Analysis of geomagnetic data using wavelet frames

这项提议的目的是建立球面小波的框架，作为地磁学中一种通用的建模工具。我们计划开发一种全球和区域磁场模拟方法，该方法可以考虑到地面地磁测量的非常不均匀的分布，以及卫星测量提供的更均匀的分布数据。该项目的重点是在地球物理上实现现在已经很成熟的称为小波框架的数学技术。与常用的球谐分析方法相比，改进的本质是基函数的区域性支持。它将允许在数据覆盖良好的区域实现高分辨率，同时避免在覆盖较少的区域出现虚假结构。到目前为止，对于标量数据，该方法可以得到改进，对于矢量数据，可以得到第一个结果。该提案计划的任务是优化(网格、度数、尺度)迄今获得的框架以改进具体的场表示，研究使用局部小波帧进行区域建模的可行性，将磁层源纳入场模型，并纳入与时间有关的数据和非线性数据(例如强度测量)。

The aim of this proposal is to establish frames of spherical wavelets as a versatile modelling tool in geomagnetism. We plan to develop a global and regional magnetic field modelling method which can take into account the very inhomogeneous distribution of ground-based geomagnetic measurements together with the more homogeneously distributed data provided by satelite measurements. The emphasis of this project is on the geophysical implementation of the by now well established mathematical technique called wavelet frames. The improvement compared to the commonly used method of spherical harmonic analysis is the essentially regional support of basis functions. It will allow high resolution in areas covered well by data while avoiding spurious structure in sparsely covered regions. By now improvements of this method could be shown for scalar data and first results for vector data could be obtained. The tasks projected in this proposal are optimizing (grid, degree, scales) the frames obtained so far to improve specific field representation, studying the feasability of regional modelling using local wavelet frames, incorporating magnetospheric sources in field models and incorporating time dependency and non-linear data (e.g. intensity measurements).