invited review plate tectonics, flood basalts and the evolution of

Invited review

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

Jun KorenagaDepartment of Geology and Geophysics, Yale University, PO Box 208109, New Haven, CT 06520-8109, USA

Introduction

The thermal history of Earth, after theinitial period of global magma ocean,is governed by the balance of surfaceheat loss and internal heat generation.An initially hot Earth has been grad-ually cooled down with time because,for most of Earth’s history, surfaceheat loss has been greater than internalheat supply by radiogenic isotopes.This simple energy balance places first-order constraints on various aspects ofphysical and chemical processes oper-ating on the surface of Earth andwithin its deep interior. There havebeen a number of theoretical studieson Earth’s thermal history (e.g.McKenzie and Weiss, 1975; Davies,1980; Schubert et al., 1980; Christen-sen, 1985; Richter, 1985; Solomatov,2001; Korenaga, 2003; Grigne et al.,

2005; Labrosse and Jaupart, 2007),and a review on so far publishedmodels on Earth’s thermal evolutionhas recently been published (Korena-ga, 2008b). Estimating a thermal his-tory involves both geophysics (thephysics of convective heat loss) andgeochemistry (the abundance of heat-producing elements), and many pub-lished models do not account for bothaspects simultaneously. Available geo-chemical and geological data place astrict constraint on the permissiblerange of thermal history, and the mostlikely scenario is briefly reviewed in thenext section.The purpose of this review article is

to discuss some of major geologicalprocesses that are directly related tothe thermal evolution of Earth, on thebasis of this latest understanding.Topics covered include the onset ofplate tectonics, the history of mantleplumes, continental growth, and theorigin and evolution of Earth’soceans. They are difficult problems,and little can be said with certainty atpresent. Because they are intimatelycoupled with thermal evolution, how-ever, we can still derive a few impor-tant constraints. These constraintsmay be counter-intuitive or not obvi-ous at first sight. Mantle plumes, for

example, are often thought to be moreactive in the past, but such temporaltrend is in direct conflict with whatthermal evolution indicates. Also, thevolume of oceans is unlikely to beconstant, and it is probably decreasingwith time. Whereas these topics tendto be considered independently, eachof them represents a different aspecton the evolution of the integratedEarth system, so a proper understand-ing of Earth’s thermal history isessential to make self-consistent pre-dictions about them.

Thermal history of earth

Global heat balance equations

The thermal history of Earth may bemodelled by integrating the followingglobal energy balance (e.g. Stevensonet al., 1983):

CmdTmðtÞ

dt¼ HmðtÞ � QðtÞ þ QCMBðtÞ;

ð1Þ

and

CcdTcðtÞ

dt¼ ðLþ EgÞ

dmicðtÞdt

þ HcðtÞ

� QCMBðtÞ; ð2Þ

ABSTRACT

The chemical composition of the bulk silicate Earth (BSE)indicates that the present-day thermal budget of Earth is likelyto be characterized by a significant excess of surface heat lossover internal heat generation, indicating an important role ofsecular cooling in Earth’s history. When combined withpetrological constraints on the degree of secular cooling, thisthermal budget places a tight constraint on permissible heat-flow scaling for mantle convection, along with implications forthe operation of plate tectonics on Earth, the history of mantleplumes and flood basalt magmatism, and the origin andevolution of Earth’s oceans. In the presence of plate tectonics,hotter mantle may have convected more slowly because itgenerates thicker dehydrated lithosphere, which could slowdown subduction. The intervals of globally synchronousorogenies are consistent with the predicted variation of platevelocity for the last 3.6 Gyr. Hotter mantle also produces

thicker, buoyant basaltic crust, and the subductability ofoceanic lithosphere is a critical factor regarding the emer-gence of plate tectonics before the Proterozoic. Moreover,sluggish convection in the past is equivalent to reducedsecular cooling, thus suggesting a more minor role of mantleplumes in the early Earth. Finally, deeper ocean basins arepossible with slower plate motion in the past, and Earth’soceans in the Archean is suggested to have had about twice asmuch water as today, and the mantle may have started as dryand have been gradually hydrated by subduction. The globalwater cycle may thus be dominated by regassing, rather thandegassing, pointing towards the impact origin of Earth’soceans, which is shown to be supported by the revisedcomposition of the BSE.

Terra Nova, 20, 419–439, 2008

Correspondence: Jun Korenaga, Depart-

ment 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:

[email protected]

This article was commissioned by the

Editors of Terra Nova to mark the Inter-

national Year of Planet Earth.

� 2008 Blackwell Publishing Ltd 419

doi: 10.1111/j.1365-3121.2008.00843.x

where the subscripts m and c denotethe mantle and core components,respectively, Ci is heat capacity, Ti(t)is average temperature, and Hi(t) isinternal heat production. Core heatflux, QCMB(t), represents heatexchange between the mantle and thecore, and Q(t) is the surface heat flux.The mass of the inner core is denotedby mic(t), and the first term on theright-hand side of Eq. (2) describes therelease of latent heat and gravitationalenergy associated with the growth ofthe inner core. As mantle evolution istracked by a single average tempera-ture, this formulation corresponds towhole-mantle convection. Thoughlayered-mantle convection has been apopular concept (e.g. Jacobsen andWasserburg, 1979; Richter, 1985; All-egre et al., 1996; Kellogg et al., 1999),whole-mantle convection is probablysufficient to explain available geophys-ical and geochemical data if the uncer-tainties of these data and thelimitation of theoretical predictionsare taken into account (Lyubetskayaand Korenaga, 2007b; Korenaga,2008b). Note that layered mantle con-vection is still possible. Because it isnot well defined (Korenaga, 2008b),however, exploring its implication forEarth’s evolution would require us todeal with more degrees of freedom.For simplicity, therefore, we restrictourselves to whole-mantle convectionin this review, which should serve asa reference when considering morecomplex convection models (Table 1presents a summary of major assump-tions made in this article).Internal heat production in the core

is controversial (e.g. Gessmann andWood, 2002; McDonough, 2003;Rama Murthy et al., 2003; Lee et al.,2004; Lassiter, 2006), but even if thecore contains potassium at 100 p.p.m.level, Hc would be only �0.7 TW atpresent. The energy release due to theinner core growth is similarly small,being on the order of �2 TW (e.g.

Stevenson et al., 1983). Thus, the firsttwo terms on the right-hand side ofEq. (2) may be neglected for simplic-ity, and Eqs (1) and (2) may becombined to yield:

CdTmðtÞ

dt� HmðtÞ � QðtÞ

þ CcdDTCMBðtÞ

dt; ð3Þ

where C is the heat capacity of theentire Earth [=Cm+Cc, �7 ·1027 J K)1 (Stacey, 1981)] andDTCMB(t) is the temperature contrastat the core–mantle boundary. Thepresent-day contrast is estimated tobe on the order of 1000 K (e.g. Boeh-ler, 1996; Williams, 1998), but how itshould change with time is not under-stood well. To estimate the temporalvariability of the temperature con-trast, we need to calculate the coreheat flux QCMB(t), which dependscritically on the poorly known rheo-logy of the lowermost mantle (e.g.Solomatov, 1996; Karato, 1998;Korenaga, 2005a) and also on othercomplications such as the presence ofchemical heterogeneities (e.g. Farne-tani, 1997; Jellinek and Manga, 2002),the post-perovskite phase transition(e.g. Murakami et al., 2004; Oganovand Ono, 2004), and drastic changesin thermal properties (e.g. Badroet al., 2004; Lin et al., 2005). We donot even know why the present-daycontrast happens to be �1000 K.Thus, it may be reasonable to treatdDTCMB(t) ⁄dt as a free parameter andsee how thermal evolution would beaffected by this term. As the simplestoption, it is set to zero here, and otherpossibilities will be explored later (seeCore heat flux and the possibility ofsuperheated core). With these simpli-fying assumptions, the global heatbalance can be expressed as:

CdTmðtÞ

dt¼ HmðtÞ � QðtÞ: ð4Þ

As the physical state of the earlyEarth is uncertain, the above differen-tial equation is integrated backward intime, starting with the present-daycondition.

Present-day thermal budget

The present-day thermal budget, i.e.Q(0) and Hm(0), may be estimated asfollows. The global heat flux is esti-mated to be 46 ± 3 TW (Jaupartet al., 2007), which is the sum of heatflux due to mantle convection, Q(0),and radiogenic heat production incontinental crust, Hcc(0). The latter isestimated to be 7.5 ± 2.5 TW (Rud-nick and Gao, 2003), so we may write

Hccð0Þ ¼ 7:5þ 2:5e1 ½TW�; ð5Þ

and

Qð0Þ ¼ 46�Hccð0Þ þ 3e2 ½TW�; ð6Þ

where e1 and e2 are random variablesfollowing the Gaussian distribution ofzero mean and unit standard devia-tion. The use of two independentrandom variables signifies that theuncertainty of the global heat fluxand that of continental heat produc-tion are not correlated. Assumingwhole-mantle convection, heat pro-duction in the bulk silicate Earth(BSE) (i.e. crust and mantle) is esti-mated to be 16 ± 3 TW (Lyubetskayaand Korenaga, 2007b), so heat pro-duction in the convecting mantle maybe expressed as:

Hmð0Þ¼ 16�Hccð0Þþ3e3 ½TW�; ð7Þ

where e3 is another random variablefollowing the same Gaussian distribu-tion, and the �convective Urey ratio’(Korenaga, 2008b) is defined as:

Ur(0) ¼ Hmð0Þ=Qð0Þ: ð8Þ

These uncertainties are relativelylarge, allowing unrealistic values [e.g.negative values for Hm(0)], so thefollowing additional constraints areimposed: 5 TW £ Hcc(0) £ 14 TW andHm(0) ‡ 3 TW. These a priori boundsare based on published compositionmodels for the continental crust andthe convecting mantle (e.g. Jochumet al., 1983; Taylor and McLennan,1985; Wedepohl, 1995; Rudnick andGao, 2003; Salters and Stracke, 2004;Workman and Hart, 2005). Theresulting probability distributionfunctions are shown in Fig. 1. It can

Table 1 List of major assumptions employed in this article.

