The evolution of terrestrial volatiles: a view from helium, neon, argon and nitrogen isotope modelling

Ž .Chemical Geology 147 1998 27–52

The evolution of terrestrial volatiles: a view from helium, neon,argon and nitrogen isotope modelling

I.N. Tolstikhin a,b,c, B. Marty a,b,)

a Centre de Recherches Petrographiques et Geochimiques, Rue Notre-Dame des PauÕres, B.P. 20, 54501 VandoeuÕre Cedex, France´ ´b Ecole Nationale Superieure de Geologie, Rue du Doyen Marcel Roubault BP 40, 54500 VandoeuÕre Cedex, France´ ´

c Geological Institute, Kola Scientific Centre Russia Academy of Sciences, Apatity 184200, Russian Federation

Abstract

In this contribution, we have developed an evolutionary model in order to identify and quantify processes which wereable to reproduce rare gas and nitrogen isotopic abundances in the main terrestrial reservoirs. The following processes appearto have played an important role in the history of terrestrial volatiles. During accretion, impact degassing could have releasedf95% of the initial rare gas abundances, which were quite similar to those typical of solar wind-implanted gases. After the

Ž .major phase of accretion and core segregation 4.50 Ga ago , some parts of the upper mantle were partially melted by giantŽ .impact s and experienced vigorous convection and solubility-controlled degassing. More than 99% of the volatile species

Ž .initially presented in the upper mantle–atmosphere reservoirs were lost during this period from 4.50 to 4.30 Ga ago . Thisloss was accompanied by elemental and isotopic fractionation of residual atmospheric constituents. The atmosphere becameretentive for Xe at 4.40 Ga but degassing, loss and fractionation of lighter rare gases and nitrogen might have taken placesome time afterwards. Therefore each gas might have undergone fractionation to various extent at different times. After

Ž . Ž .closure of the atmosphere at f4.30 Ga for all but the lightest H, He constituents, the lower mantle supplied the upperŽ .mantle with minute amounts of parent incompatible elements, rare gases and nitrogen, between ;1% 4.3 Ga ago and

Ž .;0.2% at present of their total amount in the lower mantle per Ga. The post-atmosphere closure flux of liquid silicatesfrom the upper mantle, analogue to the present-day MOR flux of basaltic melts, decreased by a factor of ;100, from

18 Ž . 16 y1 Ž . 36 Ž . 36 Ž . y4;5P10 4.3 Ga ago to 6P10 g a at present . The ratio of Ar now r Ar 4.3 Ga ;10 illustrates the totalum

degree of upper mantle degassing yielded by this flux. This rate of degassing corresponds to a present-day ratio of40Arr 36Ar )106, if no fluxes from the lower mantle and the crustal–atmospheric reservoirs had operated, and the ratiosum

of radiogenic over primordial species could have been higher in the past than those at present. The model postulates thatnitrogen trapped in the Earth–Atmosphere system was initially depleted in 15N relative to present-day atmospheric

Ž . 15 15composition ATM . Atmospheric escape enriched the ancient atmosphere in N, resulting in a d N isotopic compositionŽ .of q2.5 parts per mil ATM 4 Ga ago. Subsequent degassing of mantle nitrogen allowed this element to reach its

present-day composition in air. Because the upper mantle is extremely depleted in volatile elements, their transfer from thelower mantle is sufficient to maintain primordial rare gases and nitrogen abundances in the upper mantle approximately at asteady state. Decays of parent radioactive elements, U , Th , and K , contribute radiogenic nuclides. Recycling fluxesum um um

Ž . Ž .of sub surface materials into the upper mantle transfer surface volatiles, ;6% of surface-derived atmosphereqsedimentsN and ;0.03% of atmospheric 36Ar per Ga. Consequently, the isotopic composition of mantle nitrogen varied from itsah

initial d 15N value of y30 parts per mil to its present-day upper mantle value of y5 parts per mil. The consequence of

) Corresponding author. E-mail: [email protected]

0009-2541r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.Ž .PII S0009-2541 97 00170-8

( )I.N. Tolstikhin, B. MartyrChemical Geology 147 1998 27–5228

nitrogen recycling in the Earth–Atmosphere system is therefore partial re-homogenisation of N-isotopes, but this processwas not efficient enough to have erased early heterogeneity. Thus the present contribution proposes early formation of theEarth’s atmosphere by a combination of degassing, dissipation, and fractionation processes. Primordial rare gases andnitrogen were set in this reservoir around 4.3 Ga ago and further mantle outgassing has contributed less than 3% of thesespecies since that time. q 1998 Elsevier Science B.V. All rights reserved.

