扩展空间自相关法用于线性阵列时加权拟合问题研究
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摘要
针对扩展空间自相关法拟合问题,分析了系统误差和方差这两种加权因素,讨论了它们对估算相速度的影响。实验采用10个台站组成的线形阵列。结果表明:有无根据系统误差加权拟合,相速度差别较大;有无根据方差加权拟合,相速度差别较小,但个别值有明显改变;加权前后得到的频散曲线有明显差别。应用扩展空间自相关法时,必须根据系统误差和方差确定合理权值,才能更准确估算相速度。
For the fitting problem in the extended spatial autocorrelation method,were two weighting factors analyzed: the systematic error and the variance and discussed the effect of estimating phase velocity caused by them.Linear array which consisted of 10 stations was used in the experiment. The results indicate that whether weight fitting is based on the systematic error or not,great difference can be found in phase velocity; whether weight fitting is based on the variance or not,the difference in phase velocity is relatively slight,but individual values are significantly changed; after the weight fitting,the frequency dispersion curves are obviously different. In the application of the extended spatial autocorrelation method,reasonable weights must be determined according to the systematic error and the variance so as to estimate phase velocity in a more accurate way.
For the fitting problem in the extended spatial autocorrelation method,were two weighting factors analyzed: the systematic error and the variance and discussed the effect of estimating phase velocity caused by them.Linear array which consisted of 10 stations was used in the experiment. The results indicate that whether weight fitting is based on the systematic error or not,great difference can be found in phase velocity; whether weight fitting is based on the variance or not,the difference in phase velocity is relatively slight,but individual values are significantly changed; after the weight fitting,the frequency dispersion curves are obviously different. In the application of the extended spatial autocorrelation method,reasonable weights must be determined according to the systematic error and the variance so as to estimate phase velocity in a more accurate way.
引文
1 Okada H.The microtremor survey method.Socity of Exploration Geophysicists,2003
2 Aki K.Space and time spectra of stationary stochastic waves,with special reference to microtremors..Bulletin of the Earthquake Research Institue.1957;35:415-456
3凌甦群.关于提取微动中面波相速度的方法研究.北海道:北海道大学理学部,1994Ling S Q.Research on the estimation of phase velocities of surface waves in microtremors.Hokkaido:Hokkaido University,1994
4 Ohori M,Nobata A,Wakamatsu K.A comparison of ESAC and FKmethods of estimating phase velocity using arbitrarily shaped microtremor arrays.Bull Seismol Soc Amer,2002;92(6):2323-2332
5 Chavez-Garcia F J,Rodriguez M,Stephenson W R.Subsoil structure using SPAC measurements along a line.Bulletin of the Seismologica Society of America,2006;96(2):729-736
6李传金.微动勘查法中三种阵列的适用性研究.北京:中国科学院研究生院,2011Li C J.Study on the applicability of three arrays used in microtremor survey method.Beijing:Graduate University of Chinese Academy of Sciences,2011
7徐佩芬,李传金,凌甦群,等.利用微动勘查方法探测煤矿陷落柱.地球物理学报,2009;52(7):1923-1930Xu P F,Li C J,Ling S Q,et al.Mapping collapsed columns in coal mines utilizing microtremor survey methods.Chinese J Geophys,2009;52(7):1923-1930
8徐佩芬,侍文,凌苏群,等.二维微动剖面探测“孤石”:以深圳地铁7号线为例.地球物理学报,2012;55(6):2120-2128Xu P F,Shi W,Ling S Q,et al.Mapping spherically weathered“Boulders”using 2D microtremor profiling method:a case study along subway line 7 in Shenzhen.Chinese J Geophys,2012;55(6):2120-2128
9 Okada H.Theory of efficient array observations of microtremors with special reference to the SPAC method.Exploration Geophysics,2006;59(37):73-85
10 Cho I,Tada T,Shinozaki Y.Assessing the applicability of the spatial autocorrelation method:a theoretical approach.J Geophys.ResSolid Earth,2008;113(6):1-19
11何晓群,刘文卿.浅谈加权最小二乘法及其残差图.统计研究,2006;(4):53-57He X Q,Liu W Q.Discussion weighted least square regression and weighted residual plots.Statistical Research,2006;(4):53-57
2 Aki K.Space and time spectra of stationary stochastic waves,with special reference to microtremors..Bulletin of the Earthquake Research Institue.1957;35:415-456
3凌甦群.关于提取微动中面波相速度的方法研究.北海道:北海道大学理学部,1994Ling S Q.Research on the estimation of phase velocities of surface waves in microtremors.Hokkaido:Hokkaido University,1994
4 Ohori M,Nobata A,Wakamatsu K.A comparison of ESAC and FKmethods of estimating phase velocity using arbitrarily shaped microtremor arrays.Bull Seismol Soc Amer,2002;92(6):2323-2332
5 Chavez-Garcia F J,Rodriguez M,Stephenson W R.Subsoil structure using SPAC measurements along a line.Bulletin of the Seismologica Society of America,2006;96(2):729-736
6李传金.微动勘查法中三种阵列的适用性研究.北京:中国科学院研究生院,2011Li C J.Study on the applicability of three arrays used in microtremor survey method.Beijing:Graduate University of Chinese Academy of Sciences,2011
7徐佩芬,李传金,凌甦群,等.利用微动勘查方法探测煤矿陷落柱.地球物理学报,2009;52(7):1923-1930Xu P F,Li C J,Ling S Q,et al.Mapping collapsed columns in coal mines utilizing microtremor survey methods.Chinese J Geophys,2009;52(7):1923-1930
8徐佩芬,侍文,凌苏群,等.二维微动剖面探测“孤石”:以深圳地铁7号线为例.地球物理学报,2012;55(6):2120-2128Xu P F,Shi W,Ling S Q,et al.Mapping spherically weathered“Boulders”using 2D microtremor profiling method:a case study along subway line 7 in Shenzhen.Chinese J Geophys,2012;55(6):2120-2128
9 Okada H.Theory of efficient array observations of microtremors with special reference to the SPAC method.Exploration Geophysics,2006;59(37):73-85
10 Cho I,Tada T,Shinozaki Y.Assessing the applicability of the spatial autocorrelation method:a theoretical approach.J Geophys.ResSolid Earth,2008;113(6):1-19
11何晓群,刘文卿.浅谈加权最小二乘法及其残差图.统计研究,2006;(4):53-57He X Q,Liu W Q.Discussion weighted least square regression and weighted residual plots.Statistical Research,2006;(4):53-57