Plate tectonics, flood basalts and the evolution of Earth’s oceans


  • This article was commissioned by the Editors of Terra Nova to mark the International Year of Planet Earth.

Jun Korenaga, Department of Geology and Geophysics, Yale University, PO Box 208109, New Haven, CT 06520-8109, USA. Tel.: +1 (203) 432 7381; fax: +1 (203) 432 3134; e-mail:


The chemical composition of the bulk silicate Earth (BSE) indicates that the present-day thermal budget of Earth is likely to be characterized by a significant excess of surface heat loss over internal heat generation, indicating an important role of secular cooling in Earth’s history. When combined with petrological constraints on the degree of secular cooling, this thermal budget places a tight constraint on permissible heat-flow scaling for mantle convection, along with implications for the operation of plate tectonics on Earth, the history of mantle plumes and flood basalt magmatism, and the origin and evolution of Earth’s oceans. In the presence of plate tectonics, hotter mantle may have convected more slowly because it generates thicker dehydrated lithosphere, which could slow down subduction. The intervals of globally synchronous orogenies are consistent with the predicted variation of plate velocity for the last 3.6 Gyr. Hotter mantle also produces thicker, buoyant basaltic crust, and the subductability of oceanic lithosphere is a critical factor regarding the emergence of plate tectonics before the Proterozoic. Moreover, sluggish convection in the past is equivalent to reduced secular cooling, thus suggesting a more minor role of mantle plumes in the early Earth. Finally, deeper ocean basins are possible with slower plate motion in the past, and Earth’s oceans in the Archean is suggested to have had about twice as much water as today, and the mantle may have started as dry and have been gradually hydrated by subduction. The global water cycle may thus be dominated by regassing, rather than degassing, pointing towards the impact origin of Earth’s oceans, which is shown to be supported by the revised composition of the BSE.


The thermal history of Earth, after the initial period of global magma ocean, is governed by the balance of surface heat loss and internal heat generation. An initially hot Earth has been gradually cooled down with time because, for most of Earth’s history, surface heat loss has been greater than internal heat supply by radiogenic isotopes. This simple energy balance places first-order constraints on various aspects of physical and chemical processes operating on the surface of Earth and within its deep interior. There have been a number of theoretical studies on Earth’s thermal history (e.g. McKenzie and Weiss, 1975; Davies, 1980; Schubert et al., 1980; Christensen, 1985; Richter, 1985; Solomatov, 2001; Korenaga, 2003; Grigne et al., 2005; Labrosse and Jaupart, 2007), and a review on so far published models on Earth’s thermal evolution has recently been published (Korenaga, 2008b). Estimating a thermal history involves both geophysics (the physics of convective heat loss) and geochemistry (the abundance of heat-producing elements), and many published models do not account for both aspects simultaneously. Available geochemical and geological data place a strict constraint on the permissible range of thermal history, and the most likely scenario is briefly reviewed in the next section.

The purpose of this review article is to discuss some of major geological processes that are directly related to the thermal evolution of Earth, on the basis of this latest understanding. Topics covered include the onset of plate tectonics, the history of mantle plumes, continental growth, and the origin and evolution of Earth’s oceans. They are difficult problems, and little can be said with certainty at present. Because they are intimately coupled with thermal evolution, however, we can still derive a few important constraints. These constraints may be counter-intuitive or not obvious at first sight. Mantle plumes, for example, are often thought to be more active in the past, but such temporal trend is in direct conflict with what thermal evolution indicates. Also, the volume of oceans is unlikely to be constant, and it is probably decreasing with time. Whereas these topics tend to be considered independently, each of them represents a different aspect on the evolution of the integrated Earth system, so a proper understanding of Earth’s thermal history is essential to make self-consistent predictions about them.

Thermal history of earth

Global heat balance equations

The thermal history of Earth may be modelled by integrating the following global energy balance (e.g. Stevenson et al., 1983):




where the subscripts m and c denote the mantle and core components, respectively, Ci is heat capacity, Ti(t) is average temperature, and Hi(t) is internal heat production. Core heat flux, QCMB(t), represents heat exchange between the mantle and the core, and Q(t) is the surface heat flux. The mass of the inner core is denoted by mic(t), and the first term on the right-hand side of Eq. (2) describes the release of latent heat and gravitational energy associated with the growth of the inner core. As mantle evolution is tracked by a single average temperature, this formulation corresponds to whole-mantle convection. Though layered-mantle convection has been a popular concept (e.g. Jacobsen and Wasserburg, 1979; Richter, 1985; Allegre et al., 1996; Kellogg et al., 1999), whole-mantle convection is probably sufficient to explain available geophysical and geochemical data if the uncertainties of these data and the limitation of theoretical predictions are taken into account (Lyubetskaya and Korenaga, 2007b; Korenaga, 2008b). Note that layered mantle convection is still possible. Because it is not well defined (Korenaga, 2008b), however, exploring its implication for Earth’s evolution would require us to deal with more degrees of freedom. For simplicity, therefore, we restrict ourselves to whole-mantle convection in this review, which should serve as a reference when considering more complex convection models (Table 1 presents a summary of major assumptions made in this article).

Table 1.   List of major assumptions employed in this article.
AssumptionRelevant section
Earth’s mantle convects as a single layerThermal History of Earth
Internal heat production in the core is negligibleThermal History of Earth
Mantle dehydration by melting controls global mantle dynamicsThermal History of Earth
Mean sea level has always been close to mean continental levelHistory of Ocean Volume
Seafloor age–area relationship follows a triangular distributionHistory of Ocean Volume
Zero-age depth of seafloor has been approximately constantHistory of Ocean Volume
Average thickness of continental crust has been approximately constantHistory of Ocean Volume

Internal heat production in the core is controversial (e.g. Gessmann and Wood, 2002; McDonough, 2003; Rama Murthy et al., 2003; Lee et al., 2004; Lassiter, 2006), but even if the core contains potassium at 100 p.p.m. level, Hc would be only ∼0.7 TW at present. The energy release due to the inner core growth is similarly small, being on the order of ∼2 TW (e.g. Stevenson et al., 1983). Thus, the first two terms on the right-hand side of Eq. (2) may be neglected for simplicity, and Eqs (1) and (2) may be combined to yield:


where C is the heat capacity of the entire Earth [=Cm+Cc, ∼7 × 1027 J K−1 (Stacey, 1981)] and ΔTCMB(t) is the temperature contrast at the core–mantle boundary. The present-day contrast is estimated to be on the order of 1000 K (e.g. Boehler, 1996; Williams, 1998), but how it should change with time is not understood well. To estimate the temporal variability of the temperature contrast, we need to calculate the core heat flux QCMB(t), which depends critically on the poorly known rheology of the lowermost mantle (e.g. Solomatov, 1996; Karato, 1998; Korenaga, 2005a) and also on other complications such as the presence of chemical heterogeneities (e.g. Farnetani, 1997; Jellinek and Manga, 2002), the post-perovskite phase transition (e.g. Murakami et al., 2004; Oganov and Ono, 2004), and drastic changes in thermal properties (e.g. Badro et al., 2004; Lin et al., 2005). We do not even know why the present-day contrast happens to be ∼1000 K. Thus, it may be reasonable to treat dΔTCMB(t)/dt as a free parameter and see how thermal evolution would be affected by this term. As the simplest option, it is set to zero here, and other possibilities will be explored later (see Core heat flux and the possibility of superheated core). With these simplifying assumptions, the global heat balance can be expressed as:


As the physical state of the early Earth is uncertain, the above differential equation is integrated backward in time, starting with the present-day condition.

Present-day thermal budget

The present-day thermal budget, i.e. Q(0) and Hm(0), may be estimated as follows. The global heat flux is estimated to be 46 ± 3 TW (Jaupart et al., 2007), which is the sum of heat flux due to mantle convection, Q(0), and radiogenic heat production in continental crust, Hcc(0). The latter is estimated to be 7.5 ± 2.5 TW (Rudnick and Gao, 2003), so we may write




where ε1 and ε2 are random variables following the Gaussian distribution of zero mean and unit standard deviation. The use of two independent random variables signifies that the uncertainty of the global heat flux and that of continental heat production are not correlated. Assuming whole-mantle convection, heat production in the bulk silicate Earth (BSE) (i.e. crust and mantle) is estimated to be 16 ± 3 TW (Lyubetskaya and Korenaga, 2007b), so heat production in the convecting mantle may be expressed as:


where ε3 is another random variable following the same Gaussian distribution, and the ‘convective Urey ratio’ (Korenaga, 2008b) is defined as:


These uncertainties are relatively large, allowing unrealistic values [e.g. negative values for Hm(0)], so the following additional constraints are imposed: 5 TW ≤ Hcc(0) ≤ 14 TW and Hm(0) ≥ 3 TW. These a priori bounds are based on published composition models for the continental crust and the convecting mantle (e.g. Jochum et al., 1983; Taylor and McLennan, 1985; Wedepohl, 1995; Rudnick and Gao, 2003; Salters and Stracke, 2004; Workman and Hart, 2005). The resulting probability distribution functions are shown in Fig. 1. It can be seen that Hcc(0) ∼ 8 TW, Hm(0) ∼ 8.5 TW, Q(0) ∼ 38 TW, and Ur(0) ∼ 0.22. For the sake of simplicity, thermal evolution models in this paper are all calculated with these mean values, but it is important to keep in mind that the present-day thermal budget has non-trivial uncertainties and that some uncertainties are strongly correlated [e.g. Hm(0) and Ur(0)]. See Korenaga (2008b) for the effects of such uncertainties on the prediction of thermal histories.

