exploring the kappa conundrum: the role of recycling in the lead isotope evolution of the mantle

ELSEVIER Earth and Planetary Science Letters 169 (1999) 129–145

Exploring the kappa conundrum: the role of recycling in the leadisotope evolution of the mantle

Tim Elliott Ł, Alan Zindler 1, Bernard Bourdon 2

Lamont-Doherth Earth Observatory of Columbia University, Palisades, NY 10964, USA

Received 16 July 1998; revised version received 2 February 1999; accepted 15 March 1999

Abstract

It has long been known that the measured kappa (232Th=238U, or �) of mid-ocean ridge basalts (MORB) and, byinference, the upper mantle, is much lower than the time-integrated � recorded by Pb isotope ratios .�Pb/. We examinemodels that can reconcile this kappa conundrum by in situ decay of U and Th in the upper mantle. Monte Carlo simulationsreveal a restricted range of permissible ‘in situ’ paths of MORB mantle evolution. These solutions require a roughlyconstant 232Th=238U ratio during early Earth history, followed by a period of steadily decreasing 232Th=238U from the end ofthe Archean to the present. These model criteria make good geological sense in terms of post-Archean recycling of crustaluranium back into the mantle. Preferential recycling of uranium, relative to thorium, can result from the high aqueousmobility of uranium in the oxidising environment at the Earth’s surface. Soluble uranium is transported from continentsto the altered oceanic crust and ultimately, by subduction, back into the mantle. In contrast, insoluble thorium remainsin the weathered continental residue. This process is only likely to have become important after the marked increase inatmospheric oxygen fugacity at ¾2.2 Ga which led to a change in the predominant surface oxidation state of uranium. Theuranium fluxes required in this Post-Archean Uranium Recycling (PURE) model are compatible with estimates derivedfrom present-day fluxes of ‘excess’ continental uranium returned to the mantle by subduction, integrated over some 2Ga. Further modelling of Earth evolution in the context of differentiation into crust, depleted mantle and recycled plumereservoirs demonstrates the viability of this scenario in explaining modern-day lead isotopic signatures of both MORB and‘HIMU’ ocean island basalts. We emphasise that resolution of the kappa conundrum does not require a steady state uppermantle with its lead isotope ratios buffered by entrainment of material from another, deeper reservoir. 1999 ElsevierScience B.V. All rights reserved.

Keywords: lead; isotopes; Th=U; recycling; upper mantle

1. Introduction

Decay of the naturally occurring actinides to Pb,namely 238U–206Pb, 235U–207Pb and 232Th–208Pb,

Ł Corresponding author. Present address: Faculteit der Aardwetenschappen, Vrije Universiteit, de Boelelaan 1085, 1081 HV Amsterdam,Netherlands. E-mail: [email protected] Present address: National High Magnetic Field Laboratory and Dept. of Geology, Florida State University, Tallahassee, FL 32306, USA.2 Present address: Laboratoire de Geochimie et Cosmochimie, CNRS, IPGP 4, Place Jussieu 75252, Paris Cedex 05, France.

provides an isotopic record of the fractionation ofU=Pb, Th=Pb and hence Th=U throughout Earth his-tory. Measurements of Pb isotope ratios thus yieldpowerful simultaneous constraints on Earth evo-

0012-821X/99/$ – see front matter 1999 Elsevier Science B.V. All rights reserved.PII: S 0 0 1 2 - 8 2 1 X ( 9 9 ) 0 0 0 7 7 - 1

130 T. Elliott et al. / Earth and Planetary Science Letters 169 (1999) 129–145

lution, which indeed have proved so stringent thatgeochemists have had to couch their less-than-per-fect understanding of plumbology in terms of notone, but two paradoxes.

The first problem noted in interpreting Pb isotopedata, duly dubbed ‘the Pb paradox’ [1], concernsplanetary Pb isotopic mass balance. If the Earthis the same age as the meteorites that define theGeochron [2], then bulk Earth should likewise liesomewhere on this line. However, the two reservoirsmost likely to dominate the terrestrial lead budget,the mantle and crust, do not sum to give a composi-tion that falls on the 4.55 Ga reference line (e.g. [3]).Both reservoirs plot to the right of the Geochronrather than forming a complementary distributionabout it (Fig. 1a). This further implies a secular in-crease in the U=Pb in both crust and mantle, whichis difficult to reconcile with simple models of theMORB source as a residue of continent extraction. Itis also contrary to most expectations of the relativeincompatibilities of U and Pb during mantle melting(e.g. [4]). Nevertheless, it is the position of the es-timated bulk Earth lead isotope composition relativeto the Geochron which has been the chief dilemma.Unradiogenic lead compositions of the lower crustcould potentially counter-balance radiogenic mantleand upper-crustal reservoirs (e.g. [5]), but Pb isotopedata on granulite xenoliths has cast doubt on thisproposal [6]. Alternatively, if lead is partitioned intothe core and if the core growth continues for some100 Ma after accretion, bulk silicate Earth is ex-pected to plot to the right of the Geochron [1,3,7,8],thereby solving the problem. Recent work greatlystrengthens the arguments for this latter explanation[9,10], and so the first lead paradox is perhaps nolonger quite so puzzling.

The second concern caused by Pb isotope system-atics was originally raised by Tatsumoto [11] but wasreiterated in detail by Galer and O’Nions [12], whennew perspectives were provided by 230Th=238U dise-quilibrium data on MORB. This problem pertains tothe Th=U or, more properly, the near equivalent (atpresent day) 232Th=238U ratio of the depleted MORBmantle (DMM). The 232Th=238U ratio is commonlytermed � , and thus we refer to this second concern asthe kappa conundrum. Since 232Th decays to 208Pband 238U decays to 206Pb, the Pb isotope system pro-vides information on the time-integrated 232Th=238U

ratio. A time-integrated � , as calculated from Pbisotope ratios has been termed �Pb [12].�Pb values for MORB are remarkably homoge-

neous (3:8š 0:2, Fig. 1b) and generally much higherthan their measured � (Fig. 1c). The absence of asimple closed-system relationship between measuredparent–daughter ratios and their respective radio-genic isotopic ratios in mantle-derived rocks is by nomeans unique to the Th–U–Pb system. The simplestpotential explanation of such a mismatch is recentmelt-produced fractionation of parent and daughterelements, so that the parent–daughter ratio measuredin the melt may not be representative of the source.Indeed the Sm–Nd and Lu–Hf isotope systematicsof oceanic basalts have been rationalized within sucha framework [13–15].

