Freeboard revisited: continental growth, crustal thickness change and Earth’s thermal efficiency

The rate of growth of Earth’s continental crust is commonly estimated from the age distribution of present continental crust and from the geochemistry of ancient mantle-derived lavas. In this paper, I assess the rate of growth from relationships between the volume and thickness of continental crust. The thickness of the continental crust is governed by its total volume and by the relative buoyancy of the continental and oceanic lithospheres. The buoyancy of the oceanic lithosphere is governed by the amount of melting at mid-oceanic ridges and the mean age of the ocean floor, which are functions of the mantle temperature and its relationship to global heat loss. Thus, the relationship between continental crustal thickness, continental crustal volume and mantle temperature may be specified provided the functional dependence of global heat loss on mantle temperature is known. Using this relationship, I investigate the implications of crustal growth models for changes in continental crustal thickness over time. If Archean continental crustal volumes had been the same as or similar to modern ones, continental crustal thicknesses would have been significantly greater than today. This would be reflected in subsequently deeply eroded Archean terrains and is inconsistent with the geological record. Sigmoidal growth models, in which significant crustal growth occurred during the Proterozoic, also require several kilometers of erosion for strong dependence of heat loss on mantle temperature, but permit nearly constant continental crustal thicknesses through time if the dependence is weak. With more precise information on the erosion of Archean terrains, it will be possible to constrain both crustal growth models and the nature of the functional dependence of heat loss on mantle temperature.