Assumption Relevant section

Earth’s mantle convects as a single layer Thermal History of Earth

Internal heat production in the core is negligible Thermal History of Earth

Mantle dehydration by melting controls global mantle dynamics Thermal History of Earth

Mean sea level has always been close to mean continental level History of Ocean Volume

Seafloor age–area relationship follows a triangular distribution History of Ocean Volume

Zero-age depth of seafloor has been approximately constant History of Ocean Volume

Average thickness of continental crust has been approximately constant History of Ocean Volume

Plate tectonics, flood basalts and Earth’s oceans • J. Korenaga Terra Nova, Vol 20, No. 6, 419–439

.............................................................................................................................................................

420 � 2008 Blackwell Publishing Ltd

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 paperare all calculated with these meanvalues, but it is important to keep inmind that the present-day thermalbudget has non-trivial uncertaintiesand that some uncertainties arestrongly correlated [e.g. Hm(0) andUr(0)]. See Korenaga (2008b) for theeffects of such uncertainties on theprediction of thermal histories.

Internal heating and surface heat flux

At present, the convecting mantlecontains only �50% of heat-produc-ing elements in the BSE, but it musthave had a larger fraction when themass of continental crust was smallerin the past. This may be expressed as:

HmðtÞ ¼ Hm0ðtÞ þ ð1� FCðtÞÞHccðtÞ;ð9Þ

where Hm0(t) and Hcc(t) denote the(hypothetical) evolution of internalheating in the mantle and the conti-nental crust, respectively, withoutmass transfer between them, andFC(t) is the mass fraction of continen-tal crust with respect to the present-day value [assuming FC(t) £ 1 forall t]. The calculation of these internalheating functions is straightforwardonce the present-day values are spec-ified (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 asthere are no direct observations onglobal heat flow in the past. Thisscaling issue has been controversial

(e.g. Schubert et al., 1980; Christen-sen, 1985; Gurnis, 1989; Solomatov,1995; Conrad and Hager, 1999b; Ko-renaga, 2003). Figure 2 shows threerepresentative scaling laws (see Kore-naga (2006) for their derivations). The�conventional’ scaling predicts higherheat flux for hotter mantle, and thetemperature dependency is dictated bythe activation energy of mantle vis-cosity [a few hundred kJ mol)1, (Ka-rato and Wu, 1993)]. Even in the limitof zero activation energy (�isoviscousconvection’ in Fig. 2), the temperaturedependency of heat flow is still posi-tive because heat flow is also propor-

tional to the temperature differencebetween the surface and the interior. Ithas been repeatedly shown that thepositive temperature dependency doesnot produce a sensible thermal historyconsistent with the present-day ther-mal budget (e.g. Christensen, 1985;Korenaga, 2003). One could resolvethis problem by postulating a highUrey ratio at present (e.g. �0.7)(Davies, 1980, 1993, 2007; Schubertet al., 1980; Schubert and Reymer,1985; Williams and Pan, 1992; Mc-Namara and van Keken, 2000), butsuch high Urey ratio appears to be inconflict with geochemical data (Mc-Donough and Sun, 1995; Lyubetskayaand Korenaga, 2007a). Future anti-neutrino data should give direct con-straints on mantle radioactivity (Arakiet al., 2005; McDonough, 2005).Recently, there were some attemptsto rescue the conventional scaling byinvoking temporal fluctuations inplate tectonics (e.g. Grigne et al.,2005; Silver and Behn, 2008), butthese studies have been suggested tobe inconsistent either with known sealevel changes (Korenaga, 2007a) orwith the physics of heat transfer (Ko-renaga, 2008a). It is also important tounderstand what underlies the con-ventional scaling (e.g. Howard, 1966);

6

8

10

0.0 0.1 0.2 0.3 0.4 0.5

Ur

12

14 H

cc (T

W)

Hm

(TW

)

4

6

8

10

12

14

0.0 0.1 0.2 0.3 0.4 0.5

Ur Ur

30

32

34

36

38

40

42

44

0.0 0.1 0.2 0.3 0.4 0.5

Ur

Q (

TW

)

Ur

Fig. 1 Joint probability distribution functions for continental crust heat productionHcc, mantle heat production Hm, convective heat flux Q, and the convective Ureyratio Ur, based on Eqs (5)–(8) with the a priori bounds described in the text. Brightercolour denotes higher probability. Stars correspond to mean values, and ellipses to68% confidence regions assuming the normal distribution.

10

20

50

Q (

TW

)

100

200

1200 1300 1400 1500 1600 1700 1800

Tm(°C)

"Plate tectonics"

Isoviscous convection

Conventional scaling

Fig. 2 Three classes of heat-flow scaling for mantle convection. �Conventional’ and�isoviscous’ parametrizations are both based on the heat-flow scaling of simplethermal convection. Mantle viscosity is temperature-dependent for the former, withthe 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 asdehydration stiffening and compositional buoyancy. See Korenaga (2006) forderivations.

Terra Nova, Vol 20, No. 6, 419–439 J. Korenaga • Plate tectonics, flood basalts and Earth’s oceans

.............................................................................................................................................................


hotter mantle is predicted to yieldhigher heat flux because the boundarylayer (i.e. plates) becomes thinnerowing to greater convective instabil-ity. Conventional scaling and substan-tial boundary-layer growth are thusmutually exclusive, but mixing theseopposing concepts seems to be re-quired if intermittent plate tectonicswere to moderate surface heat flux.It appears, therefore, that some

kind of negative temperature depen-dency is essential to prevent the so-called thermal catastrophe (Fig. 3a),and such scaling may be possible if theeffects of grain growth kinetics (Solo-matov, 1996, 2001) or mantle meltingassociated with plate tectonics (Kore-naga, 2003, 2006) are important forglobal mantle dynamics. Whereas the

importance of grain growth kinetics inmantle convection (particularly in thelower mantle) is not well understoodyet, heat-flow scaling with mantlemelting depends mainly on uppermantle properties, which are reason-ably well known. Thus, the scaling ofKorenaga (2006) (�plate tectonics’ inFig. 3) is adopted for thermal historycalculations here. Note that the con-cept of hotter and stiffer mantle (So-lomatov, 1996) could enhance thenegative temperature dependency fur-ther. As will be suggested later, themantle may have been drier on aver-age, which would also help suppress-ing convective heat flux from a hottermantle in the past. These suggestionsfor unconventional heat-flow scalingare far from being established and

subject to further investigation,including fully self-consistent numeri-cal modelling. Important points arethat there is no a priori reason forEarth’s mantle to follow the conven-tional scaling, and that we now havesome physically plausible mechanismsthat may modify drastically the appar-ent temperature sensitivity of convec-tive heat flux.The calculated thermal history is

presented with three different modelsof continental growth (Fig. 3).Table 2 lists key model parametersand their (present-day) values adoptedhere. The present-day mantle poten-tial temperature is assumed to be1350 �C (e.g. Kinzler, 1997; Herzberget al., 2007). It can be observed thatthe detail of continental growth is notimportant; radically different growthmodels give rise to only �100 Kdifference in the early Earth (Fig. 3a).Perhaps the most important feature isthe robustness of model predictionsowing to a negative feedback imple-mented by the adopted heat-flow scal-ing. Lower heat flux for hotter mantleimplies that internal heating may havebeen higher than surface heat fluxsometime in the past (Fig. 3c), andalso that plate tectonics was moresluggish in the past (Fig. 3d).Before interpreting these predic-

tions any further, at least two issuesneed to be discussed. The first one isthe validity of the assumed heat-flowscaling for plate tectonics. The physicsof plate tectonics is not fully under-stood yet (e.g. Bercovici et al., 2000;Bercovici, 2003). We still do notknow, for example, why Earth exhib-its plate tectonics and other terrestrialplanets do not. There are varioussuggestions (e.g. Tozer, 1985; Regen-auer-Lieb et al., 2001; Korenaga,2007b), many of which call for theexistence of surface water, but we donot have a quantitative understandingfor under what conditions plate tec-tonics can take place. Without suchfundamental understanding, then,why should we trust the proposedscaling for plate tectonics? The answerlies in the nature of scaling laws. Heat-flow scaling prescribes the sensitivityof surface heat flow to variations inmantle temperature, and all of scalinglaws in Fig. 2 are normalized withrespect to the present-day convectiveheat flow. We know plate tectonics isoperating today, and we can estimate

Thermal catastrophe

Q

H m

Ur(0) = 0.22

Armstrong [1981]

Campbell [2003]

McLennan & Talyor [1982]

1300 Man

tle p

oten

tial t

emp.

(°C

)

Fra

ctio

n of

con

t. cr

ust

Pla

te v

eloc

ity (

cm/y

ear)

Qco

nv &

Hm

(T

W)

1400

1500

1600

1700

1800

0 1 2 3 4 Time B.P. (Ga)

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4

First G

CO

?

Ken

orlan

d

Nu

na

Ro

din

ia

Pan

gea

(Go

nd

wan

aland

)

Time B.P. (Ga)

0

20

40

60 (c)

(a) (b)

(d)

0 1 2 3 4 Time B.P. (Ga)

0

2

4

6

8

10

0 1 2 3 4 Time B.P. (Ga)

Fig. 3 Thermal evolution modelling with continental growth, starting with thepresent-day mantle temperature of 1350 �C and the present-day convective Urey ratioof 0.22. The global heat balance of Eq. (4) is assumed, and the details of integrationprocedure 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 resultwith the conventional heat-flow scaling is also shown by dashed line. (b) Three modelsof 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 maybe seen that the Urey ratio, Ur(t) = Hm(t) ⁄Q(t), gradually increases from thepresent-day value of 0.22 to higher values in the past. (d) Predicted history of averageplate velocity. Dashed lines denote the range of geological estimate based on theintervals between supercontinent assemblies or globally synchronous orogenies (Kore-naga,2006), thetimingofwhichareshownbygreenbars(Hoffman,1997;Nutman,2006).