The question of melt fractionation of Th=U ratiosduring magma genesis, however, can be rigorouslyassessed with U-series disequilibrium measurements.230Th–238U disequilibrium provides a measure ofrecent (<350,000 a) Th–U fractionation. 230Th ex-cesses of ¾20% are a common signature of MORB(see [16,17] for recent compilations), and no large238U excesses (>10%) have been observed in freshMORB glasses. The cause of prevalent 230Th ex-cesses in MORB has been a matter of some debate(see [18] for summary) and the original premiseof Galer and O’Nions [12], that the (230Th=232Th)ratio of MORB yields a more reliable estimateof the (232Th=238U) of the source than measured(232Th=238U), is probably not valid (e.g. [19]). Nev-ertheless, the presence of 230Th excesses in MORBprovides firm evidence that melting does not result inenrichments of U over Th in MORB relative to theirsources. Hence it is unequivocal that the measured,low � of MORB compared to their �Pb is repre-sentative of their upper mantle sources. Thus, moresophisticated models must be invoked to reconcilethe kappa conundrum.

2. Models of mantle lead isotope evolution

Galer and O’Nions [12] investigated the Pb iso-topic characteristics of a simple two-stage model for� evolution in the upper mantle (Fig. 2a). The firststage was assumed to have � equal to that of bulksilicate earth .�BE, 3.9 in their original model), while

T. Elliott et al. / Earth and Planetary Science Letters 169 (1999) 129–145 131

Fig. 1. U–Th–Pb systematics of MORB from a literature compilation (references available on request). Atlantic and Pacific samplesare shown as grey filled squares, whereas Indian Ocean samples are smaller open squares (the ‘DUPAL’ [59] samples of Hanan et al.[60] from the South Atlantic below 26ºS are grouped with the Indian samples). (a) 206Pb=204Pb vs. 207Pb=204Pb with reference 4.55 GaGeochron and single-stage growth curves for ¼ values of 8.0, 8.2 and 8.4 (as appropriate estimates for Bulk Earth). Various estimatesof composition continental crust (taken from a summary in [10]) are shown as diamonds. (b) 206Pb=204Pb vs. 208Pb=204Pb. The lineslabelled with � values of 3.6, 3.8 and 4.0 represent loci of domains that have evolved as closed systems for 4.55 Ga with given � fora range of different ¼. (c) Measured � against inferred time-integrated kappa, calculated from Pb isotopes, �Pb. A locus of equal � and�Pb is shown, and clearly the majority of MORB samples plot to the low � side of this line. Only samples where � has been determinedby isotope dilution mass-spectrometry are plotted (references available on request). Such data sets containing Th and U concentrationstogether with Pb isotope ratios are rare and the samples shown comprise a disproportionate number of high � samples relative to moreextensive data on Th and U concentrations alone.


the � of the second stage was set to an appropriatevalue for the present-day MORB reservoir (�DMM ¾2:5). They noted that unless the transition from bulkEarth to present-day Th=U occurred more recentlythan ¾600 Ma, then the �Pb of MORB would besignificantly lower than is observed (Fig. 2d).

As a result of such modelling, Galer and cowork-ers [12,20] proposed an open-system upper mantle,in which partial melting removes elements from theupper mantle, while entrainment of lower mantlematerial provides a counter-balancing flux. In sucha model, highly incompatible elements such as U,Th and Pb have short residence times in the uppermantle, and can rapidly reach steady-state concen-trations. The short residence time for Pb in thissteady-state upper mantle results in its Pb isotopicsignature effectively reflecting that of the entrainedlower mantle material. Thus, the Pb isotope ratios ofDMM are not supported by in situ decay of U andTh, and instead largely record the time-integratedTh–U–Pb ratios of the lower mantle [12], or otherentrained material [21].

In order to maintain a steady-state upper man-tle with � ¾ 2:5 requires that significant Th=Ufractionation be produced by the (melt) flux fromDMM in order to balance input of material withhigh � (¾4). Galer and O’Nions [12] related thisoutput as a flux of material to the continental crust.As highly incompatible elements, however, Th andU are only fractionated at very small degrees ofmelting and even then elemental Th–U fractionationshould be no greater (and is generally much smaller)than the degree of (230Th=238U) disequilibrium mea-sured in zero age lavas, which rarely exceeds 40%.Moreover, at subduction zones, the major sites ofpresent-day continental growth, 238U–230Th system-atics commonly imply no U–Th fractionation during

Fig. 2. (a–c) show three different styles of model for � evolution of DMM (� corrected for decay to present day), whilst (d–f) show loci(at different final ¼) of the present day 206Pb=204Pb and 208Pb=204Pb resulting from the corresponding evolution paths on the oppositepanel. Measured MORB isotope ratios are shown as reference. (a) The model of Galer and O’Nions [12]; (b) A continuous evolutionmodel, in which the dotted line represents a similar model to that proposed by Allegre et al. [24]; (c) the post-Archean uranium recycling(PURE) model, discussed in this manuscript. The lead isotope compositions in (d–f) were calculated using a twenty step model (equaltime steps of 0.2275 Ga), with ¼ always initially set to 8. In (e) and (f) ¼ was allowed to vary linearly to a range of final values over theperiod of change in �, whilst (d) is a simple two stage model. The same MORB data set as shown in Fig. 1 is used with Atlantic andPacific samples shown as dark outlined open squares, and Indian samples as lighter outlined open squares. As elsewhere in this paper, weprincipally attempt to model the compositions of the Atlantic and Pacific samples. Only a very recent change to a second stage (a) or anunreasonably high initial � (b) can account for MORB compositions using the first two models. See text for further discussion.

arc formation or, when disequilibrium is observed,it usually suggests an enrichment of U, not Th, inthe new crust (e.g., [22,23]). Hence, there is somedifficulty in finding a suitable mechanism to main-tain a low Th=U ratio in a putative steady state uppermantle.

