Tarduno, J. A. et al. Geodynamo, solar wind, and magnetopause 3.4 to 3.45 billion years ago. Science 327, 1238–1240 (2010).
Biggin, A. J. et al. Palaeomagnetism of Archaean rocks of the Onverwacht Group, Barberton Greenstone Belt (southern Africa): evidence for a stable and potentially reversing geomagnetic field at ca. 3.5Ga. Earth Planet. Sci. Lett. 302, 314–328 (2011).
Nimmo, F. in Treatise on Geophysics Vol. 8 (ed. Schubert, G.) 27–55 (Elsevier, 2015).
Glatzmaier, G. A. & Roberts, P. H. A three-dimensional self-consistent computer simulation of a geomagnetic field reversal. Nature 377, 203–209 (1995).
Kuang, W. & Bloxham, J. An Earth-like numerical dynamo model. Nature 389, 371–374 (1997).
Christensen, U. R., Aubert, J. & Hulot, G. Conditions for Earth-like geodynamo models. Earth Planet. Sci. Lett. 296, 487–496 (2010).
Aubert, J., Finlay, C. C. & Fournier, A. Bottom-up control of geomagnetic secular variation by the Earth’s inner core. Nature 502, 219–223 (2013).
Yadav, R. K., Gastine, T., Christensen, U. R., Wolk, S. J. & Poppenhaeger, K. Approaching a realistic force balance in geodynamo simulations. Proc. Natl Acad. Sci. 113, 12065–12070 (2016).
Schaeffer, N., Jault, D., Nataf, H.-C. & Fournier, A. Turbulent geodynamo simulations: a leap towards Earth’s core. Geophys. J. Int. 211, 1–29 (2017).
Sheyko, A., Finlay, C., Favre, J. & Jackson, A. Scale separated low viscosity dynamos and dissipation within the Earth’s core. Sci. Rep. 8, 12566 (2018).
Aubert, J. State and evolution of the geodynamo from numerical models reaching the physical conditions of Earth’s core. Geophys. J. Int. 235, 468–487 (2023).
Labrosse, S. Thermal evolution of the core with a high thermal conductivity. Phys. Earth Planet. Inter. 247, 36–55 (2015).
Davies, C. J. Cooling history of Earth’s core with high thermal conductivity. Phys. Earth Planet. Inter. 247, 65–79 (2015).
Biggin, A. J. et al. Palaeomagnetic field intensity variations suggest Mesoproterozoic inner-core nucleation. Nature 526, 245–248 (2015).
Bono, R. K., Tarduno, J. A., Nimmo, F. & Cottrell, R. D. Young inner core inferred from Ediacaran ultra-low geomagnetic field intensity. Nat. Geosci. 12, 143–147 (2019).
Bloxham, J. Sensitivity of the geomagnetic axial dipole to thermal core–mantle interactions. Nature 405, 63–65 (2000).
Landeau, M., Aubert, J. & Olson, P. The signature of inner-core nucleation on the geodynamo. Earth Planet. Sci. Lett. 465, 193–204 (2017).
Mound, J. E. & Davies, C. J. Longitudinal structure of Earth’s magnetic field controlled by lower mantle heat flow. Nat. Geosci. 16, 380–385 (2023).
Sakuraba, A. & Kono, M. Effect of the inner core on the numerical solution of the magnetohydrodynamic dynamo. Phys. Earth Planet. Inter. 111, 105–121 (1999).
Zhan, X., Zhang, K. & Zhu, R. A full-sphere convection-driven dynamo: implications for the ancient geomagnetic field. Phys. Earth Planet. Inter. 187, 328–335 (2011).
Wicht, J. & Sanchez, S. Advances in geodynamo modelling. Geophys. Astrophys. Fluid Dyn. 113, 2–50 (2019).
Roberts, P. H. & King, E. M. On the genesis of the Earth’s magnetism. Rep. Prog. Phys. 76, 096801 (2013).
Kageyama, A. & Sato, T. Computer simulation of a magnetohydrodynamic dynamo. II. Phys. Plasmas 2, 1421–1431 (1995).
Christensen, U., Olson, P. & Glatzmaier, G. A. A dynamo model interpretation of geomagnetic field structures. Geophys. Res. Lett. 25, 1565–1568 (1998).
Kida, S., Araki, K. & Kitauchi, H. Periodic reversals of magnetic field generated by thermal convection in a rotating spherical shell. J. Phys. Soc. Jpn. 66, 2194–2201 (1997).
King, E. M. & Buffett, B. A. Flow speeds and length scales in geodynamo models: the role of viscosity. Earth Planet. Sci. Lett. 371-372, 156–162 (2013).
Sakuraba, A. & Roberts, P. H. Generation of a strong magnetic field using uniform heat flux at the surface of the core. Nat. Geosci. 2, 802–805 (2009).
