参数化地震子波估计模型定阶方法研究综述
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摘要
参数化模型地震子波提取中模型阶数的确定对子波提取的精度至关重要,笔者针对因果地震子渡MA、ARMA模型,总结了目前比较成熟的四类定阶方法:相关分析法、信息量准则法、线性代数法及基于优化算法的模型定阶方法,分析比较发现这些算法都存在不同程度的缺陷,只能在各自的适用范围内得到较好的定阶结果,针对算法在子波建模应用中的不足提出了改进建议;同时分析比较了基于高阶累积量的非因果系统模型定阶的各种方法,并对非因果地震子波模型定阶进行了展望.
The choice of the order in modeling the seismic wavelet is very vital for the precision of the wavelet extraction.Based on the hypothesis that the wavelet model is MA or ARAM model which is causal,the author summarizes four broad categories of order determination to the wavelet estimation model,i.e.,the correlation analyse method,the information criterion method,the linear algebra method and the optimization-based method.Theoretical analysis shows that these methods have different levels'limitations.We can only get good order determination in the methods' own applications.In view of the limitation of the above algorithms used in seismic wavelet estimation,the author puts forward recommendations for improvement.At the same time,the author analyses the different methods based on the high order cumulant of the order determination in the non-causal system model comparatively,and prospects for the order determination of the non-causal seismic wavelet model.
The choice of the order in modeling the seismic wavelet is very vital for the precision of the wavelet extraction.Based on the hypothesis that the wavelet model is MA or ARAM model which is causal,the author summarizes four broad categories of order determination to the wavelet estimation model,i.e.,the correlation analyse method,the information criterion method,the linear algebra method and the optimization-based method.Theoretical analysis shows that these methods have different levels'limitations.We can only get good order determination in the methods' own applications.In view of the limitation of the above algorithms used in seismic wavelet estimation,the author puts forward recommendations for improvement.At the same time,the author analyses the different methods based on the high order cumulant of the order determination in the non-causal system model comparatively,and prospects for the order determination of the non-causal seismic wavelet model.
引文
[1] 戴永寿,王俊岭,王伟伟,等.基于高阶累积量的ARMA模型地震子波提取方法研究[J].地球物理学报,2008,51(6) :1851-1859．Dai Y S,Wang J L,Wang W W,et al.Seismic wavelet extraction via cumulant-based ARMA model approach with linear and nonlinear combination[J].Geophys.(in Chinese),2008,51(6) :1851-1859．
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[3] 王晓鹏,曹广超等.基于Box-Jenkins方法的青男高原降水量时间序列分析建模与预测[J].数理统计与管理2008,27(4) :555-560．Wang X P,Cao G C,Ding S X.Time series Analysis and Forecast Model of Annual Rain-Fall on South of Qinghai Plateau Based on Box-Jenkins Methods[J].Application of Statistics and Management.2008,27(4) :555-560．
[4] 陈建奇,李金珊.国库资金模型构建与预测[J].山西财经大学学报[J].2007,29(5) :97-102．Chen J Q,Li J S,Predicting and Modeling the Treasury Funds[J].Journal of Shanxi Finance and Economics University.2007,29(5) :97-102．
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[13] Giannakis G B,Mendel J M. Cumulant-based order determination of non-Gaussian ARMA models[J].IEEE Trans.Signal Processing,1990,38:1411-1423．
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[19] Tan H Z,Chow T W S.Recursive scheme for ARMA coefficient and order estimation with noisy input-output data[J].IEEE,1999,146(2) :65-71．
