole logging in transversely isotropic poroelastic formations[J]. Acoust Soc Am. 1989, 86:2397-2421.
[24]王尚旭.双相介质中弹性波问题有限元数值解和AVO问题[D].北京:石油大学, 1990
[25]张应波.Biot理论应用于地震勘探的探索[J].石油物探,1994, 33(4):29-38
[26]刘维国,包洪洋,董晓丽.双相介质中的密度反演[J].哈尔滨工业大学学报,1994, 26(6):1-5
[27]刘维国,全大勇.双相介质中孔隙率反演的一种方法[J].哈尔滨工业大学学报,1998, 30(4):1-3
[28]席道瑛,刘爱文,刘卫.低频条件下饱和流体砂岩的衰减研究[J].地震学报,1995,17(4):477-481
[29]席道瑛,张斌,易良坤,李娟.双相介质中应力波的衰减规律[J].岩石力学与工程学报, 1998,17(4):429-433
[30]徐文骏,王跃.流体饱和多孔介质(双相介质)物性参数的反演[J].石油地球物理勘探, 1995,30(5):602-608
[31]乔文孝,王宁,严炽培.声波在两种多孔介质界面上的反射和透射[J].地球物理学报, 1992,35:242-248
[32] Zhang Bixing(张碧星), Dong Hefeng, Wang Kexie.Multipole sources in a fluid-filledborehole surrounded by a transversely isotropicelastic solid[J]. Acoust Soc Am, 1994, 96:2546-2555.
[33] Zhang Bixing, Wang Kexie, Dong Qingde. Acoustic multipole logging in transversely isotropic two-phase medium[J]. Acoust. Soc Am,1995,97:3462-3472.
[34]董和风,王克协.弹性固体地层-流体井孔弹性波场的有限差分数值模拟[J].地球物理学报,1995年,38(1):205-215
[35]陶果.用于声波测井的大型三维有限差分模拟程序[J].测井技术,2001,25(4): 273-277
[36]邵秀民,蓝志凌.非均匀质各向同性弹性介质中地震波传播的数值模拟[J].地球物理学报,1995年,38(增1):39-55
[37]张剑锋.三维非均匀介质中弹性波传播的数值模拟[J].固体力学学报,2001年, 22(4):356-360
[38]牛滨华.裂隙各向异性介质2.5维弹性波场数值模拟[J].中国地质大学学报,1995, 20(1),107-111
[39]牛滨华,何樵登,孙春岩.裂隙各向异性介质波场VSP多分量记录的数值模拟[J].地球物理学报,1995年,38(4):519-527
[40]张碧星.各向异性介质地层流体井孔中多极源声测井理论与数值研究[D].长春:吉林大学,1994
[41]邵治龙,贺振华,黄德济.正交各向异性介质中地震记录的有限差分数值模拟[J].物探化探计算技术,1998,20(4),300-305
[42]张剑锋,刘铁林.各向异性介质中弹性波的数值模拟[J].固体力学学报,2000,21(3):234-242
[43]张美根,王妙月.各向异性弹性波场的有限元数值模拟[J].地球物理学进展,2002,17(3):384-389
[44]徐文骏,郭建.流体饱和多孔介质中弹性波的数值模拟[J].地球物理学报,1994年, 37(增I):424-433
[45]魏修成.双相各向异性介质中的地震波场研究[D].北京:石油大学,1995
[46]牟永光.储层地球物理学[M].北京:石油工业出版社.1996
[47]张碧星,王克协.各向异性双相介质中多极源声波测井理论研究[J].地球物理学报, 2000, 43(5):707-708
[48]刘洋,李承楚.双相各向异性介质中弹性波传播伪谱法数值模拟研究[J].地震学报,2000,22(2):32-138
[49]杨顶辉.双相各向异性介质中弹性波方程的有限元解法及波场模拟[J].地球物理学报,2002, 45(4):575-583
[50]杨宽德,杨顶辉.基于BISQ高频极限方程的交错网格法数值模拟[J].石油地球物理勘探,2002, 37(5):463-468.
[51] Cara M.Time-Frequency analysis[J]. Eos, Transactions, American Geophysical Union, 1982, 63(51):13-20.
[52] Gabor D.Theory of Communication[J].Journal of the IEEE. 1946,93:429-497.
