高精度时频分析方法与技术研究
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摘要
对信号的传统分析方法是傅里叶变换,但是对地震信号这种典型的非平稳信号而言,传统的傅里叶变换不能达到分析要求,需要进行时频联合域分析。目前时频分析技术已被广泛应用于时变滤波去噪、检测地层变化特征、提高地震资料分辨率等物探领域中。
本研究主要通过对连续小波变换和逆谱分解进行研究以形成高精度时频分析方法,并将该方法运用于理论试算和实际资料处理中。
在连续小波变换中,有三个非常重要的参数:小波函数、尺度范围及变换所选择的尺度步长。对信号采用不同的小波函数进行分析,将得到不同精度的时频分析结果;尺度与频率对应,较好的选择尺度的分析范围能够更准确的分析信号频率;变换尺度步长的选择对能否较好的分析信号的局部特征有重要影响;小波变换的结果是时间-尺度域结果,不能从变换域直接得到信号的频率信息;同时对信号的分析要满足能对信号实现的重构,分析才具有实际意义。因此本文对小波函数的选择、变换尺度范围的确定和变换时所采用的尺度步长进行了深入研究;研究了尺度与频率的对应关系,通过这种关系可以直接得到对应的频率信息;对连续小波变换的重构问题进行研究,保证用小波变换进行资料处理时具备一定的实际意义。
逆谱分解是基于连续小波反变换和约束条件的,小波函数的选择和约束条件对分解结果的精度有重要影响。逆谱分解的分析结果相对其他时频分析方法如短时傅里叶变换、小波变换而言具有更高的精度。在逆谱分解方法中,本文主要研究了L1、L2和稀疏脉冲三种约束条件对分析结果的影响,通过理论模型试算得出三种约束的分析精度是逐渐升高的,其中稀疏脉冲约束(sparse spike)具有最高的精度。
本文在对高精度时频分析方法理论研究成功的基础上,将该方法的研究运用于实际资料处理和解释中,在分频资料解释和高分辨率处理中均取得较好的应用效果。
The traditional analysis method of signal is Fourier transform, but to the typical non-stationary signal such as seismic signal, this method can’t reach the requirement, it is need to use time and frequency domain to analysis. As the widely use of time-frequency analysis method in petroleum exploration, it’s researched by many people.
This research mainly through continuous wavelet transform and inverse spectral decomposition research to form high-precision time-frequency analysis method, then use these methods in theoretical calculation and practical data processing.
In CWT, there are three important parameters: wavelet function, the space of scale and the step. Adopting different wavelet function to analyse the signal will get different resolution results; The scale is related to frequency, the much better choice of the scale range the better frequency results will be obtained; The choice of step is related to the partial feature of the signal. The result of wavelet transform is time-scale range, we can’t obtain the information of frequency directly in the transform result; Also analysis the signal need to meet the reconstruction to let it has a practical significance. So I had studied the inverse problem about wavelet transform to certain the data processing has practical significance.
The inverse spectral decomposition is based on inverse wavelet transform and constraint condition. The choice of wavelet function and constraint condition has important influence to the decomposition result. Compared with other methods such as short time Fourier transform and continuous wavelet transform this method has better time and frequency resolution. In inverse spectral decomposition, the paper mainly studied the influence of constraint condition. In theoretical models mainly used three constraints condition minimum L2 norm, minimum L1 norm and sparse spike or minimum support constraint. The accuracy of these constraints is raised, and the sparse spike has the best accuracy.
This paper use accuracy time-frequency to the processing and processing of real seismic data base on the successful research of high precision time-frequency methods, and have a good application effect in frequency data interpretation and high resolution processing.
本研究主要通过对连续小波变换和逆谱分解进行研究以形成高精度时频分析方法,并将该方法运用于理论试算和实际资料处理中。
在连续小波变换中,有三个非常重要的参数:小波函数、尺度范围及变换所选择的尺度步长。对信号采用不同的小波函数进行分析,将得到不同精度的时频分析结果;尺度与频率对应,较好的选择尺度的分析范围能够更准确的分析信号频率;变换尺度步长的选择对能否较好的分析信号的局部特征有重要影响;小波变换的结果是时间-尺度域结果,不能从变换域直接得到信号的频率信息;同时对信号的分析要满足能对信号实现的重构,分析才具有实际意义。因此本文对小波函数的选择、变换尺度范围的确定和变换时所采用的尺度步长进行了深入研究;研究了尺度与频率的对应关系,通过这种关系可以直接得到对应的频率信息;对连续小波变换的重构问题进行研究,保证用小波变换进行资料处理时具备一定的实际意义。
逆谱分解是基于连续小波反变换和约束条件的,小波函数的选择和约束条件对分解结果的精度有重要影响。逆谱分解的分析结果相对其他时频分析方法如短时傅里叶变换、小波变换而言具有更高的精度。在逆谱分解方法中,本文主要研究了L1、L2和稀疏脉冲三种约束条件对分析结果的影响,通过理论模型试算得出三种约束的分析精度是逐渐升高的,其中稀疏脉冲约束(sparse spike)具有最高的精度。
本文在对高精度时频分析方法理论研究成功的基础上,将该方法的研究运用于实际资料处理和解释中,在分频资料解释和高分辨率处理中均取得较好的应用效果。
The traditional analysis method of signal is Fourier transform, but to the typical non-stationary signal such as seismic signal, this method can’t reach the requirement, it is need to use time and frequency domain to analysis. As the widely use of time-frequency analysis method in petroleum exploration, it’s researched by many people.