Keywords: terrestrial volatiles; rare gases; nitrogen; evolution; mantle; atmosphere

1. Introduction

The isotopic abundance of terrestrial rare gasesŽsuggests a two-layered mantle reservoir Kurz et al.,

1982; O’Nions and Oxburgh, 1983; Allegre et al.,`1983, 1986r87; Kaneoka and Takaoka, 1985; Poredaand Farley, 1992; Hiyagon et al., 1992; Matsuda and

.Marty, 1995 . The lower mantle region appears to bea source of primordial, unfractionated rare gases,

Ž .some of which e.g., He, Ne being identified inŽ . Žplume PLUME materials Kurz et al., 1983; Rison

and Craig, 1983; Honda et al., 1991, 1993; Hiyagon.et al., 1992; Richard et al., 1996 . The upper part of

the mantle, as sampled by Mid-Ocean Ridge BasaltsŽ .MORB , contributes radiogenic isotopes to primor-dial rare gases transferred from the lower mantleŽAllegre et al., 1986r87; Kellogg and Wasserburg,`1990; O’Nions and Tolstikhin, 1994; Porcelli and

.Wasserburg, 1995a,b . Recyclingrcontaminationprocesses transfer some atmospheric gases into the

Žmantle Azbel and Tolstikhin, 1988, 1990, 1993;.Porcelli and Wasserburg, 1995a,b . Modelling inter-

actions between the lower and the upper mantlereservoirs shows that calculated rare gas abundancesin MORB and PLUME materials are consistent witha steady-state upper mantle feeding by plumes from

Žthe lower mantle Kellogg and Wasserburg, 1990;.Porcelli and Wasserburg, 1995a,b and outgassing at

Ža similar rate at mid-ocean ridges O’Nions andTolstikhin, 1994, 1996; Tolstikhin and O’Nions,

.1996 .The behaviour of volatile elements during and

soon after accretion is more obscure. Some of thecharacteristics of terrestrial rare gases are still notwell understood. For example, the abundances andthe isotopic ratios of atmospheric rare gases arefractionated relative to their potential extra-terrestrialprecursors, whereas mantle rare gases, at least thelight ones, more resemble those present in meteoritesor the solar wind. Notably, the atmosphere is very

depleted in xenon relative to krypton, and Xe isŽ .isotopically fractionated 3‰ per a.m.u. in compari-

son to solar-type Xe and meteoritic Xe.Accretionary processes are likely to have pro-

Žvoked efficient degassing of impacting bodies e.g.,.Gerasimov and Mukhin, 1979; Melosh et al., 1993 ,

and recent modelling suggests that only about 5% ofinitial rare gas concentrations in accreting proto-ter-restrial materials were retained inside the EarthŽ .Azbel and Tolstikhin, 1993 . Tolstikhin and O’NionsŽ .1994 proposed that, towards the end of accretionand soon afterward, gas loss from the mantle contin-ued via fractional degassing of convecting melts.Volatiles, including heavy constituents like Xe, es-caped from accreting planetesimals andror theEarth–Atmosphere system which finally retained

Žonly ;1% of the initial abundance of Xe Wetherill,1975; Azbel and Tolstikhin, 1993; Tolstikhin and

. Ž .O’Nions, 1998 . Impact erosion e.g., Ahrens, 1993Žorrand hydrogen hydrodynamic flux e.g., Pepin,

.1991, 1992 are considered to be plausible escapemechanisms which could also have produced theisotopic and elemental fractionation of atmospheric

Žgases Zahnle et al., 1988, 1990; Vityazev and Pech-.ernikova, 1996 . The atmosphere became retentive

for Xe about 150 Ma after the beginning of accre-tion. The lower mantle started to behave as a near-

Žclosed system at or before this time Tolstikhin and.O’Nions, 1998 .

This framework allows to investigate the fate ofmajor volatiles, nitrogen, carbon and water. Nitrogenis the best candidate to start with because the majorfraction of nitrogen at the Earth’s surface is now inthe atmosphere, and because its isotopic compositionin the upper mantle and its relationship to rare gasesŽ . Že.g., Ar have been documented Marty, 1995; Marty

.et al., 1996 .The first goal of this contribution is to present an

Ževolutionary model for the light rare gases He, Ne,. Ž .Ar and their parent radioactive elements U, Th, K .