[53]卫俊平.时频分析技术及应用[D].西安:电子科技大学, 2005
[54] Chakraborty A, Okaya D.Frequency-time decomposition of seismic data using wavelet-based methods[J]. Geophysics, 1995, 60(6):1906-1916.
[55] Stockwell R G, Mansinha L, Lowe R P.Locatization of the complex spectrum: the S transform[J]. IEEE Transactions on Signal Processing,1996,44(4):998-1001.
[56] Sabadell F J.Spectral.Localization of seismic data with a phase corrected wavelet transform[J]. SEG Expanded Abstarcts,2001,20:595.
[57] Taner M T, Koehler F, Sheriff R E.Complex seismic trace analysis[J]. Geophysics, 1979, 44(6):1041-1063.
[58]石春香,罗奇峰.时程信号的Hilbert-Huang变换与小波分析[J].地震学报,2003, 25(4):398-405
[59] Hardy H, Richard A, Beier, Jonathan D. Gaston.Frequency estimates of seismic traces[J]. Geophysics,2003,68(1):370-380.
[60] Choi A.Real-time fundamental frequency estimation by least-square fitting[J]. IEEE Trans. Speech Audio processing. 1997,5,201-205.
[61] Liu J L.Time-Frequency decomposition based on Ricker wavelet[J]. SEG Expanded Abstarcts,2004,23.1933.
[62] Cohen L.Generalized phase space distribution functions[J].Jour. Math. Phys, 1966,7:781-787.
[63] Jeffrey C, William J.Shift covariant time-frequency distributions of discrete signals [J]. 1999,47(1):133-146.
[64] Jeffrey C, William J.A function of time, frequency[J],lag and doppler, 1999, 47(3): 789-799.
[65] Jeffrey C and Patrick F.Virtues and vices of quartic time-frequency distributions[J]. IEEE Trans-actions on Signal Processing, 2000, 48(9):2641-2650.
[66]江万哲,章成广.时频分析方法在声波测井信息提取中的应用[J].石油天然气学报(江汉石油学院学报),2005, 12, 27(6):736-738
[67]王祝文,刘菁华,聂春燕.基于Choi-Williams时频分布的阵列声波测井信号时频分析[J].地球物理学进展,2007,10,22(5):1481-1485
[68]王祝文,刘菁华,聂春燕.时频分析的重排方法及其在声波测井信号处理中的应用[J].吉林大学学报,2007,9,37(5):1042-1046
[69]张学涛,王祝文,原镜海.利用时频分析方法在阵列声波测井中区分油水层[J].岩性油气藏,2008,3,20(1):101-104
[70]王祝文,刘菁华,聂春燕.基于Hilbter-Huang变换的阵列声波测井信号时频分析[J].地球科学—中国地质大学学报,2008,5,33(3):387-391
[71]王祝文,刘菁华,聂春燕.阵列声波测井信号的时频局域相关能量分析[J].吉林大学学报,2008,3,38(2):341-345
[2]张碧星,王克协.各向异性介质地层中多极源声波测井的现状与发展[J].地球物理学进展,1998,13(2):1-8
[3]李维彦.利用偶极横波成像测井资料评价地层的各向异性[J].江汉石油学院学报,1999,21(4):36-38
[4]陶果,邹辉.现代阵列声波测井数据处理和解释方法研究[J].石油勘探与开发,2000,27(2):76-78
[5]陈必孝,张筠.声波全波列测井资料分析处理技术及应用[J].测井技术,2002,26(5):369-372
[6]谭廷栋.天然气勘探中的测井技术[M].北京:石油工业出版社,1994
[7]杨雷,高秋涛.利用XMAC测井资料识别油气层段[J].新疆石油地质,2002,23(5):402-404
[8]赵军,李进福.测井新技术在塔里木油田气藏描术中的应用[J].天然气地球科学,2004,15(3):285-289
[9]江明,李兆阳.声波全波列测井资料的处理方法及应用[J].石油仪器,2005,19(5):53-58
[10]肖亮,初玉林.测井资料识别气层方法研究[J].工程地球物理学报,2006,3(6):470-472
[11]燕继承,刘李春.基于测井资料识别气层及适用性分析研究[J].国外测井技术, 2009,6,171:16-18
[12]章成广,江万哲,肖承文,等.声波全波资料识别气层方法研究[J].测井技术,2004,28(5):397-401
[13]令狐松,王敬农.利用偶极横波资料进行疑难气层评价[J].测井技术,2006,30(3):230-232
[14]刘有霞,裴鹏.偶极声波测井在YU地区的气层识别[J].测井技,2007,31(5):445-447
[15]高楚桥,钟兴水.测井信息识别低电阻率气层[J].江汉石油学院学,1999,21(4):15-17
[16]赵辉.阵列声波测井资料判别储层流体性质方法及应用,测井技术信息[J],2004,17(5):42-46
[17]陈雪莲,王瑞甲.多极子声波测井在低孔低渗气层中的数值研究[J].地球物理学进展,2007,12,22(6):1836~1840
[18]邵才瑞,张福明.井筒声场研究回顾与展望[J].地球物理学进展,2004,9,19(3):524-532
[19] Biot M A.Theory of elasticity and consolidation for a porous anisotropic solid [J]. Appl Phys, 1955, 26:182-185.
