Realistic modelling for Earth's magnetic field reversals – revEarth

1) Direct Numerical Simulations (DNS) of the Earth’s core will be performed employing a high-performance computer program (namely XSHELLS) to time-step the fundamental equations of core dynamics. For well-chosen parameters, magnetic field reversals can be obtained if long-enough simulations are performed.

2) Adaptive Multilevel Splitting (AMS) is an algorithm enabling a DNS to compute large numbers of rare events (such as reversals) together with their probability of occurrence, but without computing excruciatingly long simulations.
We will use it to efficiently compute reversals and associated return times in demanding three-dimensional direct simulations of the Earth’s core. In a nutshell, AMS works with an ensemble of short simulations, among which the furthest away from a reversal are discarded and replaced by new ones starting from a well chosen time among the other simulations. Ideally, in the end, an ensemble of realisations that all display reversals is obtained, and mean time between two reversals is obtained with good accuracy.

3) Mantle General Circulation Models (MGCM) are used to prescribe realistic thermal boundary conditions at the top of the core. It is not in the scope of this project to develop new mantle models. Instead, we will rely on a suite of MGCM recently constructed by Nicolas Coltice and collaborators.
More specifically, we will use a several hundred Myr-long 3D-MGCM with plate-like behaviour to explore the response of the dynamo to a set of representative CMB heat flux distributions and amplitudes.
A twin version includes chemically denser material at the base of the mantle, accounting for the seismically discovered Large Low Shear Velocity Provinces (LLSVP). This model will be used
to try to reproduce the magnetic reversal rate record of the past 300 Myr.

4) Low-dimensional models (LDM), in contrast to DNS, do not need large amount of computing resources and can be computed for geological times on personal computers. Several LDM have been proposed as toymodels or simplified models of geomagnetic reversals. Here, we will consider only stochastic models, where the stochastic forcing accounts for “turbulence” in the core.

1) The implementation of the AMS rare events method was successful and made it possible to simulate several hundred rare events (magnetic pole reversals), with increased efficiency by a factor of around 25 compared to a classic simulation.
The porting of the code for the use of GPUs (which henceforth equip the majority of recent computing machines) is in progress, with a first prototype of promising GPU code, and a communication at the EGU conference.

2) Thanks to the AMS method, we were able to obtain several hundred reversals in a parameter regime that is starting to be realistic on several indicators, both physical and paleomagnetic.
The complete analysis of the reversal sequences is underway.

3) We started by analyzing data from simulations of mantle dynamics over more than a billion years. Heat flux maps at the core-mantle interface were extracted, taking into account the displacement of the rotational axis. A principal component analysis made it possible to identify the dominant patterns of the thermal flux imposed on the surface of the nucleus by the mantle. The influence of heterogeneous heat flux on reversals started with the geodynamo simulation code XSHELLS having been adapted accordingly and validated during the year 2021.

4) A theoretical work on the nature of the magnetic field modes possibly involved in dynamos.
Boundary conditions and spatial variations in the physical properties of fluids are important. We got a theoretical result showing that different problems are assistant problems and therefore have the same dynamo thresholds.

It is still too early to talk about prospects. The rest of the project is looking good, with we hope for great discoveries on the reversals of the Earth's magnetic field and its fundamental mechanisms.

K Gwirtz, M Morzfeld, A Fournier, G Hulot, Can one use Earth’s magnetic axial dipole field intensity to predict reversals?, Geophysical Journal International,(2021), doi.org/10.1093/gji/ggaa542

Efficient spherical harmonic transforms on GPU and its use in planetary core dynamics simulations, N. Schaeffer (EGU 2021)
ui.adsabs.harvard.edu/abs/2021EGUGA..2313680S/abstract

Enhanced dynamo growth in nonhomogeneous conducting fluids F. Marcotte, B. Gallet, F. Pétrélis, and C. Gissinger (2021)
doi.org/10.1103/PhysRevE.104.015110

Improvements of the XSHELLS simulation software:
gricad-gitlab.univ-grenoble-alpes.fr/schaeffn/xshells

Improvements of the SHTNS library:
gricad-gitlab.univ-grenoble-alpes.fr/schaeffn/shtns

The magnetic field of the Earth (the geomagnetic field) forms a protective envelope against the solar wind, which may otherwise erode the atmosphere, as it happened on Mars. As such, strong planetary magnetic fields are arguably necessary for life.
The geological record shows that the geomagnetic field reversed its polarity hundreds of times in the past, at a highly variable rate. In the recent geological history (for the past 25 million years), reversals occurred approximately 4 to 5 times per million year. Further in the past, there exists periods of stable polarity (termed chrons) that lasted for several tens of millions of years. Paleomagnetic data further indicate that reversals are very short events; even if the question remains to be settled, they do not last for more than a few thousands years, which make them almost instantaneous on a geological time scale. This further complicates the detailed description of the properties of the geomagnetic field during a reversal (the transitional field henceforth).
Due to the scarcity of associated data, reversals remain largely unexplained and their consequences uncertain. Numerical simulations appear as a welcome tool to complement this partial understanding.
The magnetic field of our planet is generated and sustained by the circulation of liquid metal deep inside its core. Realistic simulations of this process (termed the geodynamo) are currently restricted to integration intervals short in comparison to the typical duration of a chron in the recent geological record (millennia as opposed to hundreds of millennia, say). By improving an existing state-of-the-art simulation code, combined with a rare event algorithm, we will reach geophysically relevant regimes in reversing geodynamo simulations over an adequate integration interval for the first time.
We plan to build an open database of at least 1000 reversals and excursions (aborted reversals), for further analysis in the framework of this project and beyond. Using our low-viscosity, strong magnetic field simulations, we will investigate the effect of several key factors of the evolution of Earth on the reversal rate and the properties of the transitional field. Particular attention will be paid to the presence and size of the inner-core, and the heterogeneities in the heat flux extracted from the core by the surrounding silicate mantle. Even if these questions have already been addressed in previous high-viscosity studies, the new regime in which our reversing geodynamo simulations operate is currently uncharted territory.
Upon completion of a parametric survey, we will produce a geodynamo simulation spanning 300 million years, subject to a realistic, heterogeneous, and time-varying heat flux extracted by the mantle, using the output of a high-fidelity general circulation model of mantle convection.
In addition, we will combine observations and simulations via data assimilation to assess and calibrate a series of reduced, low-dimensional, models of geomagnetic reversals and excursions.
We will use these simulations to shed light on the physical processes leading to a reversal, to seek robust precursors to reversals, to characterize the typical magnetic field shape and intensity during a reversal, and to estimate the consequences of a reversal for society.