In a rather different approach, Allegre et al. [24]used lead isotopic analyses of Archean mafic sam-ples and galenas to infer a high �BE (¾4.3) for theEarth. This assertion, combined with correlations of�Pb with other radiogenic isotope systems, promptedAllegre et al. [24] to propose a secular decrease in �with time related to continental extraction. It is ap-parent from Fig. 2b,e, however, that a monotonic de-crease of � , even starting from a rather high value of4.3, cannot reproduce the lead isotope systematics ofMORB. Rocholl and Jochum [25] have subsequentlyreassessed �BE from an extensive study of the Th=Uratios of chondritic meteorites. Th and U are bothhighly refractory and so chondrites should providea good estimate of �BE. Sadly, low temperature Umobility in meteorite samples impairs the record andonly enables an upper limit of �BE < 4:2 (i.e. Th=U< 4.1) to be estimated [25]. Using a lower limit of�BE > 3:8 from lead isotope analyses of meteorites,Rocholl and Jochum [25] derived a best estimate of�BE D 4:0 š 0:2. Thus, this more comprehensive in-vestigation of �BE does not remove the fundamentalproblem raised by Galer and O’Nions [12].

Previously, Tatsumoto [26] had modelled hisMORB U–Th–Pb data using a simple model of‘in-situ’ decay. Starting from a reasonable bulk Earthcomposition .�BE D 3:8–4:0/, he argued that pro-tocrust extraction elevated Archean mantle Th=Uvalues to 4.3–4.5, after which Th=U steadily de-clined to present day values. He noted that the modelhad difficulty in accounting for the lowest Th=U


samples, but these had Th=U < 2 and were probablylowered by seafloor alteration (e.g. [27]). Tatsumoto[26] only investigated a five step model, but the suc-cess of this approach suggested further explorationwould be worthwhile. Below we discuss the moregeneral behaviour of solutions to the kappa conun-drum derived from in situ decay of Th and U alone.

3. A simple model of κ evolution in DMM

The area beneath the � evolution curves in Fig. 2is essentially proportional to the time-integrated232Th=238U ratio, and therefore a good approxima-tion of �Pb. In essence, the difficulty highlighted byGaler and O’Nions [12] was in finding an evolutionpath that started at a reasonable �BE (¾4) and endedat a depleted MORB value .�DMM ¾ 2:5/, but stillretained sufficient area beneath this curve to yield�Pb ¾ 3:7.

Fig. 2c shows a hybrid of the models displayed inFig. 2a,b and is somewhat similar to the form usedby Tatsumoto [26]. This evolution trajectory hasinitially constant � which gradually decreases to 2.5over the latter half of Earth history. This fulfils theprincipal constraints we have on present-day Th=Uratios in the mantle, yet strikingly, still managesto yield �Pb ¾ 3:7 for the MORB mantle withoutresorting to a steady-state model with very shortresidence times for the elements of interest. Theeffect of increasing the ‘area under the curve’ inFig. 2c, and hence �Pb, by delaying the onset ofTh=U decrease (compared to the models in Fig. 2b)or by only gradually decreasing Th=U (relative to themodels in Fig. 2a) can be readily observed.

To investigate whether this is the only form ofsolution that satisfies both �Pb and � constraints forMORB by in-situ decay, we used a Monte Carlotechnique to investigate a range of possible � evolu-tion pathways. The forward model uses eighty equaltime steps of 0.05688 Ga. An initial � of 4.0 (all� values discussed are corrected for radioactive de-cay to present day to help comparison at differenttime periods) changed each time step by an incre-ment varied randomly between C0.15 and �0.15.This produces a smooth � evolution without anypre-determination of the sense of change, but isconsequently computationally very inefficient (eight

successful solutions in ¾16 millions trials). Success-ful solutions were deemed to be those that ended upwith � and �Pb within a range appropriate for an end-member (Atlantic or Pacific) MORB, namely 2.5–2.7 and 3.7–3.8 respectively. A wider range couldhave been allowed, but by restricting the analysisto the most ‘problematic’ samples, we focus moreclearly on the conundrum.� evolution trajectories of the eight successful

solutions are shown in Fig. 3. The general form ofthe evolution of �DMM is rather well constrained, andis similar to that sketched in Fig. 2c. A range ofbehaviour is permissible in early Earth history, andthe high � for the Archean mantle inferred from�Pb in Archean galenas ([24,28] and refs. therein), ismimicked by several solutions. The key feature ofthe model, however, is that the upper mantle evolvescontinuously toward lower � during the latter halfof Earth history. The exact timing of the onset ofdecreasing � will depend on �BE and the extent towhich � may increase in early Earth history (contrastFig. 2c and Fig. 3). In general though, it is clear thata major reduction in upper mantle � is required inthe post-Archean period.

4. Mechanisms for Post-Archean decrease inupper mantle Th=U

Is there a reasonable mechanism that may beinvoked to account for the post-Archean decrease inupper mantle Th=U predicted by the successful insitu models? Th and U are difficult to fractionate inthe mantle, as discussed above, but under the highlyoxidizing conditions at the Earth’s surface, the twoactinides show very different behaviour that canlead to large inter-element fractionations. In naturalsystems, Th is found in only one oxidation state,Th4C, but uranium exhibits a range of oxidationstates, U4C, U6C and, less importantly, U5C. At mostmantle redox conditions, U is largely tetravalent [29]and behaves very similarly to Th. At the Earth’ssurface, U can be oxidised to U6C, which, in contrastto Th4C (and U4C) is highly soluble in aqueous fluids[30]. Thus, during weathering U is preferentiallytransported into river waters, while Th remains in thesedimentary residue. Rivers carry a large flux of U tothe oceans, and in order to maintain steady-state sea


Fig. 3. Successful � evolution trajectories for a Monte Carlo inversion starting with � D 4:0, finishing at 2:5 < � < 2:6 that yield3:7 < �Pb < 3:8. An eighty time step model is used which produces smooth trajectories but is computationally inefficient, the eightsolutions here result from ¾16 million trails. See text for further details.

water composition, there must be an accompanyinglarge U sink within the oceans. Part of this sink isthe oceanic crust, which, during alteration, increasesits U concentration by an order of magnitude whileTh concentrations are virtually unaffected [27,31].Unless all the U in subducted altered oceanic crustis directly returned to the continents at subductionzones, then the effect of the plate tectonic cycle willbe to preferentially recycle continental U back tothe mantle, relative to Th. Such a recycling processshould lead to continually decreasing mantle Th=U.