[20] Biot MA.Theory of propagation of elastic waves in a fluid-saturated porous solid, I: Low-frequency range[J]. Acoust Soc Amer, 1956a,28:68-178.
[21] Biot MA.Theory of propagation of elastic waves in a fluid-saturated porous solid, II: Higher-frequency range[J]. Acoust Soc Amer,1956b, 28:179-191.
[22] Amos Nur著,许云译.双相介质中波的传播[M].北京:石油工业出版社,1986
[23] Schmitt D P.Acoustic multipole logging in transversely isotropic poroelastic formations[J]. Acoust Soc Am. 1989, 86:2397-2421.
[24]王尚旭.双相介质中弹性波问题有限元数值解和AVO问题[D].北京:石油大学, 1990
[25]张应波.Biot理论应用于地震勘探的探索[J].石油物探,1994, 33(4):29-38
[26]刘维国,包洪洋,董晓丽.双相介质中的密度反演[J].哈尔滨工业大学学报,1994, 26(6):1-5
[27]刘维国,全大勇.双相介质中孔隙率反演的一种方法[J].哈尔滨工业大学学报,1998, 30(4):1-3
[28]席道瑛,刘爱文,刘卫.低频条件下饱和流体砂岩的衰减研究[J].地震学报,1995,17(4):477-481
[29]席道瑛,张斌,易良坤,李娟.双相介质中应力波的衰减规律[J].岩石力学与工程学报, 1998,17(4):429-433
[30]徐文骏,王跃.流体饱和多孔介质(双相介质)物性参数的反演[J].石油地球物理勘探, 1995,30(5):602-608
[31]乔文孝,王宁,严炽培.声波在两种多孔介质界面上的反射和透射[J].地球物理学报, 1992,35:242-248
[32] Zhang Bixing(张碧星), Dong Hefeng, Wang Kexie.Multipole sources in a fluid-filledborehole surrounded by a transversely isotropicelastic solid[J]. Acoust Soc Am, 1994, 96:2546-2555.
[33] Zhang Bixing, Wang Kexie, Dong Qingde. Acoustic multipole logging in transversely isotropic two-phase medium[J]. Acoust. Soc Am,1995,97:3462-3472.
[34]董和风,王克协.弹性固体地层-流体井孔弹性波场的有限差分数值模拟[J].地球物理学报,1995年,38(1):205-215
[35]陶果.用于声波测井的大型三维有限差分模拟程序[J].测井技术,2001,25(4): 273-277
[36]邵秀民,蓝志凌.非均匀质各向同性弹性介质中地震波传播的数值模拟[J].地球物理学报,1995年,38(增1):39-55
[37]张剑锋.三维非均匀介质中弹性波传播的数值模拟[J].固体力学学报,2001年, 22(4):356-360
[38]牛滨华.裂隙各向异性介质2.5维弹性波场数值模拟[J].中国地质大学学报,1995, 20(1),107-111
[39]牛滨华,何樵登,孙春岩.裂隙各向异性介质波场VSP多分量记录的数值模拟[J].地球物理学报,1995年,38(4):519-527
[40]张碧星.各向异性介质地层流体井孔中多极源声测井理论与数值研究[D].长春:吉林大学,1994
[41]邵治龙,贺振华,黄德济.正交各向异性介质中地震记录的有限差分数值模拟[J].物探化探计算技术,1998,20(4),300-305
[42]张剑锋,刘铁林.各向异性介质中弹性波的数值模拟[J].固体力学学报,2000,21(3):234-242
[43]张美根,王妙月.各向异性弹性波场的有限元数值模拟[J].地球物理学进展,2002,17(3):384-389
[44]徐文骏,郭建.流体饱和多孔介质中弹性波的数值模拟[J].地球物理学报,1994年, 37(增I):424-433
[45]魏修成.双相各向异性介质中的地震波场研究[D].北京:石油大学,1995
[46]牟永光.储层地球物理学[M].北京:石油工业出版社.1996
[47]张碧星,王克协.各向异性双相介质中多极源声波测井理论研究[J].地球物理学报, 2000, 43(5):707-708
[48]刘洋,李承楚.双相各向异性介质中弹性波传播伪谱法数值模拟研究[J].地震学报,2000,22(2):32-138
[49]杨顶辉.双相各向异性介质中弹性波方程的有限元解法及波场模拟[J].地球物理学报,2002, 45(4):575-583
[50]杨宽德,杨顶辉.基于BISQ高频极限方程的交错网格法数值模拟[J].石油地球物理勘探,2002, 37(5):463-468.