( )I.N. Tolstikhin, B. MartyrChemical Geology 147 1998 27–52 29

ŽThis model is consistent with and partially con-. Ž .strained by : 1 the standard scenario of Earth accre-

Ž . Ž .tion Vityazev et al., 1990; Wetherill, 1990 ; 2ŽPu–U–I–Xe Azbel and Tolstikhin, 1993; Tolstikhin

. Žand O’Nions, 1996, 1998 , U–Th–Pb Kramers and. Ž .Tolstikhin, 1997 , and Hf–W Kramers, 1997 iso-

Ž .topic systematics; and 3 recent rare gas steady-stateŽmodels Kellogg and Wasserburg, 1990; O’Nions

and Tolstikhin, 1994, 1996; Porcelli and Wasser-.burg, 1995a,b . This model allows to investigate the

initial elemental abundances of the light rare gases,He, Ne, and Ar in proto-terrestrial materials and tocompare them with those observed in extraterrestrialreservoirs. An important result of the model is anindependent assessment of the mass fluxes betweenthe main terrestrial reservoirs during the geologicalevolution of our planet.

Second, we use this model to investigate theevolution of terrestrial nitrogen in the mantle andatmospheric reservoirs. This application is particu-larly important to document the early surface envi-ronments contemporary to the formation of the prim-itive crust and the development of life.

2. Nitrogen isotope abundances and nitrogen–raregas relationship in extra-terrestrial, mantle andatmospheric reservoirs

A summary of rare gas observational data wasŽ .given by O’Nions and Tolstikhin 1994, 1996 , Por-

Ž .celli and Wasserburg 1995a,b , Tolstikhin andŽ . Ž .O’Nions 1996 see Table 3 and only the nitrogen

isotope geochemistry and the relationship betweenthis element and rare gases are discussed below.

The large variations in the isotopic composition ofnitrogen in extraterrestrial samples reflect nebularinhomogeneities of nucleosynthetic origin as well asN isotope production processes in the pre-solar and

Žsolar nebula Kung and Clayton, 1978; Lewis et al.,.1983; Prombo and Clayton, 1993 . The isotopic

composition of nitrogen varies over 1000 parts permil in bulk stony and iron meteorites, and estimatesfor the isotopic composition of the solar wind varyover 300 parts per mil, precluding a straightforwardchoice for an initial terrestrial composition. Someconstraints are available from the oxygen isotopic

Žcharacterisation of meteorites and planets Clayton et.al., 1976; Clayton, 1993 . Indeed the oxygen isotopic

composition of the Earth is similar to that of theenstatite chondrites, suggesting that these meteoritescan provide a source material for terrestrial nitrogen

Ž . 15also Javoy and Pineau, 1983 . d N in enstatiteŽchondrites vary from y20 to y45‰ see Appendix

15 .A for definition of d N , somewhat lower then thelowest known compositions for terrestrial diamonds,

Žy12‰ Javoy et al., 1984; Boyd et al., 1992; Boyd.and Pillinger, 1994 and the present-day composition

of nitrogen in the convective upper mantle, source ofŽ .MORB, y5‰ Marty et al., 1996 . Therefore, a

15 Žtypical E-chondrite d N value of y30‰ Kung.and Clayton, 1978, Grady et al., 1986 appears to be

a reasonable choice for the initial terrestrial composi-Ž .tion and this value is used hereafter Table 1 .

An important observation on the relative abun-dance of volatiles in the Earth–Atmosphere systemis that both meteoritic and terrestrial Nrrare gasratios are much higher than those of the Sun. Forexample, chondritic Nr 36Ar ratios are within 105–107 and the atmospheric ratio is 0.5P105, whereasthe solar ratio is estimated at 30. Therefore a mete-orite-like material appears to be a more plausible

Ž .source of terrestrial volatiles except rare gases thana trapped massive proto-atmosphere of which the

Žcomposition is expected to be solar e.g., Sasaki and.Nakazawa, 1988 .