Whilst recycling of altered oceanic crust appearsto be a highly viable process for altering the Th=Uratio of the mantle, does it make sense that this onlystarted mid way through Earth history, as requiredin the models sketched in Fig. 2c and Fig. 3? Thereis much evidence that the Earth’s atmosphere be-came significantly more oxygen rich between 2.0 to2.25 Ga [32,33]. Absolute estimates of the oxygenfugacity of the evolving Proterozoic atmosphere arepoorly constrained, but it is highly likely that thedominant oxidation state of uranium at the surfacechanged from U4C to U6C at the beginning of theProterozoic.

Of particular relevance are observations whichsuggest a major change in the nature of U oredeposits with time. Prior to 2 Ga, extensive de-trital uraninite (UO2) deposits are found, but nohydrothermal U mineralization has been recorded,while after 2 Ga, the reverse is true [34]. The sur-vival of large volumes of detrital U4C oxide grainsin the sedimentary environment requires low atmo-spheric oxygen fugacities. In contrast, models ofhydrothermal uranium deposition invoke uranium tobe initially transported as U6C before being precipi-tated and concentrated by subsequent reduction [35].Hence, there appears to have been a major changein the dominant oxidation state of uranium in thenear surface environment at around 2 Ga. Many ad-ditional lines of evidence further document a markedincrease in the oxygen content of the atmosphere¾2.2 Ga [32,33].

There is also supporting evidence in continentalsediments that recycling of crustal U to the man-tle has been an important process since the earlyProterozoic. McLennan and Taylor [36] present Thand U analyses of shales with a wide range of ages.This study shows a significant increase in the mean


Th=U of shales with decreasing age, from ¾4 at theArchean–Proterozoic boundary to ¾5.5 in the latePhanerozoic. Since the U postulated to reduce theTh=U in the upper mantle must be ultimately derivedfrom the continents, this increase in Th=U of thecontinental sedimentary mass would be expected.

We are not the first to invoke recycling of Ufrom crust to mantle to account for the lead iso-topic composition of the major terrestrial reservoirs.Bi-directional transport of U, Th and Pb has beenan important aspect of a number of plumbo-tectonicmodels [5,37–40]. Zartman and Haines [38] andKramers and Tolstikhin [40] specifically discussedpreferential recycling of U relative to Th as a resultof the contrast in behaviour of U and Th in an oxidis-ing surface environment. Not surprisingly therefore,the form of upper mantle Th=U evolution shown inZartman and Haines [38] is equivalent to that inFig. 3. McCulloch [41] also discussed the impor-tance of the return of U to the upper mantle duringlatter part of Earth history, but argued for a differentmechanism to account for the change of behaviourat some 2 Ga. Despite these previous contributions,the role of U recycling in shaping upper mantle evo-lution is still often overlooked. We feel that we addfurther weight to these earlier studies with the MonteCarlo inversion above. Additionally, in the followingsection, we explore the mass balance constraints onthe effectiveness of U recycling.

5. Constraints on recycled U fluxes

The Post-Archean Uranium recycling (PURE)model is a conceptually attractive means of ac-counting for the Th–U–Pb systematics of MORB.However, we need to determine whether the magni-tude of the uranium flux from the crust to the mantlerequired by the model can be reconciled with theamount of U delivered via subduction zones.

During alteration, the upper oceanic crust isstrongly enriched in uranium, as clearly documentedin DSDP sites 417 and 418 [27,31]. Compositesof material from these holes suggest an increase ofalmost an order of magnitude in the uranium con-centration of altered oceanic upper crust. The ‘super-composite’ of Staudigel et al. [27] yields an estimateof ¾ 3 ð 108 g of uranium added during alteration

to each km2 of oceanic crust. Given an oceanic crustproduction rate of ¾3 km2=a [42] this then deliversan annual flux of ¾ 1:0 ð 109 g of ‘excess’ uranium(i.e. U fractionated from its magmatic associate, Th)into subduction zones.

The concentration of uranium in the upper 500 mof oceanic crust, as described above, is indicative ofuranium addition during largely low-temperature al-teration. Exhalations of high-temperature hydrother-mal waters at black smokers indicate that uranium isalso quantitatively stripped from the deep circulatingseawater that recharges the hydrothermal cells [43].Estimates for such high temperature uranium uptakerange from 5:2ð 108 g=a [44] to some 3:8ð 109 g=a[45]. The value cited by Klinkhammer and Palmer[45], however, seems to be an order of magnitudehigher than can be calculated from the parametersthe authors cite, and so the estimates in effect appearto be quite similar. Combined high and low-tem-perature additions of U to the oceanic crust thusgive a total excess U flux into subduction zones of¾ 1:5ð 109 g=a.

A somewhat different estimate can be made fromthe data of Klinkhammer and Palmer [45] andPalmer and Edmond [46]. These authors respec-tively provide estimates of the flux of uranium thatis fixed by reducing conditions in continental shelfsediment and the flux of uranium into the oceansfrom rivers. The difference between these two fluxes,¾ 4 ð 109 g=a, corresponds to the total uptake ofuranium required to keep seawater composition insteady state. This value potentially monitors U sinksin the oceanic crust not directly observable. The er-rors on the estimate are large; Palmer and Edmond[46] cited an uncertainty of š3:5 ð 109 g=a on theriverine U flux alone. Given such uncertainties, theagreement between the two estimates for excess Udelivered to subduction zones is reasonable and inthe range 1:5–4ð 109 g=a.

