Satellite magnetic data over the past two decades (from records of the Oersted, Champ, CryoSat-2 and Swarm missions) offer an unprecedent coverage of the dynamics within the Earth’s core [1]. Meanwhile, recent progress in simulations of the geodynamo shed new lights on the core physics, emphasizing the role played by hydro-magnetic waves [2]. The conjunction of those two (observational and numerical) constraints led to the discovery of Magneto-Coriolis modes of period about 7 years [3], which explain a significant part of the interannual magnetic field variations. As a result of the “Swarm 4D-Earth Core” project, we are now in a position to understand the physics responsible for the rapid changes observed in the rate of change of the magnetic field.

With this recent evolution of our understanding, we foresee the possibility to improve our knowledge of the base state within the Earth’s core, over which hydro-magnetic waves travel. This is the overarching goal of the “Swarm 4D-Earth Core” project continuation. We shall present the main steps envisioned to reach this target. These involve upgraded satellite datasets (including data error cross-covariances), large scale core surface flow models related to subgrid induction processes, as well as the recovery of the base state from statistical and dynamical constraints contained in the latest generation of dynamo simulations. Our project also aims at better characterizing the sensitivity of hydro-magnetic modes to the base state through eigen-mode studies [4] and direct numerical experiments. Particular care should be brought to the magnetic boundary conditions, in particular in the vicinity of the core equator, where most of the interannual magnetic signal is observed. The knowledge of the base state in the core is key for the implementation of data assimilation algorithms for geomagnetic purposes.

[1] Hammer, Finlay & Olsen. Applications for CryoSat-2 satellite magnetic data in studies of Earth's core field variations, Earth Planets Space 73, https://doi.org/10.1186/s40623-021-01365-9 (2021)
[2] Aubert & Gillet, The interplay of fast waves and slow convection in geodynamo simulations nearing Earth's core conditions, Geophys. J. Int. ggab054, https://doi.org/10.1093/gji/ggab054 (2021)
[3] Gillet, Gerick, Jault, Schwaiger, Aubert & Istas, Satellite magnetic data reveal interannual modes in Earth’s core, Proc. Nat. Acad. Sci. (in revision).
[4] Gerick, Jault and Noir. Fast Quasi-Geostrophic Magneto-Coriolis Modes in Earth's core, Geophys. Res. Lett. https://doi.org/10.1029/2020GL090803 (2021)

Low Earth orbit satellite data enable magnetic field gradient tensor elements to be estimated by taking along track and, in the case of the current Swarm constellation mission, across track differences. Here we produce time dependent core surface advective flow models by inverting geomagnetic virtual observatory (GVO) gradient tensor elements of the secular variation (SV) from Swarm satellite data every 4 months in the period 2014-2019. We apply a temporal constraint that minimises flow change between epochs, as well as spatial regularization. The data predictions show no obvious biases, and are very similar to those of the CHAOS-7 field model. Our normalised misfit to the data is 0.93, suggesting the data uncertainties have been slightly over-estimated. The greater sensitivity of the gradient tensor SV elements to higher harmonic degrees of the flow enable more coefficients to be resolved, around 160 compared to of order 100 for SV vector data. We use a variety of spatial regularizations that result in rather different flow geometries, though they all display the main features seen in previous studies, such as westward drift in an equatorial band around the equator in a region straddling the Greenwich meridian, eastward drift in an equatorial band around the equator beneath the Pacific, and the eccentric planetary gyre. Flow beneath the Pacific has non-equatorially symmetric and non-tangentially geostrophic ingredients, notably cross-equator flow in the region below Indonesia.