Sheyko, A., Finlay, C. C. & Jackson, A. Magnetic reversals from planetary dynamo waves. Nature 539, 551–554 (2016).
Aubert, J., Gastine, T. & Fournier, A. Spherical convective dynamos in the rapidly rotating asymptotic regime. J. Fluid Mech. 813, 558–593 (2017).
Aubert, J. & Finlay, C. C. Geomagnetic jerks and rapid hydromagnetic waves focusing at Earth’s core surface. Nat. Geosci. 12, 393–398 (2019).
Aubert, J., Livermore, P. W., Finlay, C. C., Fournier, A. & Gillet, N. A taxonomy of simulated geomagnetic jerks. Geophys. J. Int. 231, 650–672 (2022).
Aubert, J. Approaching Earth’s core conditions in high-resolution geodynamo simulations. Geophys. J. Int. 219, S137–S151 (2019).
Schwaiger, T., Gastine, T. & Aubert, J. Relating force balances and flow length scales in geodynamo simulations. Geophys. J. Int. 224, 1890–1904 (2021).
Dormy, E. Strong-field spherical dynamos. J. Fluid Mech. 789, 500–513 (2016).
Kent, D. V. & Smethurst, M. A. Shallow bias of paleomagnetic inclinations in the Paleozoic and Precambrian. Earth Planet. Sci. Lett. 160, 391–402 (1998).
Veikkolainen, T., Evans, D. A., Korhonen, K. & Pesonen, L. J. On the low-inclination bias of the Precambrian geomagnetic field. Precambrian Res. 244, 23–32 (2014).
Biggin, A. J. et al. Quantitative estimates of average geomagnetic axial dipole dominance in deep geological time. Nat. Commun. 11, 6100 (2020).
Jackson, A., Jonkers, A. R. T. & Walker, M. R. Four centuries of geomagnetic secular variation from historical records. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 358, 957–990 (2000).
Finlay, C. C. et al. The CHAOS-7 geomagnetic field model and observed changes in the South Atlantic Anomaly. Earth Planets Space 72, 156 (2020).
Roberts, P. H. in Treatise on Geophysics Vol. 8 (ed. Schubert, G.) 57–90 (Elsevier, 2015).
Marti, P. & Jackson, A. A fully spectral methodology for magnetohydrodynamic calculations in a whole sphere. J. Comput. Phys. 305, 403–422 (2016).
de Koker, N., Steinle-Neumann, G. & Vlček, V. Electrical resistivity and thermal conductivity of liquid Fe alloys at high P and T, and heat flux in Earth’s core. Proc. Natl Acad. Sci. 109, 4070–4073 (2012).
Pozzo, M., Davies, C., Gubbins, D. & Alfè, D. Thermal and electrical conductivity of iron at Earth’s core conditions. Nature 485, 355–358 (2012).
Greenspan, H. P. The Theory of Rotating Fluids (Cambridge Univ. Press, 1968).
Schwaiger, T., Gastine, T. & Aubert, J. Force balance in numerical geodynamo simulations: a systematic study. Geophys. J. Int. 219, S101–S114 (2019).
Calkins, M. A., Orvedahl, R. J. & Featherstone, N. A. Large-scale balances and asymptotic scaling behaviour in spherical dynamos. Geophys. J. Int. 227, 1228–1245 (2021).
Taylor, J. B. The magneto-hydrodynamics of a rotating fluid and the earth’s dynamo problem. Proc. R. Soc. Lond. A Math. Phys. Sci. 274, 274–283 (1963).
Bono, R. K. et al. The PINT database: a definitive compilation of absolute palaeomagnetic intensity determinations since 4 billion years ago. Geophys. J. Int. 229, 522–545 (2022).
Constable, C., Korte, M. & Panovska, S. Persistent high paleosecular variation activity in southern hemisphere for at least 10 000 years. Earth Planet. Sci. Lett. 453, 78–86 (2016).
Jackson, A. Intense equatorial flux spots on the surface of the Earth’s core. Nature 424, 760–763 (2003).
Marti, P. et al. Full sphere hydrodynamic and dynamo benchmarks. Geophys. J. Int. 197, 119–134 (2014).
Livermore, P. W., Jones, C. A. & Worland, S. J. Spectral radial basis functions for full sphere computations. J. Comput. Phys. 227, 1209–1224 (2007).
Lin, Y. & Jackson, A. Large-scale vortices and zonal flows in spherical rotating convection. J. Fluid Mech. 912, A46 (2021).
Wicht, J. & Christensen, U. R. Torsional oscillations in dynamo simulations. Geophys. J. Int. 181, 1367–1380 (2010).
Varga, P., Denis, C. & Varga, T. Tidal friction and its consequences in palaeogeodesy, in the gravity field variations and in tectonics. J. Geodyn. 25, 61–84 (1998).
Backus, G., Parker, R. & Constable, C. Foundations of Geomagnetism (Cambridge Univ. Press, 1996).