Incorporation of subducted material into arc mag-mas during the formation of new crust at destructiveplate margins can potentially short-circuit the recy-cling of U into the mantle. Plank [47] has assessedthe importance of subducted material to the budgetsof several key elements in arc lavas, and estimatedthat the contribution of subducted material to theU flux at arcs ranges from 0.09 to 0.27 g=a percm of arc length. Given 37,000 km of active arc


[48], this amounts to a flux of ¾ 5 ð 108 g=a fromslab to arc. This flux will comprise contributionsfrom both subducted sediment and altered oceaniccrust, and many studies have shown that the sedi-mentary flux is the dominant influence on many ofthe distinctive chemical signatures of arc lavas (e.g.[49] and refs. therein). Several workers [47,50,51]have noted, in simple input–output calculations, that¾25% of the elemental inventory in the subductedsediment pile can be accounted for in arc lavas. Aglobal sedimentary subduction (GLOSS) flux of Uhas been calculated by Plank and Langmuir [52] tobe 2:2 ð 109 g=a, and a quarter of this can readilyaccount for the 5 ð 108 g=a of subduction related Uin all arc lavas. Thus there is no need to invoke ma-jor transfer of U from the subducted altered oceaniccrust to account for U mass balance at convergentmargin volcanism.

U may also be lost from the altered oceanic crustto the subduction zone at depths shallower thansampled by arc magmatism. Quantifying this flux isdifficult but evidence from compositions of fore-arcserpentinites suggest significant loss of only B andCs at shallow depths, but not, for example, K [53]which in the absence of U data might represent areasonable proxy. The geochemistry of some in lavasproduced by back-arc rifting (e.g. [54]) also implya return flux of subducted material to the surfacebehind the arc. In forming oceanic crust, however,back-arc basin lavas will themselves ultimately besubducted, and so we regard back-arc basalts as atemporary reservoir of subducted material.

Perhaps a more important consideration is theeffect of recycling Th=U rich continental materialwhich will clearly counteract the effect of subduct-ing U-enriched altered oceanic crust. This issue canagain be approached using the GLOSS fluxes of9:03 ð 109 g=a Th and 2:2 ð 109 g=a U from Plankand Langmuir [52]. Rea and Ruff [55] independentlyestimated that 1:1 ð 1015 g=a of terrigenous sed-iment enters the subduction zones, which given acrustal [Th] of ¾10 ppm, is compatible with the fig-ure of Plank and Langmuir [52]. From the GLOSSflux, we can calculate that 1:4 ð 109 g=a of ura-nium is required to counterbalance the high Th=Uof subducted sediment, before subduction can beginto lower the Th=U of the mantle. Shortly after theonset of U recycling, much less of the U flux within

the altered oceanic crust would have been neededto off-set the sediment flux, as the difference be-tween Th=U of continents and upper mantle wouldhave been less extreme. Recycling continental Pb,with high 208Pb=206Pb, will also help diminish thekappa conundrum [56]. Quantifying the sedimentarymass-balance of Pb at subduction zones, however, iscomplex (e.g. [57]) and hindered by insufficient dataat most arcs. Without better constraints we simplynote that Galer and O’Nions [12] argued that the207Pb=206Pb ratios of MORB precluded significantamounts of recycled of continental Pb within theupper mantle.

In summary, some 2:5 ð 109 g=a of ‘excess’ Umay be recycled, although within the error of theestimates, it is also possible that very little net U isreturned to the mantle. Nevertheless, an intermediateestimate of the recycled excess U flux (1ð 109 g=a)could, for example, lower the � of an upper mantleMORB source (with 0.01 ppm Th) from 4.0 to 2.6over about 1.8 Ga. This calculation tacitly assumesthat no new continental crust is formed during thelast ¾2 Ga, maximising the effect of recycled U onthe upper mantle Th=U ratio. The fuller model ofEarth evolution discussed later accounts for some ofthese complexities and the average solution requiresa present day excess U flux of some 3:3 ð 109 g=a.The uncertainties in the above calculations makeconclusions less definitive than might be hoped, butthe estimates of recycled U fluxes by no meanspreclude the PURE model.

6. U–Th–Pb evolution of the mantle–crust system

So far we have only discussed the evolution ofTh=U and its record in 208Pb and 206Pb isotopes inthe upper mantle. In this section we extend the PUREconcept into a fuller, twenty time step model of theEarth evolution that tracks of all three lead isotopesystems within three reservoirs: depleted mantle, arecycled ‘plume’ source (made solely from recycledoceanic crust) and continental crust. Full details ofthe calculation are given in Appendix A, but theapproach to the modelling is briefly summarised be-low and shown schematically in Fig. 4. Monte Carloinversions of the forward model were run to in-vestigate ranges of parameters that could reproduce


Fig. 4. Cartoon of reservoirs and fluxes used in the fuller PURE model of Earth evolution. Different chemical reservoirs are shadeddifferent colours and open white arrows indicate mass-transport between reservoirs. The numbered arrows indicate where chemicalfractionations occurring during transport (via parameters, �frac and ¼frac at (1) and from Ð¼ and mass balance of the system at (2).The thick lines and arrows show schematically how U from the continental crust is transported to the oceans, incorporated by alterationinto the crust and then transferred to DMM (with a small amount lost at the subduction zone). The return of PR material to DMM isshown mechanistically as discrete plumes that become convectively thinned, whereas in the model, mixing is instantaneous and DMM ahomogenous reservoir. Likewise subducted oceanic crust is instantaneously mixed with PR.

lead isotopic compositions of upper mantle and a‘HIMU’ [8] plume reservoir. Christensen and Hof-mann [58] have previously developed a numericalmodel of mantle evolution involving oceanic platerecycling that similarly concentrated on producingthe salient lead isotopic features of upper mantle andHIMU reservoirs. Christensen and Hofmann [58],however, did not include the Th–Pb decay system intheir calculations and so did not address the kappaconundrum.