Rapid temporal changes in the Pacific region are seen in both SV vector field and SV gradient tensor GVO time series around 2017, most clearly in the radial SV component, and also in several of the SV gradient elements. We investigate the changes in the flow and flow accelerations associated with this geomagnetic jerk. We show that, despite the differences in the flows themselves as a result of the spatial regularization, the changes to the core surface flow beneath the Pacific associated with the jerk are consistent. In particular, the east-west component of acceleration, calculated by simple first differences of the flow with no smoothing, has the opposite sense either side of around 160 degrees W longitude, where the acceleration is very small, and changes sign at the jerk epoch. The image shows the E-W acceleration component at 170 degrees E, 160 degrees W and 130 degrees W from left to right, and for three spatial norms from top to bottom. The acceleration change is rapid (less than a year), and before and after the jerk the acceleration is essentially constant for the duration of our model. Flow accelerations in the jerk region are significantly higher than elsewhere on the core surface. There is a similarly well-defined change in the radial component of the core surface secular acceleration in the Pacific region at the jerk epoch.

Earth’s core-generated magnetic field undergoes rapid, and at present unpredictable, changes on time scales of less than a decade. These events prevent accurate forecasts of the magnetic field more than a few months ahead. Study of sub-decadal field changes has long been hampered by a lack of global coverage from ground observatories. But with more than eight years of vector magnetic field measurements now available from the Swarm mission, combined with data from the earlier CHAMP and Ørsted missions, as well as calibrated platform magnetometer data from Cryosat-2, a new, more detailed, picture of rapid core field changes is emerging. We describe observations of sub-decadal field changes captured by a regular grid of geomagnetic ‘virtual’ observatories at satellite altitude based on Swarm data. These highlight the dynamic nature of field changes in the Pacific region over the past decade, where oscillations are observed in the radial field component. Changes in the slope of the secular variation of the east-west field component have also been seen in recent years, particular in Europe, the Atlantic and Asian sectors. We describe the latest update of the CHAOS global geomagnetic field model and use it to map the origin of these sub-decadal changes at the core-mantle boundary. We reflect on the similarities between recent field changes and geomagnetic impulses observed earlier in the twentieth century and on possible explanations for the observed changes in terms of hydromagnetic waves in the core. The time series of global satellite magnetic observations is still short compared to the dynamical time scales of interest; an extended Swarm mission is therefore vital if further progress is to be made in understanding these events and using them to probe Earth’s properties and dynamics. Improvements in the temporal resolution of core signals are also needed; proposed future geomagnetic missions with improved local time coverage, in particular the NanoMagSat mission, would deliver exciting new insights on this frontier.

Geomagnetic jerks are abrupt changes in the acceleration of Earth’s magnetic field that punctuate geomagnetic records. A rich phenomenological description of these events has been constructed over the past fourty years by taking advantage of the complementary strengths of ground observatory and satellite measurements. This has raised the question whether a single physical cause can explain the important characteristics of all observed jerks. Their possible dynamical origin has been studied in recent numerical geodynamo simulations achieving a realistic interplay and time scale separation between slow convection and rapid hydromagnetic wave propagation in Earth's outer core, with these latter waves playing a key role in the generation of jerk signals. To assess the generality of this explanation, here we analyse a catalog of 14 events obtained during a 14000 year long temporal sequence from a model that is the closest to date to Earth's core conditions regarding time scale separation. The majority of jerk events are found to arise from intermittent local disruptions of the leading-order force balance between the pressure, Coriolis, buoyancy and Lorentz forces (the QG-MAC balance), that leads to an inertial compensation through the emission of rapid, non-axisymmetric, quasi-geostrophic Alfvén waves from the region where this force balance is disrupted. As in an earlier simulation, jerk events of moderate strength arise from the arrival at the core surface of hydromagnetic wave packets which originate at depth, and these account well for jerk features that have recently been documented by satellite and ground observations. The more realistic timescales in the simulation reported here allow further details to be distinguished, such as multiple temporal alternations of geomagnetic acceleration pulses at low latitudes, long-range synchronisation of pulse foci in space and rapid longitudinal westward drift of these foci at the core surface. The strongest events in the catalog arise from disruption of the leading-order force balance near or at the core surface, from the combined influence of the arrival of buoyancy plumes and magnetic field rearrangement at the core surface. The hydromagnetic waves that are sent laterally and downwards generate signals that clearly illustrate the presence of nearly synchronous 'V-shaped' magnetic variation patterns over a wide portion of Earth's surface and also at mid to high latitudes, despite the source being confined in equatorial regions of the core surface. Other well-known characteristics of strong geomagnetic jerks such as surges in the intensity of the secular variation and inflexions in the length-of-day variations are also reproduced in these events. Irrespectively of the event strength, the results therefore support the hypothesis of a single physical root cause - the emission of hydromagnetic magneto-inertial waves following a disruption of the QG-MAC balance - for jerks observed throughout the geomagnetic record.

