Modelling the effects of internal heating in the core and lowermost mantle on the earth’s magnetic history

Recently, an incompatible-element enriched reservoir, bearing a high degree of radioactive heating, has been proposed to exist at the base of the mantle. This scenario has been discussed based on parameterized thermal and magnetic models of the core [Buffett, B.A., 2002. Estimates of heat flow in the deep mantle based on the power requirements for the geodynamo. Geophys. Res. Lett. 29(12), 7], as well as on geochemical grounds [Tolstikhin, I., Hofmann, A.W., 2005. Early crust on top of the Earth’s core. Phys. Earth Plan. Int., 148, 109-130; Boyet M., Carlson, R.W., 2005. Nd142 Evidence for early (>4.53>4.53 Ga) global differentiation of the sillicate earth. Science 309, 576-581]. A high degree of radioactivity at the base of the mantle [Buffett, B.A., 2003. The thermal state of Earth’s core. Science 299, 1675-1677], or alternatively the presence of radioactivity in the core [e.g., Labrosse, S., 2003. Thermal and magnetic evolution of the Earth’s core. Phys. Earth Plan. Int. 140, 127-143; Nimmo F., Price, G.D., Brodholt, J., Gubbins, D., 2004. The influence of potassium on core and geodynamo evolution. Geophys. J. Int. 156, 363-376], have been proposed as means to allow sufficient buoyancy to power the geodynamo and maintain a magnetic field throughout most of the Earth’s history as palaeomagnetic records indicate [McElhinny, M.W., Senanayake, W.E., 1980. Paleomagnetic evidence for the existence of the geomagnetic field 3.5 Ga ago. J. Geophys. Res. 85, 3523-3528; Hale, C.J., D.J. Dunlop, 1984. Evidence for an early Archean geomagnetic field: a paleomagnetic study of the Komati Formation, Barberton Greenstone Belt, South Africa. Geophys. Res. Lett. 11, 97-100], while maintaining a sufficiently high temperature in the core. The present paper analyzes the consequences of internal heating in the core and the lowermost mantle on the core’s magnetic history using numerical simulations of convection in the mantle coupled to an energy balance model for the core. This method allows feed-back at each time step between the cooling histories in the core and mantle through the heat flux and temperature at the core-mantle boundary (CMB). We employ a two dimensional, spherical-axisymmetric model of convection in the Earth’s mantle, coupled to a heat reservoir model for the core. We calculate at each time-step the entropy available for ohmic dissipation in the core and use this result to estimate the intensity of a magnetic field generated by geodynamo action. In agreement with Nimmo et al. [Nimmo F., Price, G.D., Brodholt, J., Gubbins, D., 2004. The influence of potassium on core and geodynamo evolution. Geophys. J. Int. 156, 363-376], we find that the presence of 300 ppm potassium in the core allows for a magnetic field to have existed over the lifetime of the Earth with a reasonable final value for the temperature at the CMB. Almost all of the models with high internal heating at the base of the mantle exhibit warming of the core throughout much of the Earth’s thermal history, a state that would prohibit a functioning geodynamo. In one simulation, we are driven to a scenario where the inner core has existed over the lifetime of the Earth only to gradually melt and then refreeze, with a functioning geodynamo existing for a short time. We conclude that careful tuning of the mantle viscosity, internal heating rate and initial core temperatures would be required in order to achieve a magnetic field over the lifetime of the Earth in the presence of a basal layer with a high degree of internal heating and therefore such a scenario must be better constrained before it could present itself as viable.