Figure 1.

 Joint probability distribution functions for continental crust heat production Hcc, mantle heat production Hm, convective heat flux Q, and the convective Urey ratio Ur, based on Eqs (5)–(8) with the a priori bounds described in the text. Brighter colour denotes higher probability. Stars correspond to mean values, and ellipses to 68% confidence regions assuming the normal distribution.

Internal heating and surface heat flux

At present, the convecting mantle contains only ∼50% of heat-producing elements in the BSE, but it must have had a larger fraction when the mass of continental crust was smaller in the past. This may be expressed as:


where Hm0(t) and Hcc(t) denote the (hypothetical) evolution of internal heating in the mantle and the continental crust, respectively, without mass transfer between them, and FC(t) is the mass fraction of continental crust with respect to the present-day value [assuming FC(t) ≤ 1 for all t]. The calculation of these internal heating functions is straightforward once the present-day values are specified (e.g. Spohn and Breuer, 1993; Grigne and Labrosse, 2001).

The evolution of surface heat flux Q(t) has to be estimated through heat-flow scaling for mantle convection as there are no direct observations on global heat flow in the past. This scaling issue has been controversial (e.g. Schubert et al., 1980; Christensen, 1985; Gurnis, 1989; Solomatov, 1995; Conrad and Hager, 1999b; Korenaga, 2003). Figure 2 shows three representative scaling laws (see Korenaga (2006) for their derivations). The ‘conventional’ scaling predicts higher heat flux for hotter mantle, and the temperature dependency is dictated by the activation energy of mantle viscosity [a few hundred kJ mol−1, (Karato and Wu, 1993)]. Even in the limit of zero activation energy (‘isoviscous convection’ in Fig. 2), the temperature dependency of heat flow is still positive because heat flow is also proportional to the temperature difference between the surface and the interior. It has been repeatedly shown that the positive temperature dependency does not produce a sensible thermal history consistent with the present-day thermal budget (e.g. Christensen, 1985; Korenaga, 2003). One could resolve this problem by postulating a high Urey ratio at present (e.g. ∼0.7) (Davies, 1980, 1993, 2007; Schubert et al., 1980; Schubert and Reymer, 1985; Williams and Pan, 1992; McNamara and van Keken, 2000), but such high Urey ratio appears to be in conflict with geochemical data (McDonough and Sun, 1995; Lyubetskaya and Korenaga, 2007a). Future antineutrino data should give direct constraints on mantle radioactivity (Araki et al., 2005; McDonough, 2005). Recently, there were some attempts to rescue the conventional scaling by invoking temporal fluctuations in plate tectonics (e.g. Grigne et al., 2005; Silver and Behn, 2008), but these studies have been suggested to be inconsistent either with known sea level changes (Korenaga, 2007a) or with the physics of heat transfer (Korenaga, 2008a). It is also important to understand what underlies the conventional scaling (e.g. Howard, 1966); hotter mantle is predicted to yield higher heat flux because the boundary layer (i.e. plates) becomes thinner owing to greater convective instability. Conventional scaling and substantial boundary-layer growth are thus mutually exclusive, but mixing these opposing concepts seems to be required if intermittent plate tectonics were to moderate surface heat flux.

Figure 2.

 Three classes of heat-flow scaling for mantle convection. ‘Conventional’ and ‘isoviscous’ parametrizations are both based on the heat-flow scaling of simple thermal convection. Mantle viscosity is temperature-dependent for the former, with the activation energy of 300 kJ mol−1, and it is constant for the latter. ‘Plate tectonics’ scaling incorporates the effects of mantle melting beneath mid-ocean ridges such as dehydration stiffening and compositional buoyancy. See Korenaga (2006) for derivations.

It appears, therefore, that some kind of negative temperature dependency is essential to prevent the so-called thermal catastrophe (Fig. 3a), and such scaling may be possible if the effects of grain growth kinetics (Solomatov, 1996, 2001) or mantle melting associated with plate tectonics (Korenaga, 2003, 2006) are important for global mantle dynamics. Whereas the importance of grain growth kinetics in mantle convection (particularly in the lower mantle) is not well understood yet, heat-flow scaling with mantle melting depends mainly on upper mantle properties, which are reasonably well known. Thus, the scaling of Korenaga (2006) (‘plate tectonics’ in Fig. 3) is adopted for thermal history calculations here. Note that the concept of hotter and stiffer mantle (Solomatov, 1996) could enhance the negative temperature dependency further. As will be suggested later, the mantle may have been drier on average, which would also help suppressing convective heat flux from a hotter mantle in the past. These suggestions for unconventional heat-flow scaling are far from being established and subject to further investigation, including fully self-consistent numerical modelling. Important points are that there is no a priori reason for Earth’s mantle to follow the conventional scaling, and that we now have some physically plausible mechanisms that may modify drastically the apparent temperature sensitivity of convective heat flux.

Figure 3.

 Thermal evolution modelling with continental growth, starting with the present-day mantle temperature of 1350 °C and the present-day convective Urey ratio of 0.22. The global heat balance of Eq. (4) is assumed, and the details of integration procedure can be found in Korenaga (2006). The heat-flow scaling of plate tectonics (Fig. 2) is adopted. (a) The history of mantle potential temperature Tm. The result with the conventional heat-flow scaling is also shown by dashed line. (b) Three models of continental growth: ‘instantaneous’ growth (Armstrong, 1981), ‘gradual’ growth (McLennan and Taylor, 1982), and somewhere in-between (Campbell, 2003). (c) Predicted history of convective heat flux (solid) and mantle internal heating (dashed). Different colours correspond different models of continental growth. It may be seen that the Urey ratio, Ur(t) = Hm(t)/Q(t), gradually increases from the present-day value of 0.22 to higher values in the past. (d) Predicted history of average plate velocity. Dashed lines denote the range of geological estimate based on the intervals between supercontinent assemblies or globally synchronous orogenies (Korenaga, 2006), the timing of which are shown by green bars (Hoffman, 1997; Nutman, 2006).

The calculated thermal history is presented with three different models of continental growth (Fig. 3). Table 2 lists key model parameters and their (present-day) values adopted here. The present-day mantle potential temperature is assumed to be 1350 °C (e.g. Kinzler, 1997; Herzberg et al., 2007). It can be observed that the detail of continental growth is not important; radically different growth models give rise to only ∼100 K difference in the early Earth (Fig. 3a). Perhaps the most important feature is the robustness of model predictions owing to a negative feedback implemented by the adopted heat-flow scaling. Lower heat flux for hotter mantle implies that internal heating may have been higher than surface heat flux sometime in the past (Fig. 3c), and also that plate tectonics was more sluggish in the past (Fig. 3d).

Table 2.   Key parameters used in mantle and ocean evolution modelling.
  1. *For parameters that depend on time t, present-day values are listed.

  2. †Past heat production is calculated based on the present-day value and U : Th : K of 1 : 4 : 1.27 × 104 [see Eq. (3) and Table 1 of Korenaga (2006)]. The effect of continental growth is taken into account by Eq. (9).

  3. ‡Past convective heat flux is calculated using the ‘plate tectonics’ scaling law shown in Fig. 2.

  4. §This is assumed to be constant in Figs 3, 4 and 9. The effect of its possible temporal variation on mantle evolution is minor (see Section on Core heat flux and the possibility of superheated core), though it is important for the thermal history of the core (Fig. 5).

  5. ¶Past heat production in the continental crust is calculated in a similar way to that in the mantle but with U : Th : K of 1 : 5 : 104.

  6. **The triangular distribution of seafloor age-depth is assumed [Eq. (15)].

  7. ††Past plate velocity is calculated using its relationship to convective heat flux, vinline image (Q/Tm)2 [Eq. (18) of Korenaga (2006)].

  8. ‡‡This is assumed to be constant in Fig. 9.

