Correlation based modelling of the Earth magnetic field

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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.