.............................................................................................................................................................


how potential energy release is bal-anced by viscous dissipation for thepresent-day mantle (e.g. Conrad andHager, 1999a). Heat-flow scaling isconstructed by considering how thisenergy balance should change fordifferent temperatures. As far as platetectonics is operating, therefore, theassumed heat flow scaling is unlikelyto be grossly in error, though thedetails of viscous dissipation in themantle could be debatable. Thisbrings up the second issue, which isthe onset of plate tectonics on Earth.Figure 3 shows the backward inte-gration of global heat balance to thebeginning of Earth’s history (4.6 Ga),and this is equivalent to assuming thatplate tectonics started as soon asEarth was created. However, if platetectonics started at 3 Ga, for example,model predictions for older times bearlittle significance. This issue isdiscussed in detail next.

Onset of plate tectonics

Geological and geochemical evidence

The assembly of continental massesand associated collisional processes

require the closure of ocean basinsthat existed between different conti-nents. The subduction of oceanic lith-osphere should be involved in closingocean basins, so the timing of ancientorogenies provides important con-straints on the first emergence of platetectonics on Earth. The oldest �super-continent’ Kenorland was assembledat c. 2.7 Ga (Hoffman, 1997), so itwould be reasonable to assume theoperation of plate tectonics in the lateArchean. Whether Kenorland was atrue supercontinent or not (Bleeker,2003) is not so important in thecurrent context; there is field evidencefor globally synchronous orogeny atc. 2.7 Ga, which is sufficient for discus-sion here. Also, recycling of oceaniccrust by subduction back to c. 3 Ga issupported by the age of eclogite xeno-liths from subcontinental lithosphericmantle (e.g. Jacob et al., 1994; Shireyet al., 2001). As noted by Korenaga(2006), the time intervals of so farknown five supercontinents (Pangea,Gondwanaland, Rodinia, Nuna andKenorland) may be used to estimatethe spatially and temporally averagedrate of plate motion, and such esti-mate appears to be consistent with the

prediction based on thermal evolutionmodelling (Fig. 3d). One could ques-tion this connection between the his-tory of supercontinents and the vigourof plate tectonics by suggesting thatplate tectonics could have been pro-ceeding vigorously for long periodswith no significant change in conti-nental configuration, but as notedearlier (see Internal heating and sur-face heat flux), more vigorous convec-tion (i.e. higher heat flow) in the pastmay not allow us to construct areasonable thermal history. Nonethe-less, the speed of continental motionmay be better regarded as a minimumestimate on the global average, so theagreement with model predictionshould not be taken at face value.The interpretation of geological

records prior to c. 3 Ga has beencontroversial. It is important to keepin mind that, even if plate tectonicswas operating in the early Archean, itdoes not have to resemble modern-style plate tectonics. The most impor-tant ingredient is the subduction ofoceanic lithosphere, and other aspectsof plate tectonics could have beendifferent. It follows that a mere changein the style of tectonics [e.g. atc. 3.2 Ga as suggested by the geologyof the Pilbara Craton in Australia(Van Kranendonk et al., 2007)] doesnot necessarily coincide with the emer-gence of plate tectonics. Plates cancoexist with vertical tectonics, as cur-rently observed at the Basin andRange (Sleep, 2007). In fact, theoperation of plate tectonics as earlyas 3.7–3.8 Ga was suggested by Ko-miya et al. (1999) based on the Isuasupracrustal belt in Greenland, andthe age of episodic granite productionrecorded in the Istaq Gneiss Complexof Greenland (Nutman et al., 2002) aswell as the Narryer Gneiss Complex ofWestern Australia (Kinny and Nut-man, 1996) may point to an earlyglobal collisional orogeny at c. 3.6 Ga(Nutman, 2006). Interestingly, thistiming is consistent with what thermalevolution indicates (Fig. 3d).The possibility of plate tectonics in

even earlier times has also been widelydebated, and it is centred on theinterpretation of the Hadean(>4 Ga) detrital zircons (e.g. Mojzsiset al., 2001; Wilde et al., 2001; Harri-son et al., 2005; Valley et al., 2005;Coogan and Hinton, 2006; Grimeset al., 2007). Some authors have

Table 2 Key parameters used in mantle and ocean evolution modelling.

Parameter Definition Value* Note

C Heat capacity of the entire Earth 7 · 1027 J K)1 Eqs (3) and (4)

Tm(t) Mantle potential temperature 1350 �C Eqs (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 TW Eqs (3), (4) and (6); Fig. 1

Cc Heat capacity of the core 1.3 · 1027 J K)1 Eq. (3)

DTCMB(t) Temperature contrast at CMB§ �1000 K Eq. (3)

Hcc(t) Heat production in continental crust– �8 TW Eq. (9); Fig. 1

smax(t) Maximum age of seafloor** 180 Ma Eq. (23)

v(t) Average plate velocity�� 4 cm yr)1 Eq. (23)

Ao(t) Total area of ocean basins 3.1 · 1014 m3 Eqs (16) and (23)

G(t) Plate creation rate 3.45 km2 yr)1 Eqs (22), (15) and (23)

V(t) Total ocean volume 1.51 · 1018 m3 Eq. (18)

d0(t) Zero-age depth of seafloor 2654 m�� Eq. (19)

b(t) Seafloor subsidence rate 323 m Myr)1 ⁄ 2 Eqs (19) and (20)

*For parameters that depend on time t, present-day values are listed.

�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).

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

§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).

–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.

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

��Past plate velocity is calculated using its relationship to convective heat flux, v / (Q ⁄ Tm)2 [Eq. (18) of

Korenaga (2006)].

��This is assumed to be constant in Fig. 9.


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suggested the existence and recyclingof continental crust as early as 4.5 Ga(Harrison et al., 2005), which impliesthe operation of plate tectonics (orjust recycling of oceanic lithosphere)shortly after the formation of Earth.The interpretation of out-of-contextdetrital zircons is, however, not un-ique especially for the Hadean era(e.g. Sleep, 2007), unless we invokeUniformitarianism for relevant geo-logical processes. What the Hadeanzircons actually constrain seems to bean open question. A related issue isthat, if continental crust existed in theHadean, how voluminous it couldhave been then, and it will be dis-cussed later (see Continental growth:instantaneous, gradual, or discontinu-ous?).

A note on late heavy bombardment

On the basis of the lunar crateringrecord, it has been suggested thatEarth experienced a spike of meteoritebombardment at 4.0–3.8 Ga (Hart-mann et al., 2000; Ryder, 2002). Thisevent is called as the late heavybombardment, and it is sometimesdiscussed as if it could have had astrong influence on the stability oflithosphere (and thus the operation ofplate tectonics) (e.g. Shirey et al.,2008). The total mass of impactorsthat hit the Moon during this period isestimated to be �3 · 1018 kg (Ryder,2002), and by extrapolation, Earth isexpected to have been hit by a few big(>300 km diameter) impactors andnumerous smaller ones (about a dozenof �200-km-diameter impactors, ahundred of �100-km-diameter impac-tors, and so on) (e.g. Sleep, 2007). Themass of a 300-km-diameter impactorwould be �4 · 1019 kg, and its influ-ence of the thermal state of Earth’slithosphere may be estimated byequating its potential energy and theenergy required to heat up the litho-sphere by DT as:

MLcpDT � GMEmrE

; ð10Þ

where ML is the mass of lithosphere(�1.7 · 1023 kg for the thickness of100 km), cp is its specific heat (�103J kg)1 K)1), G is the gravitationalconstant (6.67 · 10)11 m3 kg)1 s)2),ME is the mass of Earth (�6 ·1024 kg), m is the mass of the impac-tor, and rE is the radius of Earth

(�6.4 · 106 m). For a 300-km-diame-ter impactor, DT is only �15 K. Ofcourse, impact heating is a highlylocalized phenomenon, and a muchgreater temperature rise is expected inthe vicinity of an impact site. The lateheavy bombardment is certainlyimportant for surface conditions as itcould vaporize at least a part ofoceans. The above order-of-magni-tude estimate is probably sufficient,however, to show that the effect ofeven the biggest impactor during thelate bombardment would not besignificant for global mantle dynam-ics such as the operation of platetectonics.

