Assimilation of geomagnetic data into dynamo models, an archeomagnetic study

The magnetic field measured at the Earth's surface is the superposition of a plurality of sources, the main component of which originates in the core. The core field is generated by a natural dynamo mechanism, which evolves on a variety of time scales. Its longer term dynamics are only accessible by indirect observations, the archeomagnetic data. The heterogeneous spatial and temporal character of the archeomagnetic data catalog, however, does not allow for a well-constrained inversion of the core field. Instead, the inverse problem is generally regularized by imposing prior constraints limiting the complexity of the field. Here we introduce the concept of using prior information derived from numerical models of the Earth's dynamo. This study is divided into two parts. The first part considers the static aspects of this inversion and its consequences for archeomagnetic field modeling. The prior information, built on a dynamo model, is connected to the surface data in terms of the directions and intensity of the field, by means of nonlinear and linearized observation operators. This yields an estimate, or analysis, of the core field given the available data. By means of these two pieces of information and the archeomagnetic dataset from the last three thousand years it is possible to quantify the archeomagnetic data resolution. Our results show that the archeomagnetic field is well-resolved up to spherical harmonic degree 3 for the first millennium BC, up to degree 4 for the first millennium AD and close to degree 5 for the past thousand years. The second part of the study explores how a sequential data assimilation framework can help improving the estimation of the field in the archeomagnetic context. In this case, the static inversion performed in the first part of the thesis is propagated in time by the numerical dynamo model in a sequence of forecast-and-analysis cycles. This methodology allows for the estimation of not only the observable, but also of the hidden variables of the dynamo system, the magnetic field in depth, the flow throughout the core and the density anomalies for instance. The assimilation, tested in the framework of closed-loop experiments for archeomagnetic-like synthetic observations, shows good performance in terms of accuracy and precision of the core state estimation. In particular, the assimilation is robust even in the case where observations are only available over one hemisphere. This thesis opens the possibility for the assimilation of real archeomagnetic observations and the subsequent estimation of the physical processes operating in the core on secular time scales.