地震研究

时域最小二乘配置求定点形变特征曲线与异常识别的应用研究^*

贾鹏,张希,唐红涛,李瑞莎

(中国地震局第二监测中心,陕西西安 710054)

Application Study of Least Square Collocation in Fixed Point Deformation Characteristic Curve and Anomaly Identification

JIA Peng,ZHANG Xi,TANG Hong-tao,LI Rui-sha

(The Second Monitoring and Application Center,CEA,Xi'an 710054,Shannxi,China)

Keywords：least square collocation; fixed point deformation; fitting; extrapolation

备注

收稿日期:2012-03-12
基金项目:星火计划项目“青藏块体东北缘前兆系统结构分析与异常识别”(XH12072)资助.

摘要

全文

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参考文献

将最小二乘配置方法的高斯型经验协方差函数模型应用于定点形变特征曲线的异常辅助识别,通过两个不同算例说明最小二乘配置滤波、内插和外推可以进行定点形变曲线的趋势模拟和辅助查找其短期、中长期的异常特征,对于定点形变曲线异常识别有一定的意义。

The Gauss-Function covariance model based on least square collocation was applied in the anomaly assisted identification of fixed point deformation characteristic curves. We used two different examples to show that the filtering,interpolation and extrapolation of least square collocation can be simulated the trend of fixed point deformation curves and assisted searching their anomaly characteristics in short-,medium-and long-term. The least square collocation method has certain significance for identifying the fixed point deformation.

引言
1 最小二乘配置方法原理
2 定点形变曲线与异常识别应用实例
3 结论与讨论

图1 四川姑咱台钻孔应变东西分量日均值观测曲线<br/>Fig.1 Daily mean observation cruve of E-W borehole strain at Guzan Station in Sichuan

图1 四川姑咱台钻孔应变东西分量日均值观测曲线
Fig.1 Daily mean observation cruve of E-W borehole strain at Guzan Station in Sichuan

图2 姑咱台钻孔应变东西分量在不同相关范围下日均值与拟合值曲线对比,绝对差值曲线<br/>及二倍均方差(参考区间为2008年1月1日至2011年12月31日)<br/>(a)k=0.896;(b)k=2;(c)k=4<br/>Fig.2 Comparison between daily mean and fitting curves of E-W borehole strain at Guzan Station,absolute difference curve and the double mean square error between daily mean and fitting values in different relevance range(time scale is from 2008-01-01 to 2011-12-31)

图2 姑咱台钻孔应变东西分量在不同相关范围下日均值与拟合值曲线对比,绝对差值曲线
及二倍均方差(参考区间为2008年1月1日至2011年12月31日)
(a)k=0.896;(b)k=2;(c)k=4
Fig.2 Comparison between daily mean and fitting curves of E-W borehole strain at Guzan Station,absolute difference curve and the double mean square error between daily mean and fitting values in different relevance range(time scale is from 2008-01-01 to 2011-12-31)

图3 姑咱台钻孔应变东西分量在不同参考区间内的日均值与拟合值曲线对比、绝对值差异曲线<br/>及二倍均方差(相关范围取缺省值)<br/>(a)2008-01-01至2011-06-30;(b)2008-01-01至2011-09-30<br/>Fig.3 Comparison between daily mean and fitting curves of E-W borehole strain at Guzan Station,absolute difference curve and the double mean square error between daily mean and

图3 姑咱台钻孔应变东西分量在不同参考区间内的日均值与拟合值曲线对比、绝对值差异曲线
及二倍均方差(相关范围取缺省值)
(a)2008-01-01至2011-06-30;(b)2008-01-01至2011-09-30
Fig.3 Comparison between daily mean and fitting curves of E-W borehole strain at Guzan Station,absolute difference curve and the double mean square error between daily mean and

图4 云南永胜台垂直摆倾斜北南分量<br/>日均值观测曲线<br/>Fig.4 Daily mean observational records of N-S vertical pendulum tiltmeter at Yongsheng Station in Yunnan

图4 云南永胜台垂直摆倾斜北南分量
日均值观测曲线
Fig.4 Daily mean observational records of N-S vertical pendulum tiltmeter at Yongsheng Station in Yunnan

图5 永胜台垂直摆倾斜北南分量在不同参考区间内日均值与拟合值曲线对比、绝对值差异曲线<br/>及二倍均方差(相关范围取缺省值)<br/>(a)2008-01-01至2011-12-31;(b)2008-01-01至2011-06-30;(c)2008-01-01至2011-09-30<br/>Fig.5 Comparison between daily mean and fitting curves of N-S vertical pendulum tiltmeter at Yongsheng Station, absolute difference curve and the double mean square error between daily mean and fitting values in different time scale(k=0.896)

图5 永胜台垂直摆倾斜北南分量在不同参考区间内日均值与拟合值曲线对比、绝对值差异曲线
及二倍均方差(相关范围取缺省值)
(a)2008-01-01至2011-12-31;(b)2008-01-01至2011-06-30;(c)2008-01-01至2011-09-30
Fig.5 Comparison between daily mean and fitting curves of N-S vertical pendulum tiltmeter at Yongsheng Station, absolute difference curve and the double mean square error between daily mean and fitting values in different time scale(k=0.896)