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Fig. 5.6. Evolution of upper-mantle temperature (black curve) and surface heat flux (blue curve) vs. time. This model does not take into account plate tectonics and may be more appropriate for Venus or for Mars. The present-day heat flux (80mW/m2) is indicated by a grey arrow assuming that it has decreased during the last billions years. The present temperature is indicated by a black dash arrow assuming a cooling of 100K/Ga. This figure shows the efficiency of plate tectonics to cool down a planet

Numerical experiments have been tested against laboratory experiments and were then applied for conditions closer to those existing on Earth (or other planets). After the onset of convection, there is a transient period (between t1 and t2 on Fig. 5.6). During that period, heat transfer is controlled by cold down-welling as described in Plate 5.2 and Fig. 5.5. Isotopic anomalies of 142Nd in the 3.78Ga old Isua supracrustal belt samples are better described by convection in a conductive-lid regime rather than by convection with plate tectonics (Boyet et al., 2003). After the transient period, scaling laws (e.g. Choblet and Sotin, 2000) can be used to predict evolution of heat flux and mantle temperature (Fig. 5.6). Note that the Earth cools down when the surface heat flux becomes greater than the power produced by the decay of the long-lived radioactive elements. According to Fig. 5.6, this event occurred about 1.8Ga after accretion.

One important limitation of the present model is that it does not take into account plate tectonics in the Earth's evolution. But no model developed so far is able to simulate plate tectonics and thermal convection for temperature-dependent viscosity. One difficulty is that cooling is dominated by 3D structures, which impose 3D modelling and huge computer requirements to account for both the 3D structures and the temperature-dependent viscosity. Figure 5.6 shows that the present value of heat flux (mantle temperature) is higher (lower) than that predicted by the conductive-lid regime of mantle convection. This is consistent with the fact that plate tectonics is much more efficient than conductive-lid convection to transfer heat. Was plate tectonics triggered during the transient period by the cold downwellings? Or did it occur when the Earth started cooling down (maximum of mantle temperature in Fig. 5.6)? The Archaean greenstone belts can be explained by different steps of subduction of an oceanic crust under these Archaean shields (Moorbath, 1979). These observations suggest that subduction existed at least 2.5Ga ago. It could be as old as 3.8Ga if one believes that the oldest rocks found on Earth have undergone transformations linked to plate-tectonics processes.

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