[51] Cara M.Time-Frequency analysis[J]. Eos, Transactions, American Geophysical Union, 1982, 63(51):13-20.
[52] Gabor D.Theory of Communication[J].Journal of the IEEE. 1946,93:429-497.
[53]卫俊平.时频分析技术及应用[D].西安:电子科技大学, 2005
[54] Chakraborty A, Okaya D.Frequency-time decomposition of seismic data using wavelet-based methods[J]. Geophysics, 1995, 60(6):1906-1916.
[55] Stockwell R G, Mansinha L, Lowe R P.Locatization of the complex spectrum: the S transform[J]. IEEE Transactions on Signal Processing,1996,44(4):998-1001.
[56] Sabadell F J.Spectral.Localization of seismic data with a phase corrected wavelet transform[J]. SEG Expanded Abstarcts,2001,20:595.
[57] Taner M T, Koehler F, Sheriff R E.Complex seismic trace analysis[J]. Geophysics, 1979, 44(6):1041-1063.
[58]石春香,罗奇峰.时程信号的Hilbert-Huang变换与小波分析[J].地震学报,2003, 25(4):398-405
[59] Hardy H, Richard A, Beier, Jonathan D. Gaston.Frequency estimates of seismic traces[J]. Geophysics,2003,68(1):370-380.
[60] Choi A.Real-time fundamental frequency estimation by least-square fitting[J]. IEEE Trans. Speech Audio processing. 1997,5,201-205.
[61] Liu J L.Time-Frequency decomposition based on Ricker wavelet[J]. SEG Expanded Abstarcts,2004,23.1933.
[62] Cohen L.Generalized phase space distribution functions[J].Jour. Math. Phys, 1966,7:781-787.
[63] Jeffrey C, William J.Shift covariant time-frequency distributions of discrete signals [J]. 1999,47(1):133-146.
[64] Jeffrey C, William J.A function of time, frequency[J],lag and doppler, 1999, 47(3): 789-799.
[65] Jeffrey C and Patrick F.Virtues and vices of quartic time-frequency distributions[J]. IEEE Trans-actions on Signal Processing, 2000, 48(9):2641-2650.
[66]江万哲,章成广.时频分析方法在声波测井信息提取中的应用[J].石油天然气学报(江汉石油学院学报),2005, 12, 27(6):736-738
[67]王祝文,刘菁华,聂春燕.基于Choi-Williams时频分布的阵列声波测井信号时频分析[J].地球物理学进展,2007,10,22(5):1481-1485
[68]王祝文,刘菁华,聂春燕.时频分析的重排方法及其在声波测井信号处理中的应用[J].吉林大学学报,2007,9,37(5):1042-1046
[69]张学涛,王祝文,原镜海.利用时频分析方法在阵列声波测井中区分油水层[J].岩性油气藏,2008,3,20(1):101-104
[70]王祝文,刘菁华,聂春燕.基于Hilbter-Huang变换的阵列声波测井信号时频分析[J].地球科学—中国地质大学学报,2008,5,33(3):387-391
[71]王祝文,刘菁华,聂春燕.阵列声波测井信号的时频局域相关能量分析[J].吉林大学学报,2008,3,38(2):341-345