Terrestrial N in sedimentary and crystalline rocksgenerally shows enrichment in 15N relative to atmo-spheric N, with d 15 N between q2‰ and q10‰ for

Ž .organic N in marine sediments Peters et al., 1978 ,and between q2‰ and q15‰ for ammoniacal N in

Žmeta-sediments and S-type granites Haendel et al.,.1986; Bebout and Fogel, 1992; Boyd et al., 1993 .

15 ŽThe mean d N at the Earth’s surface atmosphere.qcrust is approximately q1‰. Sedimentary rocks

and basalts involved in subduction metamorphismrelease nitrogen, and d 15 N in residual N increases

Žtogether with the metamorphic grade Bebout and.Fogel, 1992, Fig. 1 . Consequently, N recycled at

subduction zones is likely to be enriched in 15NŽ 15 .d N)0‰ , and the effect of subduction can betreated as the addition of N with a d 15 N higher by5‰ than that of the surface reservoir into the upper

Ž .mantle Fig. 1 . Such case might not have been validin the far past because the N isotope fractionation


Table 1Input parameters

Ž .Parameters, dimensions, and time scales Ga Value Notes

Ž .Proto-terrestrial material t s0in27Mass of proto-terrestrial material, 10 g 5.98

Metalrtotal mass ratio 0.33238 17Initial abundance of U, 10 mol 7.37 1232 238Atomic Thr U ratio 2.4140 238Atomic Kr U ratio 56.3 240 36Arr Ar 0.01 320 22Ner Ne 13.721 22Ner Ne 0.03273 22Her Ne 4.54 3Her He 2560

15d N, ‰ y30 4Ž .Fractionation parameters: core segregation 0, 0.06

Fraction of liquid silicates, F 0.5 5u m ,c rŽ .Fraction of solid silicates, F ss 0.47u m ,c r

Ž .Fraction of metal, F met 0.03u m ,c rŽ .Partition coefficients t , tin fin

Solidrmelt part. coef. for rare gases and N 0.001 6i Ž .Metalrmelt part. coef. for rare gases, D met 0.01 7u m ,c rN Ž .Metalrmelt part. coef. for nitrogen, D met 0.1 8u m ,c r

y9 y1 y1Solubility coefficients, 10 mol g barHe 36 9Ne 6.7Ar, N 3.5Kr 2.2Xe 1.1

Ž .1 Initial abundances of U and Th are from a chondritic model of the Earth. The values correspond to the present-day bulk mantle238 Ž . 232 238Us22 ppb Jacobsen and Wasserburg, 1979; Morgan and Anders, 1980; Hofmann, 1988; Galer et al., 1989 and Thr Us3.9Ž .Stacey and Kramers, 1975; Galer and O’Nions, 1985; O’Nions and McKenzie, 1993 .Ž . Ž .2 Corresponds to a present-day KrU ratio of 12,500 Jochum et al., 1983 .Ž . Ž . Ž .1, 2 Decay constants, yields and production ratios are from Ozima and Podosek 1983 and Mamyrin and Tolstikhin 1984 .Ž . Ž . Ž . Ž . Ž . Ž .3 From Black 1972a,b , Begemann et al. 1976 , Bernatowicz and Podosek 1978 , Anders and Grevesse 1989 , Bochsler et al. 1990 .Ž . Ž .4 Within the range typical of E-chondrites Section 2 .Ž . Ž .5 From Azbel et al. 1993 .Ž . Ž .6 Rare gases and nitrogen are treated as incompatible elements e.g., Marty and Lussiez, 1993; Marty, 1995 .Ž . Ž .7 Rare gas metalrliquid silicate partition coefficients are from Matsuda et al. 1993 for a moderate pressure of 30 kbar.Ž . Ž .8 From comparison of N contents in iron and stony meteorites Kung and Clayton, 1978; Grady et al., 1986; Prombo and Clayton, 1993 .Ž . Ž . Ž .9 Rare gas data from Jambon et al. 1986 and Lux 1987 . Nitrogen solubility from Marty et al., 1995.

may be linked to biologic activity before sedimenta-tion, but the impact of this simplification on theresults is limited and the general view of the nitrogenevolution given in this work is not qualitativelydependent on this simplification.

The isotope composition of nitrogen in the mantlebelow continents is mainly available from analysesof diamonds. Both positive and negative d 15 N val-

Žues have been observed Javoy et al., 1984; Boyd et.al., 1987; Boyd, 1988; Boyd and Pillinger, 1994 .

