Thermal history of the Earth: a corollary concerning non-linear mantle rheology

Mantle rheology and the convective cooling process exert a close mutual control on one another, so that the cooling rate can be calculated with only a rudimentary idea of the material properties of the mantle. However, the distinction between linear, i.e. Newtonian, viscous behaviour and non-linear or power-law rheology, in which the creep rate ε{lunate} depends upon stress σ as σ with n > 1, it isportant. We find that the present rate of loss of residual heat is almost twice as great with n = 3 as it si tn the linear case (n = 1). Since this net heat loss is simply the difference between the observed total mantle heat flux and the radiogenic heat input, the radioactive content of the mantle is predicted to be substantially less in the non-linear case. An examination of the plausible ranges of the U, Th and K contents of the mantle shows that the requirement for radiogenic heat by the linear model us unreasonably high. This observation strengthens an earlier very tentative conclusion, based on temperatures of komatiite lavas, that convective mantle rheology is non-linear. The alternative conclusion would be that the Earth contains ≈ 30 ppb of U compared with carbonaceous chondrites (20 ppb) or ordinary chondrites (15 ppb)