高阶统计量方法在地球物理学中的应用与展望
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摘要
高阶统计量方法是研究非高斯过程,非线性系统和非最小相位信号的有力工具。一些使用相关函数或功率谱进行分析与处理而得不到满意结果的问题都可以使用高阶统计量方法。本文介绍了高阶统计量在地球物理学中的应用现状。
Higher-order statistics is a useful tool for studying non-Gaussian processes,nonlinear systems and non-minimum phase systems.Some problems,which cannot be solved satisfactorily using power spectrum or correlation functions,can be worthy of using higher-order statistics method.In this paper,the main theoretical results about applications of high-order statistics in geophysics are summarized.
Higher-order statistics is a useful tool for studying non-Gaussian processes,nonlinear systems and non-minimum phase systems.Some problems,which cannot be solved satisfactorily using power spectrum or correlation functions,can be worthy of using higher-order statistics method.In this paper,the main theoretical results about applications of high-order statistics in geophysics are summarized.
引文
[1]Rosenblatt M,Van Ness J W.Estimation of the bispeetrum[J].Ann.Math.Statist.,1965,36(1):1120-1136.
[2]Brillinger D R.An introduction tO polyspectra[J].Ann.Math.Statist.,1965,36(1):1351-1374.
[3]王书明,等.地球物理学中的高阶统计量方法[M].北京:科学出版社,2006.
[4]李宏伟,程乾生.高阶统计量与随机信号分析[M].武汉:中国地质大学出版社,2002.
[5]张贤达.时间序列分析——高阶统计量方法[M].北京:清华大学出版社,1996.
[6]尹成,伍志明,邓怀群,等.高阶统计计量方法在地震勘探中的应用[J].地球物理学进展.2003,18(3):546-550.
[7]Mendel J M.Optimal Seismic Deconvolution.An Estimation Based Approach[M].NewYork:Academic Press,1983.
[8]Lazear G L.Mixed-phase wavelet estimation using fourth order cu-mulants[J].Geophysics,1993,7:1042-1051.
[9]Velis D R,ulrych Tj.Simulated annealing wavelet estimation via fourth-order cumulant matching[J].Geophysics,1996,61(6):1939-1948.
[10]Liang G H,Cai X P,Li Q Y.Using high-order cumulants to ex-trapolate spatially variant seismic wavelets[J].Geophyscis,2002,67(6):1869-1876.
[11]尹成,唐兵,谢桂生.地震子波估计——高阶累积量矩阵方程法[J].信号处理,2000,16(增刊):83-87.
[12]Matsuoka T,Ulrych T J.Phase estimation using the bispectrum[J].Proc.IEEE,1984,72:1403-1411.
[13]Pan R,Nikias C L.Phase reconstruction in the trispectrum do-main[J].IEEE Trans.Acoustics Speech,Signal Processing,1987,35:895-897.
[14]Sundaramoorthy G,Raghuveer MR,Dianat S A.Bispectral recon-struction of signals in noise:Amplitude reconstruction issues[J].IEEE Trans.Acoustics Speech,Signal Processing,1990,38:1297-1306.
[15]石玉梅,刘天放,谢桂生.一种断层解释的新方法.双相干相关法[J].煤炭学报,2000,25(2):117-121.
[16]石玉梅,刘天放,谢桂生.三阶累计量法在断层检测和落差估算中的应用[J].地质与勘探,2001,37(4):73-75.
[17]谢桂生,石玉梅.双相干相关法在断层解释及落差估算中的应用[J].石油地球物理勘探,2000,35(6):719-722.
[18]熊晓军,贺振华,尹成,等.高阶统计量在油气地球物理勘探中的新应用[J].地质科技情报,2005,24(2):78-84.
[19]Nikias C L,Raghuveer M R.Bispectrum estimation:a digital sig-nal processing framework[J].IEEE,1987,75(5):869-891.
[20]Mendel J M,Tutorial on higher-order statistics in signal and sys-tem theory:theoretical results and some applications,process[J].IEEE,1991,79(3):278-305.
[21]杜宁平,史军,朱红涛,等.高阶统计量分析在油气预测中的应用[J].海洋地质动态,2004,20(8):27-29.
[22]Tugnait J K.Time delay estimation with unknown spatially corre-lated gaussian noise[J].IEEE Trans.Acoustics apeech,SignalProcessing,1993,41:549-558.