The structure of the model is set by the � evolu-tion of the upper mantle, as deduced from the earlierdiscussion. Initial and final values of � and ¼ areallowed to vary within reasonable ranges for bulkEarth and MORB respectively (see Appendix A).�DMM evolves unchanged, apart from radioactive de-cay, until a time TD at which it starts to steadilydecrease to the present day value of �DMM. All modelsolutions therefore produce �DMM evolution trajec-tories like those in Fig. 3, but permit variations inthe time at which �DMM starts to decrease. Recycledoceanic crust accumulates in a homogenised reser-

voir (PR) which is returned to DMM with a charac-teristic half-time that is varied between runs .−PR/.Continental crust is allowed to reach its present daysize (2:6 ð 1025 g) by exponential growth rates witha range of half-times, −CC. The concentration of Thof the continental crust ([Th]CC) is assumed constantthrough Earth history, but this value varied betweenruns. Some U–Pb fractionation is allowed duringcontinent formation (via parameter ∆¼), and U–Th–Pb fractionation is permitted during subduction ofoceanic crust. Given this framework, U, Th and Pbfluxes between the reservoirs, and consequently theirPb isotope ratios, can be calculated. All input pa-rameters are given in Appendix A, together with atable (Table A1) of the randomly selected variablesand their permitted range (see also Fig. 5). 1178 suc-cessful model solutions were generated from ¾6.8million trials. The results of the modelling are sum-marized in Figs. 5 and 6.

The Pb isotopic compositions of model solutionsare shown in Fig. 6, which illustrates that mostof the permitted range is reproduced. The model

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Fig. 5. Histograms of various parameters used in the Monte Carlo PURE inversion, for the 1178 successful solutions (grey bars) and for only those solutions with a3:8 < �BE < 4:0 (points joined by black line). The scale shown illustrates the permitted range of input values (except in (d), (g) and (h) where the values were notpre-determined). For definition of parameters see text.


Fig. 6. Plots of lead isotope ratios for successful solutions of thefull PURE model. Compositions of the different reservoirs areshown (squares, DMM; triangles, PR; and diamonds, CC). Thebigger symbols represent the mean of the 1178 successful solu-tions, which itself satisfies the Monte Carlo criteria. Referencelines as in Fig. 1.

results may be interpreted from two end-memberviews of the MORB mantle. At one extreme, onemay envision a DMM which is heterogeneous onthe scale sampled by MORB melting. Such hetero-geneity may result from different parcels of DMM

following slightly different evolutionary pathways.Admittedly we model a number of different wholeEarth evolution paths rather than tracking multipleparcels of mantle on a single Earth. Nevertheless,individual solutions can be averaged to produce amean result that we empirically found to fulfil theselection criteria of the model. Alternatively, onemay imagine that the heterogeneity in DMM resultsfrom the incorporation of variable amounts of en-riched PR material in a matrix of DMM. In thiscase, the MORB Pb isotopic arrays may be thoughtof as being produced by mixing between a DMMcomposition which falls to the low 206Pb=204Pb sideof the array and a PR composition that falls to thehigh side.

The compositions of average continental crustgenerated by the model, which unlike the DMMand PR reservoirs were not pre-determined, are alsoshown in Fig. 6. Since the crust contains the majorityof Pb within the silicate Earth, the crust must lieclose to the Geochron. Our model did not allow anyloss of lead during a finite period of core forma-tion. Hence, the Geochron to which our continentalcrust is tied is probably not appropriate [8,10] andshould be shifted to higher values of 206Pb=204Pb.The absolute values of our model continental crusttherefore need refining, but their positions relativeto the other reservoirs is significant. Most successfulmodel solutions require some preferential enrich-ment of U relative to Pb during continent formation(i.e. non zero ∆¼), as illustrated in Fig. 5k. Thisresults in a slightly higher U=Pb of the continen-tal crust relative to the upper mantle in early Earthhistory and hence the generally elevated 207Pb=204Pbat a given 206Pb=204Pb relative to the MORB array(Fig. 6a). The onset of recycling of U later in Earthhistory then reverses the sense of change of ¼ inthese two reservoirs. This helps explain one aspectof the first lead paradox. Although U is generallymore incompatible than lead during melting, the ef-fects of recycling in latter Earth history subsequentlycounteract this effect. Thus, our mean model MORBplots to the right of the Geochron even though itwas relatively depleted in U relative to Pb by earlycontinent formation.

Fig. 5 shows histograms to illustrate the rangeof some key parameters in successful solutions. Thelarge number of variables used in the model result


in a large degree of freedom, and few good corre-lations exist between parameters. For example, themodelling is insensitive to ¼ of bulk Earth (Fig. 5e),the volume of differentiable mantle (not shown) andhalf-time of continental extraction (not shown, butwhich tends towards large half-times and thus nearlinear growth). Perhaps the clearest covariation ofparameters is between �BE and TD; the lower the ini-tial � of the Earth, the later the onset of U recycling.Allowing bulk Earth � to vary between the full rangeof possible chondritic compositions (Fig. 5a) causesa rather broad peak in TD (Fig. 5i). By restrictingthe range to 3:9 š 0:1 (which most importantly ex-cludes the possibility of high �BE), the peak of TD isnarrowed and mean value shifted to ¾2.2 Ga (blackline, Fig. 5i). The latter is more compatible with esti-mates of the change in atmospheric oxygen fugacity[32,33]. The insensitivity of other key parametersto this restriction of �BE can be observed in Fig. 5.The time constant of the plume reservoir is tightlyconstrained (Fig. 5j) and this is a consequence of thewell defined slope of mantle derived leads on a plotof 206Pb=204Pb vs. 207Pb=204Pb.