Geodynamical considerations

Estimating the onset of plate tectonicson a purely theoretical ground isdifficult because the very physics ofplate-tectonic convection is not wellunderstood (e.g. Bercovici et al.,2000). There still exist, however, cer-tain physical constraints that have tobe considered when discussing thestyle and vigour of mantle convectionin the early Earth. In particular, theinterpretation of geochemical data isoften assisted by or compared togeodynamical considerations (some-times subconsciously), and this iswhere a preconception could poten-tially lead to biased interpretations.For example, vigorous convection isoften assumed for the Hadean dynam-ics (e.g. Sleep and Zahnle, 2001), but itis not clear if such vigour can really beattained in the early Earth. Thoughconvection in a magma ocean shouldhave been extremely vigorous (Solo-matov, 2007), the transition from suchintense liquid convection to solid-statemantle convection is currently poorlyunderstood [see Sleep (2007) for thepossibility of �mush ocean’]. If mantleconvection was in the mode of platetectonics, for example, the scaling ofKorenaga (2006) might be applicable,which predicts slower, not faster, platemotion. Even without calling for thisparticular scaling, however, a simplephysical argument centred on thesubductability of oceanic lithosphere(e.g. Bickle, 1986; Davies, 1992) seemsto question rapid convection whenEarth was much hotter than today.For the top boundary layer to berecycled into the interior by free con-vection, the boundary layer must be

negatively buoyant, at least on aver-age, with respect to the hot interior.This buoyancy constraint is not anissue for simple thermal convectionwith a homogeneous material becausethe top thermal boundary layer isalways denser than the hot interior.Convection in Earth’s mantle, how-ever, induces pressure-release meltingand differentiates the shallow mantleinto basaltic crust and depleted mantlelithosphere, both of which are lessdense than the mantle before meltingif compared at the same temperature.For the top boundary layer to becomedenser than the interior, therefore, ithas to be cooled for a sufficiently longtime so that negative buoyancy due tothermal contraction overcomes theintrinsic chemical buoyancy [note thatbasalt is transformed to denser eclo-gite at �60 km depth (Ringwood andGreen, 1964), so this chemical buo-yancy issue is important only for theinitiation of subduction, not for itscontinuous operation]. For the pres-ent-day condition, this time-scale isestimated to be c. 20 Myr, but whenthe mantle is hotter than present by200–300 K, the time-scale could be onthe order of 100 Myr (Davies, 1992).That is, when the mantle was hotter inthe Hadean, it must have had thickerbuoyant crust as well, which couldreturn to the interior only after c. 100-Myr long surface cooling. This time-scale is comparable to the present-daytime-scale to renew ocean basins.Vigorously convecting hotter mantlecould be at odds with more copiousmelting expected for such mantle.The subductability argument may

be countered because thick oceaniccrust such as oceanic plateaus doessubduct at present (e.g. Sleep andWindley, 1982), but such thick crustis localized at present as opposed to itslikely global occurrence in the Arche-an. The argument may also be ques-tioned because the seafloor iscurrently subducting irrespective ofits age (Parsons, 1982). Indeed, nearzero-age crust is subducting under thewestern margin of the North Ameri-can plate, whereas the oldest crust inthe Atlantic (c. 180 Ma) is not sub-ducting at all, so the simple buoyancyargument may seem to be irrelevant toactual plate dynamics. Young sub-ducting seafloor is, however, attachedto an older, already subducted plate,and the presence of old, non-subduct-


.............................................................................................................................................................


ing seafloor tells us that negativebuoyancy alone is not sufficient toinitiate subduction. Probably a moreadequate measure is the global aver-age of the age of subducting seafloor,which is c. 49 Ma (rate average) orc. 61 Ma (area average) [based onTable 1 of Parsons (1982)]. In eithercase, it is old enough to achievesufficient negative buoyancy underthe present-day condition.The concept of subductability

depends on two factors: thermal dif-fusivity and intrinsic chemical buoy-ancy. Whereas the former is virtuallyconstant under plausible mantle con-ditions, the chemical buoyancy is afunction of mantle temperature, andthe functionality is less certain. Topredict the density of oceanic crust,one has to first calculate the compo-sition of primary mantle melt for arange of mantle temperature, and thencalculate the density of mineral aggre-gates expected to be solidified from agiven melt composition. The currentunderstanding of mid-ocean ridgemagmatism is probably sufficient toconduct the first step with moderateaccuracy (e.g. Langmuir et al., 1992;Kinzler, 1997; Walter, 1998), but thesecond step is more uncertain becausethe details of crystallizing phasesdepend on the temperature and pres-sure conditions within newly formingcrust and thus on how exactly crust isconstructed. Even for the present-dayoceanic crust, the physical mechanismof crustal accretion is still underdebates (e.g. Phipps Morgan andChen, 1993; Korenaga and Kelemen,1998; Wilson et al., 2006), and we donot know, from first principles, how toconstruct much thicker crust corre-sponding to hotter mantle. The sub-ductability calculation by Korenaga(2006), for example, depends on thecrustal density parametrization ofKorenaga et al. (2002), which assumeslow-pressure crystallization. Futurestudies on the crustal structure oflarge igneous provinces may provideimportant field constraints on thisissue.Provided that intrinsic chemical

buoyancy remains significant for hot-ter mantle, subductability is a robustphysical constraint, but its use needssome care. Davies (1992), for example,argued that plate tectonics was un-likely when the mantle was muchhotter because the time-scale for

negative buoyancy would be too long(i.e. c. 100 Myr) to be achieved invigorously convecting mantle, but thisargument depends on the conventionalheat-flow scaling (Fig. 2). Also, vanThienen et al. (2004) suggested thatplate tectonics may not be possiblewhen the mantle potential temperatureis higher than 1500 �C based on sub-ductability, but their calculation as-sumes the so-called plate model for theevolution of oceanic lithosphere (Par-sons and Sclater, 1977; Stein and Stein,1992), in which the growth of litho-sphere is inhibited after c. 80 Myr.Though convective instability can limitthe growth of lithosphere (Parsons andMcKenzie, 1978), this instability is afunction of mantle viscosity, and it isdifficult to justify the use of a constantmaximum thickness over a range ofmantle temperature (cf. Korenaga,2003). Note that the plate model con-tains an artificial bottom boundarycondition to suppress cooling, and arecent global analysis of seafloortopography casts a doubt on theobservational basis for this model(Korenaga and Korenaga, 2008).Recently, Davies (2006) proposed

that the subductability issue wouldnot present a major obstacle forthe operation of plate tectonics if themantle was already depleted in theearly Earth by earlier melting events.In his numerical model, subduction isforced by a surface velocity condition,and subducted oceanic crust segre-gates from depleted mantle litho-sphere and sinks to the lower mantle,leading to a gradual depletion of theupper mantle, the melting of whichdoes not yield thick oceanic crust.This scenario, however, requires somekind of tectonics (other than platetectonics) that can subduct oceaniccrust, and a time-scale to achieve therequired mantle depletion is uncertain[in the model of Davies (2006), sub-duction was achieved by assuming thecontinuous operation of plate tecton-ics]. The once highly depleted uppermantle would also need to be refertil-ized later to explain the present-dayupper mantle. In other words, theupper mantle needs to change itscomposition so that melting alwaysyields relatively thin oceanic crustregardless of its temperature. Theplausibility of this mechanism seemsto hinge on a delicate balance betweenmantle mixing and secular cooling.

Subductability thus remains to bean important factor to be considered,and the backward integration ofEarth’s thermal history seems to pro-vide an important perspective relatedto subductability, namely, the role ofinternal heating on the initiation ofplate tectonics. Figure 4 shows twokinds of lithospheric thickness. One isthe minimum thickness of subductableoceanic lithosphere [which is equiva-lent to the �critical thickness’ definedby Korenaga (2006)]; lithosphere mustexceed this thickness to become neg-atively buoyant. This thickness is afunction of mantle temperature, so itstemporal variation is determined byan assumed thermal history (Fig. 3a).The other is the equilibrium thicknessof a hypothetical stagnant lid, which isa function of internal heat generationas (Korenaga, 2006):

�hSL �kATm

Hm; ð11Þ

where k is thermal conductivity and Ais the total surface area of Earth.At a thermal equilibrium, lithosphereshould become thinner for higherinternal heating, and Fig. 4 indicatesthat the equilibrium thickness mayhave been less than the minimumthickness before c. 2.5–3 Ga. In theArchean and the Hadean, the amountof internal heat generation in themantle was greater than present by afactor of >2 (Fig. 3c), and this highinternal heating may have suppressedthe growth of the top thermal bound-ary layer and thus prevented litho-sphere to become negatively buoyant.This argument is, however, probablytoo simplistic because the equilibriumthickness is unlikely to be achievedinstantaneously. The thermal adjust-ment time-scale can be long, on theorder of 1 Gyr (Daly, 1980), and thislong time-scale in a sense justifiesEq. (1), in which surface heat fluxQ(t) is usually parameterized as afunction of mantle temperature(Fig. 2) and can vary independentlyfrom internal heat production Hm(t).The physics of thermal adjustment is,however, not fully explored for mantleconvection with realistic rheology,and the significance of the thicknesscrossover in Fig. 4 is an open ques-tion. As noted by Sleep (2000) andStevenson (2003), a change in themode of mantle convection may leadto non-monotonic thermal histories.


.............................................................................................................................................................


Though it could be a coincidence, thetiming of crossover is close to theArchean-Proterozoic boundary, atwhich surviving continental crust be-gan to emerge in abundance. A quan-titative relationship between mantleconvection and continental recyclingthroughout Earth’s history is one ofthe subjects that should be exploredby future geodynamical studies.To go beyond this simple buoyancy

argument, it is imperative to advanceour understanding of the physics ofplate tectonics. Though plate-tectonic-like convection can be successfullysimulated 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 treatthe strength of oceanic lithosphere as afree parameter, which must be ad-justed to achieve plate tectonics. It isdifficult to discuss the onset of platetectonics on the basis of those modelsbecause the free parameter may not beconstant over the geological time. Itwould desirable to predict the strengthof lithosphere from first principlesbased on tangible physical processes;such research effort is still in itsinfancy (e.g. Korenaga, 2007b).

Secular cooling and flood basaltvolcanism

Did mantle plumes exist in theArchean?