[23]Giannakis G B,Mendel J M.Identification of nonminimum phase systems using higher-order statistics[J].IEEE Trans.Acoustics Speech,Signal Processing,1989,37:360-377.
[24]Tugnait J K.Newresults on FIR system identification using gigher order statistics[J].IEEE Trans.Acoustics apeech,Signal Pro-cessing,1994,42(10):2854-2858.
[25]王书明,王家映.大地电磁信号统计特征分析[J].地震学报,2004,26(6):669-674.
[26]王书明,王家映.高阶统计量对大地电磁测深资料处理方法的改进[J].石油地球物理勘探,2004,39(增刊):1-3.
[27]王书明,王家映.利用高阶谱重构功率谱抑制高斯有色噪声[J].科学技术与工程,2004,4(2):69-73.
[28]Tugnait J K.Time delay estimation with unknown spatially corre-lated Gaussian noise[J].IEEE Trans.Acoustics apeech,Signal Processing,1993:41:549-558.
[29]邢贞贞,韩立国,王宇,等.高阶统计量方法在地震信号分析中的应用[J].吉林大学学报,2007,37(增刊):139-142.
[30]Yung S K,Ikellez L T.An example of seismic time picking by third-order bicoherence[J].Geophysics,1997,62(6):1947-1951.
[31]周彦文,刘希强.地震事件自动检测新方法[J].西北地震学报,2008年,30(2):102-106.
[32]刘希强,周彦文,曲均浩,等.应用单台垂向记录进行区域地震事件实时检测和直达P波初动自动识别[J].地震学报,2009,31(3):260-271.
[33]刘希强,周彦文,李红,等.双谱估计在地震前兆数字化资料分析中的应用[J].西北地震学报,2007,29(3):201-206.
[34]杨涛,刘庆生,付媛媛,等.泾阳MS4.8地震磁效应的高阶统计量方法研究[J].地震,2005,25(1):97-102.
[35]张贤达.时间序列分析一高阶统计量方法[M].北京:清华大学出版社,1996.
[36]杨字山,李媛嫒,刘天佑.高阶统计量在地震弱信号及"磁亮点"识别中的应用[J].石油地球物理学报,2005,40(1):103-107.
[37]杨字山,等.高阶统计量弱信号识别方法在识别地质孔洞中的应用[J].长江科学院院报.2005,22(4):30-33.
[38]张浩,赵正予,谢树果,等.地磁脉动信号的双谱分析[J].武汉大学学报(理学版),2001,47(3):351-354.
[39]孙骏,陈淑珍,邹炼.Wigner高阶矩谱在分析相控阵探地雷达数据中的应用[J].武汉大学学报(理学版),2004,50(5):637-640.
[2]Brillinger D R.An introduction tO polyspectra[J].Ann.Math.Statist.,1965,36(1):1351-1374.
[3]王书明,等.地球物理学中的高阶统计量方法[M].北京:科学出版社,2006.
[4]李宏伟,程乾生.高阶统计量与随机信号分析[M].武汉:中国地质大学出版社,2002.
[5]张贤达.时间序列分析——高阶统计量方法[M].北京:清华大学出版社,1996.
[6]尹成,伍志明,邓怀群,等.高阶统计计量方法在地震勘探中的应用[J].地球物理学进展.2003,18(3):546-550.
[7]Mendel J M.Optimal Seismic Deconvolution.An Estimation Based Approach[M].NewYork:Academic Press,1983.
[8]Lazear G L.Mixed-phase wavelet estimation using fourth order cu-mulants[J].Geophysics,1993,7:1042-1051.
[9]Velis D R,ulrych Tj.Simulated annealing wavelet estimation via fourth-order cumulant matching[J].Geophysics,1996,61(6):1939-1948.
[10]Liang G H,Cai X P,Li Q Y.Using high-order cumulants to ex-trapolate spatially variant seismic wavelets[J].Geophyscis,2002,67(6):1869-1876.
[11]尹成,唐兵,谢桂生.地震子波估计——高阶累积量矩阵方程法[J].信号处理,2000,16(增刊):83-87.
[12]Matsuoka T,Ulrych T J.Phase estimation using the bispectrum[J].Proc.IEEE,1984,72:1403-1411.
