Time-Space Dependent Multiscale Modelling of the Magnetic Field Using Satellite Data (i.e. CHAMP-data)

使用卫星数据（即 CHAMP 数据）对磁场进行时空相关多尺度建模

• 批准号: 5249766
• 负责人: Professor Dr. Willi Freeden
• 金额: --
• 依托单位: Fachbereich Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2000
• 资助国家: 德国
• 起止时间: 1999-12-31 至 2009-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5249766?language=en
• 关键词: Time; Space; Dependent; Multiscale; Modelling

The purpose of the project MAMF is to introduce a multiscale method using trial fields for the time-space dependent computation of the Earth`s magnetic field from satellite data within source regions of ionospheric and magnetospheric currents.On the one hand, space-dependent modelling will be essentially based on two geomagnetic keystones, namely the Mie-representa- tion of a solenoidal vector field (such as the Earth`s magnetic field) in terms of toroidal and poloidal parts and the Helmholtz decomposition of tangential fields on a spherical orbit. Vector wavelets will be shown to provide adequate tools for multiscale geomagnetic modelling in form of a multiresolu- tion analysis, thereby completely circumventing the numerical obstacles caused by vector harmonics.On the other hand, time-dependent modelling will be proposed as a multiscale technique by means of (one-dimensional) Legendre- wavelets.Altogether, an integrated wavelet concept of time-space depen- dent (MAMF) resolution (in quasi-static formulation) is proposed as a twofold multiscale procedure (in tensor-product form) using satellite data, (for example, CHAMP-data).

MAMF项目的目的是介绍一种使用试验场的多尺度方法，根据电离层和磁层电流源区域内的卫星数据，根据时空计算地球磁场。一方面，与空间相关的建模将主要基于两个地磁关键，即螺线线矢量场（如地球磁场）在环面和极面部分的mie表示和切向场在球面轨道上的亥姆霍兹分解。矢量小波将以多分辨率分析的形式为多尺度地磁建模提供足够的工具，从而完全绕过矢量谐波造成的数值障碍。另一方面，时间相关建模将被提出作为一种多尺度技术，利用（一维）勒让德小波。总之，一个集成的小波概念的时空相关（MAMF）分辨率（准静态公式）被提出作为一个双重多尺度过程（张量积形式）使用卫星数据，（例如，champ数据）。