地磁场模型误差分析中的几个问题  

An Analysis of Errors in Geomagnetic field models

作　　者：徐文耀[1] 区家明[1] 杜爱民[1] 

机构地区：[1]中国科学院地质与地球物理研究所,北京100029

出　　处：《地球物理学进展》2011年第5期1485-1509,共25页Progress in Geophysics

基　　金：自然科学基金委项目(40874089;40931056);国家重点基础研究发展计划(973计划)(2008CB425704)项目联合资助

摘　　要：地磁场全球建模和局域建模理论是编绘全球地磁图和区域地磁图(如国家地磁图)的基础.区域磁场是全球磁场的一部分,因此,区域模型系数与全球模型系数之间存在着确定的关系.这些关系既是检验区域建模的分析方法是否合理,结果是否正确的判据,又是估计区域模型误差的出发点.全球建模的标准方法是球谐分析,而局域建模方法很多,大体可分为基于观测值的纯数值模型和基于磁位理论的数学模型两类.前一类是数值方法,着眼于对观测值的最佳拟合,常用的拟合函数有幂函数、指数函数、三角函数、样条函数、简谐样条函数、本征函数等等,拟合结果实用价值大,但在物理上有一定缺陷.后一类建模方法主要有等效源法、球冠谐和分析(SCHA)、修正球冠谐和分析(R-SCHA)、矩谐分析(RHA)等,这些模型在物理上满足无源无旋性质,而数值偏差却往往大于前者.本文从误差理论出发,探讨地磁模型中测值误差、截断误差、舍入误差、系统误差等各种误差的分布规律,研究地壳场、外源场的存在对模型误差的影响,用仿真算例,分析地磁场局域模型中的边界效应、长波误差、中短波误差、延拓误差、数据噪声误差,讨论由于台站分布不均匀、成片地区缺资料等因素引起的模型误差.通过对比分析,总结不同方法的优缺点和适用场合.Theory of global and regional magnetic field modeling is the basis of compilation of global and national magnetic charts. The coefficients of a regional model have definite relationship with the coefficients of global model, which is not only theoretical basis of assessing the adequacy of modelling methods, but also the start point of estimating model errors. The standard technique for global modelling is spherical harmonic analysis （SHA）, while commonly used methods for regional modeling are grouped into two categories. The first group is for pure numerical models, ignoring the physical property of the potential field and using data fitting by various functions, such as power function, triangle function, spline function, and eigen function. The second group is based on potential theory, such as spherical cap harmonic analysis （SCHA）, revised spherical cap harmonic analysis（R-SCHA）, and rectangular harmonic analysis （RHA）. This paper, starting from error theory, analyses error sources in magnetic models, including inherent errors in applied methods and the errors from measurements. Case studies are carried out to survey the errors in various wave-length components, extrapolation and continuation. Effects of random errors in data on fitting accuracy and stability are also considered. Boundary distortions and their behaviors are discussed.

关 键 词：地磁场建模 局域地磁场模型 球谐分析(SHA) 矩谐分析(RHA) 冠谐分析(SCHA) 勒让德函数 圆锥函数 误差 

分 类 号：P318[天文地球—固体地球物理学]