Wave-like motions and torques in Earth's core as inferred from geomagnetic data: a synthetic study

International audienceHere, we present a synthetic validation for the inversion of transient fluid motions at the surface of Earth’s core. It is based on a numerical simulation of the geodynamo in which the main time-scales (based on rotation, magnetic field and velocity) are sufficiently separated to give rise to a variety of hydro-magnetic waves. We focus the study on wave-like motions with periods commensurate to the Alfvén time, which is based on the strength of the magnetic field in the core interior. Synthetic magnetic data are generated over 90 Alfvén times, representative of the era covered by observatory and satellite measurements. These synthetic data are inverted to estimate a magnetic field model. Thereafter, we apply the pygeodyn data assimilation tool to recover core surface flows. We investigate the quality of their reconstruction as a function of their time scale. The success of the reconstruction depends on the data accuracy and coverage and on the magnitude of the flow. We also retrieve axi-symmetric torsional Alfvén waves, despite their relatively weak magnitude. We use the synthetic data to investigate the exchanges of angular momentum between core and mantle that induce length-of-day (LOD) changes. These exchanges result from the electromagnetic torque between the fluid core and the mantle and the gravitational torque between the inner core and the mantle. The inverted flows convincingly predict LOD variations in the dynamo calculation. We find that core surface zonal motions match well with the geostrophic (axially invariant) motions at the origin of the LOD changes, on all considered time-scales. We also investigate the different contributions to the electro-magnetic torque. In the dynamo simulation, only a small part can beattributed to the leakage torque caused by electrical currents flowing from the core to the mantle. The relative contribution from the poloidal field induced in the mantle, which amounts to about 1/3 of the total torque, is significantly larger than estimated in previous studies, based on geomagnetic observations. The remaining torque, which is associated with the toroidal induced field, mostly stems from the solid body rotation interacting with the radial magnetic field up to spherical harmonic degree 30