Thermal History and Degassing of the Earth: Some Simple Calculations

The temperature below the zone of melt formation (here given at 100 km) has decreased from about 1630°C at 2.7 B.Y.B.P. for komatiite studied by Arndt (1977) and 1780°C at 3.3 B.Y.B.P. for komatiite studied by Green et al. (1975) to 1400°C at present. As this komatiite probably formed from a small additional amount of melting of a depleted residuum after basalt formation, the difference between eruption and source temperatures is similar to that of primitive basalts. Cooling of the earth by about 300°C over the last 3 B.Y. would supply 1 heat flow unit of surface heat flux compared with the present heat loss of 1.5 heat flow units from the mantle. An analytical formulation was obtained relating the cooling rate of the earth, the amount of radioactive heat generation in the mantle, and the global rate of sea-floor spreading. The release of Ar⁴⁰ produced by K in the mantle provides another relationship between sea-floor spreading and radioactivity, as the mantle ratio K : U : Th is constrained by analyses of samples. Excessive amounts of K in the mantle require rapid sea-floor spreading to produce the observed cooling of the earth and result in excessive Ar⁴⁰ loss. Insufficient K requires slow sea-floor spreading and gives too little Ar⁴⁰. The preferred range of mantle is around 120 ppm with up to 200 ppm (mantle equivalent) K in the core. Global spreading rates have averaged between 3 and 6 km²/yr during the last 3 B.Y.