Thermal evolution of the Earth: effects of volatile exchange between atmosphere and interior

A parameterized model of mantle convection that includes the effects of volatile exchange between the mantle and the surface reservoir and the softening of the mantle by the dissolved volatiles is used to study the thermal history of the Earth. It is assumed that the activation energy for temperature-dependent solid-state creep is a linear function of weight percent of volatiles. The mantle degassing rate is taken to be directly proportional to the rate of seafloor spreading which depends on the mantle heat flow. The rate of regassing also varies with the seafloor spreading rate, but it depends on other factors as well, including the mass of the atmosphere-hydrosphere system and the efficiency of volatile recycling through island arc volcanoes. Because the degassing/regassing rates are a function of convective vigor which is regulated by mantle volatile content (through the volatile dependence of viscosity), the devolatilization/revolatilization of the mantle is self-consistently calculated. Model results indicate that mantle degassing and regassing rates quickly equifibrate during an early stage of rapid Earth cooling and adjust to regulate a more gradual cooling of the Earth over most of geologic time. These adjustments occur in the first several hundred million years of Earth's history. Most of the net volatile release from the mantle (or in some cases, net volatile absorption into the mantle) occurs early, in accord with isotopic evidence for rapid formation of the atmosphere. The net mass of volatiles released from the mantle is easily comparable to that of Earth's oceans. When mantle viscosity depends on both volatile content and temperature, changes in volatile content are compensated by changes in temperature so that the mantle evolves with the viscosity and convective vigor required to transfer its internally generated heat. Thus, the mantle is hotter (colder) as a consequence of degassing (regassing) compared to a mantle with volatile-independent rheology. The ratio of internal heat generation to total heat flow (the Urey ratio) is regulated by the temperature dependence of viscosity; models with high initial Urey ratios build up high temperatures very rapidly, thereby enhancing heat flow and reducing the Urey ratio. Early volatile loss from the mantle leads to a more rapid buildup of high temperature; thus, the "corrective" heat flow occurs even faster. Due to these feedback effects, the present value of the Urey ratio cannot exceed unity.