Apart from metal-silicate segregationthat took place within the first hun-dred million years of Earth’s history(e.g. Halliday, 2003), chemical differ-entiation in Earth’s interior refers tothe melting of silicate rocks. Themelting of shallow upper mantle usu-ally takes one of the following threetypes of surface manifestation: mid-ocean ridge magmatism, arc magma-tism and hotspot magmatism (e.g.Wilson, 1989; McBirney, 1993). Thefirst two are associated with platetectonics. Here, the term hotspotmagmatism is used in a broad senseto cover not only hotspots such asHawaii and Iceland but also continen-tal and oceanic flood basalt provincessuch as the Deccan Traps and theOntong Java Plateau (Coffin and Eld-holm, 1994). This type of magmatismis commonly explained by the upwell-ing of mantle plumes (e.g. Morgan,1971; Richards et al., 1989; Campbelland Griffiths, 1990; White andMcKenzie, 1995) though the origin

of hotspot magmatism has been con-troversial (e.g. Anderson, 1998; Foul-ger et al., 2005). Thermal anomaliessuch as mantle plumes are certainlyone way to generate hotspot islandsand flood basalts, but not the onlyway because chemical and ⁄or dynam-ical anomalies may also result insimilar magmatic activities (e.g. Sleep,1984; Tackley and Stevenson, 1993;Korenaga and Jordan, 2002; Ander-son, 2005; Ito and Mahoney, 2005;Korenaga, 2005b).For the sake of discussion, however,

let us assume that most of hotspotsand flood basalts are formed by themelting of mantle plumes that origi-nate in the core–mantle boundaryregion. In this case, the thermal evo-lution of Earth suggests that hotspotmagmatism should have been morereduced in the past. As will beexplained shortly, this is a straightfor-ward consequence of a geologicallyplausible thermal history (Sleep et al.,1988), though this fact does not seemto be widely recognized. For example,a plume-dominated regime is oftensuggested as an alternative mode ofmantle convection in the Archean (i.e.instead of the plate-tectonic regime)(e.g. Fyfe, 1978; Van Kranendonket al., 2007), and some models forcontinental growth call for a promi-nent role of flood basalts or mantleplumes in the early Earth (e.g. Abbottand Mooney, 1995; Albarede, 1998).Along with the notion of more vigor-ous convection, plume activities in theArchean are commonly assumed tohave been similar to or higher thantoday. Indeed, the vigor of mantleconvection and the intensity of plumesmay be related through the thermalbudget of Earth, but their temporalvariations do not have to be positivelycorrelated. It is possible, for example,to have a reduced plume flux whilemaintaining the vigor of convection,and the thermal history shown inFig. 3 indicates that such possibilityis likely. To discuss this further, weneed to relax one of the assumptionsbehind Eq. (4) and consider the pos-sibility of differential core coolingusing Eq. (3).

Core heat flux and the possibility ofsuperheated core

The reconstructed thermal history ofFig. 3 is based on Eq. (4), in which the

0

50

100

150

200

250

300

350

Pla

te th

ickn

ess

[km

]

0 1 2 3 4

Time B.P. [Ga]

Minimum thickness of"subductable" oceanic lithosphere

"Equilibrium" thicknessof stagnant lid

Phanerozoic Proterozoic Archean Hadean

Fig. 4 The predicted variation of the minimum thickness of subductable oceaniclithosphere and the equilibrium thickness of stagnant lid, based on the thermal historyshown in Fig. 3. The equilibrium lid thickness is thinner in the past due to highermantle heat production, and is thinner than the minimum subductable thicknessbefore the Proterozoic, suggesting that the subductability of oceanic lithosphere is akey factor for the emergence of plate tectonics in the early Earth.


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mantle and the core are assumed tohave cooled at the same rate. That is,the temperature contrast at the core–mantle boundary is assumed to havebeen constant. In this case, the coreheat flux is directly related to thesecular cooling of the mantle as:

QCMBðtÞ ¼ �CcdTmðtÞ

dtð12Þ

[from Eq. (2)]. The history of coreheat flux with this assumption isshown as case 1 in Fig. 5. The pres-ent-day core heat flux is estimated tobe �6 TW, and more important, thepast core heat flux is lower than the

present-day value and is predicted tobe negative before the early Archean(i.e. core heating instead of coolingshould take place then). With thenearly constant surface heat flux butwith gradually decaying radiogenicheat source (Fig. 3c), the secular cool-ing of Earth and thus the core heatflux are likely to have been lower inthe past.The details of the predicted core

evolution are, however, subject tolarge uncertainties. The temperaturecontrast DTCMB, which is assumed tobe constant, is almost a free parametergiven our limited knowledge of the

dynamics of the core–mantle bound-ary region; the rheology of the lower-most mantle is currently unknown. Toexplore the significance of time-depen-dent DTCMB, two different variationsare considered (cases 2 and 3 inFig. 5b). In case 2, the contrastdecreases linearly by 500 K over theentire Earth history, whereas in case 3it decreases quadratically by a similaramount. Thermal evolution wassolved again, but using Eq. (3), andthe corresponding core heat flux wascalculated as:

QCMBðtÞ¼�CcdTmðtÞ

dt�Cc

dDTCMBðtÞdt

:

ð13Þ

It may be seen that differential corecooling could modify substantiallypredicted core heat flux (Fig. 5a). Onthe other hand, the thermal history ofthe mantle (not shown) is not affectedmuch by this modification. This isexpected because the differential corecooling of case 2, for example, pro-vides additional core heat flux of �4TW, which is significant for the corethermal budget, but not for the mantlethermal budget. Cases 1 through 3 areall consistent with the observationalconstraints on the present-day coreheat flux [6)12 TW, (Buffett, 2003)].At the core–mantle boundary, the

core side is considered to be hotterthan the mantle side by at least�1000 K at present (Williams, 1998).The present-day contrast is uncertainbecause the estimate of the core-sidetemperature is based on the phasediagram of the core, which dependson its chemical composition and inparticular on the (uncertain) light ele-ment composition (e.g. McDonough,2003). Nevertheless, a temperaturecontrast more than a few hundred Kis probably robust, and this suggestseither (1) that there was no contrast atthe beginning of the Earth history, butthe mantle cooled faster than the core,or (2) that the core was initially hotterthan the mantle, and the temperaturecontrast has not been entirelyremoved. The first scenario seemsunlikely because it would predict coreheat flux lower than case 1 and thusbecomes incompatible with the pres-ent-day core heat flux estimate andalso with the history of the geo-magnetic field (e.g. McElhinny andSenanayake, 1980; Buffett, 2002;

0

2

4

6

8

10

12

Cor

e he

at fl

ux [T

W]

0 1 2 3 4

Time B.P. (Ga)

0

100

200

300

400

500

600

ΔTC

MB(t

)–ΔT

CM

B(0

) (K

)

0 1 2 3 4

Time B.P. (Ga)

(a)

(b)

Case 1

Case 1

Case 2

Case 2

Case 3

Case 3

Fig. 5 (a) Predicted history of core heat flux QCMB incorporating the effect ofdifferential core cooling. Different colours correspond to different models ofcontinental 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 rateof differential cooling (temperature contrast at the core–mantle boundary linearlydecrease by 500 K over 4.6 Gyr), and 3, decreasing rate of differential cooling (heatflux due to differential cooling decreases linearly from 10 TW at 4.6 Ga to zero atpresent).


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Tarduno et al., 2007). The secondpossibility is physically plausible be-cause either the gravitational segrega-tion of the core or the Moon-forminggiant impact is expected to deposit aconsiderable amount of heat into thecore (Solomatov, 2007). The initialtemperature of this superheated coreand its later evolution are uncertain,but it would be fortuitous if the initialtemperature contrast has been main-tained to the present day; it is possible,but it would require a specific dynam-ics of the core-boundary boundaryregion. Figure 5(a) suggests that thepossibility of differential core cooling(or the current uncertainty of the core–mantle boundary dynamics) providesimportant degrees of freedom for thecoupled core–mantle evolution.Explaining both the present-day coreheat flux and the history of the geo-magnetic field has been a conundrumfor 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 free-dom may help to resolve it.A linear decrease in the tempera-

ture contrast (case 2) shifts core heatflux almost uniformly, thus unaffect-ing the trend of lower heat flux in thepast. To reverse this trend, we needto invoke a greater temporal varia-tion in the past (e.g. case 3), but thereis a negative feedback mechanism tosuppress core heat flux in the earlyEarth. Higher differential core cool-ing is equivalent to higher internalheating in the mantle [Eq. (3)], whichwould then reduce the secular coolingof the entire Earth (i.e. including thecore). This is why even case 3 pre-dicts vanishing core heat flux in theearly Earth (Fig. 5a). It appears thatcore heat flux was probably lowerthan (cases 1 and 2) or similar to(case 3) the present-day value, andsubstantially higher core heat flux inthe early Earth probably requires anunrealistic degree of differential corecooling.

Origins of flood basalts andpreservation bias

With reduced core heat flux, it wouldbe difficult to expect more vigorousplume activities in the early Earth.Furthermore, plume heat flux is likelyto be smaller than the total core heatflux (e.g. Davies, 1993; Labrosse,

2002). If the average plume sizeremains similar through time, then,the number of plumes should havebeen lower, and if we instead assumethe constant frequency of plume for-mation, the average plume size shouldhave been smaller. In either case, weexpect a reduced volume of floodbasalt magmatism in the past as acorollary of the mantle plume hypo-thesis. This does not necessarily meanthat we cannot expect greater floodbasalt magmatism in the past. First ofall, �normal’ mantle in the Archean islikely to be �300 K hotter than pres-ent (Fig. 3a), so flood basalt magma-tism in the Archean may notnecessarily require an unusual sourcemantle. High temperature alone, how-ever, is probably insufficient to explainfocused magmatic events such as floodbasalts, and there are a few non-plumemechanisms as discussed below.One popular concept is the episodic

overturn of layered-mantle convection(e.g. Stein and Hofmann, 1994; Con-die, 1998; Rino et al., 2004). In thelayered-mantle convection mode, thelower mantle cools less efficiently andthus becomes hotter than the uppermantle. Numerical modelling in theearly 1990s suggested that, whereas itis difficult to maintain a purely layeredstate, episodically layered convectionmay take place with the endothermicphase change at the base of the mantletransition zone (i.e. at the 660-kmdiscontinuity) (e.g. Machetel andWeber, 1991; Honda et al., 1993;Tackley et al., 1993; Solheim andPeltier, 1994). When a temporallylayered state is broken, a large volumeof the hot lower mantle material canbe brought to the surface, potentiallyresulting in massive melting events.Note that the plausibility of episodicoverturns depends critically on themagnitude of the (negative) Clapeyronslope for the endothermic phasechange. To insulate the lower mantlefrom cooling due to subducted slabsand make it substantially hotter thanthe upper mantle, subducted slabsmust be supported globally by thephase change for several hundredmillion years. Recent experimentalstudies suggest that the Clapeyronslope is not as strongly negative aspreviously thought (Katsura et al.,2003; Fei et al., 2004), potentiallyundermining the physical basis forepisodically layered convection.

