The method of natural orthogonal components (NOC) is used to analyze the earth抯 main magnetic field IGRF 1900—2000, and the NOC model of the field is established. The first step of the analysis is to calculate eigen...The method of natural orthogonal components (NOC) is used to analyze the earth抯 main magnetic field IGRF 1900—2000, and the NOC model of the field is established. The first step of the analysis is to calculate eigen modes of the field from the Gauss coefficients of IGRF 1900—2000. Then the magnetic field for each epoch is expanded in a series at the basic function set constructed by the eigen modes, and the intensity coefficients of the eigen modes are calculated. Test of the convergency and stability of the NOC model shows that the model has very short series and much rapid convergency in comparison with the conventional spherical harmonic models of IGRF. Comparison of the eigen modes obtained from different IGRF model groups indicates that the low-degree eigen modes are rather stable, while the high-degree modes show a relatively large variability. The physical meaning of the eigen modes in the NOC model is discussed, and an interesting relationship is found between the spatial structure of the main field and its secular variation.展开更多
This paper deals with the order of magnitude of the partial sums of the spherical harmonic series and its convergence rate in Bessel potential spaces. The partial results obtained in the paper are the analogue of tho...This paper deals with the order of magnitude of the partial sums of the spherical harmonic series and its convergence rate in Bessel potential spaces. The partial results obtained in the paper are the analogue of those on the circle.展开更多
Ⅰ. INTRODUCTION Let ∑<sub>n</sub>= {u∈R<sup>n+1</sup>; |u|=1} be the unit sphere in （n+1）dimensional Euclidean space. For any functionf on ∑<sub>n</sub>, we associate its expa...Ⅰ. INTRODUCTION Let ∑<sub>n</sub>= {u∈R<sup>n+1</sup>; |u|=1} be the unit sphere in （n+1）dimensional Euclidean space. For any functionf on ∑<sub>n</sub>, we associate its expansion in spherical harmonics:展开更多
为研究适用于区域电离层总电子含量(total electron content, TEC)建模的方法和估计策略,对传统单层假设下的几种建模方法和估计策略进行了比较分析.基于我国中纬度武汉地区17个连续运行参考站的数据进行TEC建模,建模方法分别采用4...为研究适用于区域电离层总电子含量(total electron content, TEC)建模的方法和估计策略,对传统单层假设下的几种建模方法和估计策略进行了比较分析.基于我国中纬度武汉地区17个连续运行参考站的数据进行TEC建模,建模方法分别采用4×3阶多项式模型、2阶多项式模型、4阶球谐级数模型,估计策略使用分段常数估计策略和分段线性估计策略.在传统单层假设的基础上,本文还提出了三层电离层TEC模型,该模型可以分别给出底部电离层、峰高电离层和顶部电离层的TEC.研究结果表明,几种模型的天顶方向总电子含量拟合效果和欧洲轨道确定中心公布的电离层格网地图均具有较好的一致性,其中4阶球谐级数模型和分段线性估计策略效果最佳.通过三层电离层模型,可以得到TEC与电离层高度之间的关系,多层电离层模型对空间目标监视和低轨卫星航天测控具有重要应用价值.展开更多
基金the National Natural Science Foundation of China(Grant Nos.49734140, 49974014).
文摘The method of natural orthogonal components (NOC) is used to analyze the earth抯 main magnetic field IGRF 1900—2000, and the NOC model of the field is established. The first step of the analysis is to calculate eigen modes of the field from the Gauss coefficients of IGRF 1900—2000. Then the magnetic field for each epoch is expanded in a series at the basic function set constructed by the eigen modes, and the intensity coefficients of the eigen modes are calculated. Test of the convergency and stability of the NOC model shows that the model has very short series and much rapid convergency in comparison with the conventional spherical harmonic models of IGRF. Comparison of the eigen modes obtained from different IGRF model groups indicates that the low-degree eigen modes are rather stable, while the high-degree modes show a relatively large variability. The physical meaning of the eigen modes in the NOC model is discussed, and an interesting relationship is found between the spatial structure of the main field and its secular variation.
文摘This paper deals with the order of magnitude of the partial sums of the spherical harmonic series and its convergence rate in Bessel potential spaces. The partial results obtained in the paper are the analogue of those on the circle.
基金Project supported by the National Natural Science Foundation of China
文摘Ⅰ. INTRODUCTION Let ∑<sub>n</sub>= {u∈R<sup>n+1</sup>; |u|=1} be the unit sphere in （n+1）dimensional Euclidean space. For any functionf on ∑<sub>n</sub>, we associate its expansion in spherical harmonics:
文摘为研究适用于区域电离层总电子含量(total electron content, TEC)建模的方法和估计策略,对传统单层假设下的几种建模方法和估计策略进行了比较分析.基于我国中纬度武汉地区17个连续运行参考站的数据进行TEC建模,建模方法分别采用4×3阶多项式模型、2阶多项式模型、4阶球谐级数模型,估计策略使用分段常数估计策略和分段线性估计策略.在传统单层假设的基础上,本文还提出了三层电离层TEC模型,该模型可以分别给出底部电离层、峰高电离层和顶部电离层的TEC.研究结果表明,几种模型的天顶方向总电子含量拟合效果和欧洲轨道确定中心公布的电离层格网地图均具有较好的一致性,其中4阶球谐级数模型和分段线性估计策略效果最佳.通过三层电离层模型,可以得到TEC与电离层高度之间的关系,多层电离层模型对空间目标监视和低轨卫星航天测控具有重要应用价值.