[20] 谭洪舟,毛宗源.基于高阶统计特性的非高斯AR模型的阶次辨识[J].控制理论与应用,2000,17(2) :281-285．Tan H Z,Mao Z Y.Order Identification of Non-Gaussian AR Models Based on Higher-order Statistics[J].Control Theory and Applications,2000,17(2) :281-285．
[21] 郑明辉,蓝敏俐.高阶谱应用中模型定阶问题分析[J].机电技术,2007,(2) :21-23． Zheng M H,Lan M L.Application of high-end spectrum analysis model order determination[J].Electrical Technology,2007,(2) :21-23．
[22] 李亚峻,李月,高颖.基于双谱值和相位重构的地震子波提取[J].地球物理学进展,2007,22(3) :947-952．Li Y J,Li Y,Gao Y.A method of extracting seismic wavelet based on bispectrum amplitude and phase reconstruction[J].Progress in Geophysics,2007,22(3) :947-952．
[23] 章珂,张学工,刘贵忠.一种新的地震子波估计方法[J].信号处理,1998,14(9) :226-132．Zhang K,Zhang X G,Liu G Z.A new seismic wavelet estimation method[J].Signal Processing,1998,14(9) :226-132．
[24] 陈果.基于遗传算法的ARMA模型定阶新技术[J].机械工程学报,2005,41(1) :40-44．Chen G.A new technology of ARMA model order determination based on Genetic Algorithm[J].Chinese Journal of Mechanical Engineering,2005,41(1) :40-44．
[25] 赵锡凯,张贤达.基于最大峰度准则的非因果AR系统盲辨识[J].电子学报,1999,27(12) :126-128．Zhao X K,Zhang X D.Blind Identification of Noncausal AR System Based on Maximum Kurtosis Criteria[J].Arta Electronica Sinica,1999,27(12) :126-128．
[26] Tugnait J K.Fitting noncausal autoregressive signal plus noise model to noisy non-gaussian linear processes[J].IEEE Trans Automatic Control,1987,(6) :547-552．
[27] 陈滨宁,张贤达.基于倒谱的非因果自回归系统自适应辨识[J].清华大学学报,1997,37(9) :90-94．Chen B N,Zhang X D.Cepstrum-based non-causal adaptive autoregressive identification system[J].Journal of Tsinghua University,1997,37(9) :90-94．
[28] 李会方.非高斯信号的非因果非最小相位ARMA模型辨识[J].西北工业大学学报,1995,13(3) :418-423．Li H F.Non-causal non-minimum phase ARMA model identification of non-Gaussian signals[J].Journal of Northwestern Polytechnical University,1995,13(3) :418-423．
[29] Giannakis G B.On Estimating Noncausal Nonminimum Phase ARMA Models of Non-Gaussian Processes[J].IEEE,1990,38(3) :478-495．
[30] Tugnait,Counterexamples to“On Estimating Noncausal Nonminimum Phase ARMA Models of Non-Gaussian Processes”[J].IEEE,1992,40(4) :1011-1013．
[2] 袁三一,陈小宏.一种新的地震子波提取与层速度反演方法[J].地球物理学进展,2008,23(1) :198-205．Yuan S Y,Chen X H.A new method for seismic wavelet extraction and interval velocity inversion[J].Progress in Geophysics,2008,23(1) :198-205．
[3] 王晓鹏,曹广超等.基于Box-Jenkins方法的青男高原降水量时间序列分析建模与预测[J].数理统计与管理2008,27(4) :555-560．Wang X P,Cao G C,Ding S X.Time series Analysis and Forecast Model of Annual Rain-Fall on South of Qinghai Plateau Based on Box-Jenkins Methods[J].Application of Statistics and Management.2008,27(4) :555-560．
[4] 陈建奇,李金珊.国库资金模型构建与预测[J].山西财经大学学报[J].2007,29(5) :97-102．Chen J Q,Li J S,Predicting and Modeling the Treasury Funds[J].Journal of Shanxi Finance and Economics University.2007,29(5) :97-102．
[5] 芩冠军.ARIMA模型在小菜蛾幼虫种群动态中的应用[J].华南农业大学学报.2008,29(1) :109-113．Cen G J.The Application of ARIMA Model to the Larva’s Population Dynamic of Plutella xylostella[J].Journal of South China Agricultural University.2008,29(1) :109-113．
[6] Akaike H.Power spectrum estimation through autoregression model fitting[J].Ann.Inst.Stat.Math,1969,21:407-419．
[7] Akaike H.A new look at the statistical model identification[J].IEEE Trans.Automatic Contorl,1974,19:716-723．
[8] Kashyap R.Inconsistency of the AIC rule for estimating the order of autoregressive models[J].IEEE Trans.Automatic Control.1980 ,36:101-1012．
[9] Parzen E.Some recent advances in time series modeling[J].IEEE Trans.Automat.Contr.1974,19:723-730．
[10] Rissanen J.A universal prior for intergers and estimation by minimum descriptive lengt [J].Ann.Stat,1983,11:431-466．