Ž . 15Javoy et al. 1984 reported an average d N ofŽ .y5.1‰ for Mbuji Mayi diamonds Zaıre with ex-¨

Ž .treme values down to y12‰ Fig. 1 . Studies ofdiamonds from different localities and origins con-firmed the occurrence of a 15N-depleted end-memberand also showed that positive d 15 N values are oftenassociated with rather light carbon, which combina-tion is consistent with subduction of both species

Žtogether with crustal materials Boyd et al., 1987;.Boyd, 1988; Boyd and Pillinger, 1994 .


It is not clear however wether volatiles trapped indiamonds are representative of the astenospheric up-per mantle. Earlier measurements of d 15 N in oceanic

Ž .basalts originating in the convecting mantle weresomewhat contradictory, with d 15 N values varyingbetween y0.4‰ to q17‰ for Hawaii, and fromy4.5‰ to q7.5‰ for Mid-Ocean Ridge BasaltsŽ . ŽMORB Becker and Clayton, 1977; Sakai et al.,

. Ž .1984; Exley et al., 1987 . Javoy and Pineau 1991reported a d 15 N value in the range y2;y5‰ forN extracted from a gas-rich MORB glass by crush-ing. Variations of d 15 N in MORB glasses could be

Ž .the result of mixing between sub surface and mantleN. The best way to control this effect is to analyse

Žboth N and Ar isotope compositions Marty et al.,.1996 . Indeed Ar is an extremely sensitive tracer of

atmospheric contamination, and simultaneous analy-sis of N and Ar isotopes in gases extracted fromvesicles of MORB glasses has allowed to identify anupper mantle component with 40Arr 36Arf40,000

15 Ž .and d Nfy5‰ Marty et al., 1996 . At present

Fig. 1. Carbon versus nitrogen isotopic ratios in various sets ofŽ .terrestrial samples modified after Boyd and Pillinger, 1994 . The

convergence of MORB and diamond data towards a mean ofy5‰ indicates that this value is typical of the mantle, the uppermantle in the case of MORB. Meta-sediments from the Catalinafossil subduction zone show d 15 N increasing with metamorphicgrade, suggesting 15 N enrichment in subducted crustal N. Source

Ž .of data: Finsch, Premier, Williamson diamonds from Boyd 1988 ,Ž . Ž .Boyd and Pillinger 1994 ; Zaıre diamonds a from Javoy et al.¨

Ž . Ž . Ž . Ž .1984 , b from Boyd et al. 1987 , Boyd 1988 ; gases extractedfrom MORB glasses and those from geothermal fluids, Nesjavel-

Ž . Žlir, Hengill area Icelandic plume are from Marty et al. 1991,. Ž .1996 ; meta-sediment data are from Bebout and Fogel, 1992 .

36 40 36 Ž .Fig. 2. Mantle N r Ar versus Arr Ar in MORB. Normal N2Ž .MORB represent best the depleted upper mantle, enriched E

MORB are generally associated with geochemical heterogeneityin the mantle source, and PLUME data comprise samples showing3Her 4 He isotopic ratios higher than those of MORB’s. Theshaded area represents a mixing domain between the atmospheric

Ž .component air or air-saturated water and the deep componentcharacterised by mean N r 40Ar f80, corresponding to a mix-2 u m

ture of 70% N-MORB and 30% E-MORB, as suggested byŽstatistical analysis of MORB chemical composition Ito et al.,

.1987 . Only gases extracted by crushing of submarine basaltŽglasses or separated minerals are presented Marty, 1995; Marty et

.al., 1996 .

there is little doubt that the upper mantle is depleted15 Ž 15 .in N relative to surface nitrogen d N sy5‰ .um

Central to our approach is the relationship be-tween nitrogen and argon in MORB vesicles. A

40 Ž .striking N – Ar correlation Fig. 2 suggests that:2Ž .1 N and Ar have a similar solubility in basaltic2

melts; therefore these species are not significantlyŽ .fractionated during magma degassing; 2 the MORB

mantle source is characterised by a near-constant40 ) ŽN r Ar ratio of 80"20 Marty, 1995; Marty et2

.al., 1996 .The N r 40Ar ) ratio and d 15 N of the lower man-2

tle are not defined at present and should result frommodelling.