This research mainly through continuous wavelet transform and inverse spectral decomposition research to form high-precision time-frequency analysis method, then use these methods in theoretical calculation and practical data processing.
In CWT, there are three important parameters: wavelet function, the space of scale and the step. Adopting different wavelet function to analyse the signal will get different resolution results; The scale is related to frequency, the much better choice of the scale range the better frequency results will be obtained; The choice of step is related to the partial feature of the signal. The result of wavelet transform is time-scale range, we can’t obtain the information of frequency directly in the transform result; Also analysis the signal need to meet the reconstruction to let it has a practical significance. So I had studied the inverse problem about wavelet transform to certain the data processing has practical significance.
The inverse spectral decomposition is based on inverse wavelet transform and constraint condition. The choice of wavelet function and constraint condition has important influence to the decomposition result. Compared with other methods such as short time Fourier transform and continuous wavelet transform this method has better time and frequency resolution. In inverse spectral decomposition, the paper mainly studied the influence of constraint condition. In theoretical models mainly used three constraints condition minimum L2 norm, minimum L1 norm and sparse spike or minimum support constraint. The accuracy of these constraints is raised, and the sparse spike has the best accuracy.
This paper use accuracy time-frequency to the processing and processing of real seismic data base on the successful research of high precision time-frequency methods, and have a good application effect in frequency data interpretation and high resolution processing.
引文
[1]唐向宏,李齐良.时频分析与小波变换[M].北京:科学出版社,2008.
[2]王西文.地震资料处理和解释中的小波分析方法[M].北京:石油工业出版社,2004.
[3]张贤达.现代信号处理[M].北京:清华大学出版社,2002.
[4]李振春,张军华.地震数据处理方法[M].北京:石油大学出版社,2004.
[5]牟永光,陈小宏,李国发,等.地震数据处理方法[M].北京:石油工业出版社,2007.
[6]俞寿朋.高分辨率地震勘探[M].北京:石油工业出版社,1993.
[7] Jianlei Liu.Spectral decomposition and its application in mapping stratigraphy and hydrocarbons[D].The Faculty of the Department of Geosciences University of Houston.
[8] Oleg Portniaguine and John Castagna.Inverse spectral decomposition[C].SEG Int’l Exposition and 7th Annual Meeting,10-15 October 2004.
[9] Charles I Puryear and John P Castagna.An algorithm for calculation of bed thickness and reflection coefficients from amplitude spectrum[C].SEG/New Orleans 2006 Annual Meeting.
[10] Chakraborty,A. and Okaya,D.Frequency-time decompositon of seismic data using wavelet based methods[J].Geophysics,1995.
[11] Castagna,J.p,S.Sun and R.W.Siegfried.Instantaneous spectral analysis:Detection of low-frequency shadows associated with hudrocarbons[J].The leading Edge,2003.
[12] Satinder Chopra,Jhon Castagna and Oleg Porniaguine.Seismic resolution and thin-bed reflectivity inversion[J].Cseg Recorder,2006.
[13] Sarinder Chopra,John Castagna and Oleg Porniaguine.Thin-bed reflectivity inversion[C].SEG/New Orleans 2006 Annual Meeting.
[14] Portniaguine,O.and J.P.Castagna.Spectral inversion:Lessons from modeling and Boonesville case study[C].75th SEG Meeting,2005.
[15] Charles I Puryear and John P Castagna.An algorithm for calculation of bed thickness and reflection coefficients from amplitude spectrum[C].SEG/New Orleans 2006 Annual Meeting.
[16] Gregory A.Partyka.Seismic Thickness Estimation:Three Approaches,Pros and Cons[C].SEG Int’l Exposition and Annual Meeting,2001.
[17] Greg Partyka,James Gridley and John Lopez.Interpretational application of spectral decomposition in reservoir characterization[J].The Leading Edge,1999.
[18]施云惠.一维连续小波变换[J].高等学校计算机数学学报,2007,29(1):1-6.
