A SIMPLE PARAMETERIZED MODEL OF EARTHS THERMAL HISTORY WITH THE TRANSITION FROM LAYERED TO WHOLE MANTLE CONVECTION

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 beta of < 0.1 (the index of the power-law relation between the Nusselt and Rayleigh numbers) is required for a low Urey ratio (similar to 0.4) Earth. For the layered case the Urey ratio, beta 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 beta (e.g., < 0.1) and low Urey ratio (similar to 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 beta (< 0.1) with a low Urey ratio (similar to 0.4) or for high beta (> 0.2) with a high Urey ratio (similar to 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 now 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.