Another mechanism that may pro-duce large igneous provinces is theupwelling of chemically anomalousmantle that has been fertilized byrecycled oceanic or continental crust(e.g. Korenaga and Kelemen, 2000;Yaxley, 2000; Anderson, 2005). Morefertile mantle is usually intrinsicallydenser (O’Hara, 1975), so its upwell-ing probably requires special tectonicenvironments (Korenaga, 2004,2005b). Compensating chemical den-sity anomalies by thermal buoyancy ispossible, but it would require unreal-istically hotter mantle [e.g. DT�500)600 K (Lin and van Keken,2005)], which may not be consistentwith available petrological constraints(DT � 100)300 K) (e.g. White andMcKenzie, 1995; Herzberg, 2004).Setting aside this dynamical difficulty,it is also unclear how abundant suchfertile mantle would have been in thepast. For one thing, the recycling rateof oceanic crust is controlled by platemotion, which may not have beendifferent from present as discussedearlier (Internal heating and surfaceheat flux). On the other hand, therecycling of continental crust is freefrom this constraint, and primordialheterogeneities created during themagma ocean may have been abun-dant in the early Earth. The possibilityof fertile mantle is a wild card, as ourunderstanding of the dynamics ofchemically heterogeneous mantle isstill immature (Korenaga, 2008b).Geological indicators for flood bas-

alts are common in Archean terranes(e.g. Campbell et al., 1989; Ernst andBuchan, 2003; Sandiford et al., 2004),which is probably the basis for thenotion of more active plume activities.One way to reconcile the apparentdiscrepancy between the theoreticalexpectation and the field observationis to call for preservation bias; thecontinental crust with flood basaltsmay have better survived for thefollowing reason. The genesis of floodbasalts, produced by either thermal orchemical anomalies, involves the melt-ing of a large volume of the mantle.Because mantle melting also deh-ydrates and stiffens the residual man-tle (Karato, 1986; Hirth andKohlstedt, 1996), this large-scale melt-ing would produce a voluminous, stiffmantle root, which could protect theoverlying continental crust fromtectonic disturbances. It is unclear


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how much of such dehydrated residualmantle has contributed to what wecall today as continental tectosphere(Jordan, 1988; Pearson, 1999), but therole of dehydrated mantle in ancientcontinental dynamics is an importantdynamical problem to consider (e.g.Doin et al., 1997;Lenardic andMoresi,1999). Oceanic crust older thanc. 180 Myr old is all subducted, andwe have only continental crust to dis-cuss anything older. It is natural tohope for a minimal preservation bias,but when interpreting billion-years-oldcontinental crust, it would be hard tooverestimate preservation bias.

Continental growth and the historyof ocean volume

Continental growth: instantaneous,gradual, or discontinuous?

When the continental crust emerged inthe Earth history and how it hasevolved to its preset figure have beendebated over several decades (e.g.Hurley and Rand, 1969; O’Nionset al., 1979; DePaolo, 1980; Arm-strong, 1981; Taylor and McLennan,1985; Jacobsen, 1988; Collerson andKamber, 1999; Campbell, 2003; Har-rison et al., 2005), and continentalgrowth is still a highly controversialtopic. Being highly enriched in heat-producing elements, its growth historycan influence the thermal evolution ofEarth by depleting the convectingmantle [Eq. (9)], but this type ofinfluence is of relatively minor impor-tance (Fig. 3). Probably a moreimportant aspect is whether the pro-duction of continental crust has beencontinuous or discontinuous. Gradualgrowth models (e.g. McLennan andTaylor, 1982; Jacobsen, 1988; Camp-bell, 2003) are obviously continuous,and instantaneous growth models (e.g.Armstrong, 1981; Harrison et al.,2005) are also mostly continuous inthis sense, because the constant conti-nental mass is assumed to have beenmaintained by balancing continuousproduction and destruction. These�continuous’ growth models are com-patible with the continuous operationof plate tectonics. �Discontinuous’growth models (e.g. Rino et al.,2004; Hawkesworth and Kemp,2006; Parman, 2007), on the otherhand, suggest that the mode of mantleconvection may have changed at least

a few times in the past, and the use ofsingle heat-flow scaling in thermalevolution modelling, as done in mostof previous studies, may becomeoverly simplistic in this case. Thus,the debate over continental growthhas a critical relevance to the theoret-ical formulation of thermal evolutionmodelling.The episodic overturn of layered-

mantle convection has been a popularconcept as a plausible mechanism thatmay explain the episodic growth ofcontinental growth (e.g. Stein andHofmann, 1994), but as discussedearlier, this idea is based on earlynumerical convection models with astrong endothermic phase transition,the assumption of which does notseem to be valid in light of recentexperimental studies. Recently, O’Ne-ill et al. (2007) proposed that platetectonics itself might have been inter-mittent in the Precambrian. Whereastheir argument using palaeomagneticdata is weak given the likelihood oftrue power wander (Evans, 2003),they offer a plausible dynamical rea-soning. Mantle convection modelswith pseudo-plastic rheology areknown to exhibit three modes ofconvection (stagnant-lid, intermittentplate tectonics, and continuous platetectonics), depending on the assumedstrength of lithosphere (or its maxi-mum yield strength) (e.g. Moresi andSolomatov, 1998; Stein et al., 2004).When the mantle was hotter in thepast, its internal viscosity may belower due to temperature dependency,so convective stress could become toolow to sustain the continuous opera-tion of plate tectonics. In this case,intermittent plate tectonics is possiblefor a certain range of maximum yieldstress. Unlike the model proposed bySilver and Behn (2008), however, thisoriginal version of intermittent platetectonics proposed by Moresi andSolomatov (1998) hardly modifiesconventional heat-flow scaling, be-cause low heat flux during the stag-nant-lid mode is compensated by highheat flux during the plate tectonicsmode [see, for example, Figure 3 ofMoresi and Solomatov (1998)]. So itmay be able to explain continentalgrowth but not thermal evolution.Also, as noted earlier, the pseudo-plastic model of Moresi and Soloma-tov (1998) needs to assume thestrength of lithosphere (i.e. its

maximum yield stress), which maynot be constant over Earth’s history.Equally important, mantle viscosity isa function of not only temperature,but also other parameters such asgrain size and water content (e.g.Karato and Wu, 1993; Hirth andKohlstedt, 2003; Korenaga and Ka-rato, 2008). Solomatov (1996), forexample, suggested that hotter mantlecould become more viscous if grain-size-dependent viscosity is considered.Assuming weaker convective stressfrom a hotter mantle is equivalent toholding these other variables constantthrough time, which may not bewarranted. In fact, as shown in thenext section, the present-day thermalbudget indicates that the mantle wasprobably drier in the past, which maycompensate a decrease in viscosity dueto temperature dependency.The diversity of continental growth

models is partly because differentgeochemists place different weightson relevant geochemical data such as143Nd ⁄ 144Nd and Nb ⁄Th. For exam-ple, a significant volume of continen-tal crust in the Hadean, as implied bythe hafnium isotope data of ancientzircons (Harrison et al., 2005), seemsto be incompatible with the Th–U–Nbsystematics of depleted-mantle-de-rived rocks (Collerson and Kamber,1999). The interpretation of geochem-ical data in terms of geological pro-cesses, however, often depends onsimple box models (e.g. DePaolo,1980; Jacobsen, 1988), which in turnassumes rapid mantle mixing (Colticeet al., 2000). Also, geochemical inter-pretations usually require the chemi-cal or isotopic composition of the BSEas a reference baseline, but the uncer-tainty of such reference value is nottrivial. Continental growth modelsbased on the Nd isotope evolution(e.g. Bennett, 2003), for example,assumes that the Sm ⁄Nd ratio of theBSE is identical to that of chondriteswithin 1% uncertainty [the �strong’version of chondrite assumption (Ko-renaga, 2008b)]. Available isotopicdata from terrestrial samples, on theother hand, require only the �weak’version of chondrite assumption, i.e.the ratios of refractory lithophile ele-ments such as Sm and Nd should notbe different from the chondritic aver-age more than a few per cents (Lyu-betskaya and Korenaga, 2007b). Thistype of uncertainty may be essential


.............................................................................................................................................................


when constructing a geochemicalmodel that can reconcile differentgeochemical data simultaneously.

Global water cycle and net waterinflux

Frequent inundations throughout thePhanerozoic suggest that the mean sealevel has always been close to themean continental level, which isknown as the constant freeboard(Wise, 1974). This constancy is atleast geologically reasonable; conti-nental crust is subject to erosion whenit is above the sea level, and when apart of continents subsides below thesea level, it would likely be the locus ofdeposition. The abundant occurrenceof submarine flood basalt magmatismin the Archean and Proterozoic(Arndt, 1999), however, implies thatthe mean sea level had been highenough to inundate a substantial frac-tion of continents through the Pre-cambrian. The constant freeboard isthus probably too simplified anassumption, but the following pointseems to be robust: there has alwaysbeen a sufficient volume of water to fillup the ocean basins, at least to themean continental level. In otherwords, the constant freeboard is stilluseful to quantify the lower bound onthe ocean volume.Reymer and Schubert (1984) cou-

pled the constant freeboard with thethermal evolution of Earth and esti-mated the history of continentalgrowth assuming that the ocean vol-ume has been constant (Fig. 6a). Theirmodel is based on the conventionalheat-flow scaling (Fig. 2), which pre-dicts faster plate motion (i.e. higherheat flow) for hotter mantle in thepast. Faster plate motion means youn-ger and thus shallower seafloor, andto maintain the constant freeboardwithout changing the ocean volume,continental mass needs to be reduced.Note that the conventional scalingcannot reconstruct a reasonable ther-mal history unless internal heat pro-duction in the convecting mantle ismuch higher than geochemical con-straints (see Internal heating andsurface heat flux). This important facttends to be overlooked, and thenotion of more vigorous convectionin the past has been entrenched in theliterature on the continental freeboardor the history of ocean volume (e.g.

