Correlation based modelling of the Earth magnetic field

模拟地球磁场是理解地球外核动态过程的重要一步。在那里，产生了主导地球表面观测到的磁场的“核心场”。然而，只有考虑到岩石圈、电离层、磁层和其他较弱信号的影响，才能揭示其快速变化。这些对磁场测量的不同贡献的分离仍然是建立磁场模型的主要挑战之一。在过去几年中，由于高质量卫星数据的可用性，已经推导出了精确的地球磁场模型。然而，科学家至今未能提供磁场模型协方差矩阵的可接受估计。尽管如此，这些矩阵对于这些模型的进一步开发，特别是对地磁场同化方法的实施是必要的。这些方法已被证明是了解地核演化和状态的重要工具。此外，一旦这些矩阵已知，模型估计的不确定性就可用了。因此，鉴于同化方法的发展，本项目的目的是建立与可接受的协方差矩阵相关的精确磁场模型。为了达到这个目标，我们将不得不引入不同的方法来模拟地磁场的不同来源。我们提出利用地磁场各分量及其观测数据的全时空相关结构建立一个模型。这包括主场、地壳、电离层和测量噪声等各种噪声源。这样，我们的方法可以被看作是基于调和样条的模型。因此，我们要开发的地磁应用方法与重力场建模中使用的“配位法”密切相关。对磁场的不同贡献的分离是基于与经典球谐分析中使用的原理完全不同的原理。在我们的方法中，可以获得场分量分离的精确统计意义。这与传统的特设方法形成对比，在传统方法中，低于一定程度的所有谐波都归为核心场。此外，我们希望能够更好地揭示相对较短的空间和时间尺度的领域。尽管在过去的十年里做出了巨大的努力，但对地核磁场的这种微小变化仍然知之甚少。

Modelling the Earth magnetic field is an essential step towards understanding the dynamic processes at work in the Earth's outer core. There, is generated the ''core field`` that dominates the observed magnetic field at the Earth's surface. However, its rapid variations can be revealed only if contributions from the lithosphere, ionosphere, magnetosphere and other weaker signals are accounted for. The separation of these different contributions to magnetic field measurements remains one of the main challenges in building magnetic field models. Accurate models of the Earth's magnetic field have been derived over the past few years, thanks to the availability of high quality satellite data. However scientists have so far failed in providing acceptable estimates of the magnetic field model covariance matrices. These matrices are nonetheless necessary for the further exploitation of these models, particularly for the implementation of assimilation methods for the geomagnetic field. These methods have already proved to be remarkable tools for the understanding of the Earth's core evolution and state. Moreover the uncertainty of the model estimates become available once these matrices are known. The aim of this project is therefore to build accurate magnetic field models associated with acceptable covariance matrices in view of the development of assimilation methods. To reach this goal we will have to introduce alternative ways of modelling the different sources of the geomagnetic field. We propose to build a model that is based on the use of the full spacetime correlation structure of all the components of the geomagnetic field and its observations. This comprises the various sources as main field, crust, ionosphere and the measurement noise. In this way our approach can be seen to be of the class of harmonic spline based models. The method we want to develop for geomagnetic application is therefore closely related to the ''collocation method`` used in the modelling of the gravity field. The separation of the different contributions to the magnetic field is based on principles radically different than those used in classic spherical harmonic analysis. In our approach a precise statistical meaning of the field component separation becomes available. This contrasts with the traditional ad hoc approach, where all harmonics below a certain degree are attributed the core field. Moreover we expect to be able to better reveal relatively short spatial and temporal scales of the fields. Despite mojor efforts over the last ten years, such small variations of the core magnetic field remain poorly understood.