CHeat capacity of the entire Earth7 × 1027 J K−1Eqs (3) and (4)
Tm(t)Mantle potential temperature1350 °CEqs (3) and (4)
Hm(t)Heat production in the mantle†∼8.5 TW Eqs (3), (4) and (7); Fig. 1
Q(t)Convective heat flux‡∼38 TWEqs (3), (4) and (6); Fig. 1
CcHeat capacity of the core1.3 × 1027 J K−1Eq. (3)
ΔTCMB(t) Temperature contrast at CMB§∼1000 KEq. (3)
Hcc(t) Heat production in continental crust¶∼8 TWEq. (9); Fig. 1
τmax(t) Maximum age of seafloor**180 Ma Eq. (23)
v(t) Average plate velocity††4 cm yr−1Eq. (23)
Ao(t) Total area of ocean basins3.1 × 1014 m3Eqs (16) and (23)
G(t)Plate creation rate3.45 km2 yr−1Eqs (22), (15) and (23)
V(t) Total ocean volume1.51 × 1018 m3Eq. (18)
d0(t) Zero-age depth of seafloor2654 m‡‡Eq. (19)
b(t) Seafloor subsidence rate323 m Myr−1/2Eqs (19) and (20)

Before interpreting these predictions any further, at least two issues need to be discussed. The first one is the validity of the assumed heat-flow scaling for plate tectonics. The physics of plate tectonics is not fully understood yet (e.g. Bercovici et al., 2000; Bercovici, 2003). We still do not know, for example, why Earth exhibits plate tectonics and other terrestrial planets do not. There are various suggestions (e.g. Tozer, 1985; Regenauer-Lieb et al., 2001; Korenaga, 2007b), many of which call for the existence of surface water, but we do not have a quantitative understanding for under what conditions plate tectonics can take place. Without such fundamental understanding, then, why should we trust the proposed scaling for plate tectonics? The answer lies in the nature of scaling laws. Heat-flow scaling prescribes the sensitivity of surface heat flow to variations in mantle temperature, and all of scaling laws in Fig. 2 are normalized with respect to the present-day convective heat flow. We know plate tectonics is operating today, and we can estimate how potential energy release is balanced by viscous dissipation for the present-day mantle (e.g. Conrad and Hager, 1999a). Heat-flow scaling is constructed by considering how this energy balance should change for different temperatures. As far as plate tectonics is operating, therefore, the assumed heat flow scaling is unlikely to be grossly in error, though the details of viscous dissipation in the mantle could be debatable. This brings up the second issue, which is the onset of plate tectonics on Earth. Figure 3 shows the backward integration of global heat balance to the beginning of Earth’s history (4.6 Ga), and this is equivalent to assuming that plate tectonics started as soon as Earth was created. However, if plate tectonics started at 3 Ga, for example, model predictions for older times bear little significance. This issue is discussed in detail next.

Onset of plate tectonics

Geological and geochemical evidence

The assembly of continental masses and associated collisional processes require the closure of ocean basins that existed between different continents. The subduction of oceanic lithosphere should be involved in closing ocean basins, so the timing of ancient orogenies provides important constraints on the first emergence of plate tectonics on Earth. The oldest ‘supercontinent’ Kenorland was assembled at c. 2.7 Ga (Hoffman, 1997), so it would be reasonable to assume the operation of plate tectonics in the late Archean. Whether Kenorland was a true supercontinent or not (Bleeker, 2003) is not so important in the current context; there is field evidence for globally synchronous orogeny at c. 2.7 Ga, which is sufficient for discussion here. Also, recycling of oceanic crust by subduction back to c. 3 Ga is supported by the age of eclogite xenoliths from subcontinental lithospheric mantle (e.g. Jacob et al., 1994; Shirey et al., 2001). As noted by Korenaga (2006), the time intervals of so far known five supercontinents (Pangea, Gondwanaland, Rodinia, Nuna and Kenorland) may be used to estimate the spatially and temporally averaged rate of plate motion, and such estimate appears to be consistent with the prediction based on thermal evolution modelling (Fig. 3d). One could question this connection between the history of supercontinents and the vigour of plate tectonics by suggesting that plate tectonics could have been proceeding vigorously for long periods with no significant change in continental configuration, but as noted earlier (see Internal heating and surface heat flux), more vigorous convection (i.e. higher heat flow) in the past may not allow us to construct a reasonable thermal history. Nonetheless, the speed of continental motion may be better regarded as a minimum estimate on the global average, so the agreement with model prediction should not be taken at face value.

The interpretation of geological records prior to c. 3 Ga has been controversial. It is important to keep in mind that, even if plate tectonics was operating in the early Archean, it does not have to resemble modern-style plate tectonics. The most important ingredient is the subduction of oceanic lithosphere, and other aspects of plate tectonics could have been different. It follows that a mere change in the style of tectonics [e.g. at c. 3.2 Ga as suggested by the geology of the Pilbara Craton in Australia (Van Kranendonk et al., 2007)] does not necessarily coincide with the emergence of plate tectonics. Plates can coexist with vertical tectonics, as currently observed at the Basin and Range (Sleep, 2007). In fact, the operation of plate tectonics as early as 3.7–3.8 Ga was suggested by Komiya et al. (1999) based on the Isua supracrustal belt in Greenland, and the age of episodic granite production recorded in the Istaq Gneiss Complex of Greenland (Nutman et al., 2002) as well as the Narryer Gneiss Complex of Western Australia (Kinny and Nutman, 1996) may point to an early global collisional orogeny at c. 3.6 Ga (Nutman, 2006). Interestingly, this timing is consistent with what thermal evolution indicates (Fig. 3d).

The possibility of plate tectonics in even earlier times has also been widely debated, and it is centred on the interpretation of the Hadean (>4 Ga) detrital zircons (e.g. Mojzsis et al., 2001; Wilde et al., 2001; Harrison et al., 2005; Valley et al., 2005; Coogan and Hinton, 2006; Grimes et al., 2007). Some authors have suggested the existence and recycling of continental crust as early as 4.5 Ga (Harrison et al., 2005), which implies the operation of plate tectonics (or just recycling of oceanic lithosphere) shortly after the formation of Earth. The interpretation of out-of-context detrital zircons is, however, not unique especially for the Hadean era (e.g. Sleep, 2007), unless we invoke Uniformitarianism for relevant geological processes. What the Hadean zircons actually constrain seems to be an open question. A related issue is that, if continental crust existed in the Hadean, how voluminous it could have been then, and it will be discussed later (see Continental growth: instantaneous, gradual, or discontinuous?).

A note on late heavy bombardment

On the basis of the lunar cratering record, it has been suggested that Earth experienced a spike of meteorite bombardment at 4.0–3.8 Ga (Hartmann et al., 2000; Ryder, 2002). This event is called as the late heavy bombardment, and it is sometimes discussed as if it could have had a strong influence on the stability of lithosphere (and thus the operation of plate tectonics) (e.g. Shirey et al., 2008). The total mass of impactors that hit the Moon during this period is estimated to be ∼3 × 1018 kg (Ryder, 2002), and by extrapolation, Earth is expected to have been hit by a few big (>300 km diameter) impactors and numerous smaller ones (about a dozen of ∼200-km-diameter impactors, a hundred of ∼100-km-diameter impactors, and so on) (e.g. Sleep, 2007). The mass of a 300-km-diameter impactor would be ∼4 × 1019 kg, and its influence of the thermal state of Earth’s lithosphere may be estimated by equating its potential energy and the energy required to heat up the lithosphere by ΔT as:


where ML is the mass of lithosphere (∼1.7 × 1023 kg for the thickness of 100 km), cp is its specific heat (∼103 J kg−1 K−1), G is the gravitational constant (6.67 × 10−11 m3 kg−1 s−2), ME is the mass of Earth (∼6 × 1024 kg), m is the mass of the impactor, and rE is the radius of Earth (∼6.4 × 106 m). For a 300-km-diameter impactor, ΔT is only ∼15 K. Of course, impact heating is a highly localized phenomenon, and a much greater temperature rise is expected in the vicinity of an impact site. The late heavy bombardment is certainly important for surface conditions as it could vaporize at least a part of oceans. The above order-of-magnitude estimate is probably sufficient, however, to show that the effect of even the biggest impactor during the late bombardment would not be significant for global mantle dynamics such as the operation of plate tectonics.