Galer, 1991; Kasting and Holm, 1992;Galer and Mezger, 1998; Harrison,1999; Hynes, 2001; Rupke et al., 2004;Kasting et al., 2006).The present-day thermal budget

characterized by a low Urey ratioinstead suggests less vigorous convec-tion thus slower plate motion, thecorollary of which is older and deeperocean basins in the past (Fig. 6b). Inthis case, the volume of Earth’s oceansmay have been greater to maintain theconstant freeboard, as many geochem-ical studies suggest smaller continentalmass in the Archean. This interestingpossibility has not been seriously con-sidered probably because it is difficultto test. It can be demonstrated, how-ever, that the constant ocean volumeis inconsistent with the present-daythermal budget, without using anyheat-flow scaling law.A key concept is that, for a given

continental growth history, theassumptions of constant freeboardand constant ocean volume are suffi-cient to determine oceanic heat flux,which represents a major fraction ofconvective heat flux. In general, oce-anic heat flux at a time t, Qo(t), maybe expressed as:

QoðtÞ ¼Z smax

0

dAo

dsðs; tÞqðs; tÞds; ð14Þ

where dAo ⁄dt(s) is the area–age dis-tribution of seafloor, and q(s) is heatflow from a seafloor of age s . Both ofthem can also be a function of ageological time t. The present-dayarea–age distribution is best approxi-mated by a triangular distribution (i.e.the area of younger seafloor is greaterthan that of older seafloor), and weassume this distribution for oldertimes because it arises naturally fromsubduction irrespective of seafloor age(Parsons, 1982). Thus we have

dAo

dsðs; tÞ ¼ GðtÞ 1� s

smaxðtÞ

� �; ð15Þ

where smax(t) is the age of the oldestseafloor. The coefficient G(t) is con-strained by the total area of oceanbasins, Ao(t), as:

AoðtÞ ¼ A�AcðtÞ ¼GðtÞ

2smaxðtÞ; ð16Þ

where A is the total area of Earth’ssurface and Ac(t) is the total area ofcontinents. Seafloor heat flow is as-sumed to follow half-space cooling as:

qðs; tÞ ¼ Bffiffiffisp TmðtÞ

Tmð0Þ; ð17Þ

where B is 550 mW m)2 Myr)1 ⁄ 2

(Korenaga and Korenaga, 2008). Atpresent (i.e. t = 0), G(0)=3.45

Present

Continentalcrust

Continentalcrust

Faster plate motion Slower platemotion

Younger, shallowerocean basin

Archean

Present

Archean

Deeperocean basin

(a) Constant ocean volume[e.g., Reymer & Schubert, 1984]

(b) Variable ocean volume

Fig. 6 Cartoon illustrating possible relations among heat-flow scaling, continentalgrowth, and ocean volume, under the assumption of the constant freeboard. (a) Whenthe ocean volume is assumed to be constant, plate motion must have been faster tocreate younger and shallower seafloor when there was less continental crust. Fasterplate motion (i.e. higher heat flux) in the past, however, results in thermalcatastrophe. (b) Slower plate motion, which is more consistent with the present-daythermal budget, predicts a greater ocean volume in the past.


.............................................................................................................................................................


km2 yr)1 and smax(0)=180 Myr (Par-sons, 1982), and Eq. (14) gives �34TW for the total oceanic heat flux,which is in good agreement with theactual estimate [32 ± 2 TW (Pollacket al., 1993; Jaupart et al., 2007)].Similarly, assuming the constant free-board, the total ocean volume may beexpressed as:

V ðtÞ ¼Z smax

0

dAo

dsdðs; tÞds; ð18Þ

where d(s) is the seafloor depth as afunction of seafloor age,

dðs; tÞ ¼ d0ðtÞ þ bðtÞffiffiffisp; ð19Þ

Here d0 is the zero-age depth (averagedepth to mid-ocean ridge axis), and bis the subsidence rate due to half-spacecooling. At the present, we haved0(0) = 2654 m and b(0) = 323 mMyr)1 ⁄ 2 (Korenaga and Korenaga,2008). The subsidence rate is linearlyproportional to a temperature con-trast between the surface and theinterior (e.g. Turcotte and Schubert,1982), so we have

bðtÞ ¼ bð0Þ TmðtÞTmð0Þ

: ð20Þ

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

smaxðtÞ ¼15

8bðtÞV ð0ÞAoðtÞ

� d0ðtÞ� �� 2

;

ð21Þ

and Q(t) can then be calculated bycombining Eqs (15)–(17). The totalarea of continents in Eq. (16) iscalculated from a given history ofcontinental growth, assuming that theaverage thickness of continental crusthas been approximately constant at�35–45 km (Durrheim and Mooney,1991; Galer and Mezger, 1998). Notethat Galer and Mezger (1998) sug-gested that continental crust couldhave been thicker in the Archean thanat present by �5 km, based on origi-nal burial pressures estimated forexposed Archean granite-greenstonesegments. Thicker crust in the pastwould only substantiate the followingargument because it means moreocean basins [Eq. (16)] and flatterseafloor topography to satisfy theconstant freeboard.We used the oceanic heat flux of

Eq. (14) as the lower bound on the

total convective heat flux (i.e. subcon-tinental heat flux is neglected), andsolved the heat balance of Eq. (4)starting with the present-day Ureyratio of 0.22. Here the zero-age sea-floor depth d0 is assumed to be con-stant. This assumption may bejustified because the existence of vol-canogenic massive sulphide depositssince the Archean (e.g. Nisbet et al.,1987) indicates that the depth of mid-ocean ridges should always be greaterthan �2 km below sea level (Ohmoto,1996). As shown in Fig. 7a, this cal-culation leads to thermal catastropheeven for the instantaneous growthmodel, in which no net continentalgrowth takes place during the last4 Gyr. This is because hottermantle byitself results in greater thermal sub-sidence [Eq. (20)], so to keep the sameocean volume, the maximum seafloorage should decrease (Fig. 7c), i.e. sea-floor should become younger on aver-age, resulting in an increase in oceanicheat flux (Fig. 7b). This positive corre-lation betweenmantle temperature and

oceanic heat flux may be summarizedas �empirical’ heat-flow scaling(Fig. 7d). Alternatively, we may fixthe maximum seafloor age as 180-Myr-old, and solve Eq. (18) for thezero-age depth.Results for this case areshown in Fig. 8. The temperature oftheArcheanmantle is still toohigh, andthe predicted zero-age depth in theArchean is probably too shallow(Ohmoto, 1996; Kitajima et al., 2001).The constant ocean volume, there-

fore, seems to be incompatible withthe thermal budget of Earth, and thepossibility of time-dependent oceanvolume deserves some attention. As apreliminary attempt, the thermal his-tory of Fig. 3 may be used to calculatethe history of ocean volume (Fig. 9).First, noting that the coefficient G(t)in the area–age distribution can beexpressed as:

GðtÞ ¼ LvðtÞ; ð22Þ

where L is the total length of divergentplate boundaries and v(t) is the aver-age spreading rate, the maximum age

1300

1400

1500

1600

1700

1800

Man

tle p

oten

tial t

emp.

(°C

)

0 1 2 3 4

Time B.P. (Ga)

0

50

100

150

200Q

conv

& H

m (

TW

)

0 1 2 3 4

Time B.P. (Ga)

0

50

100

150

200

τ max

(M

a)

0 1 2 3 4

Time B.P. (Ga)

10

20

50

100

200

Qco

nv (

TW

)

1200 1400 1600 1800

Mantle potential temp. (°C)

Qconv

Hm

Convective urey ratio = 0.22 @ present

(a)

(b)

(c) (d)

Fig. 7 A possible consequence of the constant ocean volume, with the assumption ofthe constant zero-age depth. The modelling procedure is identical to that used forFig. 3, expect that convective heat flux is based on Eq. (14). (a) Mantle potentialtemperature as a function of time. (b) Convective heat flux and internal heating.(c) Maximum age of seafloor. (d) A posteriori relationship between convective heatflux and mantle temperature. For comparison, three heat-flow scaling laws of Fig. 2are shown in grey. Legend is the same as Fig. 3; note that the cases of McLennan andTaylor (1982) (blue) and Campbell (2003) (black) are identical in (a) and (d).


