Analysis of geomagnetic data using wavelet frames

该建议的目的是建立一个通用的地磁建模工具的球面小波框架。我们计划开发一种全球和区域磁场建模方法，该方法可以考虑地基地磁测量的非常不均匀分布以及卫星测量提供的更均匀分布的数据。该项目的重点是对地球物理的实施，到现在为止，建立良好的数学技术称为小波框架。与常用的球谐分析方法相比，改进之处在于基函数的区域支持。它将允许在数据覆盖良好的区域中实现高分辨率，同时避免在稀疏覆盖区域中出现虚假结构。到目前为止，这种方法的改进可以显示为标量数据和矢量数据的第一个结果可能会得到。本提案中预计的任务是优化（网格、度、尺度）迄今为止获得的框架，以改进具体的磁场表示，研究使用局部小波框架进行区域建模的可行性，将磁层源纳入磁场模型，并纳入时间依赖性和非线性数据（例如强度测量）。

The aim of this proposal is to establish frames of spherical wavelets as a versatile modellingtool in geomagnetism. We plan to develop a global and regional magnetic field modellingmethod which can take into account the very inhomogeneous distribution of ground-basedgeomagnetic measurements together with the more homogeneously distributed data providedby satelite measurements. The emphasis of this project is on the geophysical implementationof the by now well established mathematical technique called wavelet frames. Theimprovement compared to the commonly used method of spherical harmonic analysis is theessentially regional support of basis functions. It will allow high resolution in areas coveredwell by data while avoiding spurious structure in sparsely covered regions. By nowimprovements of this method could be shown for scalar data and first results for vector datacould 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 ofregional modelling using local wavelet frames, incorporating magnetospheric sources in fieldmodels and incorporating time dependency and non-linear data (e.g. intensity measurements).