Geodynamical considerations

Estimating the onset of plate tectonics on a purely theoretical ground is difficult because the very physics of plate-tectonic convection is not well understood (e.g. Bercovici et al., 2000). There still exist, however, certain physical constraints that have to be considered when discussing the style and vigour of mantle convection in the early Earth. In particular, the interpretation of geochemical data is often assisted by or compared to geodynamical considerations (sometimes subconsciously), and this is where a preconception could potentially lead to biased interpretations. For example, vigorous convection is often assumed for the Hadean dynamics (e.g. Sleep and Zahnle, 2001), but it is not clear if such vigour can really be attained in the early Earth. Though convection in a magma ocean should have been extremely vigorous (Solomatov, 2007), the transition from such intense liquid convection to solid-state mantle convection is currently poorly understood [see Sleep (2007) for the possibility of ‘mush ocean’]. If mantle convection was in the mode of plate tectonics, for example, the scaling of Korenaga (2006) might be applicable, which predicts slower, not faster, plate motion. Even without calling for this particular scaling, however, a simple physical argument centred on the subductability of oceanic lithosphere (e.g. Bickle, 1986; Davies, 1992) seems to question rapid convection when Earth was much hotter than today. For the top boundary layer to be recycled into the interior by free convection, the boundary layer must be negatively buoyant, at least on average, with respect to the hot interior. This buoyancy constraint is not an issue for simple thermal convection with a homogeneous material because the top thermal boundary layer is always denser than the hot interior. Convection in Earth’s mantle, however, induces pressure-release melting and differentiates the shallow mantle into basaltic crust and depleted mantle lithosphere, both of which are less dense than the mantle before melting if compared at the same temperature. For the top boundary layer to become denser than the interior, therefore, it has to be cooled for a sufficiently long time so that negative buoyancy due to thermal contraction overcomes the intrinsic chemical buoyancy [note that basalt is transformed to denser eclogite at ∼60 km depth (Ringwood and Green, 1964), so this chemical buoyancy issue is important only for the initiation of subduction, not for its continuous operation]. For the present-day condition, this time-scale is estimated to be c. 20 Myr, but when the mantle is hotter than present by 200–300 K, the time-scale could be on the order of 100 Myr (Davies, 1992). That is, when the mantle was hotter in the Hadean, it must have had thicker buoyant crust as well, which could return to the interior only after c. 100-Myr long surface cooling. This time-scale is comparable to the present-day time-scale to renew ocean basins. Vigorously convecting hotter mantle could be at odds with more copious melting expected for such mantle.

The subductability argument may be countered because thick oceanic crust such as oceanic plateaus does subduct at present (e.g. Sleep and Windley, 1982), but such thick crust is localized at present as opposed to its likely global occurrence in the Archean. The argument may also be questioned because the seafloor is currently subducting irrespective of its age (Parsons, 1982). Indeed, near zero-age crust is subducting under the western margin of the North American plate, whereas the oldest crust in the Atlantic (c. 180 Ma) is not subducting at all, so the simple buoyancy argument may seem to be irrelevant to actual plate dynamics. Young subducting seafloor is, however, attached to an older, already subducted plate, and the presence of old, non-subducting seafloor tells us that negative buoyancy alone is not sufficient to initiate subduction. Probably a more adequate measure is the global average of the age of subducting seafloor, which is c. 49 Ma (rate average) or c. 61 Ma (area average) [based on Table 1 of Parsons (1982)]. In either case, it is old enough to achieve sufficient negative buoyancy under the present-day condition.

The concept of subductability depends on two factors: thermal diffusivity and intrinsic chemical buoyancy. Whereas the former is virtually constant under plausible mantle conditions, the chemical buoyancy is a function of mantle temperature, and the functionality is less certain. To predict the density of oceanic crust, one has to first calculate the composition of primary mantle melt for a range of mantle temperature, and then calculate the density of mineral aggregates expected to be solidified from a given melt composition. The current understanding of mid-ocean ridge magmatism is probably sufficient to conduct the first step with moderate accuracy (e.g. Langmuir et al., 1992; Kinzler, 1997; Walter, 1998), but the second step is more uncertain because the details of crystallizing phases depend on the temperature and pressure conditions within newly forming crust and thus on how exactly crust is constructed. Even for the present-day oceanic crust, the physical mechanism of crustal accretion is still under debates (e.g. Phipps Morgan and Chen, 1993; Korenaga and Kelemen, 1998; Wilson et al., 2006), and we do not know, from first principles, how to construct much thicker crust corresponding to hotter mantle. The subductability calculation by Korenaga (2006), for example, depends on the crustal density parametrization of Korenaga et al. (2002), which assumes low-pressure crystallization. Future studies on the crustal structure of large igneous provinces may provide important field constraints on this issue.

Provided that intrinsic chemical buoyancy remains significant for hotter mantle, subductability is a robust physical constraint, but its use needs some care. Davies (1992), for example, argued that plate tectonics was unlikely when the mantle was much hotter because the time-scale for negative buoyancy would be too long (i.e. c. 100 Myr) to be achieved in vigorously convecting mantle, but this argument depends on the conventional heat-flow scaling (Fig. 2). Also, van Thienen et al. (2004) suggested that plate tectonics may not be possible when the mantle potential temperature is higher than 1500 °C based on subductability, but their calculation assumes the so-called plate model for the evolution of oceanic lithosphere (Parsons and Sclater, 1977; Stein and Stein, 1992), in which the growth of lithosphere is inhibited after c. 80 Myr. Though convective instability can limit the growth of lithosphere (Parsons and McKenzie, 1978), this instability is a function of mantle viscosity, and it is difficult to justify the use of a constant maximum thickness over a range of mantle temperature (cf. Korenaga, 2003). Note that the plate model contains an artificial bottom boundary condition to suppress cooling, and a recent global analysis of seafloor topography casts a doubt on the observational basis for this model (Korenaga and Korenaga, 2008).

Recently, Davies (2006) proposed that the subductability issue would not present a major obstacle for the operation of plate tectonics if the mantle was already depleted in the early Earth by earlier melting events. In his numerical model, subduction is forced by a surface velocity condition, and subducted oceanic crust segregates from depleted mantle lithosphere and sinks to the lower mantle, leading to a gradual depletion of the upper mantle, the melting of which does not yield thick oceanic crust. This scenario, however, requires some kind of tectonics (other than plate tectonics) that can subduct oceanic crust, and a time-scale to achieve the required mantle depletion is uncertain [in the model of Davies (2006), subduction was achieved by assuming the continuous operation of plate tectonics]. The once highly depleted upper mantle would also need to be refertilized later to explain the present-day upper mantle. In other words, the upper mantle needs to change its composition so that melting always yields relatively thin oceanic crust regardless of its temperature. The plausibility of this mechanism seems to hinge on a delicate balance between mantle mixing and secular cooling.

Subductability thus remains to be an important factor to be considered, and the backward integration of Earth’s thermal history seems to provide an important perspective related to subductability, namely, the role of internal heating on the initiation of plate tectonics. Figure 4 shows two kinds of lithospheric thickness. One is the minimum thickness of subductable oceanic lithosphere [which is equivalent to the ‘critical thickness’ defined by Korenaga (2006)]; lithosphere must exceed this thickness to become negatively buoyant. This thickness is a function of mantle temperature, so its temporal variation is determined by an assumed thermal history (Fig. 3a). The other is the equilibrium thickness of a hypothetical stagnant lid, which is a function of internal heat generation as (Korenaga, 2006):


where k is thermal conductivity and A is the total surface area of Earth. At a thermal equilibrium, lithosphere should become thinner for higher internal heating, and Fig. 4 indicates that the equilibrium thickness may have been less than the minimum thickness before c. 2.5–3 Ga. In the Archean and the Hadean, the amount of internal heat generation in the mantle was greater than present by a factor of >2 (Fig. 3c), and this high internal heating may have suppressed the growth of the top thermal boundary layer and thus prevented lithosphere to become negatively buoyant. This argument is, however, probably too simplistic because the equilibrium thickness is unlikely to be achieved instantaneously. The thermal adjustment time-scale can be long, on the order of 1 Gyr (Daly, 1980), and this long time-scale in a sense justifies Eq. (1), in which surface heat flux Q(t) is usually parameterized as a function of mantle temperature (Fig. 2) and can vary independently from internal heat production Hm(t). The physics of thermal adjustment is, however, not fully explored for mantle convection with realistic rheology, and the significance of the thickness crossover in Fig. 4 is an open question. As noted by Sleep (2000) and Stevenson (2003), a change in the mode of mantle convection may lead to non-monotonic thermal histories. Though it could be a coincidence, the timing of crossover is close to the Archean-Proterozoic boundary, at which surviving continental crust began to emerge in abundance. A quantitative relationship between mantle convection and continental recycling throughout Earth’s history is one of the subjects that should be explored by future geodynamical studies.

Figure 4.

 The predicted variation of the minimum thickness of subductable oceanic lithosphere and the equilibrium thickness of stagnant lid, based on the thermal history shown in Fig. 3. The equilibrium lid thickness is thinner in the past due to higher mantle heat production, and is thinner than the minimum subductable thickness before the Proterozoic, suggesting that the subductability of oceanic lithosphere is a key factor for the emergence of plate tectonics in the early Earth.

