Energetics of mantle convection and the fate of fossil heat

Reconstructing the thermal history of the Earth, consistent with the low concentration of heat-producing elements in convecting mantle as well as with modest secular cooling required by geological records, has been a major challenge in geophysics and geochemistry. By developing the self-consistent energetics of plate-tectonic mantle convection, we show that the low Urey ratio of convecting mantle can yield a geologically reasonable solution in the thermal evolution model of the Earth. The effect of dehydration on mantle rheology during plate formation with mantle melting results in more sluggish plate tectonics (i.e., lower heat flow) for hotter mantle. This inverse relationship between mantle temperature and surface heat flux leads to the efficient storage of fossil heat, preventing the drastic secular cooling of the Earth.