The Monte Carlo model developed here success-fully demonstrates the viability of the PURE modelin accounting for �DMM evolution in a planetarycontext. The model incorporates a depleting MORBmantle, growing continental crust and a plume reser-voir with HIMU characteristics. In dealing with anexchanging plume reservoir, we have admittedlymade an open system upper mantle, although thisshould not detract from the fact that it is the recy-cling of U from the continental crust, rather thanreturn of plume material to the upper mantle that isthe important control on its lead isotope ratios.

7. Conclusions

The mismatch between measured Th=U and in-ferred time integrated Th=U of the upper mantle,the kappa conundrum, can be readily explained byin-situ decay of U and Th. Resolution of the co-nundrum suggests near constant Th=U of the uppermantle in early Earth history followed by a steadydecrease after the Archean. This model requirementhas a striking resonance with independent geologicalconstraints. After the dramatic increase in oxygen

fugacity of the atmosphere at the end of the Archean,U can be readily weathered from the continents inits highly soluble, oxidised state. Alteration of theoceanic crust incorporates U delivered from the con-tinents to the sea, and recycles it into the mantlepreferentially relative to insoluble Th. The flux ofrecycled U necessary to appropriately lower uppermantle Th=U is within the bounds obtained by inte-grating present day fluxes of subducted ‘excess’ Ufor ¾2 Ga. The post-Archean U recycling (PURE)model provides a solution to the kappa conundrumthat does not require the lead isotope ratios of theupper mantle to predominantly reflect the signatureof entrained material from another reservoir.

Acknowledgements

Although none of the authors are presently lo-cated at Lamont-Doherty Earth Observatory, thework presented here grew from discussions begunthere during an exciting period of Th isotopicinquiry. The intellectual atmosphere provided byour Lamont colleagues, Vincent Salters and Char-lie Langmuir chief among them, was clearly veryimportant to the process. Thanks to Chris Germanand Hubert Staudigel for advice on oceanic crustalteration, and Anthony Koppers for help in codingthe inversions. We are grateful to Bill White, KenSims, Claude Allegre and two anonymous reviewersfor comments on versions of this manuscript. Thiswork was made possible by support to AZ from theNSF and FSU, to TE from NATO and VU, and toBB from the CNRS. [FA]

Appendix A

The Monte Carlo simulation runs a 20 equal time step, for-ward model of the lead evolution of the Earth. Time runs fromthe formation of the Earth at T D 0 to the present day atT D 4:55 ð 109 a. Parent=daughter ratios vary by both frac-tionation and radioactive decay. In order to help comparison ofdegrees of fractionation at different times of Earth history, werefer to parent=daughter ratios (unless otherwise specified) cor-rected to present day, indicated by a superscript 0. For example,�DMM.2:5/0, refers to the 232Th=238U ratio of the depleted man-tle reservoir at 2.5 Ga, corrected for decay to present day. Thereare 13 randomly varied parameters listed together with their per-mitted ranges in Table A1. The Earth is modelled as three main


Table A1Summary of variables used in the PURE Monte Carlo inversion;permitted ranges of the variables, units and a brief descriptionare given

Parameter Range Units Description

�DMM 2.3–2.8 232Th=238U of depleted mantlereservoir (present-day)

�PR 3.0–3.8 232Th=238U of plume reservoir(present-day)

�BE 3.7–4.2 232Th=238U of bulk silicateEarth (present-day)

¼BE 7.9–8.4 238U=204Pb of bulk silicateEarth (present-day)

TD 0.5–3.5 Ga Onset of decreasing �DMM (timefrom accretion)

−CC 1–50 Ga Half-time of continental crustproduction

−PR 0.77–2.31 Ga Half-time of plume reservoirreturn to DMM

FDM 0.3–1 Fraction of silicate Earth thatdifferentiates (into DMM, PRand CC)

[Th]CC 2–12 µg=g Concentration of Th incontinental crust (present-day)

[Th]PR 0.025–0.2 µg=g Concentration of Th insubducted oceanic crust(present-day)

∆¼ 0–0.3 Incremental lowering of238U=204Pb in DMM in earlyEarth history (before TD)

�frac 1–1.3 Fractional increase in232Th=238U during ‘subduction’(i.e. plume formation)

¼frac 1–4 Fractional increase in238U=204Pb during ‘subduction’(i.e. plume formation)

reservoirs; depleted mantle, a plume reservoir and continentalcrust. A fourth reservoir, ‘subducted MORB’, is briefly storedbefore being added to the plume reservoir. These four reservoirscomprise the differentiable silicate Earth, and only this portionof the Earth is modelled. The fraction of differentiable Earth.FDM/ is allowed to vary randomly from run to run (Table A1).Masses of bulk silicate Earth and continental crust are taken tobe 4:06ð 1027 g and 2:6ð 1025 g respectively. The size of theother reservoirs are variable, as described below.The primary aimof this study is to find possible evolution paths of � in the uppermantle, that can produce present day MORB lead isotope ratiosby in situ decay. The structure of the calculation is therefore setby the � of the upper mantle reservoir. From our initial analysisit was apparent that trajectories such as those shown in Fig. 2cand Fig. 3 can account for the Th=U and 208Pb=206Pb systematicsof the upper mantle. Thus we used this basic form but extendedthe model to include all the lead decay schemes and investigate

the implications of this evolution on other mantle reservoirs. Theevolution of � in the upper mantle is thus different in early andlate Earth history. The time at which the change in behaviouroccurs (i.e. the onset of U recycling) is allowed to vary randomlybetween models, and is defined by variable TD. In stage one.0–TD/, � changes by decay alone from an initial chondriticvalue. In the second stage (TD–4:55 Ga), �0 decreases linearly toa randomly selected present day value, appropriate for a MORBsource .�DMM/.

