Alexandre Fournier

International Geomagnetic Reference Field: the 12th generation

The 12th generation of the International Geomagnetic Reference Field (IGRF) was adopted in December 2014 by the Working Group V-MOD appointed by the International Association of Geomagnetism and Aeronomy (IAGA). It updates the previous IGRF generation with a definitive main field model for epoch 2010.0, a main field model for epoch 2015.0, and a linear annual predictive secular variation model for 2015.0-2020.0. Here, we present the equations defining the IGRF model, provide the spherical harmonic coefficients, and provide maps of the magnetic declination, inclination, and total intensity for epoch 2015.0 and their predicted rates of change for 2015.0-2020.0. We also update the magnetic pole positions and discuss briefly the latest changes and possible future trends of the Earth’s magnetic field.

Fast torsional waves and strong magnetic field within the Earth’s core

The magnetic field inside the Earth’s fluid and electrically conducting outer core cannot be directly probed. The root-mean-squared (r.m.s.) intensity for the resolved part of the radial magnetic field at the core–mantle boundary is 0.3 mT, but further assumptions are needed to infer the strength of the field inside the core. Recent diagnostics obtained from numerical geodynamo models indicate that the magnitude of the dipole field at the surface of a fluid dynamo is about ten times weaker than the r.m.s. field strength in its interior, which would yield an intensity of the order of several millitesla within the Earth’s core. However, a 60-year signal found in the variation in the length of day has long been associated with magneto-hydrodynamic torsional waves carried by a much weaker internal field. According to these studies, the r.m.s. strength of the field in the cylindrical radial direction (calculated for all length scales) is only 0.2 mT, a figure even smaller than the r.m.s. strength of the large-scale (spherical harmonic degree n ≤ 13) field visible at the core–mantle boundary. Here we reconcile numerical geodynamo models with studies of geostrophic motions in the Earth’s core that rely on geomagnetic data. From an ensemble inversion of core flow models, we find a torsional wave recurring every six years, the angular momentum of which accounts well for both the phase and the amplitude of the six-year signal for change in length of day detected over the second half of the twentieth century. It takes about four years for the wave to propagate throughout the fluid outer core, and this travel time translates into a slowness for Alfvén waves that corresponds to a r.m.s. field strength in the cylindrical radial direction of approximately 2 mT. Assuming isotropy, this yields a r.m.s. field strength of 4 mT inside the Earth’s core.

Bottom-up control of geomagnetic secular variation by the Earth’s inner core

Temporal changes in the Earth’s magnetic field, known as geomagnetic secular variation, occur most prominently at low latitudes in the Atlantic hemisphere (that is, from −90 degrees east to 90 degrees east), whereas in the Pacific hemisphere there is comparatively little activity. This is a consequence of the geographical localization of intense, westward drifting, equatorial magnetic flux patches at the core surface. Despite successes in explaining the morphology of the geomagnetic field, numerical models of the geodynamo have so far failed to account systematically for this striking pattern of geomagnetic secular variation. Here we show that it can be reproduced provided that two mechanisms relying on the inner core are jointly considered. First, gravitational coupling aligns the inner core with the mantle, forcing the flow of liquid metal in the outer core into a giant, westward drifting, sheet-like gyre. The resulting shear concentrates azimuthal magnetic flux at low latitudes close to the core–mantle boundary, where it is expelled by core convection and subsequently transported westward. Second, differential inner-core growth, fastest below Indonesia, causes an asymmetric buoyancy release in the outer core which in turn distorts the gyre, forcing it to become eccentric, in agreement with recent core flow inversions. This bottom-up heterogeneous driving of core convection dominates top-down driving from mantle thermal heterogeneities, and localizes magnetic variations in a longitudinal sector centred beneath the Atlantic, where the eccentric gyre reaches the core surface. To match the observed pattern of geomagnetic secular variation, the solid material forming the inner core must now be in a state of differential growth rather than one of growth and melting induced by convective translation.

