地球物理学报  2016, Vol. 59 Issue (6): 1948-1956 PDF

Study of regional geomagnetic model of Fujian and adjacent areas based on 3D Taylor Polynomial model
ZHANG Su-Qin, FU Chang-Hua, ZHAO Xu-Dong
Institute of Geophysics, China Earthquake Administration, Beijing 100081, China
Abstract: Based on 256 measured geomagnetic vector data (Element D, I and H) in Fujian and adjacent areas, combined with the grid data of Global Land One-kilometer Base Elevation Project and the latest 12th International Geomagnetic Referenced Field (IGRF12) model, the regional geomagnetic model has been created by using three-dimensional (3D) Taylor Polynomial model. Through comparing the Root-Mean-Square error (RMS), geomagnetic distribution and residuals, two main conclusions are drawn: (1) Truncation degree N=2 of 3D Taylor model basically produce the same calculation result as truncation degree N=6 of 2D Taylor model; (2) 3D Taylor model can calculate conveniently and has high precision, but it also has the probability of producing Runge Phenomenon. So, both calculation precision and boundary effect problem should be considered when determining truncation degree..
Key words: Geomagnetic model      3D Taylor polynomial model      Fujian and adjacent areas      Root-Mean-Square error
1 引言

2 数据与方法 2.1 实测数据及补充点的选取

 图 1 福建及邻近地区地磁测点分布图 Fig. 1 Distribution chart of all measured data over Fujian and its adjacent areas
2.2 Taylor多项式模型

 (1)

 (2)

2.3 测点高度的选取

 图 2 福建及邻近地区的三维高程 Fig. 2 3D elevation map of Fujian and its adjacent areas
3 结果 3.1 截断阶数的确定

 (3)

 图 3 N=1～10时二维和三维模型RMS的变化 Fig. 3 The RMS variation between 2D and 3D models while N=1～10

 图 4 N=1～5时二维和三维模型RMS的变化 Fig. 4 The RMS variation between 2D and 3D models while N=1～5

3.2 基于三维模型的福建及邻近地区的地磁场分布

 图 5 福建及邻近地区的三维Taylor模型的地磁场分布(N=2) Fig. 5 The geomagnetic field distribution of Fujian and its adjacent areas base on 3D Taylor model (N=2)

3.3 模型误差分析

 图 6 所有测点及二维(N=6)、三维(N=2)模型值相比较 Fig. 6 The comparison among all measured data, 2D (N=6) and 3D (N=2) model values

 图 7 二维(N=6)、三维(N=2)模型的残差值的比较 Fig. 7 The comparison of residuals between 2D (N=6) and 3D (N=2) model values

4 结论与讨论

(1) 与二维Taylor多项式模型相比,三维Taylor模型增加了对高度因素的考虑.在福建及邻近地区,海拔高度范围为-0.5～1.16 km左右,故磁场强度应有-10～20 nT左右的误差,因此三维Taylor模型在精度上要好于二维模型.本研究使用了高精度的台站和复测点的矢量数据,基于此建立的三维模型,比国际地磁参考场IGRF12模型的精度更高.

(2) 本文用到的三维Taylor多项式模型为完整展开形式,其系数约为相同截断阶数下的经典二维展开模型的2N倍,因此三维模型在较低的截断阶数下反映出更多的地磁场信息,从而提高模拟效率.另外需要注意的是由于系数数量随截断阶数的增加呈现指数式上升,三维模型也较易出现龙格现象.文中当截断阶数N>5时,出现了明显的龙格现象.因此区域磁场建模时,截断阶数的选取和边界效应的控制是两个关键性问题(徐文耀和朱岗昆,1984Feng et al., 2015),在确定模型的截断阶数时,除了考虑模型拟和精度外,还需要避免龙格现象的出现.

(3) 本文研究表明较低截数的三维模型,其均方偏差RMS与较高阶数的二维模型接近,通过对比两种模型在不同截断阶数下的RMS、磁场分布以及残差,可基本确定三维模型所对应的二维模型的阶数.

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