.............................................................................................................................................................


of seafloor may be calculated from thepredicted plate velocity as:

smaxðtÞ ¼2AoðtÞGð0Þ

vð0ÞvðtÞ : ð23Þ

Here, L is assumed to be constantbecause the average size of plates isunlikely to change substantially withtime (Korenaga, 2006). The totalocean volume can then be calculatedfrom Eq. (18), assuming the constantfreeboard as well as the constant zero-age depth (Fig. 9b). Results indicatethat Archean ocean basins may havebeen deep enough to hold twice asmuch water as today.Obviously, the predicted history of

ocean volume should not be taken atface value, as it is based on a numberof assumptions with varying credibil-ity (Table 1). At the same time, how-ever, losing one-ocean-worth watersince the Archean is not surprising,or may even be expected in light of theglobal water cycle. It has long beenknown that water flux into the mantlefrom the hydrosphere by subductionexceeds water flux out of the mantleby mid-ocean magmatism by an orderof magnitude (e.g. Ito et al., 1983;Jarrard, 2003). Most of such waterinflux is usually believed to quicklyreturn to the surface through arc

magmatism, so the net water influxmay close to be zero. It is difficult,however, to completely dehydratesubducting slabs because nominallyanhydrous minerals can hold anon-trivial amount of water (e.g. Hir-schmann et al., 2005). Continuoussubduction at the current rate couldeasily bring one-ocean-worth waterinto the deep mantle over a few billionyears (Smyth and Jacobsen, 2006). Theaverage rate of the predicted influx forthe last 2 Gyr is also compatible withthe estimated range of present-dayinflux (Jarrard, 2003) (Fig. 9c).The continental crust contains �1

wt% water on average (e.g. Wed-epohl, 1995), equivalent to �0.18ocean. The MORB-source mantle isestimated to have 142 ± 85 p.p.m.water (Saal et al., 2002), and theglobal mass balance of silicate reser-voirs, on the basis of the new compo-sition model of Earth’s primitivemantle (Lyubetskaya and Korenaga,2007a), indicates that the MORB-source mantle is representative forthe bulk of the mantle (Lyubetskayaand Korenaga, 2007b), so the mantlemay hold �0.42 ± 0.25 ocean ofwater. Thus, the amount of watercurrently stored in the BSE (crustand mantle), �0.5–1 ocean, is similar

to what is estimated to have been lostfrom Earth’s oceans (Fig. 9b). Thiscoincidence may suggest that the man-tle was dry in the Hadean and hasbeen progressively hydrated by sub-duction. As mentioned earlier, suchgradual hydration may be importantfor the continuous operation of platetectonics. Note that the dry Archeanmantle does not preclude the �wet’origin of komatiite (Allegre, 1982;Parman et al., 1997; Grove and Par-man, 2004), because arc environmentscan be locally hydrated by subduction.The regassing-dominated global watercycle suggests that the most of terres-trial water may have originated atEarth’s surface, pointing towards theimpact origin of Earth’s oceans. Asdiscussed next, this issue has anintriguing connection to the thermalbudget of Earth.

The origin of terrestrial water

The origin of Earth’s oceans, or howthis planet acquired its presentamount of water in the early solarsystem, depends on a number offactors that are currently not knownprecisely enough, such as the relativetiming of Earth accretion, core segre-gation, the dissipation of the solarnebula, and the disappearance of themassive 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 withthis information alone, Earth’s oceanscould have been derived simply fromthe accretion of chondritic materials,or from the solar nebula with isotopicfractionation, or from the mixing ofmultiple sources (e.g. Dauphas et al.,2000; Drake, 2005; Genda and Ikoma,2008). When combined with carbonand nitrogen isotope constraints, how-ever, the late accretion (i.e. accretionafter the core formation) of chondriticmaterials appear to be the most likelysource of terrestrial water (Marty andYokochi, 2006), and indeed, such lateaccretion with 0.5–1% Earth’s mass issuggested by the abundance of highlysiderophile elements (HSE) in Earth’smantle (e.g. Morgan, 1986) and is alsophysically plausible according tothe dynamical simulations of plane-tary accretion (e.g. Morbidelli et al.,

1300

1400

1500

1600

1700

1800

Man

tle p

oten

tial t

emp.

(°C

)

0 1 2 3 4

Time B.P. (Ga)

0

20

40

60

80

100

Qco

nv &

Hm

(T

W)

0 1 2 3 4

Time B.P. (Ga)

0

1000

2000

3000

d o (

m)

0 1 2 3 4

Time B.P. (Ga)

10

20

50

100

200Q

conv

(T

W)

1200 1400 1600 1800

Mantle potential temp. (°C)

Qconv

Hm

Convective urey ratio = 0.22 @ present

(a) (b)

(c) (d)

Fig. 8 Same as Fig. 7, but with the assumption of the constant maximum age ofseafloor. The history of zero-age depth is shown in (c).


.............................................................................................................................................................


2000). Also, the Moon-forming giantimpact could have been this lateveneer if a fraction of the impactor’score were mechanically mixed with theEarth’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 impedi-ment to this late accretion hypothesisfor Earth’s oceans (Meisel et al., 1996,2001). Mantle samples such as mantlexenoliths and massif peridotites exhi-bit a linear correlation between thisisotopic ratio and the index of meltdepletion such as Al2O3 (Fig. 10), and

the isotopic ratio for the BSE may beestimated based on the elemental com-position model of BSE. With theconventional estimate for the BSEAl2O3 content (�4.2 wt%), the ob-served correlation suggests the BSEisotope ratio of 0.1289–0.1304 (95%confidence limit) (Meisel et al., 2001).On the other hand, the so far observedrange of the 187Os ⁄ 188Os ratio is0.1255–0.1270 for carbonaceous chon-drites, 0.1270–0.1305 for ordinarychondrites and 0.1270–0.1290 forenstatite chondrites (Meisel et al.,1996). Thus, Earth’s 187Os ⁄ 188Os isconsistent with ordinary or enstatitechondrites, but not with carbonaceouschondrites. Ordinary and enstatitechondrites are, however, much drier(<1% H2O) than carbonaceous chon-drites (�10% H2O) (Robert, 2003), sothe addition of 0.5–1% Earth’s masscould account for only a small fractionof Earth’s water budget. The osmiumconstraint has motivated a variety ofmore elaborate ways to deliver waterto Earth and satisfy geochemical con-straints at the same time (e.g. Dauphasand Marty, 2002; Drake and Righter,2002; Marty and Yokochi, 2006).This argument may not be so robust

because, if the late accretion of HSEwere made by the Moon-formingimpactor (or similarly large impac-tors) and partial core addition, therewould be no simple relationship be-tween the added masses of HSE andwater. Even if we limit ourselves tosimple end-member mixing, however,the osmium constraint has one weak-ness that has been overlooked. Thecomposition model of BSE is basedprimarily on noisy geochemical trendsexhibited by mantle rocks, but themodel uncertainty has not been wellquantified. A new statistical methodwas recently built to address this issue,resulting in not only quantifying theuncertainty but also revising the mod-el itself in a non-trivial manner (Lyu-betskaya and Korenaga, 2007a). Thenew BSE model suggests the Al2O3

content of 3.52 ± 0.60 wt%. Revisit-ing the correlation, we would obtainthe new 95% confidence limit of0.1267–0.1277 for BSE 187Os ⁄ 188Os,which turns out to be consistent withany kind of chondrites (Fig. 10). Notethat this confidence limit is derivedfrom the uncertainty of the lineartrend and does not reflect the uncer-tainty of the BSE model. With the

(c)

(b)

(a)

Present-dayinflux

100

200

300

400

500

600

τ max

(M

a)

0 1 2 3 4

Time B.P. (Ga)

0.5

1.0

1.5

2.0

2.5

3.0

Vo(

t)/V

o(0)

Wat

er in

flux

(101

4 g/

year

)

0 1 2 3 4

Time B.P. (Ga)

0

10

20

30

0 1 2 3 4Time B.P. (Ga)

Fig. 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-dayvolume. (c) Net water influx from the hydrosphere to the mantle, assuming that thepredicted change of ocean volume shown in (b) is due to the hydration of the mantleby subduction. Legend is the same as in Fig. 3.


.............................................................................................................................................................


uncertainty of ±0.60 wt%, the likelyrange of the BSE 187Os ⁄ 188Os wouldbe widened as 0.1253–0.1291. Theother potential water sources can stillcontribute to some degree, but themost dominant source may well becarbonaceous chondrites.It is noted that efforts to quantify

the reliability of the BSE model weremotivated solely by a need to build aself-consistent geochemical model,which is important for long-standingdebates over the structure and evolu-tion of Earth’s mantle (Lyubetskayaand Korenaga, 2007b; Korenaga,2008b). The relevance to the lateaccretion hypothesis is entirely seren-dipitous. Though the new BSE modelis not a final answer and should berevised in future when additional databecome available, it does seem tobring us towards simpler, less arbi-trary hypotheses for the structure ofmantle convection as well as the originof Earth’s oceans.

Acknowledgements

The author thanks Alfred Kroner forinvitation to write a review paper on thethermal evolution of Earth, and KentCondie, Norm Sleep, Geoff Davies, andan anonymous reviewer for constructivereviews. This work was sponsored by theU.S. National Science Foundation undergrant EAR-0449517.

References

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Ordinarychondrites

Enstatitechondrites

Carbonaceouschondrites

New

BS

E estim

ate3.52 ±

0.60 wt%

Old B

SE

estimate

4.2 wt%

0.110

0.115

0.120

0.125

0.130

0.135

187 O

s/18

8 Os

0 1 2 3 4 5

Al2O3 (wt%)

Southwest USCanadaAustraliamassif

EuropeMexicoPacificAsia

Fig. 10 Covariation of Al2O3 and 187Os ⁄ 188Os for mantle xenoliths and massifperidotites [data are from Meisel et al. (2001) and references therein]. Differentsymbols denote different localities as indicated by the legend. Linear regression byMeisel et al. (2001) is shown by solid dash line (y = 0.1160 + 0.003253x). Linearregression 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 smalldifference from the original regression probably reflects that unpublished Mexicosamples used by Meisel et al. (2001) are not used here. The 95% confidence limit onthe osmium isotope rate is shown for the case with the old BSE Al2O3 content (4.2wt%) 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 theuncertainty of the new BSE model (±0.60 wt%) is indicated by light blue arrow. Theosmium isotope ranges observed for three major types of chondrites are also indicated(blue, carbonaceous; red, ordinary; green, enstatite).


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Received 2 April 2008; revised versionaccepted 5 September 2008


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