Modelling magnetic diffusion and decadal geomagnetic secular variation

Changes in the magnetic field generated within Earth's core that occur over years to centuries are known as geomagnetic secular variation (SV). These temporal variations arise from motions of the electrically conducting outer core fluid, and magnetic diffusion. Diffusive field changes are often considered much slower than those associated with fluid flow. For yearly to decadal SV, diffusion is therefore neglected in the widely adopted frozen-flux approximation. However, several studies have stressed the incompatibility of frozen flux with the SV observed over the 20th century. In particular, the approximation conflicts with the emergence of reversed-flux patches (RFPs) on the core-mantle boundary (CMB), which are regions where the sign of radial magnetic field differs from the otherwise prevalent dipole field aligned with Earth's rotation axis (i.e. the axial dipole field). In this thesis, we first introduce a method to characterise RFPs and their evolution. Subsequently, we show how these features have proliferated, strengthened, and migrated towards the geographic poles, matching the observed weakening of the axial dipole. We introduce a formalism allowing the inversion of the observed SV for an initial magnetic field throughout the core, assuming purely diffusive SV. With this method we demonstrate that pure diffusion is consistent with the SV over several decades, and can reproduce fundamental SV characteristics such as westward drift, recent North Magnetic Pole acceleration, and reversed-flux emergence. We also use our inverse formalism to augment frozen-flux models for core fluid motion by including magnetic diffusion. This hybrid scheme is shown to more accurately predict yearly SV than steady core flow, in particular that of South Atlantic RFPs. Finally, we use this hybrid forecasting method to compute a candidate model for the 2020.0 International Geomagnetic Reference Field. Our predictions also show how future axial dipole decay is no longer due to poleward migration of RFPs.