On the partitioning of mantle heat loss below oceans and continents over time and its relationship to the Archaean paradox

The Archaean paradox stems from the fact that while certain lines of evidence suggest that Archaean continental geotherms were similar to those at present, other lines of evidence suggest that the average mantle heat flux was considerably greater. The simplest qualitative solution, which holds that a greater proportion of heat loss was carried by the creation and subduction of oceanic lithosphere in the Earth's past, has lacked a clear physical basis. At a fundamental level, it requires that the ratio of mantle heat loss below oceans to that below continents be an increasing function of overall convective vigour and, to date, no self-consistent model has been used to suggest a means by which this could be so. A simple means is suggested by models that allow accumulations of chemically light near-surface material, analogues to continents, to form within the upper thermal boundary layer of a thermally convecting and chemically dense fluid, an analogue to the mantle. The physical properties of continental crust cause the thermal coupling condition between a model continent and the convectively unstable mantle below to be different from that which exists at the interface between mantle and oceans. For the latter, a spatially constant temperature condition holds due to (1) the participation of oceanic crust in convective mantle overturn and (2) the large effective thermal conductivity of oceans relative to the mantle. For the former, a spatially near-constant equilibrium heat flux condition holds due to (1) the long-term stability of continental crust against remixing into the mantle and (2) the comparable thermal conductivities of distinct rock types. This leads to a laterally variable thermal condition at the surface of the convecting mantle, which, in turn, leads to different local mantle heat flux behaviour in continental versus oceanic regions. As a result, heat flux below continents can increase at a slower rate, with increasing convective vigour, than it does elsewhere. Model heat-flux scalings are used to assess the degree to which continental geotherms can be time-stabilized by this means. Results suggest that the thermal surface heterogeneity imposed on the mantle by the presence of continental crust can prevent wide-scale crustal melting in the Archaean by forcing oceans to carry a greater proportion of the Earth's heat-loss load in the past.