基于高阶累积量ARMA模型线性非线性结合的地震子波提取方法研究
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摘要
在地震子波非因果、混合相位的假设下,本文应用自回归滑动平均(ARMA)模型对地震子波进行参数化建模,并提出利用线性(矩阵方程法)和非线性(ARMA拟合方法)相结合的参数估计方式对该模型进行参数估计.在利用矩阵方程法确定模型参数范围的基础上,利用累积量拟合法精确估计参数.理论分析和仿真结果表明,该方式有较好的适应性:一方面提高了子波估计精度,避免单独使用矩阵方程法在短数据地震记录情况下可能带来的估计误差;另一方面提高了子波提取运算效率,降低了ARMA模型拟合方法参数范围确定的复杂性,避免了单纯使用滑动平均(MA)模型拟合法估计过多参数所导致的运算规模过大问题.初步应用结果表明该方法是有效可行的.
ARMA model was used to describe the seismic wavelet on the assumption that the seismic wavelet is non-causal and mixed phase.A cumulant-based parametric estimation approach was proposed to estimate the wavelet parameters which synthesized both the linear(matrix equation) and nonlinear(cumulant matching) methods.In this approach,the cumulant matching approach is used for accurate parameter estimation,on the basis of the initial guess generated from matrix equations.Theoretic analysis and numerical simulation demonstrate the feasibility of the approach.Compared with the potential computational error of the linear methods,this approach can improve parameter estimation precision.Moreover,it extracts wavelet with high computational efficiency by avoiding the use of cumulant matching method under MA model description,and reduces the complexity of initial guess via ARMA model matching approach.The preliminary application results show that this approach is effective and feasible.
ARMA model was used to describe the seismic wavelet on the assumption that the seismic wavelet is non-causal and mixed phase.A cumulant-based parametric estimation approach was proposed to estimate the wavelet parameters which synthesized both the linear(matrix equation) and nonlinear(cumulant matching) methods.In this approach,the cumulant matching approach is used for accurate parameter estimation,on the basis of the initial guess generated from matrix equations.Theoretic analysis and numerical simulation demonstrate the feasibility of the approach.Compared with the potential computational error of the linear methods,this approach can improve parameter estimation precision.Moreover,it extracts wavelet with high computational efficiency by avoiding the use of cumulant matching method under MA model description,and reduces the complexity of initial guess via ARMA model matching approach.The preliminary application results show that this approach is effective and feasible.
引文
[1]梁光河.地震子波的时变与短程微曲多次反射.石油物探,1997,36(3):18~27Liang G H.The ti me-variant seismic wavelet and the peg-legmultiple.Geophysical Prospecting for Petroleum(inChinese),1997,36(3):18~27
[2]O′Doherty R F,Anstey N A.Reflections on amplitudes.Geophysical Procpecting,1971,19:430~458
[3]Banik N C,Lerche L,Shuey R T.Stratigraphic filtering,Part I:Derivation of the O′Doherty-Anstey formula.Geophysics,1985,50(12):2768~2774
[4]Serguei A,Zien H.The O′Doherty-Anstey formula andlocalization of seismic wave.Geophysics,1993,58(5):736~740
[5]张贤达.现代信号处理(第二版).北京:清华大学出版社,2002.263~308Zhang X D.Model Signal Processing(Second edition).Beijing:Tsinghua University Press,2002.263~308
[6]Lazear G D.Mixed-phase wavelet esti mation using fourth-order cumulants.Geophysics,1993,58(7):1042~1051
[7]Velis D R,Ulrych T J.Si mulated annealing waveletesti mation via fourth-order cumulant matching.Geophysics,1996,61(6):1939~1948
[8]梁光河.地震子波提取方法研究.石油物探,1998,37(1):31~39Liang G H.On the methods of seismic wavelet extraction.Geophysical Prospecting for Petroleum(in Chinese),1998,37(1):31~39
[9]唐斌,尹成.基于高阶统计的非最小相位地震子波恢复.地球物理学报,2001,44(3):404~410Tang B,Yin C.Non-mini mum phase seismic waveletreconstruction based on higher order statistics.Chinese J.Geophys.(in Chinese),2001,44(3):404~410
[10]戴永寿,魏磊,霍志勇.基于高阶累积量的线性化子波提取方法研究.中国石油大学学报,2006,30(4):24~29Dai Y S,Wei L,Huo Z Y.Research on wavelet extractionvia linear equation approach based on higher-order cumulant.Journal of China University of Petroleum(in Chinese),2006,30(4):24~29
[11]Giannakis G B,Swami A.On esti mating non-causal non-mini mum phase ARMA models of non-Gaussian process.IEEE Transactions on Acoustics,Speech,and SignalProcessing,1990,38(3):478~495
[12]陈滨宁,张贤达.高斯ARMA噪声中非因果非最小相位系统的辨识.电子学报,1996,24(4):24~28Chen B N,Zhang X D.Identification of a non-causal non-mini mum phase system in a Gaussian ARMA noise.ActaElectronica Sinica(in Chinese),1996,24(4):24~28
