高效ARMA模型高分辨率地震子波提取方法
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摘要
ARMA模型的最大优点是用较少的参数描述一个精确的子波,超定阶容易造成计算量大、运算速度慢,欠定阶不能满足精确子波描述的要求。针对高阶累积量对特殊切片敏感,且在短时数据下应用效果差的问题,本文采用基于自相关函数的奇异值分解(SVD)法确定AR模型阶数,同时将信息量准则法与高阶累积量法相结合,提出了一种新的MA模型定阶法。数值仿真和实际地震数据处理结果均表明,本文所用方法可有效地压制加性高斯色噪声,信息量准则法可有效提高MA定阶的准确率,在保证子波精度的同时尽可能降低模型阶数,实现运算高效率。
The most importantly advantage of ARMA(autoregressive moving average) model is to describe an exact wavelet with fewer parameters.Order over-determination easily leads to large calculation costs while order under-determination cannot meet the wavelet requirements.Higher-order cumulants are sensitive to special slices and it causes poor results with short time data series.This paper focuses on the model order determination.Singular value decomposition(SVD) based on autocorrelation function is exploded to determine the AR model order.Combining the information theoretic criteria method with the cumulant-based method,the author proposes a new MA model order determination method.Numerical simulations and real data processing show that additional Gaussian colored noise is suppressed,and the MA model order determination precision is improved by the information theoretic criteria method.With this approach,the wavelet gets high resolution and the model order number is reduced as much as possible in order to improve the computation efficiency.
The most importantly advantage of ARMA(autoregressive moving average) model is to describe an exact wavelet with fewer parameters.Order over-determination easily leads to large calculation costs while order under-determination cannot meet the wavelet requirements.Higher-order cumulants are sensitive to special slices and it causes poor results with short time data series.This paper focuses on the model order determination.Singular value decomposition(SVD) based on autocorrelation function is exploded to determine the AR model order.Combining the information theoretic criteria method with the cumulant-based method,the author proposes a new MA model order determination method.Numerical simulations and real data processing show that additional Gaussian colored noise is suppressed,and the MA model order determination precision is improved by the information theoretic criteria method.With this approach,the wavelet gets high resolution and the model order number is reduced as much as possible in order to improve the computation efficiency.
引文
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[3]Akaike H.Power spectrum estimation through au-toregressive model fitting.Annals of the Institute ofStatistical Mathematics,1969,21(1):407～419
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[5]王少水,戴永寿,王芳等.参数化地震子波估计模型定阶方法研究综述.地球物理学进展,2009,24(4):1405～1410Wang Shao-shui,Dai Yong-shou,Wang Fang et al.The summarization of the research on the order deter-mination of the seismic wavelet parameterized estima-tion model.Progress in Geophys(in Chinese),2009,24(4):1405～1410
[6]李振春,张军华.地震数据处理方法.山东东营:中国石油大学出版社,2004,1～109
[7]吴镇扬.数字信号处理.北京:高等教育出版社,2004
[8]张贤达.现代信号处理.北京:清华大学出版社,2002,263～334
[9]李翠萍,谢红卫.基于高阶累积量方法的非高斯非最小相位ARMA模型辨识.上海大学学报(自然科学版),2001,7(5):438～453Li Cui-ping,Xie Hong-wei.Identification of non-gaussian and non-Minimum phase ARMA modelsbased on Higher-Order cumulants.Journal ofShanghai University(Natural Science),2001,7(5):438～453
[10]Cadzow J A.Spectral estimation:An overdeterminedrational model equation approach.Proceedings of theIEEE,1982,70(9):907～939
[11]Giannakis G B,Mendel J M.Cumulant-based orderdetermination of non-Gaussian ARMA models,signalprocessing.IEEE on Transactions,1990,38(8):1411～1423
[12]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 Bin,Yin Cheng.Non-minimum phase seismicwavelet reconstruction based on higher order statis-tics.Chinese J Geophys(in Chinese),2001,44(3):404～410
[13]Zhang X D,Zhang Y S.Singular value decomposi-tion-based MA order determination of non-GaussianARMA model,signal processing.IEEE on Transac-tions,1993,41(8):2657～2664
[2]戴永寿,王俊岭,王伟伟等.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.地球物理学报,2008,51(6):1851～1859Dai Yong-shou,Wang Jun-ling,Wang Wei-wei et al.Seismic wavelet extraction via cumulant-based ARMAmodel approach with linear and nonlinear combina-tion.Chinese J Geophys(in Chinese),2008,51(6):1851～1859
[3]Akaike H.Power spectrum estimation through au-toregressive model fitting.Annals of the Institute ofStatistical Mathematics,1969,21(1):407～419
[4]Akaike H.A new look at the statistical model identifi-cation,Automatic Control.IEEE Transactions on,1974,19(6):716～723
[5]王少水,戴永寿,王芳等.参数化地震子波估计模型定阶方法研究综述.地球物理学进展,2009,24(4):1405～1410Wang Shao-shui,Dai Yong-shou,Wang Fang et al.The summarization of the research on the order deter-mination of the seismic wavelet parameterized estima-tion model.Progress in Geophys(in Chinese),2009,24(4):1405～1410
[6]李振春,张军华.地震数据处理方法.山东东营:中国石油大学出版社,2004,1～109
[7]吴镇扬.数字信号处理.北京:高等教育出版社,2004
[8]张贤达.现代信号处理.北京:清华大学出版社,2002,263～334
[9]李翠萍,谢红卫.基于高阶累积量方法的非高斯非最小相位ARMA模型辨识.上海大学学报(自然科学版),2001,7(5):438～453Li Cui-ping,Xie Hong-wei.Identification of non-gaussian and non-Minimum phase ARMA modelsbased on Higher-Order cumulants.Journal ofShanghai University(Natural Science),2001,7(5):438～453
[10]Cadzow J A.Spectral estimation:An overdeterminedrational model equation approach.Proceedings of theIEEE,1982,70(9):907～939
[11]Giannakis G B,Mendel J M.Cumulant-based orderdetermination of non-Gaussian ARMA models,signalprocessing.IEEE on Transactions,1990,38(8):1411～1423
[12]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 Bin,Yin Cheng.Non-minimum phase seismicwavelet reconstruction based on higher order statis-tics.Chinese J Geophys(in Chinese),2001,44(3):404～410
[13]Zhang X D,Zhang Y S.Singular value decomposi-tion-based MA order determination of non-GaussianARMA model,signal processing.IEEE on Transac-tions,1993,41(8):2657～2664
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