To go beyond this simple buoyancy argument, it is imperative to advance our understanding of the physics of plate tectonics. Though plate-tectonic-like convection can be successfully simulated in numerical models (e.g. Moresi and Solomatov, 1998; Tackley, 2000; Richards et al., 2001; Ogawa, 2003; Gurnis et al., 2004; Stein et al., 2004), currently available models treat the strength of oceanic lithosphere as a free parameter, which must be adjusted to achieve plate tectonics. It is difficult to discuss the onset of plate tectonics on the basis of those models because the free parameter may not be constant over the geological time. It would desirable to predict the strength of lithosphere from first principles based on tangible physical processes; such research effort is still in its infancy (e.g. Korenaga, 2007b).

Secular cooling and flood basalt volcanism

Did mantle plumes exist in the Archean?

Apart from metal-silicate segregation that took place within the first hundred million years of Earth’s history (e.g. Halliday, 2003), chemical differentiation in Earth’s interior refers to the melting of silicate rocks. The melting of shallow upper mantle usually takes one of the following three types of surface manifestation: mid-ocean ridge magmatism, arc magmatism and hotspot magmatism (e.g. Wilson, 1989; McBirney, 1993). The first two are associated with plate tectonics. Here, the term hotspot magmatism is used in a broad sense to cover not only hotspots such as Hawaii and Iceland but also continental and oceanic flood basalt provinces such as the Deccan Traps and the Ontong Java Plateau (Coffin and Eldholm, 1994). This type of magmatism is commonly explained by the upwelling of mantle plumes (e.g. Morgan, 1971; Richards et al., 1989; Campbell and Griffiths, 1990; White and McKenzie, 1995) though the origin of hotspot magmatism has been controversial (e.g. Anderson, 1998; Foulger et al., 2005). Thermal anomalies such as mantle plumes are certainly one way to generate hotspot islands and flood basalts, but not the only way because chemical and/or dynamical anomalies may also result in similar magmatic activities (e.g. Sleep, 1984; Tackley and Stevenson, 1993; Korenaga and Jordan, 2002; Anderson, 2005; Ito and Mahoney, 2005; Korenaga, 2005b).

For the sake of discussion, however, let us assume that most of hotspots and flood basalts are formed by the melting of mantle plumes that originate in the core–mantle boundary region. In this case, the thermal evolution of Earth suggests that hotspot magmatism should have been more reduced in the past. As will be explained shortly, this is a straightforward consequence of a geologically plausible thermal history (Sleep et al., 1988), though this fact does not seem to be widely recognized. For example, a plume-dominated regime is often suggested as an alternative mode of mantle convection in the Archean (i.e. instead of the plate-tectonic regime) (e.g. Fyfe, 1978; Van Kranendonk et al., 2007), and some models for continental growth call for a prominent role of flood basalts or mantle plumes in the early Earth (e.g. Abbott and Mooney, 1995; Albarède, 1998). Along with the notion of more vigorous convection, plume activities in the Archean are commonly assumed to have been similar to or higher than today. Indeed, the vigor of mantle convection and the intensity of plumes may be related through the thermal budget of Earth, but their temporal variations do not have to be positively correlated. It is possible, for example, to have a reduced plume flux while maintaining the vigor of convection, and the thermal history shown in Fig. 3 indicates that such possibility is likely. To discuss this further, we need to relax one of the assumptions behind Eq. (4) and consider the possibility of differential core cooling using Eq. (3).

Core heat flux and the possibility of superheated core

The reconstructed thermal history of Fig. 3 is based on Eq. (4), in which the mantle and the core are assumed to have cooled at the same rate. That is, the temperature contrast at the core–mantle boundary is assumed to have been constant. In this case, the core heat flux is directly related to the secular cooling of the mantle as:


[from Eq. (2)]. The history of core heat flux with this assumption is shown as case 1 in Fig. 5. The present-day core heat flux is estimated to be ∼6 TW, and more important, the past core heat flux is lower than the present-day value and is predicted to be negative before the early Archean (i.e. core heating instead of cooling should take place then). With the nearly constant surface heat flux but with gradually decaying radiogenic heat source (Fig. 3c), the secular cooling of Earth and thus the core heat flux are likely to have been lower in the past.

Figure 5.

 (a) Predicted history of core heat flux QCMB incorporating the effect of differential core cooling. Different colours correspond to different models of continental growth (Fig. 3b). (b) Three cases of differential cooling are shown: 1, no differential cooling (the core cools at the same rate as the mantle), 2, constant rate of differential cooling (temperature contrast at the core–mantle boundary linearly decrease by 500 K over 4.6 Gyr), and 3, decreasing rate of differential cooling (heat flux due to differential cooling decreases linearly from 10 TW at 4.6 Ga to zero at present).

The details of the predicted core evolution are, however, subject to large uncertainties. The temperature contrast ΔTCMB, which is assumed to be constant, is almost a free parameter given our limited knowledge of the dynamics of the core–mantle boundary region; the rheology of the lowermost mantle is currently unknown. To explore the significance of time-dependent ΔTCMB, two different variations are considered (cases 2 and 3 in Fig. 5b). In case 2, the contrast decreases linearly by 500 K over the entire Earth history, whereas in case 3 it decreases quadratically by a similar amount. Thermal evolution was solved again, but using Eq. (3), and the corresponding core heat flux was calculated as:


It may be seen that differential core cooling could modify substantially predicted core heat flux (Fig. 5a). On the other hand, the thermal history of the mantle (not shown) is not affected much by this modification. This is expected because the differential core cooling of case 2, for example, provides additional core heat flux of ∼4 TW, which is significant for the core thermal budget, but not for the mantle thermal budget. Cases 1 through 3 are all consistent with the observational constraints on the present-day core heat flux [6−12 TW, (Buffett, 2003)].

At the core–mantle boundary, the core side is considered to be hotter than the mantle side by at least ∼1000 K at present (Williams, 1998). The present-day contrast is uncertain because the estimate of the core-side temperature is based on the phase diagram of the core, which depends on its chemical composition and in particular on the (uncertain) light element composition (e.g. McDonough, 2003). Nevertheless, a temperature contrast more than a few hundred K is probably robust, and this suggests either (1) that there was no contrast at the beginning of the Earth history, but the mantle cooled faster than the core, or (2) that the core was initially hotter than the mantle, and the temperature contrast has not been entirely removed. The first scenario seems unlikely because it would predict core heat flux lower than case 1 and thus becomes incompatible with the present-day core heat flux estimate and also with the history of the geomagnetic field (e.g. McElhinny and Senanayake, 1980; Buffett, 2002; Tarduno et al., 2007). The second possibility is physically plausible because either the gravitational segregation of the core or the Moon-forming giant impact is expected to deposit a considerable amount of heat into the core (Solomatov, 2007). The initial temperature of this superheated core and its later evolution are uncertain, but it would be fortuitous if the initial temperature contrast has been maintained to the present day; it is possible, but it would require a specific dynamics of the core-boundary boundary region. Figure 5(a) suggests that the possibility of differential core cooling (or the current uncertainty of the core–mantle boundary dynamics) provides important degrees of freedom for the coupled core–mantle evolution. Explaining both the present-day core heat flux and the history of the geomagnetic field has been a conundrum for the thermal history of Earth’s core (e.g. Labrosse et al., 2001; Buffett, 2003; Nimmo et al., 2004; Butler et al., 2005), and these extra degrees of freedom may help to resolve it.

A linear decrease in the temperature contrast (case 2) shifts core heat flux almost uniformly, thus unaffecting the trend of lower heat flux in the past. To reverse this trend, we need to invoke a greater temporal variation in the past (e.g. case 3), but there is a negative feedback mechanism to suppress core heat flux in the early Earth. Higher differential core cooling is equivalent to higher internal heating in the mantle [Eq. (3)], which would then reduce the secular cooling of the entire Earth (i.e. including the core). This is why even case 3 predicts vanishing core heat flux in the early Earth (Fig. 5a). It appears that core heat flux was probably lower than (cases 1 and 2) or similar to (case 3) the present-day value, and substantially higher core heat flux in the early Earth probably requires an unrealistic degree of differential core cooling.

