Modelling diurnal variation magnetic fields due to ionospheric currents

Accurate models of the spatial structure of ionospheric magnetic fields in the diurnal variation (DV) band (periods of a few hours to a day) would enable use of magneto-variational methods for 3-D imaging of upper mantle and transition zone electrical conductivity. Constraints on conductivity at these depths, below what is typically possible with magnetotellurics, would in turn provide valuable constraints on mantle hydration and Earths deep water cycle. As a step towards this objective, we present here a novel approach to empirical modelling of global DV magnetic fields. First, we apply frequency domain (FD) principal components analysis (PCA) to ground-based geomagnetic data, to define the dominant spatial and temporal modes of source variability. Spatial modes are restricted to the available data sites, but corresponding temporal modes are effectively continuous in time. Secondly, we apply FD PCA to gridded surface magnetic fields derived from outputs of the physics-based Thermosphere-Ionosphere Electrodynamics General Circulation Model (TIEGCM), to determine the dominant modes of spatial variability. The TIEGCM spatial modes are then used as basis functions, to fit (or interpolate) the sparsely sampled data spatial modes. Combining the two steps, we have a FD model of DV band global magnetic fields that is continuous in both space and time. We show that the FD model can easily be transformed back to the time domain (TD) to directly fit time-series data, allowing the use of satellite, as well as ground-based, data in the empirical modelling scheme. As an illustration of the methodology we construct global FD and TD models of DV band source fields for 1997-2018. So far, the model uses only ground-based data, from 127 geomagnetic observatories. We show that the model accurately reproduces surface magnetic fields in both active and quiet times, including those at sites not used for model construction. This empirical model, especially with future enhancements, will have many applications: improved imaging of electrical conductivity, ionospheric studies and improved external field corrections for core and crustal studies.