[19]高静怀,汪文秉,朱光明,等.地震资料处理中小波函数的选取研究[J].地球物理学报,1996,39(3):392-398.
[20]李世雄.小波变换及其应用[J].高等数学研究,2002,5(2):36-38.
[21]刘葵,刘招君,朱建伟.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):282-284.
[22]董建华,顾汉明,张星.几种时频分析方法的比较及应用[J].工程地球物理学报,2007,4(4):312-315.
[23]刘喜武,张宁,勾永峰,等.地震勘探信号时频分析方法对比与应用分析[J].地球物理学进展,2008,23(3):743-753.
[24]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[J].勘探地球物理进展,2004,27(4):246-250.
[25]陈洁.时频分析方法小结[J].中国水运,2009,9(2):87-89.
[26]陈学华.时频分布与地震信号谱分析研究[D].成都理工大学,2006.
[27]刘丽娟.时频分析技术及其应用[D].成都理工大学,2008.
[28]蔡希玲,吕英梅.地震数据时频分析与分频处理[J].勘探地球物理进展,2005,28(4):265-270.
[29]姜弢,刘庆普,胡留军.地震信号去噪的小波方法研究[J].哈尔滨工程大学学报,2002,23(4):86-90.
[30]王西文,高静怀,李幼铭.高分辨率地震资料处理中导数小波函数的构造[J].石油物探,2000,39(2):64-71.
[31]贾丽华,吴长江,刘小娟,等.地震资料高分辨率处理技术[J].石油物探,2002,41(4):484-488.
[32]盛怀洁,钟子发,吴彦华.连续小波变换中基小波的尺度伸缩与应用[J].无线电工程,1999,29(6):55-57.
[33]陈文超,高静怀,汪文秉,小波变换用于提高过井地震资料分辨率的方法研究[J].西安交通大学学报,1998,32(12):44-47.
[34]刘维国,杨兆进,郭惠娟,等.小波变换及其在地震资料处理中的应用[J].哈尔滨工业大学学报,1995,27(1):1-3.
[35]彭波,郭树祥,赵晨曦.高分辨率资料处理[J].勘探地球物理进展,2004,27(6):415-421.
[36]赵军龙,李娜.小波变换在高分辨率层序地层分析中的应用[J].地球物理学进展,2008,23(4):1230-1235.
[37]何光明,高如曾,韩德贵,等.小波变换在地震资料高分辨率处理中的应用[J].石油物探,1996,35(2):44-53.
[38]易宗富.地震资料的保幅宽频高分辨率处理[J].油气地球物理,2006,4(3):13-18.
[39]冯智慧,王世煜,刘财,等.高分辨率地震信号瞬时特征分析方法[J].吉林大学学报,2007,37:82-85.
[40]高静怀,吴茜,陈文超,等.小波变换域地震资料瞬时频率分析方法[J].石油物探,2007,46(6):534-540.
[41]马朋善,王继强,刘来祥,等.Morlet小波分频处理在提高地震资料分辨率中的应用[J].石油物探,2007,46(3):283-287.
[42]卢新城,龚沈光,周骏,等.基于Morlet小波的高分辨率信号频谱估计[J].武汉理工大学学报,2002,26(5):632-635.
[43]高静怀,朱光明,汪文秉等.小波变换与地震资料谱白化[J],煤田地质与勘探,1997,6(3):44-48.
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[48]张进铎,杨平,王云雷.地震信息的谱分解技术及其应用[J].勘探地球物理进展,2006,29(4):235-238.
[49]杜世通.用地震反演技术实现资料高分辨率处理[J].油气地球物理,2004,2(2):59-65.
[50]杨贵祥.基于调谐频率与分频处理的高分辨率反演技术[J].石油物探,2006,45(3):242-244.
[51] Partyka G,Gridley J and Lopez J.Interpretational applications of spectral decomposition in reservoir characterization[J].The Leading Edge,1999.
[52]师学明,王家映.地球物理资料非线性反演方法讲座—模拟退火法[J].工程地球物理学报,2007,4(3):166-174.
[2]王西文.地震资料处理和解释中的小波分析方法[M].北京:石油工业出版社,2004.
[3]张贤达.现代信号处理[M].北京:清华大学出版社,2002.
[4]李振春,张军华.地震数据处理方法[M].北京:石油大学出版社,2004.
[5]牟永光,陈小宏,李国发,等.地震数据处理方法[M].北京:石油工业出版社,2007.
[6]俞寿朋.高分辨率地震勘探[M].北京:石油工业出版社,1993.
[7] Jianlei Liu.Spectral decomposition and its application in mapping stratigraphy and hydrocarbons[D].The Faculty of the Department of Geosciences University of Houston.
[8] Oleg Portniaguine and John Castagna.Inverse spectral decomposition[C].SEG Int’l Exposition and 7th Annual Meeting,10-15 October 2004.