Origins of flood basalts and preservation bias

With reduced core heat flux, it would be difficult to expect more vigorous plume activities in the early Earth. Furthermore, plume heat flux is likely to be smaller than the total core heat flux (e.g. Davies, 1993; Labrosse, 2002). If the average plume size remains similar through time, then, the number of plumes should have been lower, and if we instead assume the constant frequency of plume formation, the average plume size should have been smaller. In either case, we expect a reduced volume of flood basalt magmatism in the past as a corollary of the mantle plume hypothesis. This does not necessarily mean that we cannot expect greater flood basalt magmatism in the past. First of all, ‘normal’ mantle in the Archean is likely to be ∼300 K hotter than present (Fig. 3a), so flood basalt magmatism in the Archean may not necessarily require an unusual source mantle. High temperature alone, however, is probably insufficient to explain focused magmatic events such as flood basalts, and there are a few non-plume mechanisms as discussed below.

One popular concept is the episodic overturn of layered-mantle convection (e.g. Stein and Hofmann, 1994; Condie, 1998; Rino et al., 2004). In the layered-mantle convection mode, the lower mantle cools less efficiently and thus becomes hotter than the upper mantle. Numerical modelling in the early 1990s suggested that, whereas it is difficult to maintain a purely layered state, episodically layered convection may take place with the endothermic phase change at the base of the mantle transition zone (i.e. at the 660-km discontinuity) (e.g. Machetel and Weber, 1991; Honda et al., 1993; Tackley et al., 1993; Solheim and Peltier, 1994). When a temporally layered state is broken, a large volume of the hot lower mantle material can be brought to the surface, potentially resulting in massive melting events. Note that the plausibility of episodic overturns depends critically on the magnitude of the (negative) Clapeyron slope for the endothermic phase change. To insulate the lower mantle from cooling due to subducted slabs and make it substantially hotter than the upper mantle, subducted slabs must be supported globally by the phase change for several hundred million years. Recent experimental studies suggest that the Clapeyron slope is not as strongly negative as previously thought (Katsura et al., 2003; Fei et al., 2004), potentially undermining the physical basis for episodically layered convection.

Another mechanism that may produce large igneous provinces is the upwelling of chemically anomalous mantle that has been fertilized by recycled oceanic or continental crust (e.g. Korenaga and Kelemen, 2000; Yaxley, 2000; Anderson, 2005). More fertile mantle is usually intrinsically denser (O’Hara, 1975), so its upwelling probably requires special tectonic environments (Korenaga, 2004, 2005b). Compensating chemical density anomalies by thermal buoyancy is possible, but it would require unrealistically hotter mantle [e.g. ΔT∼500−600 K (Lin and van Keken, 2005)], which may not be consistent with available petrological constraints (ΔT∼ 100−300 K) (e.g. White and McKenzie, 1995; Herzberg, 2004). Setting aside this dynamical difficulty, it is also unclear how abundant such fertile mantle would have been in the past. For one thing, the recycling rate of oceanic crust is controlled by plate motion, which may not have been different from present as discussed earlier (Internal heating and surface heat flux). On the other hand, the recycling of continental crust is free from this constraint, and primordial heterogeneities created during the magma ocean may have been abundant in the early Earth. The possibility of fertile mantle is a wild card, as our understanding of the dynamics of chemically heterogeneous mantle is still immature (Korenaga, 2008b).

Geological indicators for flood basalts are common in Archean terranes (e.g. Campbell et al., 1989; Ernst and Buchan, 2003; Sandiford et al., 2004), which is probably the basis for the notion of more active plume activities. One way to reconcile the apparent discrepancy between the theoretical expectation and the field observation is to call for preservation bias; the continental crust with flood basalts may have better survived for the following reason. The genesis of flood basalts, produced by either thermal or chemical anomalies, involves the melting of a large volume of the mantle. Because mantle melting also dehydrates and stiffens the residual mantle (Karato, 1986; Hirth and Kohlstedt, 1996), this large-scale melting would produce a voluminous, stiff mantle root, which could protect the overlying continental crust from tectonic disturbances. It is unclear how much of such dehydrated residual mantle has contributed to what we call today as continental tectosphere (Jordan, 1988; Pearson, 1999), but the role of dehydrated mantle in ancient continental dynamics is an important dynamical problem to consider (e.g. Doin et al., 1997; Lenardic and Moresi, 1999). Oceanic crust older than c. 180 Myr old is all subducted, and we have only continental crust to discuss anything older. It is natural to hope for a minimal preservation bias, but when interpreting billion-years-old continental crust, it would be hard to overestimate preservation bias.

Continental growth and the history of ocean volume

Continental growth: instantaneous, gradual, or discontinuous?

When the continental crust emerged in the Earth history and how it has evolved to its preset figure have been debated over several decades (e.g. Hurley and Rand, 1969; O’Nions et al., 1979; DePaolo, 1980; Armstrong, 1981; Taylor and McLennan, 1985; Jacobsen, 1988; Collerson and Kamber, 1999; Campbell, 2003; Harrison et al., 2005), and continental growth is still a highly controversial topic. Being highly enriched in heat-producing elements, its growth history can influence the thermal evolution of Earth by depleting the convecting mantle [Eq. (9)], but this type of influence is of relatively minor importance (Fig. 3). Probably a more important aspect is whether the production of continental crust has been continuous or discontinuous. Gradual growth models (e.g. McLennan and Taylor, 1982; Jacobsen, 1988; Campbell, 2003) are obviously continuous, and instantaneous growth models (e.g. Armstrong, 1981; Harrison et al., 2005) are also mostly continuous in this sense, because the constant continental mass is assumed to have been maintained by balancing continuous production and destruction. These ‘continuous’ growth models are compatible with the continuous operation of plate tectonics. ‘Discontinuous’ growth models (e.g. Rino et al., 2004; Hawkesworth and Kemp, 2006; Parman, 2007), on the other hand, suggest that the mode of mantle convection may have changed at least a few times in the past, and the use of single heat-flow scaling in thermal evolution modelling, as done in most of previous studies, may become overly simplistic in this case. Thus, the debate over continental growth has a critical relevance to the theoretical formulation of thermal evolution modelling.

The episodic overturn of layered-mantle convection has been a popular concept as a plausible mechanism that may explain the episodic growth of continental growth (e.g. Stein and Hofmann, 1994), but as discussed earlier, this idea is based on early numerical convection models with a strong endothermic phase transition, the assumption of which does not seem to be valid in light of recent experimental studies. Recently, O’Neill et al. (2007) proposed that plate tectonics itself might have been intermittent in the Precambrian. Whereas their argument using palaeomagnetic data is weak given the likelihood of true power wander (Evans, 2003), they offer a plausible dynamical reasoning. Mantle convection models with pseudo-plastic rheology are known to exhibit three modes of convection (stagnant-lid, intermittent plate tectonics, and continuous plate tectonics), depending on the assumed strength of lithosphere (or its maximum yield strength) (e.g. Moresi and Solomatov, 1998; Stein et al., 2004). When the mantle was hotter in the past, its internal viscosity may be lower due to temperature dependency, so convective stress could become too low to sustain the continuous operation of plate tectonics. In this case, intermittent plate tectonics is possible for a certain range of maximum yield stress. Unlike the model proposed by Silver and Behn (2008), however, this original version of intermittent plate tectonics proposed by Moresi and Solomatov (1998) hardly modifies conventional heat-flow scaling, because low heat flux during the stagnant-lid mode is compensated by high heat flux during the plate tectonics mode [see, for example, Figure 3 of Moresi and Solomatov (1998)]. So it may be able to explain continental growth but not thermal evolution. Also, as noted earlier, the pseudo-plastic model of Moresi and Solomatov (1998) needs to assume the strength of lithosphere (i.e. its maximum yield stress), which may not be constant over Earth’s history. Equally important, mantle viscosity is a function of not only temperature, but also other parameters such as grain size and water content (e.g. Karato and Wu, 1993; Hirth and Kohlstedt, 2003; Korenaga and Karato, 2008). Solomatov (1996), for example, suggested that hotter mantle could become more viscous if grain-size-dependent viscosity is considered. Assuming weaker convective stress from a hotter mantle is equivalent to holding these other variables constant through time, which may not be warranted. In fact, as shown in the next section, the present-day thermal budget indicates that the mantle was probably drier in the past, which may compensate a decrease in viscosity due to temperature dependency.

The diversity of continental growth models is partly because different geochemists place different weights on relevant geochemical data such as 143Nd/144Nd and Nb/Th. For example, a significant volume of continental crust in the Hadean, as implied by the hafnium isotope data of ancient zircons (Harrison et al., 2005), seems to be incompatible with the Th–U–Nb systematics of depleted-mantle-derived rocks (Collerson and Kamber, 1999). The interpretation of geochemical data in terms of geological processes, however, often depends on simple box models (e.g. DePaolo, 1980; Jacobsen, 1988), which in turn assumes rapid mantle mixing (Coltice et al., 2000). Also, geochemical interpretations usually require the chemical or isotopic composition of the BSE as a reference baseline, but the uncertainty of such reference value is not trivial. Continental growth models based on the Nd isotope evolution (e.g. Bennett, 2003), for example, assumes that the Sm/Nd ratio of the BSE is identical to that of chondrites within 1% uncertainty [the ‘strong’ version of chondrite assumption (Korenaga, 2008b)]. Available isotopic data from terrestrial samples, on the other hand, require only the ‘weak’ version of chondrite assumption, i.e. the ratios of refractory lithophile elements such as Sm and Nd should not be different from the chondritic average more than a few per cents (Lyubetskaya and Korenaga, 2007b). This type of uncertainty may be essential when constructing a geochemical model that can reconcile different geochemical data simultaneously.