In order to understand the processes involved in the deep interior of the Earth and explaining its evolution, in particular the dynamics of the Earth’s fluid iron-rich outer core, only indirect satellite and ground observations are available. They each provide invaluable information about the core flow but are incomplete on their own:
- The time dependent magnetic field, originating mainly within the core, can be used to infer the motions of the fluid at the top of the core on decadal and subdecadal time scales.
- The time dependent gravity field variations that reflect changes in the mass distribution within the Earth and at its surface occur on a broad range of time scales. Decadal and interannual variations include the signature of the flow inside the core, though they are largely dominated by surface contributions related to the global water cycle and climate-driven land ice losses.
- Earth rotation changes (or variations in the length of the day) also occur on these time scales, and are largely related to the core fluid motions through exchange of angular momentum between the core and the mantle at the core-mantle boundary.
The “core contributions” on these observations are all related to the core flow that can also be modelled. In terms of modelling, we consider that the core is fully coupled with the mantle and allow for viscosity, magnetic field and rotation to intervene.
Here, we present the main activities proposed in the frame of the GRACEFUL ERC project, which aims to combine information about the core deduced from the gravity field, from the magnetic field and from the Earth rotation in synergy, in order to examine in unprecedented depth the dynamical processes occurring inside the core and at the core-mantle boundary.

The lateral and vertical thermochemical heterogeneity in the mantle is a long-standing question in geodynamics. The forces that control mantle flow and therefore Plate Tectonics arise from the density and viscosity lateral and vertical variations. A common approach to estimate the density field for geodynamical purposes is to simply convert seismic tomography anomalies sometimes assuming constraints from mineral physics. Such converted density field does not match in general with the observed gravity field, typically predicting anomalies the amplitudes of which are too large. Knowledge on the lateral variations in lithospheric density is essential to understand the dynamic/residual isostatic components of the Earth’s topography linking deep and surface processes. The cooling of oceanic lithosphere, the bathymetry of mid oceanic ridges, the buoyancy and stability of continental cratons or the thermochemical structure of mantle plumes are all features central to Plate Tectonics that are dramatically related to mantle temperature and composition.We present a new global thermochemical model of the lithosphere and underlying upper mantle constrained by state-of-the-art seismic waveform inversion, satellite gravity (geoid and gravity anomalies and gradiometric measurements from ESA's GOCE mission), surface elevation and heat flow data: WINTERC-G. The model is based upon an integrated geophysical-petrological approach where mantle seismic velocities and density are computed within a thermodynamically self-consistent framework, allowing for a direct parameterization in terms of the temperature and composition variables. The complementary sensitivities of the data sets allow us to constrain the geometry of the lithosphere-asthenosphere boundary, to separate thermal and compositional anomalies in the mantle, and to distinguish dynamic vs isostatic surface-elevation contributions. At long spatial wavelengths, our model is generally consistent with previous seismic (or seismically derived) global models and earlier integrated studies incorporating surface-wave data at lower lateral resolution. At finer scales, the temperature, composition and density distributions in WINTERC-G offer a new state of the art image at a high resolution globally (225 km average inter-knot spacing).