Dynamo constraints on the long-term evolution of Earth’s magnetic field strength

Abstract

SUMMARY Elucidating the processes in the liquid core that have produced observed palaeointensity changes over the last 3.5 Gyr is crucial for understanding the dynamics and long-term evolution of Earth’s deep interior. We combine numerical geodynamo simulations with theoretical scaling laws to investigate the variation of Earth’s magnetic field strength over geological time. Our approach follows the study of Aubert et al., adapted to include recent advances in numerical simulations, mineral physics and palaeomagnetism. We first compare the field strength within the dynamo region and on the core–mantle boundary (CMB) between a suite of 314 dynamo simulations and two power-based theoretical scaling laws. The scaling laws are both based on a Quasi-Geostropic (QG) force balance at leading order and a Magnetic, Archimedian, and Coriolis (MAC) balance at first order and differ in treating the characteristic length scale of the convection as fixed (QG-MAC-fixed) or determined as part of the solution (QG-MAC-free). When the data set is filtered to retain only simulations with magnetic to kinetic energy ratios greater than at least two we find that the internal field together with the root-mean-square and dipole CMB fields exhibit power-law behaviour that is compatible with both scalings within uncertainties arising from different heating modes and boundary conditions. However, while the extrapolated intensity based on the QG-MAC-free scaling matches Earth’s modern CMB field, the QG-MAC-fixed prediction shoots too high and also significantly overestimates palaeointensities over the last 3.5 Gyr. We combine the QG-MAC-free scaling with outputs from 275 realizations of core–mantle thermal evolution to construct synthetic true dipole moment (TDM) curves spanning the last 3.5 Gyr. Best-fitting TDMs reproduce binned PINT data during the Bruhnes and before inner core nucleation (ICN) within observational uncertainties, but PINT does not contain the predicted strong increase and subsequent high TDMs during the early stages of inner core growth. The best-fitting models are obtained for a present-day CMB heat flow of 11–16 TW, increasing to 17–22 TW at 4 Ga, and predict a minimum TDM at ICN.

Early Cambrian renewal of the geodynamo and the origin of inner core structure

“…This relatively rapid recovery agrees with expectations of new energy sources to power the geodynamo from inner core growth. We note that the rapid increase is predicted by thermal evolution/geodynamo models employing scaling laws 6,40,41 .…”

Combined dynamical and morphological characterisation of geodynamo simulations

“…Moving along the path towards Earth-like conditions they found increasing ratios of magnetic to kinetic energy and ohmic to viscous dissipation, which are expected on theoretical grounds (Davidson, 2013). Davies et al (2022) pointed out that QG-MAC theory smoothly links the root-mean-square (RMS) magnetic field strength both in the bulk and at the CMB as well as the CMB dipole field strength between simulations and estimates for present-day Earth. However, while some QG-MAC dynamos have been shown to exhibit Earth-like magnetic fields according to the compliance test (Aubert et al, 2013(Aubert et al, , 2017, a systematic link between the dynamo dynamics, as measured by the force balance, and the observed field morphology, as measured by the compliance criteria, has yet to be established.…”

Large hot provinces at the base of the mantle stabilise the palaeomagnetic field

“…Our results provide evidence of remarkable stability in the palaeosecular variation of the magnetic field over the last 3 billion years and indicate that the assumption of uniformitarian GAD-like field behaviour over most of geological time is not unreasonable. That long-term average PSV has displayed such invariance is a somewhat surprising finding given that the secular evolution of Earth's core is expected to have radically affected the dynamo process responsible for generating this field during its long history [24][25][26] . To deduce possible mechanisms for producing this long-term stability, we investigated the capacity of numerical models to replicate our PSV observations using the outputs of a set of 88 geodynamo simulations (51 of which have been previously published 27,28 29 ) each run with unique input parameters (Table S1; Methods).…”