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

MAMF项目的目的是引入一种多尺度方法，利用试探场从电离层和磁层流源区内的卫星数据中计算地球磁场的时空相关。一方面，空间相关的模拟基本上将基于两个地磁关键点，即螺线矢量场(如地球磁场)的环向和极向部分的Mie表示和球面轨道上切向场的Helmholtz分解。矢量小波将以多分辨率分析的形式为多尺度地磁模拟提供足够的工具，从而完全绕过矢量调和造成的数值障碍。另一方面，时间相关建模将被提出作为一种(一维)勒让德小波的多尺度技术。同时，利用卫星数据(例如，CHAMP数据)，提出了时间-空间相关(MAMF)分辨率(准静态形式)的集成小波概念，作为一种双重多尺度过程(以张量积形式)。

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).