Global water cycle and net water influx

Frequent inundations throughout the Phanerozoic suggest that the mean sea level has always been close to the mean continental level, which is known as the constant freeboard (Wise, 1974). This constancy is at least geologically reasonable; continental crust is subject to erosion when it is above the sea level, and when a part of continents subsides below the sea level, it would likely be the locus of deposition. The abundant occurrence of submarine flood basalt magmatism in the Archean and Proterozoic (Arndt, 1999), however, implies that the mean sea level had been high enough to inundate a substantial fraction of continents through the Precambrian. The constant freeboard is thus probably too simplified an assumption, but the following point seems to be robust: there has always been a sufficient volume of water to fill up the ocean basins, at least to the mean continental level. In other words, the constant freeboard is still useful to quantify the lower bound on the ocean volume.

Reymer and Schubert (1984) coupled the constant freeboard with the thermal evolution of Earth and estimated the history of continental growth assuming that the ocean volume has been constant (Fig. 6a). Their model is based on the conventional heat-flow scaling (Fig. 2), which predicts faster plate motion (i.e. higher heat flow) for hotter mantle in the past. Faster plate motion means younger and thus shallower seafloor, and to maintain the constant freeboard without changing the ocean volume, continental mass needs to be reduced. Note that the conventional scaling cannot reconstruct a reasonable thermal history unless internal heat production in the convecting mantle is much higher than geochemical constraints (see Internal heating and surface heat flux). This important fact tends to be overlooked, and the notion of more vigorous convection in the past has been entrenched in the literature on the continental freeboard or the history of ocean volume (e.g. Galer, 1991; Kasting and Holm, 1992; Galer and Mezger, 1998; Harrison, 1999; Hynes, 2001; Rüpke et al., 2004; Kasting et al., 2006).

Figure 6.

 Cartoon illustrating possible relations among heat-flow scaling, continental growth, and ocean volume, under the assumption of the constant freeboard. (a) When the ocean volume is assumed to be constant, plate motion must have been faster to create younger and shallower seafloor when there was less continental crust. Faster plate motion (i.e. higher heat flux) in the past, however, results in thermal catastrophe. (b) Slower plate motion, which is more consistent with the present-day thermal budget, predicts a greater ocean volume in the past.

The present-day thermal budget characterized by a low Urey ratio instead suggests less vigorous convection thus slower plate motion, the corollary of which is older and deeper ocean basins in the past (Fig. 6b). In this case, the volume of Earth’s oceans may have been greater to maintain the constant freeboard, as many geochemical studies suggest smaller continental mass in the Archean. This interesting possibility has not been seriously considered probably because it is difficult to test. It can be demonstrated, however, that the constant ocean volume is inconsistent with the present-day thermal budget, without using any heat-flow scaling law.

A key concept is that, for a given continental growth history, the assumptions of constant freeboard and constant ocean volume are sufficient to determine oceanic heat flux, which represents a major fraction of convective heat flux. In general, oceanic heat flux at a time t, Qo(t), may be expressed as:


where dAo/dt(τ) is the area–age distribution of seafloor, and q(τ) is heat flow from a seafloor of age τ . Both of them can also be a function of a geological time t. The present-day area–age distribution is best approximated by a triangular distribution (i.e. the area of younger seafloor is greater than that of older seafloor), and we assume this distribution for older times because it arises naturally from subduction irrespective of seafloor age (Parsons, 1982). Thus we have


where τmax(t) is the age of the oldest seafloor. The coefficient G(t) is constrained by the total area of ocean basins, Ao(t), as:


where A is the total area of Earth’s surface and Ac(t) is the total area of continents. Seafloor heat flow is assumed to follow half-space cooling as:


where B is 550 mW m−2 Myr−1/2 (Korenaga and Korenaga, 2008). At present (i.e. = 0), G(0)=3.45 km2 yr−1 and τmax(0)=180 Myr (Parsons, 1982), and Eq. (14) gives ∼34 TW for the total oceanic heat flux, which is in good agreement with the actual estimate [32 ± 2 TW (Pollack et al., 1993; Jaupart et al., 2007)]. Similarly, assuming the constant freeboard, the total ocean volume may be expressed as:


where d(τ) is the seafloor depth as a function of seafloor age,


Here d0 is the zero-age depth (average depth to mid-ocean ridge axis), and b is the subsidence rate due to half-space cooling. At the present, we have d0(0) = 2654 m and b(0) = 323 m Myr−1/2 (Korenaga and Korenaga, 2008). The subsidence rate is linearly proportional to a temperature contrast between the surface and the interior (e.g. Turcotte and Schubert, 1982), so we have


By assuming the constant ocean volume, therefore, we can solve Eq. (18) for the maximum seafloor age as:


and Q(t) can then be calculated by combining Eqs (15)–(17). The total area of continents in Eq. (16) is calculated from a given history of continental growth, assuming that the average thickness of continental crust has been approximately constant at ∼35–45 km (Durrheim and Mooney, 1991; Galer and Mezger, 1998). Note that Galer and Mezger (1998) suggested that continental crust could have been thicker in the Archean than at present by ∼5 km, based on original burial pressures estimated for exposed Archean granite-greenstone segments. Thicker crust in the past would only substantiate the following argument because it means more ocean basins [Eq. (16)] and flatter seafloor topography to satisfy the constant freeboard.

We used the oceanic heat flux of Eq. (14) as the lower bound on the total convective heat flux (i.e. subcontinental heat flux is neglected), and solved the heat balance of Eq. (4) starting with the present-day Urey ratio of 0.22. Here the zero-age seafloor depth d0 is assumed to be constant. This assumption may be justified because the existence of volcanogenic massive sulphide deposits since the Archean (e.g. Nisbet et al., 1987) indicates that the depth of mid-ocean ridges should always be greater than ∼2 km below sea level (Ohmoto, 1996). As shown in Fig. 7a, this calculation leads to thermal catastrophe even for the instantaneous growth model, in which no net continental growth takes place during the last 4 Gyr. This is because hotter mantle by itself results in greater thermal subsidence [Eq. (20)], so to keep the same ocean volume, the maximum seafloor age should decrease (Fig. 7c), i.e. seafloor should become younger on average, resulting in an increase in oceanic heat flux (Fig. 7b). This positive correlation between mantle temperature and oceanic heat flux may be summarized as ‘empirical’ heat-flow scaling (Fig. 7d). Alternatively, we may fix the maximum seafloor age as 180-Myr-old, and solve Eq. (18) for the zero-age depth. Results for this case are shown in Fig. 8. The temperature of the Archean mantle is still too high, and the predicted zero-age depth in the Archean is probably too shallow (Ohmoto, 1996; Kitajima et al., 2001).

Figure 7.

 A possible consequence of the constant ocean volume, with the assumption of the constant zero-age depth. The modelling procedure is identical to that used for Fig. 3, expect that convective heat flux is based on Eq. (14). (a) Mantle potential temperature as a function of time. (b) Convective heat flux and internal heating. (c) Maximum age of seafloor. (d) A posteriori relationship between convective heat flux and mantle temperature. For comparison, three heat-flow scaling laws of Fig. 2 are shown in grey. Legend is the same as Fig. 3; note that the cases of McLennan and Taylor (1982) (blue) and Campbell (2003) (black) are identical in (a) and (d).

Figure 8.

 Same as Fig. 7, but with the assumption of the constant maximum age of seafloor. The history of zero-age depth is shown in (c).

The constant ocean volume, therefore, seems to be incompatible with the thermal budget of Earth, and the possibility of time-dependent ocean volume deserves some attention. As a preliminary attempt, the thermal history of Fig. 3 may be used to calculate the history of ocean volume (Fig. 9). First, noting that the coefficient G(t) in the area–age distribution can be expressed as:


where L is the total length of divergent plate boundaries and v(t) is the average spreading rate, the maximum age of seafloor may be calculated from the predicted plate velocity as:


Here, L is assumed to be constant because the average size of plates is unlikely to change substantially with time (Korenaga, 2006). The total ocean volume can then be calculated from Eq. (18), assuming the constant freeboard as well as the constant zero-age depth (Fig. 9b). Results indicate that Archean ocean basins may have been deep enough to hold twice as much water as today.

