短时傅立叶变换与Wigner-Ville分布联合确定地震信号瞬时频率
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摘要
地震信号属于非平稳信号,利用短时傅立叶变换对地震信号进行时频分析时会受窗口大小的影响,利用Wigner-Ville分布的方法时会产生交叉项。基于这些原因,提出了把二者结合起来的方法计算时频分布,并且利用时频剖面得到信号的瞬时频率。从理论数据出发,分别计算利用短时傅立叶变换、Wigner-Ville及二者结合得到的时频剖面。通过比较得出:2类方法联合后获取的瞬时频率与原始的瞬时频率最接近,说明二者结合的方法对获取瞬时频率更有效。
Seismic signal is non-stable signal.The time-frequency analysis result of short-time Fourier transform is affected by the window size.The time-frequency analysis result of Wigner-Ville is affected by the cross part.Based on the advantage and disadvantage of linear time-frequency method and non-linear time-frequency method,the author proposes to obtain the time-frequency profile using the method of combination for linear time-frequency and non-linear time-frequency method.Then the instantaneous frequency can be obtained in the time-frequency profile.The author computes the time-frequency distribution using the short-time Fourier transform method,Wigner-Ville method and the combination of short-time Fourier transform and Wigner-Ville method for theoretical data.A comparison indicates that the result of combination of short-time Fourier transform and Wigner-Ville method is very close to the theoretical instantaneous frequency.The method is effective for computing instantaneous frequency.
Seismic signal is non-stable signal.The time-frequency analysis result of short-time Fourier transform is affected by the window size.The time-frequency analysis result of Wigner-Ville is affected by the cross part.Based on the advantage and disadvantage of linear time-frequency method and non-linear time-frequency method,the author proposes to obtain the time-frequency profile using the method of combination for linear time-frequency and non-linear time-frequency method.Then the instantaneous frequency can be obtained in the time-frequency profile.The author computes the time-frequency distribution using the short-time Fourier transform method,Wigner-Ville method and the combination of short-time Fourier transform and Wigner-Ville method for theoretical data.A comparison indicates that the result of combination of short-time Fourier transform and Wigner-Ville method is very close to the theoretical instantaneous frequency.The method is effective for computing instantaneous frequency.
引文
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[9]刘喜武,张宁,勾永峰,等.地震勘探信号时频分析方法对比及应用研究[J].地球物理学进展,2008,23(3):743-753.LIU Xi-wu.ZHANG Ning,GOU Yong-feng.The comparison and application of time-frequency analysis methods to seismicsignal[J].Progress in Geophysics.2008,23(3):743-753.
[10]杨海涛,朱仕军,文中平,等.基于Wigner-Ville的谱分解效果分析[J].勘探地球物理进展,2009,32(1):37-39.YANG Hai-tao,ZHU Shi-jun,WEN Zhong-ping,et al.Effect analysis of spectral decomposition based on Wigner-Ville distri-bution[J].Progress in Exploration Geophysics.2009,32(1):37-39.
[2]Taner M T,Koehler F,Sheriff R E.Complex seismic trace analysis[J].Geophysics,1979,44(6):1 041-1 063.
[3]张贤达,保铮.非平稳信号分析与处理[M].北京:国防工业出版社,1998.ZHANG Xian-da,BAO Zheng.Nonstationary signal analysis and processing[M].Beijing:,National Defence Press,1998.
[4]张贤达.现代信号处理[M].北京:清华大学出版社,2002.ZHANG Xian-da.Modern signal processing[M].Beijing:Tsinghua University Press,2002.
[5]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.GAO Jing-huai,WU Qian,CHEN Wen-chao,et al.Instantaneous frequency analysis of seismic data in wavelet transform do-main[J].Geophysical Prospecting for Petroleum,2007,46(6):534-540.
[6]赵淑红,朱光明.用小波变换谱均衡法提高地震资料的分辨率[J].西安科技大学学报,2007,27(2):255-259.ZHAO Shu-hong,ZHU Guang-ming.Using combined method of wavelet transform and spectrum equalization to improve seis-mic data resolution[J].Journal of Xi′an University of Science and Technology,2007,27(2):255-259.
[7]赵淑红,王璇.S变换时频滤波与其它滤波方法比较[J].西北地震学报,2007,29(3):224-229.ZHAO Shu-hong,WANG Xuan.Comparison between the time-frequency filtering of S transform method and other filter method[J].Northwestern Seismological Journal,2007,29(3):224-229.
[8]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.ZOU Hong-xing,ZHOU Xiao-bo,LI Yan-da.Time-frequency analysis-a survey[J].ACTA Electronica SINICA,2000,28(9):78-84.
[9]刘喜武,张宁,勾永峰,等.地震勘探信号时频分析方法对比及应用研究[J].地球物理学进展,2008,23(3):743-753.LIU Xi-wu.ZHANG Ning,GOU Yong-feng.The comparison and application of time-frequency analysis methods to seismicsignal[J].Progress in Geophysics.2008,23(3):743-753.
[10]杨海涛,朱仕军,文中平,等.基于Wigner-Ville的谱分解效果分析[J].勘探地球物理进展,2009,32(1):37-39.YANG Hai-tao,ZHU Shi-jun,WEN Zhong-ping,et al.Effect analysis of spectral decomposition based on Wigner-Ville distri-bution[J].Progress in Exploration Geophysics.2009,32(1):37-39.
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