A simple parameterized model of Earth's thermal history with the transition from layered to whole mantle convection

Abstract

Recent studies of mantle convection suggest a possible scenario for Earth's history in which the convection has changed its style from layered to whole mantle because of the existence of an endothermic phase boundary. To understand the possible thermal consequence of this ‘transition’, we shall re-examine the thermal history of Earth with different types of convection mode (i.e., whole mantle convection, layered mantle convection and convection with a transition) using a simple parameterized scheme. For the whole mantle convection model we shall confirm the results presented by previous workers (i.e., a small β of <0.1 (the index of the power-law relation between the Nusselt and Rayleigh numbers) is required for a low Urey ratio (∼ 0.4) Earth. For the layered case the Urey ratio, β and the concentration of the radiogenic heat source in the lower mantle are restricted by the melting constraints. In order to avoid massive melting of the mantle at present and in the past, a depleted lower mantle is required, which confirms the results of the previous studies, although the amount of depletion is not so large as previous estimates. We shall also show that a low β (e.g., < 0.1) and low Urey ratio (∼ 0.4) Earth are not favourable for layered convection models, because they will predict massive melting of the mantle in the past and at the present. For the transition-type convection model, we find that early transition (e.g., older than 1 Ga B.P. is allowed for low β (< 0.1) with a low Urey ratio (∼ 0.4) or for high β (> 0.2) with a high Urey ratio (∼ 0.8). This is almost identical to the whole mantle case. The implication is that, because whole mantle convection is powerful enough, Earth may loose the memory of early layering that may have existed more than 1 Ga B.P. The change in flow velocity associated with the transition is expected to be a factor of five or more. The temperature of the upper mantle before the transition took place may be lower than the present mantle temperature.