Changes in rotation induced by Pleistocene ice masses with stratified analytical Earth models

The rotational response of the Earth to Pleistocene deglaciation is studied by means of a multilayered, viscoelastic Earth model based on the preliminary reference Earth model (PREM). Incompressible viscoelastic deformation is evaluated from a self-compressed initial state. The novelty of our approach stands on the application of a fully analytical normal mode theory to the response of the Earth to surface loads and variations in the centrifugal potential for large numbers of viscoelastic layers, as requested by PREM. Assuming that both present-day true polar wander (TPW) and changes in the second-degree component of the geopotential are solely due to Pleistocene postglacial rebound, we obtain for a two-layer viscosity model that the upper mantle viscosity must be lowered to about 1–5×1020 Pa s with respect to the classical value of 1021 Pa s. This upper mantle viscosity is accompanied by an increase of the lower mantle viscosity by a factor of 25, in agreement with some recent relative sealevel (RSL) data analyses and convectively supported long-wavelength geoid anomalies. When the viscosity contrast is located at 1470 km depth, TPW and require a viscosity of 1021 Pa s in the upper part of the mantle (above 1470 km depth), with a moderate viscosity increase in the lowermost portion of the mantle. This result indicates that a viscosity of 1021 Pa s is appropriate for a wider portion of the mantle than the upper mantle, in agreement with Haskells [1935] estimate that was not limited to the seismically inferred 670 km boundary.

Dynamical similarity of geomagnetic field reversals

No consensus has been reached so far on the properties of the geomagnetic field during reversals or on the main features that might reveal its dynamics. A main characteristic of the reversing field is a large decrease in the axial dipole and the dominant role of non-dipole components. Other features strongly depend on whether they are derived from sedimentary or volcanic records. Only thermal remanent magnetization of lava flows can capture faithful records of a rapidly varying non-dipole field, but, because of episodic volcanic activity, sequences of overlying flows yield incomplete records. Here we show that the ten most detailed volcanic records of reversals can be matched in a very satisfactory way, under the assumption of a common duration, revealing common dynamical characteristics. We infer that the reversal process has remained unchanged, with the same time constants and durations, at least since 180 million years ago. We propose that the reversing field is characterized by three successive phases: a precursory event, a 180° polarity switch and a rebound. The first and third phases reflect the emergence of the non-dipole field with large-amplitude secular variation. They are rarely both recorded at the same site owing to the rapidly changing field geometry and last for less than 2,500 years. The actual transit between the two polarities does not last longer than 1,000 years and might therefore result from mechanisms other than those governing normal secular variation. Such changes are too brief to be accurately recorded by most sediments.

A case for variational geomagnetic data assimilation: insights from a one-dimensional, nonlinear, and sparsely observed MHD system

Secular variations of the geomagnetic field have been measured with a continuously improving accuracy during the last few hundred years, culminating nowadays with satellite data. It is however well known that the dynamics of the magnetic field is linked to that of the velocity field in the core and any attempt to model secular variations will involve a coupled dynamical system for magnetic field and core velocity. Unfortunately, there is no direct observation of the velocity. Independently of the exact nature of the above-mentioned coupled system – some version being currently under construction – the question is debated in this paper whether good knowledge of the magnetic field can be translated into good knowledge of core dynamics. Furthermore, what will be the impact of the most recent and precise geomagnetic data on our knowledge of the geomagnetic field of the past and future? These questions are cast into the language of variational data assimilation, while the dynamical system considered in this paper consists in a set of two oversimplified one-dimensional equations for magnetic and velocity fields. This toy model retains important features inherited from the induction and Navier-Stokes equations: non-linear magnetic and momentum terms are present and its linear response to small disturbances contains Alfven waves. It is concluded that variational data assimilation is indeed appropriate in principle, even though the velocity field remains hidden at all times; it allows us to recover the entire evolution of both fields from partial and irregularly distributed information on the magnetic field. This work constitutes a first step on the way toward the reassimilation of historical geomagnetic data and geomagnetic forecast.

