基于三维曲面Spline模型研究中国不同地区的磁场分布

3D modeling of different areas of China based on the 3D Surface Spline model

利用地面台站以及子午工程测点,CHAMP卫星实测数据,建立了中国地区主磁场的三维曲面Spline(3DSS)模型。基于该模型进行了我国的高原地区(青藏高原28°N-38°N,78°E-102°E)、平原地区(长江中下游平原27°N-34°N,111°E-122°E)以及海洋地区(东海和南海部分区域16°N-30°N,123°E-136°E)的磁场模拟。分别基于高原及平原的实测数据建立了各自的3DSS模型。另外分别建立了对应的二维Taylor(2DTY)、三维Taylor多项式(3DTY)模型以比较验证。建模时考虑了所有测点的场源移除、地面及卫星数据间的数据真空、边界效应等问题。为了考察模型相对于实测值的模拟精度,对三个地区分别选取若干个测点不参与建模,将所建模型分别模拟这些测点,并计算残差、变化率及均方根偏差(RMSE)。结果显示无论是全国3DSS模型还是小区域3DSS模型,其变化率除了Y分量略大,其余分量都在1%以内,模拟精度均要好于2DTY和3DTY模型。小区域(高原及平原)3DSS模型能较好反映区域磁场分布。模型对高原的拟合最好,平原次之,海洋地区最差,说明3DSS模型不需要太多的测点即可完成建模,但建模精度依赖于测点的数量及分布。

This study creates a three-dimensional surface spline(3DSS)model of China's Mainland based on surface and CHAMP satellite observations.Through this model,the magnetic field analyses of domestic plateau(Qinghai–Tibet Plateau 28°N–38°N,78°E–102°E),plain(middle and lower reaches of Yangtze River Plain 27°N–34°N,111°E–122°E),and marine(parts of the East and South China Seas 16°N–30°N,123°E–136°E)areas have been investigated.Single models of plateau and plain have also been created.To compare and verify results,the corresponding two-dimensional(2DTY)and three-dimensional(3DTY)Taylor polynomial models have been derived.Issues such as the removal of disturbing geomagnetic fields,the data gap between surface and satellite level,and boundary effect are all seriously considered.With an aim to evaluate the resulting model,some randomly selected points are not join the modeling,by which we thereby inspected the results in terms of residuals,change rate absolutes,and Root Mean Square Error(RMSE).Results show that except component Y,the change rate absolutes of other components are less than 1%both in domestic and single models,which means that the modeling result of 3DSS is better than the other two models.Plateau and plain 3DSS models reflect the fine distribution of the magnetic field after comparison with domestic distribution.The 3DSS model fits the plateau best,followed by the plain,while the worst fit is in the marine area.This means that the modeling precision depends mainly on the number and distribution of measuring points.