Response to Comment on “ Intermittent Plate Tectonics ? ”

The realization that Earth may have lost heat more slowly in the past than at present has motivated the search for mechanisms to reduce the efficiency of plate tectonics in the past. Several mechanisms have been proposed, such as the resistance to subduction of thick plates (1) produced by deeper melting at higher mantle temperatures (2). We (3) proposed an alternative mechanism, namely subduction termination by continent-continent collision. Our basic argument is that if plate tectonics has worked at roughly half of its modern efficiency, through intermittency, this could explain the reduced loss of heat throughout Earth’s history. The primary issue raised by Korenaga (4) is that we have underestimated Earth’s heat flux during periods without plate tectonics. Korenaga argues for a modification of our heat-flux parameterization for variable-efficiency plate tectonics [equation 1 in (4)] by introducing a term, Qmin, the heat flux in the absence of plate tectonics [equation 2 in (4)]. In using equation 1, we have implicitly assumed that Qmin is small and can be ignored, and equation 2 reduces to equation 1 in this limit. In contrast, Korenaga (4) argues that Qmin is sufficiently large that intermittent plate tectonics does not prevent “thermal catastrophe.” In this view, plate tectonics is only marginally more efficient than stagnant-lid convection in removing heat. The main issue, therefore, is the magnitude of Qmin. Korenaga suggests that for Qmin to be small (roughly an order of magnitude below present-day heat flux), the thermal boundary layer should be about an order of magnitude larger than its present value. Thus far, we agree with this assessment. He then argues that such an outcome is unlikely for two reasons: (i) there is an upper limit of ~100 km for the thickness of oceanic lithosphere, and (ii) even if lithospheric thickness could become thicker, it would take much longer for Q to approach Qmin than is assumed by our model. We address both of these points below. Our assumption thatQmin is small is based on extensive literature discussing heat flux associated with stagnant-lid convection (5–9). These studies show that for a given internal temperature, the difference in heat flux between platetectonic and stagnant-lid modes is greater than an order of magnitude [see figure 4 in (6)]. Indeed, Solomatov and Moresi (5) calculated a reduction by a factor of 5 in heat flux after an instantaneous change from plate tectonics to stagnant-lid tectonics for Venus [see figure 13 in (5)]. Thus, the maximum thickness of the thermal boundary layer is critical in determining the magnitude of heat flux during stagnant-lid convection. To illustrate this point, we show calculations of Earth’s thermal evolution for three cases in which the normalized heat flow during stagnant-lid periods (e.g., Q%min 1⁄4 Qmin=QPT ) is a factor of 0.5, 0.2, and 0.1 of the modern plate tectonic heat flow (QPT ~ 36 TW) (Fig. 1). These cases correspond to effective boundary-layer thicknesses of ~100 km [the case considered in (4)], 250 km, and 500 km, respectively. We find that although Q%min 1⁄4 0:5 results in “thermal catastrophe,” the other two cases are consistent with the available geologic evidence, particularly over the past 3 billion years where the calculated extrapolation from the present is most robust. Indeed, the predicted thermal evolution forQ%min 1⁄4 0:2 is similar to that for a large initial Urey ratio (e.g., g0 = 0.7), a model frequently proposed as a means by which “thermal catastrophe” could be avoided [e.g., (9)]. The question raised by Korenaga (4) is thus whether the thermal boundary-layer thickness in oceanic regions is limited to ~100 km. We contend that there is no strong evidence for this limit. There has been a long-standing controversy as to whether the half-space cooling (HSC) model or a plate model is more appropriate for Earth. Indeed, several studies [e.g., (10, 11)], including one by Korenaga (12), have argued that HSC is preferable. Moreover, even if such a limit currently exists, it is likely produced by plate tectonics itself. The strainrate dependence of viscosity in the dislocation creep regime implies that as plate tectonics slows and ultimately stops, asthenospheric viscosity would increase and the lid thickness would grow. Indeed, the cratonic roots of continents, which are most removed from plate tectonic activity, approach thicknesses ≥250 km (13). The second issue raised in (4) is the time scale over which the thermal boundary layer thickens. Korenaga assumes an instantaneous switch from plate tectonics to stagnant lid. However, our model for intermittent plate tectonics is tied to the long-term history of subduction. Slab flux does not instantaneously drop to zero in the Proterozoic but instead goes from a maximum at 2.5 billion years ago (Ga) to a minimum at 1.0 Ga. During this time, lid thickness should conTECHNICALCOMMENT