[13]Tugnait J K.Parameter esti mation for noncausal ARMAmodels of non-Gaussian signal via cumulant matching.IEEETransaction on Signal Processing,1995,43(4):886~893
[14]杨文采.地球物理反演的遗传算法.石油物探,1995,34(1):116~122Yang W C.Genetic algorithm for geophysical inversion.Geophysical Prospect for Petroleum(in Chinese),1995,34(1):122~130
[15]师学明,王家映,易远元等.一种新的地球物理反演方法—模拟原子跃迁反演法.地球物理学报,2007,50(1):305~312Shi X M,Wang J Y,Yi Y Y,et al.Astudy onthe si mulatedatomic transition algorithmfor geophysical inversion.ChineseJ.Geophys.(in Chinese),2007,50(1):305~312
[16]师学明,王家映,张胜业等.多尺度逐次逼近遗传算法反演大地电磁资料.地球物理学报,2000,43(1):122~130Shi X M,Wang J Y,Zhang S Y,et al.Multi-scale GeneticAlgorithmandits applicationin magnetotelluric sounding datainversion.Chinese J.Geophys.(in Chinese),2000,43(1):122~130
[17]杨文采.非线性地球物理反演方法:回顾与展望.地球物理学进展,2002,17(2):255~261Yang WC.Non-linear geophysical inversion methods:reviewand perspective.Process in Geophysics(in Chinese),2002,17(2):255~261
[18]王家映.地球物理资料非线性反演方法讲座(一):地球物理反演问题概述.工程地球物理学报,2007,4(1):1~3Wang J Y.Lecture on non-linear inverse methods ingeophysics(1):introduction to geophysical inverse problems.Chinese Journal of Engineering Geophysics(in Chinese),2007,4(1):1~3
[2]O′Doherty R F,Anstey N A.Reflections on amplitudes.Geophysical Procpecting,1971,19:430~458
[3]Banik N C,Lerche L,Shuey R T.Stratigraphic filtering,Part I:Derivation of the O′Doherty-Anstey formula.Geophysics,1985,50(12):2768~2774
[4]Serguei A,Zien H.The O′Doherty-Anstey formula andlocalization of seismic wave.Geophysics,1993,58(5):736~740
[5]张贤达.现代信号处理(第二版).北京:清华大学出版社,2002.263~308Zhang X D.Model Signal Processing(Second edition).Beijing:Tsinghua University Press,2002.263~308
[6]Lazear G D.Mixed-phase wavelet esti mation using fourth-order cumulants.Geophysics,1993,58(7):1042~1051
[7]Velis D R,Ulrych T J.Si mulated annealing waveletesti mation via fourth-order cumulant matching.Geophysics,1996,61(6):1939~1948
[8]梁光河.地震子波提取方法研究.石油物探,1998,37(1):31~39Liang G H.On the methods of seismic wavelet extraction.Geophysical Prospecting for Petroleum(in Chinese),1998,37(1):31~39
[9]唐斌,尹成.基于高阶统计的非最小相位地震子波恢复.地球物理学报,2001,44(3):404~410Tang B,Yin C.Non-mini mum phase seismic waveletreconstruction based on higher order statistics.Chinese J.Geophys.(in Chinese),2001,44(3):404~410
[10]戴永寿,魏磊,霍志勇.基于高阶累积量的线性化子波提取方法研究.中国石油大学学报,2006,30(4):24~29Dai Y S,Wei L,Huo Z Y.Research on wavelet extractionvia linear equation approach based on higher-order cumulant.Journal of China University of Petroleum(in Chinese),2006,30(4):24~29
[11]Giannakis G B,Swami A.On esti mating non-causal non-mini mum phase ARMA models of non-Gaussian process.IEEE Transactions on Acoustics,Speech,and SignalProcessing,1990,38(3):478~495
[12]陈滨宁,张贤达.高斯ARMA噪声中非因果非最小相位系统的辨识.电子学报,1996,24(4):24~28Chen B N,Zhang X D.Identification of a non-causal non-mini mum phase system in a Gaussian ARMA noise.ActaElectronica Sinica(in Chinese),1996,24(4):24~28
[13]Tugnait J K.Parameter esti mation for noncausal ARMAmodels of non-Gaussian signal via cumulant matching.IEEETransaction on Signal Processing,1995,43(4):886~893
[14]杨文采.地球物理反演的遗传算法.石油物探,1995,34(1):116~122Yang W C.Genetic algorithm for geophysical inversion.Geophysical Prospect for Petroleum(in Chinese),1995,34(1):122~130
[15]师学明,王家映,易远元等.一种新的地球物理反演方法—模拟原子跃迁反演法.地球物理学报,2007,50(1):305~312Shi X M,Wang J Y,Yi Y Y,et al.Astudy onthe si mulatedatomic transition algorithmfor geophysical inversion.ChineseJ.Geophys.(in Chinese),2007,50(1):305~312
[16]师学明,王家映,张胜业等.多尺度逐次逼近遗传算法反演大地电磁资料.地球物理学报,2000,43(1):122~130Shi X M,Wang J Y,Zhang S Y,et al.Multi-scale GeneticAlgorithmandits applicationin magnetotelluric sounding datainversion.Chinese J.Geophys.(in Chinese),2000,43(1):122~130
[17]杨文采.非线性地球物理反演方法:回顾与展望.地球物理学进展,2002,17(2):255~261Yang WC.Non-linear geophysical inversion methods:reviewand perspective.Process in Geophysics(in Chinese),2002,17(2):255~261
[18]王家映.地球物理资料非线性反演方法讲座(一):地球物理反演问题概述.工程地球物理学报,2007,4(1):1~3Wang J Y.Lecture on non-linear inverse methods ingeophysics(1):introduction to geophysical inverse problems.Chinese Journal of Engineering Geophysics(in Chinese),2007,4(1):1~3
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