线性Errors-in-Variables模型在确定汶川地震主震断层面中的应用
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摘要
首先介绍线性Errors-in-Variables模型,给出求解回归系数的奇异值分解(SVD)算法和MATLAB源代码,其次指出在模型中所有变量均具有不可忽略的误差时,全最小二乘法得到回归系数估计更接近于模型中的真实系数,并通过理论分析和计算机仿真说明了这一结果,最后将线性模型和算法用于确定汶川大地震主震断层面,取得了与震源机制解一致的结果,说明了模型和算法的有效性。
At first,the linear errors-in-variables model is introduced,the algorithm of singular value decomposition method and its MATLAB code for parameters estimation of the linear model coefficient is given.Subsequently,the theory analysis,numerical experimentations and figures verified the validity of the linear errors-in-variables model when all the random errors of variables in linear model can't be neglected.At last,the linear errors-in-variables model is employed for determination fault plane parameters of Wenchuan earthquake and the results is much closed to focal mechanism solution which show that the model and the algorithm is valid.
At first,the linear errors-in-variables model is introduced,the algorithm of singular value decomposition method and its MATLAB code for parameters estimation of the linear model coefficient is given.Subsequently,the theory analysis,numerical experimentations and figures verified the validity of the linear errors-in-variables model when all the random errors of variables in linear model can't be neglected.At last,the linear errors-in-variables model is employed for determination fault plane parameters of Wenchuan earthquake and the results is much closed to focal mechanism solution which show that the model and the algorithm is valid.
引文
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[2]Markovsky I,Huffel V S.Overview of total least-squares methods[J].IEEE Trans.Signal Processing, 2007,87(10):2283-2302.
[3]Fuller A W.Measurement Error Model[M].New York:John Wiley,1987.
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[6]程龙生.基于errors-in-variables的预测模型及其应用[J].数理统计与管理,2005,24(2):55-59.
[7]Anderson T W.The 1982 WALD memorial lectures:Estimating linear statistical relationship[J]. The Annals Statistics,1984,12(1):1-45.
[8]刘瑞丰,陈运泰,任枭等.中国地震台网震级的对比[J].地震学报,2007,29(5):467-476.
[9]胡玉锁,陈宗海.一种新的基于线性EIV模型的鲁棒估计算法[J].计算机研究与发展,2006,43(3): 483-488.
[10]Schuermans M,Markovsky I,Wentzell D P,etc.On the equivalence between total least squares and maximum likelihood PCA[J].Analytica Chimica Acta,2005,544:254-267.
[11]万永革,沈正康,刁桂苓等.利用小震分布和区域应力场确定大震断层面参数方法研究及其在唐山地震序列中的应用[J].地球物理学报,2008,51(3):793-804.
[12]王福昌,万永革,胡顺田.粒子群算法在主震断层面参数估计中的应用[J].地震研究,2008,31(2):149- 153.
[13]四川汶川8.0级地震及余震的速报目录及统计结果[EB/OL]. http://www.csndmc.ac.cn/newweb/wenchuan/wenchuan_aftershocks.htm,2008-07-12.
[14]吴可法,梁怡,徐宗本等.关于加权全最小一乘的探讨[J].应用数学学报,2002,3:439-447.
[15]万永革,吴忠良,周公威等.根据震源的两个节面的走向角和倾角求滑动角[J].地震地磁观测技术,2000, 21(5):26-30.
[16]王卫民,姚振兴,赵连锋.2008年5月12日汶川特大地震震源特性分析报告[EB/OL]. http://www.csi.ac.cn/sichuan/sichuan080512_cs2.htm,2008-7-13.
[2]Markovsky I,Huffel V S.Overview of total least-squares methods[J].IEEE Trans.Signal Processing, 2007,87(10):2283-2302.
[3]Fuller A W.Measurement Error Model[M].New York:John Wiley,1987.
[4]Cui H J.Asymptotic normality of M-estimates in the EV model[J].J.Sys.Sci.and Math.Scis., 1997,10(3):225-236.
[5]Cui H J,Chen S X.Empirical likelihood confidence region for parameter in the errors-in-variables models[J].J.Multivariate Anal.,2003,84:101-115.
[6]程龙生.基于errors-in-variables的预测模型及其应用[J].数理统计与管理,2005,24(2):55-59.
[7]Anderson T W.The 1982 WALD memorial lectures:Estimating linear statistical relationship[J]. The Annals Statistics,1984,12(1):1-45.
[8]刘瑞丰,陈运泰,任枭等.中国地震台网震级的对比[J].地震学报,2007,29(5):467-476.
[9]胡玉锁,陈宗海.一种新的基于线性EIV模型的鲁棒估计算法[J].计算机研究与发展,2006,43(3): 483-488.
[10]Schuermans M,Markovsky I,Wentzell D P,etc.On the equivalence between total least squares and maximum likelihood PCA[J].Analytica Chimica Acta,2005,544:254-267.
[11]万永革,沈正康,刁桂苓等.利用小震分布和区域应力场确定大震断层面参数方法研究及其在唐山地震序列中的应用[J].地球物理学报,2008,51(3):793-804.
[12]王福昌,万永革,胡顺田.粒子群算法在主震断层面参数估计中的应用[J].地震研究,2008,31(2):149- 153.
[13]四川汶川8.0级地震及余震的速报目录及统计结果[EB/OL]. http://www.csndmc.ac.cn/newweb/wenchuan/wenchuan_aftershocks.htm,2008-07-12.
[14]吴可法,梁怡,徐宗本等.关于加权全最小一乘的探讨[J].应用数学学报,2002,3:439-447.
[15]万永革,吴忠良,周公威等.根据震源的两个节面的走向角和倾角求滑动角[J].地震地磁观测技术,2000, 21(5):26-30.
[16]王卫民,姚振兴,赵连锋.2008年5月12日汶川特大地震震源特性分析报告[EB/OL]. http://www.csi.ac.cn/sichuan/sichuan080512_cs2.htm,2008-7-13.
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