Turbulent geodynamo simulations: a leap towards Earth’s core

We present an attempt to reach realistic turbulent regime in direct numerical simulations of the geodynamo. We rely on a sequence of three convection-driven simulations in a rapidly rotating spherical shell. The most extreme case reaches towards the Earths core regime by lowering viscosity (magnetic Prandtl number Pm=0.1) while maintaining vigorous convection (magnetic Reynolds number Rm>500) and rapid rotation (Ekman number E=1e-7), at the limit of what is feasible on todays supercomputers. A detailed and comprehensive analysis highlights several key features matching geomagnetic observations or dynamo theory predictions – all present together in the same simulation – but it also unveils interesting insights relevant for Earths core dynamics. In this strong-field, dipole-dominated dynamo simulation, the magnetic energy is one order of magnitude larger than the kinetic energy. The spatial distribution of magnetic intensity is highly heterogeneous, and a stark dynamical contrast exists between the interior and the exterior of the tangent cylinder (the cylinder parallel to the axis of rotation that circumscribes the inner core). In the interior, the magnetic field is strongest, and is associated with a vigorous twisted polar vortex, whose dynamics may occasionally lead to the formation of a reverse polar flux patch at the surface of the shell. Furthermore, the strong magnetic field also allows accumulation of light material within the tangent cylinder, leading to stable stratification there. Torsional Alfven waves are frequently triggered in the vicinity of the tangent cylinder and propagate towards the equator. Outside the tangent cylinder, the magnetic field inhibits the growth of zonal winds and the kinetic energy is mostly non-zonal. Spatio-temporal analysis indicates that the low-frequency, non-zonal flow is quite geostrophic (columnar) and predominantly large-scale: an m=1 eddy spontaneously emerges in our most extreme simulations, without any heterogeneous boundary forcing. Our spatio-temporal analysis further reveals that (i) the low-frequency, large-scale flow is governed by a balance between Coriolis and buoyancy forces – magnetic field and flow tend to align, minimizing the Lorentz force; (ii) the high-frequency flow obeys a balance between magnetic and Coriolis forces; (iii) the convective plumes mostly live at an intermediate scale, whose dynamics is driven by a 3-term 1 MAC balance – involving Coriolis, Lorentz and buoyancy forces. However, small-scale (E^{1/3}) quasi-geostrophic convection is still observed in the regions of low magnetic intensity.

Spherical convective dynamos in the rapidly rotating asymptotic regime

Self-sustained convective dynamos in planetary systems operate in an asymptotic regime of rapid rotation, where a balance is thought to hold between the Coriolis, pressure, buoyancy and Lorentz forces (the MAC balance). Classical numerical solutions have previously been obtained in a regime of moderate rotation where viscous and inertial forces are still significant. We define a unidimensional path in parameter space between classical models and asymptotic conditions from the requirements to enforce a MAC balance and to preserve the ratio between the magnetic diffusion and convective overturn times (the magnetic Reynolds number). Direct numerical simulations performed along this path show that the spatial structure of the solution at scales larger than the magnetic dissipation length is largely invariant. This enables the definition of large-eddy simulations resting on the assumption that small-scale details of the hydrodynamic turbulence are irrelevant to the determination of the large-scale asymptotic state. These simulations are shown to be in good agreement with direct simulations in the range where both are feasible, and can be computed for control parameter values far beyond the current state of the art, such as an Ekman number

Deciphering records of geomagnetic reversals

E=10^{-8}

Hydromagnetic quasi-geostrophic modes in rapidly rotating planetary cores

. We obtain strong-field convective dynamos approaching the MAC balance and a Taylor state to an unprecedented degree of accuracy. The physical connection between classical models and asymptotic conditions is shown to be devoid of abrupt transitions, demonstrating the asymptotic relevance of classical numerical dynamo mechanisms. The fields of the system are confirmed to follow diffusivity-free, power-based scaling laws along the path.