[11] 胡基福,姜宏川,周庆满,等.自回归模型的最优定阶及其在长期预报中的应用[J].应用气象学报,1994,5(2) :196-202．Hu J F,Jiang H C,Zhou Q M,et al.Optimal autoregressive model order determination and its application in the application of long-term forecast[J].Quarterly Journal of Applied Meteorology.1994,5(2) :196-202．
[12] CadzowJ A.Spectral estimation:An overdetermined rational model equation approach[J].IEEE.1982,70(9) :907-939．
[13] Giannakis G B,Mendel J M. Cumulant-based order determination of non-Gaussian ARMA models[J].IEEE Trans.Signal Processing,1990,38:1411-1423．
[14] Zhang X D,Zhang Y S.Singular value decomposition-basedMA Order Determination of Non-Gaussian ARMA Model[J].IEEE transactions on signal processing,1993,41(8) :2657-2664．
[15] Chan Y T,JAMES C.WOOD.A New Order Determination Technique for ARMA Processes[J].IEEE,1984,32(3) :517-521．
[16] Liang G,Wilkes D M,Cadzow J A.ARMA model order estimation based on the eigenvalues of the covariance Matrix[J].IEEE Trans.on Signal Processing,1993,41(10) :3003-3009．
[17] Al-Smadi A,Wilkes D W.On estimating ARMA model orders[J].IEEE.1996,20(2) :505-508．
[18] Davila C E,Chiang H L.An algorithm for pole-zero system model order estimation[J].IEEE Trans.Signal Processing.1995,43:1013-1016．
[19] Tan H Z,Chow T W S.Recursive scheme for ARMA coefficient and order estimation with noisy input-output data[J].IEEE,1999,146(2) :65-71．
[20] 谭洪舟,毛宗源.基于高阶统计特性的非高斯AR模型的阶次辨识[J].控制理论与应用,2000,17(2) :281-285．Tan H Z,Mao Z Y.Order Identification of Non-Gaussian AR Models Based on Higher-order Statistics[J].Control Theory and Applications,2000,17(2) :281-285．
[21] 郑明辉,蓝敏俐.高阶谱应用中模型定阶问题分析[J].机电技术,2007,(2) :21-23． Zheng M H,Lan M L.Application of high-end spectrum analysis model order determination[J].Electrical Technology,2007,(2) :21-23．
[22] 李亚峻,李月,高颖.基于双谱值和相位重构的地震子波提取[J].地球物理学进展,2007,22(3) :947-952．Li Y J,Li Y,Gao Y.A method of extracting seismic wavelet based on bispectrum amplitude and phase reconstruction[J].Progress in Geophysics,2007,22(3) :947-952．
[23] 章珂,张学工,刘贵忠.一种新的地震子波估计方法[J].信号处理,1998,14(9) :226-132．Zhang K,Zhang X G,Liu G Z.A new seismic wavelet estimation method[J].Signal Processing,1998,14(9) :226-132．
[24] 陈果.基于遗传算法的ARMA模型定阶新技术[J].机械工程学报,2005,41(1) :40-44．Chen G.A new technology of ARMA model order determination based on Genetic Algorithm[J].Chinese Journal of Mechanical Engineering,2005,41(1) :40-44．
[25] 赵锡凯,张贤达.基于最大峰度准则的非因果AR系统盲辨识[J].电子学报,1999,27(12) :126-128．Zhao X K,Zhang X D.Blind Identification of Noncausal AR System Based on Maximum Kurtosis Criteria[J].Arta Electronica Sinica,1999,27(12) :126-128．
[26] Tugnait J K.Fitting noncausal autoregressive signal plus noise model to noisy non-gaussian linear processes[J].IEEE Trans Automatic Control,1987,(6) :547-552．
[27] 陈滨宁,张贤达.基于倒谱的非因果自回归系统自适应辨识[J].清华大学学报,1997,37(9) :90-94．Chen B N,Zhang X D.Cepstrum-based non-causal adaptive autoregressive identification system[J].Journal of Tsinghua University,1997,37(9) :90-94．
[28] 李会方.非高斯信号的非因果非最小相位ARMA模型辨识[J].西北工业大学学报,1995,13(3) :418-423．Li H F.Non-causal non-minimum phase ARMA model identification of non-Gaussian signals[J].Journal of Northwestern Polytechnical University,1995,13(3) :418-423．
[29] Giannakis G B.On Estimating Noncausal Nonminimum Phase ARMA Models of Non-Gaussian Processes[J].IEEE,1990,38(3) :478-495．
[30] Tugnait,Counterexamples to“On Estimating Noncausal Nonminimum Phase ARMA Models of Non-Gaussian Processes”[J].IEEE,1992,40(4) :1011-1013．
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