Figure 9.

 (a) The maximum age of seafloor predicted from the thermal history of Fig. 3 [Eq. (23)]. (b) The predicted history of ocean volume normalized by the present-day volume. (c) Net water influx from the hydrosphere to the mantle, assuming that the predicted change of ocean volume shown in (b) is due to the hydration of the mantle by subduction. Legend is the same as in Fig. 3.

Obviously, the predicted history of ocean volume should not be taken at face value, as it is based on a number of assumptions with varying credibility (Table 1). At the same time, however, losing one-ocean-worth water since the Archean is not surprising, or may even be expected in light of the global water cycle. It has long been known that water flux into the mantle from the hydrosphere by subduction exceeds water flux out of the mantle by mid-ocean magmatism by an order of magnitude (e.g. Ito et al., 1983; Jarrard, 2003). Most of such water influx is usually believed to quickly return to the surface through arc magmatism, so the net water influx may close to be zero. It is difficult, however, to completely dehydrate subducting slabs because nominally anhydrous minerals can hold a non-trivial amount of water (e.g. Hirschmann et al., 2005). Continuous subduction at the current rate could easily bring one-ocean-worth water into the deep mantle over a few billion years (Smyth and Jacobsen, 2006). The average rate of the predicted influx for the last 2 Gyr is also compatible with the estimated range of present-day influx (Jarrard, 2003) (Fig. 9c).

The continental crust contains ∼1 wt% water on average (e.g. Wedepohl, 1995), equivalent to ∼0.18 ocean. The MORB-source mantle is estimated to have 142 ± 85 p.p.m. water (Saal et al., 2002), and the global mass balance of silicate reservoirs, on the basis of the new composition model of Earth’s primitive mantle (Lyubetskaya and Korenaga, 2007a), indicates that the MORB-source mantle is representative for the bulk of the mantle (Lyubetskaya and Korenaga, 2007b), so the mantle may hold ∼0.42 ± 0.25 ocean of water. Thus, the amount of water currently stored in the BSE (crust and mantle), ∼0.5–1 ocean, is similar to what is estimated to have been lost from Earth’s oceans (Fig. 9b). This coincidence may suggest that the mantle was dry in the Hadean and has been progressively hydrated by subduction. As mentioned earlier, such gradual hydration may be important for the continuous operation of plate tectonics. Note that the dry Archean mantle does not preclude the ‘wet’ origin of komatiite (Allegre, 1982; Parman et al., 1997; Grove and Parman, 2004), because arc environments can be locally hydrated by subduction. The regassing-dominated global water cycle suggests that the most of terrestrial water may have originated at Earth’s surface, pointing towards the impact origin of Earth’s oceans. As discussed next, this issue has an intriguing connection to the thermal budget of Earth.

The origin of terrestrial water

The origin of Earth’s oceans, or how this planet acquired its present amount of water in the early solar system, depends on a number of factors that are currently not known precisely enough, such as the relative timing of Earth accretion, core segregation, the dissipation of the solar nebula, and the disappearance of the massive asteroid belt (e.g. Abe et al., 2000; Marty and Yokochi, 2006). The hydrogen isotope ratio (D/H) is ∼150 × 10−6 for Earth’s oceans, ∼25 × 10−6 for the solar nebula, ∼310 × 10−6 for comets and ∼130–180 × 10−6 for chondrites, and with this information alone, Earth’s oceans could have been derived simply from the accretion of chondritic materials, or from the solar nebula with isotopic fractionation, or from the mixing of multiple sources (e.g. Dauphas et al., 2000; Drake, 2005; Genda and Ikoma, 2008). When combined with carbon and nitrogen isotope constraints, however, the late accretion (i.e. accretion after the core formation) of chondritic materials appear to be the most likely source of terrestrial water (Marty and Yokochi, 2006), and indeed, such late accretion with 0.5–1% Earth’s mass is suggested by the abundance of highly siderophile elements (HSE) in Earth’s mantle (e.g. Morgan, 1986) and is also physically plausible according to the dynamical simulations of planetary accretion (e.g. Morbidelli et al., 2000). Also, the Moon-forming giant impact could have been this late veneer if a fraction of the impactor’s core were mechanically mixed with the Earth’s mantle.

Osmium is one of those HSEs, however, and its isotopic ratio, 187Os/188Os, of Earth’s mantle is known to present a serious impediment to this late accretion hypothesis for Earth’s oceans (Meisel et al., 1996, 2001). Mantle samples such as mantle xenoliths and massif peridotites exhibit a linear correlation between this isotopic ratio and the index of melt depletion such as Al2O3 (Fig. 10), and the isotopic ratio for the BSE may be estimated based on the elemental composition model of BSE. With the conventional estimate for the BSE Al2O3 content (∼4.2 wt%), the observed correlation suggests the BSE isotope ratio of 0.1289–0.1304 (95% confidence limit) (Meisel et al., 2001). On the other hand, the so far observed range of the 187Os/188Os ratio is 0.1255–0.1270 for carbonaceous chondrites, 0.1270–0.1305 for ordinary chondrites and 0.1270–0.1290 for enstatite chondrites (Meisel et al., 1996). Thus, Earth’s 187Os/188Os is consistent with ordinary or enstatite chondrites, but not with carbonaceous chondrites. Ordinary and enstatite chondrites are, however, much drier (<1% H2O) than carbonaceous chondrites (∼10% H2O) (Robert, 2003), so the addition of 0.5–1% Earth’s mass could account for only a small fraction of Earth’s water budget. The osmium constraint has motivated a variety of more elaborate ways to deliver water to Earth and satisfy geochemical constraints at the same time (e.g. Dauphas and Marty, 2002; Drake and Righter, 2002; Marty and Yokochi, 2006).

Figure 10.

 Covariation of Al2O3 and 187Os/188Os for mantle xenoliths and massif peridotites [data are from Meisel et al. (2001) and references therein]. Different symbols denote different localities as indicated by the legend. Linear regression by Meisel et al. (2001) is shown by solid dash line (= 0.1160 + 0.003253x). Linear regression by the bootstrap resampling method is shown by red dashed line (y = 0.1161 + 0.003170x) with pink shade for the 95% confidence limit. The small difference from the original regression probably reflects that unpublished Mexico samples used by Meisel et al. (2001) are not used here. The 95% confidence limit on the osmium isotope rate is shown for the case with the old BSE Al2O3 content (4.2 wt%) and the original regression (grey arrow) and for that with the new BSE Al2O3 content (3.52 wt%) and the bootstrap regression (blue arrow). The influence of the uncertainty of the new BSE model (±0.60 wt%) is indicated by light blue arrow. The osmium isotope ranges observed for three major types of chondrites are also indicated (blue, carbonaceous; red, ordinary; green, enstatite).

This argument may not be so robust because, if the late accretion of HSE were made by the Moon-forming impactor (or similarly large impactors) and partial core addition, there would be no simple relationship between the added masses of HSE and water. Even if we limit ourselves to simple end-member mixing, however, the osmium constraint has one weakness that has been overlooked. The composition model of BSE is based primarily on noisy geochemical trends exhibited by mantle rocks, but the model uncertainty has not been well quantified. A new statistical method was recently built to address this issue, resulting in not only quantifying the uncertainty but also revising the model itself in a non-trivial manner (Lyubetskaya and Korenaga, 2007a). The new BSE model suggests the Al2O3 content of 3.52 ± 0.60 wt%. Revisiting the correlation, we would obtain the new 95% confidence limit of 0.1267–0.1277 for BSE 187Os/188Os, which turns out to be consistent with any kind of chondrites (Fig. 10). Note that this confidence limit is derived from the uncertainty of the linear trend and does not reflect the uncertainty of the BSE model. With the uncertainty of ±0.60 wt%, the likely range of the BSE 187Os/188Os would be widened as 0.1253–0.1291. The other potential water sources can still contribute to some degree, but the most dominant source may well be carbonaceous chondrites.

It is noted that efforts to quantify the reliability of the BSE model were motivated solely by a need to build a self-consistent geochemical model, which is important for long-standing debates over the structure and evolution of Earth’s mantle (Lyubetskaya and Korenaga, 2007b; Korenaga, 2008b). The relevance to the late accretion hypothesis is entirely serendipitous. Though the new BSE model is not a final answer and should be revised in future when additional data become available, it does seem to bring us towards simpler, less arbitrary hypotheses for the structure of mantle convection as well as the origin of Earth’s oceans.


The author thanks Alfred Kröner for invitation to write a review paper on the thermal evolution of Earth, and Kent Condie, Norm Sleep, Geoff Davies, and an anonymous reviewer for constructive reviews. This work was sponsored by the U.S. National Science Foundation under grant EAR-0449517.