[9] Charles I Puryear and John P Castagna.An algorithm for calculation of bed thickness and reflection coefficients from amplitude spectrum[C].SEG/New Orleans 2006 Annual Meeting.
[10] Chakraborty,A. and Okaya,D.Frequency-time decompositon of seismic data using wavelet based methods[J].Geophysics,1995.
[11] Castagna,J.p,S.Sun and R.W.Siegfried.Instantaneous spectral analysis:Detection of low-frequency shadows associated with hudrocarbons[J].The leading Edge,2003.
[12] Satinder Chopra,Jhon Castagna and Oleg Porniaguine.Seismic resolution and thin-bed reflectivity inversion[J].Cseg Recorder,2006.
[13] Sarinder Chopra,John Castagna and Oleg Porniaguine.Thin-bed reflectivity inversion[C].SEG/New Orleans 2006 Annual Meeting.
[14] Portniaguine,O.and J.P.Castagna.Spectral inversion:Lessons from modeling and Boonesville case study[C].75th SEG Meeting,2005.
[15] Charles I Puryear and John P Castagna.An algorithm for calculation of bed thickness and reflection coefficients from amplitude spectrum[C].SEG/New Orleans 2006 Annual Meeting.
[16] Gregory A.Partyka.Seismic Thickness Estimation:Three Approaches,Pros and Cons[C].SEG Int’l Exposition and Annual Meeting,2001.
[17] Greg Partyka,James Gridley and John Lopez.Interpretational application of spectral decomposition in reservoir characterization[J].The Leading Edge,1999.
[18]施云惠.一维连续小波变换[J].高等学校计算机数学学报,2007,29(1):1-6.
[19]高静怀,汪文秉,朱光明,等.地震资料处理中小波函数的选取研究[J].地球物理学报,1996,39(3):392-398.
[20]李世雄.小波变换及其应用[J].高等数学研究,2002,5(2):36-38.
[21]刘葵,刘招君,朱建伟.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):282-284.
[22]董建华,顾汉明,张星.几种时频分析方法的比较及应用[J].工程地球物理学报,2007,4(4):312-315.
[23]刘喜武,张宁,勾永峰,等.地震勘探信号时频分析方法对比与应用分析[J].地球物理学进展,2008,23(3):743-753.
[24]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[J].勘探地球物理进展,2004,27(4):246-250.
[25]陈洁.时频分析方法小结[J].中国水运,2009,9(2):87-89.
[26]陈学华.时频分布与地震信号谱分析研究[D].成都理工大学,2006.
[27]刘丽娟.时频分析技术及其应用[D].成都理工大学,2008.
[28]蔡希玲,吕英梅.地震数据时频分析与分频处理[J].勘探地球物理进展,2005,28(4):265-270.
[29]姜弢,刘庆普,胡留军.地震信号去噪的小波方法研究[J].哈尔滨工程大学学报,2002,23(4):86-90.
[30]王西文,高静怀,李幼铭.高分辨率地震资料处理中导数小波函数的构造[J].石油物探,2000,39(2):64-71.
[31]贾丽华,吴长江,刘小娟,等.地震资料高分辨率处理技术[J].石油物探,2002,41(4):484-488.
[32]盛怀洁,钟子发,吴彦华.连续小波变换中基小波的尺度伸缩与应用[J].无线电工程,1999,29(6):55-57.
[33]陈文超,高静怀,汪文秉,小波变换用于提高过井地震资料分辨率的方法研究[J].西安交通大学学报,1998,32(12):44-47.
[34]刘维国,杨兆进,郭惠娟,等.小波变换及其在地震资料处理中的应用[J].哈尔滨工业大学学报,1995,27(1):1-3.
[35]彭波,郭树祥,赵晨曦.高分辨率资料处理[J].勘探地球物理进展,2004,27(6):415-421.
[36]赵军龙,李娜.小波变换在高分辨率层序地层分析中的应用[J].地球物理学进展,2008,23(4):1230-1235.
[37]何光明,高如曾,韩德贵,等.小波变换在地震资料高分辨率处理中的应用[J].石油物探,1996,35(2):44-53.
[38]易宗富.地震资料的保幅宽频高分辨率处理[J].油气地球物理,2006,4(3):13-18.
[39]冯智慧,王世煜,刘财,等.高分辨率地震信号瞬时特征分析方法[J].吉林大学学报,2007,37:82-85.
[40]高静怀,吴茜,陈文超,等.小波变换域地震资料瞬时频率分析方法[J].石油物探,2007,46(6):534-540.
[41]马朋善,王继强,刘来祥,等.Morlet小波分频处理在提高地震资料分辨率中的应用[J].石油物探,2007,46(3):283-287.
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