The ¼ of the upper mantle is treated similarly. However, inthe first stage some fractionation between U and Pb is allowed,mimicking the potential effects of melting in continent produc-tion. No fractionation of Th=U was assumed for this processas these elements are so incompatible that melt fractionation isunlikely. The fractionation of ¼DMM in the first stage is modelledby subtracting a constant (∆¼) from ¼DMM for each time stepbefore TD. The parameter, ∆¼, is a constant for each run, butrandomly varied between runs. As discussed at length above, webelieve that recycled U decreases Th=U in the upper mantle andsuch recycling must also have a proportional effect on U=Pb.However, in addition to effect of U recycling, other processesmay affect Pb and hence ¼DMM. Thus, present day ¼DMM isallowed to vary randomly to 30% greater or less than a value of¼ for DMM corrected for U recycling. The latter is calculatedby multiplying ¼DMM.TD/

0 by [�DMM.TD/0=[�DMM.0/0]. From

TD, ¼0DMM follows a linear evolution to the present day ¼DMM.In

our model, the plume reservoir is derived from recycled oceaniccrust and so is related to the composition of the upper mantle.Creation of the plume reservoir does not start until the third timestep, accounting for the possibility of a global magma ocean, orstrong convective homogenisation early in Earth history. Subse-quently plume material is created by fractionation of the uppermantle reservoir, via the parameters �frac and ¼frac. The �.t/0

and ¼.t/0 of newly formed plume material is simply calculatedby multiplying �.t/0DMM and ¼.t/0DMM by �frac and ¼frac re-spectively. This mimics net fractionations after alteration andsubduction and is required, in particular, to create the radiogeniclead isotope compositions characteristic of the (HIMU) plumesource. After these fractionations, the newly formed plume ma-terial then evolves in isolation for a single time-step (accountingfor the time taken to be deep subducted) before being added andhomogenised with the plume reservoir.The masses of additionsto the plume source need to be considered. The mass of theplume reservoir at time step tn can be written:

MPR.tn/ D MPR.tn�1/[exp.� ln 2=−PR.tn � tn�1//]

C 4c0.tn � tn�1/[exp.�3:05ð 10�10tn�1/] (1)

where c0 is annual present day oceanic crustal production andMPR and MDMM are the masses of the plume reservoir andthe depleted MORB mantle, respectively. The rationale behindthe mass of the plume reservoir is that it is created at anexponentially declining rate due to cooling of the Earth andslowing plate subduction. The mass of plume formation is scaledfrom present day rate of oceanic crust creation (taken to be5:4 ð 1016 g=a), and it is assumed that this was higher inthe past. Initial creation of oceanic plates, and hence plumematerial, in early Earth history is conservatively taken to be


four times greater than at present, and this production ratedecays exponentially to present day values. The plume reservoiris also believed to be ‘destroyed’ by return to the convectingupper mantle, in the form of plumes. We assume that rate ofreturn is proportional to the reservoir size. The half time ofthe reservoir is varied from run to run using the parameter−PR.Continental growth rate is assumed to decrease exponentiallyfrom the beginning of Earth history, such that:

MCC.tn/ D MCC.tn�1/C c[exp.ln 2=−CC.tn � tn�1//] (2)

where MCC.tn/ is the mass of the continental crust at time atthe start of the nth time step, −CC is the half time for crustalproduction, and c is a constant which varies with −CC to ensurethat today (tn D 4:55 Ga) MCC D 2:6ð1025 g. The time constantof continental growth is allowed to vary considerably, such thatgrowth can approach a near linear form (Table A1). The conti-nents grow to create a present day mass of Th in the continentalcrust controlled by the variable [Th]CC (Table A1). [Th]CC isassumed to be constant (aside from radioactive decay) throughtime.A flux of Th to the plume reservoir can be calculated fromthe mass-flux of subducted material (discussed above) multipliedby a Th content appropriate for a MORB melt. This variable,ThPR, is assumed to have been a factor 2 higher at 4.55 Ga (dueto a less melt depleted upper mantle) and decreases linearly withtime to the value ThPR for current production of plume material.Given the mass fluxes into and out of plume reservoir, the Thheld in the plume reservoir can readily be computed. Thus themasses of Th in CC and PR reservoirs are known and the mass ofTh left in DMM in any time step can then be calculated by massbalance.Since the � and ¼ of DMM are set, knowing the Thconcentration of the DMM at any time allows the calculation ofU and Pb abundances. Since the � and ¼ fractionation betweenDMM and plume material is also set by �frac and ¼frac, the massof U and Pb in the plume reservoir can further be calculated. Theconcentration of U and Pb in the continents can then be com-puted by mass balance. Radiogenic lead produced in each timestep can be calculated and mixed according to isotope ratios andlead fluxes.Successful solutions are required to generate presentday lead isotope ratios. The MORB and PR fields in Fig. 6 covermost of the permitted range. Successful solutions are deemedto fall in the following quadrilaterals: MORB in 206Pb=204Pbvs. 207Pb=204Pb space with apices at (17, 15.288) (17, 15.363)(19.5, 15.593) (19.5, 15.668); PR in 206Pb=204Pb vs. 207Pb=204Pbspace with apices at (19.0, 15.532) (19.0, 15.607) (22, 15.897)(22, 15.972); MORB in 206Pb=204Pb vs. 208Pb=204Pb space withapices at (17, 36.1) (17, 36.6) (19.5, 38.918) (19.5, 39.418);PR in 206Pb=204Pb vs. 208Pb=204Pb space with apices at (19.0,38.354) (19.0, 38.854) (22, 41.735) (22, 42.235). Furthermoresolutions were only accepted if the slope defined by the MORBand PR solutions was >0.092 and <0.152 in 206Pb=204Pb vs.207Pb=204Pb space and >0.957 and <1.297 in 206Pb=204Pb vs.208Pb=204Pb space. Some further constraints are also set. A mini-mum, present day uranium concentration for the depleted mantleof 0.002 µg=g and a minimum uranium content continental crustof 5:6ð 1016 moles are set. Solutions that generate negative Th,U or Pb concentrations for any time step in the depleted mantleare also rejected. Finally, the amount of U recycled in any step

is calculated and any solution that requires this flux to be greaterthan 3:84ð 1015 mol=a, or three times our current day estimateof ‘excess’ U carried in the altered oceanic crust, is also rejected.

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exploring the kappa conundrum: the role of recycling in the lead isotope evolution of the mantle

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