[13]Pan R,Nikias C L.Phase reconstruction in the trispectrum do-main[J].IEEE Trans.Acoustics Speech,Signal Processing,1987,35:895-897.
[14]Sundaramoorthy G,Raghuveer MR,Dianat S A.Bispectral recon-struction of signals in noise:Amplitude reconstruction issues[J].IEEE Trans.Acoustics Speech,Signal Processing,1990,38:1297-1306.
[15]石玉梅,刘天放,谢桂生.一种断层解释的新方法.双相干相关法[J].煤炭学报,2000,25(2):117-121.
[16]石玉梅,刘天放,谢桂生.三阶累计量法在断层检测和落差估算中的应用[J].地质与勘探,2001,37(4):73-75.
[17]谢桂生,石玉梅.双相干相关法在断层解释及落差估算中的应用[J].石油地球物理勘探,2000,35(6):719-722.
[18]熊晓军,贺振华,尹成,等.高阶统计量在油气地球物理勘探中的新应用[J].地质科技情报,2005,24(2):78-84.
[19]Nikias C L,Raghuveer M R.Bispectrum estimation:a digital sig-nal processing framework[J].IEEE,1987,75(5):869-891.
[20]Mendel J M,Tutorial on higher-order statistics in signal and sys-tem theory:theoretical results and some applications,process[J].IEEE,1991,79(3):278-305.
[21]杜宁平,史军,朱红涛,等.高阶统计量分析在油气预测中的应用[J].海洋地质动态,2004,20(8):27-29.
[22]Tugnait J K.Time delay estimation with unknown spatially corre-lated gaussian noise[J].IEEE Trans.Acoustics apeech,SignalProcessing,1993,41:549-558.
[23]Giannakis G B,Mendel J M.Identification of nonminimum phase systems using higher-order statistics[J].IEEE Trans.Acoustics Speech,Signal Processing,1989,37:360-377.
[24]Tugnait J K.Newresults on FIR system identification using gigher order statistics[J].IEEE Trans.Acoustics apeech,Signal Pro-cessing,1994,42(10):2854-2858.
[25]王书明,王家映.大地电磁信号统计特征分析[J].地震学报,2004,26(6):669-674.
[26]王书明,王家映.高阶统计量对大地电磁测深资料处理方法的改进[J].石油地球物理勘探,2004,39(增刊):1-3.
[27]王书明,王家映.利用高阶谱重构功率谱抑制高斯有色噪声[J].科学技术与工程,2004,4(2):69-73.
[28]Tugnait J K.Time delay estimation with unknown spatially corre-lated Gaussian noise[J].IEEE Trans.Acoustics apeech,Signal Processing,1993:41:549-558.
[29]邢贞贞,韩立国,王宇,等.高阶统计量方法在地震信号分析中的应用[J].吉林大学学报,2007,37(增刊):139-142.
[30]Yung S K,Ikellez L T.An example of seismic time picking by third-order bicoherence[J].Geophysics,1997,62(6):1947-1951.
[31]周彦文,刘希强.地震事件自动检测新方法[J].西北地震学报,2008年,30(2):102-106.
[32]刘希强,周彦文,曲均浩,等.应用单台垂向记录进行区域地震事件实时检测和直达P波初动自动识别[J].地震学报,2009,31(3):260-271.
[33]刘希强,周彦文,李红,等.双谱估计在地震前兆数字化资料分析中的应用[J].西北地震学报,2007,29(3):201-206.
[34]杨涛,刘庆生,付媛媛,等.泾阳MS4.8地震磁效应的高阶统计量方法研究[J].地震,2005,25(1):97-102.
[35]张贤达.时间序列分析一高阶统计量方法[M].北京:清华大学出版社,1996.
[36]杨字山,李媛嫒,刘天佑.高阶统计量在地震弱信号及"磁亮点"识别中的应用[J].石油地球物理学报,2005,40(1):103-107.
[37]杨字山,等.高阶统计量弱信号识别方法在识别地质孔洞中的应用[J].长江科学院院报.2005,22(4):30-33.
[38]张浩,赵正予,谢树果,等.地磁脉动信号的双谱分析[J].武汉大学学报(理学版),2001,47(3):351-354.
[39]孙骏,陈淑珍,邹炼.Wigner高阶矩谱在分析相控阵探地雷达数据中的应用[J].武汉大学学报(理学版),2004,50(5):637-640.
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