奇异谱分析在地磁数据研究中的应用  

Application of singular spectrum analysis in geomagnetic data research

作　　者：于畅 路来君[1] 于洪池[3] 吕铁鑫[4] 魏美璇 陈卓[2] YU Chang;LU Lai-jun;YU Hong-chi;LYU Tie-xin;WEI Mei-xuan;CHEN Zhuo(College of Earth Sciences,Jilin University,Changchun 130061,China;Jilin Seismic Station,Jilin Earthquake Agency,Changchun 130117,China;Helong Seismic Station,Jilin Earthquake Agency,Changchun 130200,China;Siping Branch,Jishi Media Co.Ltd.,Siping 136000,Jilin,China;Information Center,Jilin Earthquake Agency,Changchun 130117,China)

机构地区：[1]吉林大学地球科学学院,长春130061 [2]吉林省地震局吉林地震台,长春130117 [3]吉林省地震局合隆地震台,长春130200 [4]吉视传媒股份有限公司四平分公司,吉林四平136000 [5]吉林省地震局信息中心,长春130117

出　　处：《世界地质》2021年第2期459-466,共8页World Geology

基　　金：国家自然科学基金项目(41872243)。

摘　　要：为验证奇异谱分析在地磁数据中的拟合效果,笔者选取2017年1月至2019年7月吉林省长春地磁台FHDZ-M15仪采集的Z、H、D、F4个分量进行奇异谱分析。通过构造轨迹矩阵、分解奇异值和重构序列等步骤提取信号的趋势项和噪声等成分,得出原始序列奇异谱分析拟合值。构建原始序列的一元线性回归分析作为对比模型并计算拟合值,运用RMSE(均方根误差)、MAE(平均绝对误差)和MSPE(均方百分比误差)3项误差评价指标对奇异谱分析和一元线性回归分析的拟合结果进行误差分析,结果表明奇异谱分析拟合结果具有更高的精度。构建ARMA模型并对奇异谱拟合后的序列进行数值预测,给出置信区间并分析预测性能。ARMA预测模型显示,预测值序列与原始序列的变化趋势一致,且预测值均未超出置信区间的范围,表明在预测期内将无地磁异常发生。In order to verify the fitting effect of singular spectrum analysis in geomagnetic data,the authors conduct singular spectrum analysis by using Z,H,D and F components,which have been collected by the FHDZ-M15 instrument located in Changchun Geomagnetic Station during the period from January 2017 to July 2019.By constructing trajectory matrix,decomposing singular values and reconstructing series,we extract the trend term,noise term and finally obtain the fitting values of original series.We create unary linear regression as a contrast model and calculate the fitting values.RMSE(root mean square error),MAE(mean absolute error)and MSPE(mean square percentage error)have been used to make error analysis on the fitting results of singular spectrum analysis and unary linear regression analysis.The results show that the fitting results of singular spectrum analysis have higher accuracy.The ARMA model has been constructed to make value prediction on the singular spectrum fitting sequence.The confidence interval has been given and the prediction performance has been analyzed.ARMA prediction model shows that changes in the trend of the predicted value is consistent with that of the original sequence,and the predicted value does not exceed the confidence interval,which indicates that there will be no geomagnetic anomaly in the prediction period.

关 键 词：奇异谱分析 一元线性回归分析 ARMA模型 数值拟合 地磁数据 

分 类 号：P318[天文地球—固体地球物理学]