Local estimation of quasi-geostrophic flows in Earth's core

The inference of fluid motion below the core–mantle boundary from geomagnetic observations presents a highly non-unique inverse problem. We propose a new method that provides a unique local estimate of the velocity field, assuming quasi-geostrophic flow in the core interior (which implies equatorial mirror symmetry) and negligible magnetic diffusion. These assumptions remove the theoretical underdetermination, enabling us to invert for the flow at each point of a spherical grid representing the core surface. The unreliable reconstruction of small-scale flows, which arises because only large-scale observations are available, is mitigated by smoothing the locally estimated velocity field using a Gaussian process regression. Application of this method to synthetic data provided by a state-of-the-art geodynamo simulation suggests that using this approach, the large-scale flow pattern of the core surface flow can be well reconstructed, while the flow amplitude tends to be underestimated. We compare these results with a core flow inversion using a Bayesian framework that incorporates statistics from numerical geodynamo models as prior information. We find that whether the latter method provides a more accurate recovery of the reference flow than the local estimation depends heavily on how realistic/relevant the chosen prior information is. Application to real geomagnetic data shows that both methods are able to reproduce the main features found in previous core flow studies.