3. The model

3.1. ReserÕoirs, fluxes of mass and species

In this contribution, reservoirs are large homoge-neous domains of the Earth characterised by differ-


ŽFig. 3. Reservoirs and fluxes. f , f , f , f , f are mass fluxes from the terrestrial feeding zone proto-terrestrialp m ,u m u m ,c r u m ,l m u m ,o c u m ,c c.material into the upper mantle, from the upper mantle into the core, lower mantle, oceanic crust and continental crust, respectively. f l m ,u m

and f are fluxes from the lower mantle and oceanic crust into the upper mantle. iL , i

L , and iL are the dissipation,o c ,u m a h a h ,u m c c ,a h

Ž .atmosphere – upper mantle recycling and crustal degassing transport coefficients, respectively. Numbers in brackets show time interval GaŽ .during which a given flux is evaluated see Appendices A and B for the definitions and equations, respectively .

Ž .ent evolution and composition Fig. 3 . Each reser-Žvoir j is characterised by its mass with the excep-

.tion of the atmo-hydrosphere which mass is ignored ,Ž . i Ž . iM t 'M , the amount of species i, N t ' N ,j j j j

i Ž . i iand the concentration of i, C t ' C ' NrM .j j j

Fluxes of mass and species and fluxes of speciesŽ .unsupported by mass fluxes operating between thereservoirs change these characteristics. This is in facta generalised case of the transport problem proposed

Ž .by Jacobsen and Wasserburg 1979 . The numericaltreatment of this multi-reservoirs and multi-fluxes

Ž .direct problem Appendix B was developed by Az-Ž .bel and Tolstikhin 1985, 1988, 1990, 1993 and

Ž .Asming and Tolstikhin 1998 . The accuracy inferredfrom comparison of analytical and numerical solu-tions is "0.01%.

3.2. Formation of the Earth

( )3.2.1. Initial conditions ts t '0in

The initial time t s0 is defined as the timein

when material able to retain rare gases had beenformed in the solar nebula. This time had beenrecorded by the retention of 129 Xe) , product of 129 I

Ž .decay T s17 Ma , in chondrites, with an initial1r2

129 127 Ž . y4isotopic ratio of iodine of Ir I t s1=10inŽHohenberg et al., 1967a,b; Lewis and Anders, 1975;Crabb et al., 1982; Swindle and Podosek, 1988;

.Podosek and Cassen, 1994 . Pb–Pb model age ofphosphate inclusions in some of these chondrites is

Ž .close to 4.55 Ga Allegre et al., 1995 therefore`t s0 corresponds to the age T s4.55 Ga.in in

We assume that the terrestrial feeding zone,termed as a reservoir of proto-terrestrial materialŽ .subscript pm was formed at t , and that the totalin

initial mass M and the metalrbulk ratio were thepmŽsame as those of the present-day Earth see Tables 1

.and 2 . This reservoir contained fixed initial abun-dances of U, Th, K, and undetermined abundances ofHe, Ne, Ar and N which need to be constrained bymodelling. The initial isotopic compositions of raregases are assumed to be solar by analogy with

Ž .mantle Ne Honda et al., 1993 . The case of N is lessŽ .straightforward Section 2 and we assume an initial

15 Žd N of y30‰ by analogy with E-chondrites Javoy.and Pineau, 1983 .

( )3.2.2. Accretion and core segregation t , tin b eŽHomogeneous Safronov-type accretion Vityazev

.et al., 1990; Wetherill, 1990 is described as a mass


Table 2Parameters derived from modelling

Ž .Parameters, dimensions, and time scales Ga Value Notes

Ž .Proto-terrestrial material t s0in36 18Initial abundance of Ar, 10 mol 2.0 122 17Initial abundance of Ne, 10 mol 9.414 23Initial abundance of N, 10 mol 4.9 2

Ž .Accretion 0, 0.060Ž .Retention coefficient for rare gases L bulk 0.04 3p m ,u m

Retention coefficient for N 1 4i iy1 Ž .Dissipation parameters: L , Ga , t , tah b e a h

36 40 Ž .Ar and Ar 0.06, 0.19 166 520 Ž .Ne, 0.06, 0.225 25121 Ž .Ne, 0.06, 0.225 23622 Ž .Ne, 0.06, 0.225 22614 Ž .N 0.06, 0.230 29415 Ž .N 0.06, 0.230 291

Upper mantle degassing and fractionationFraction of liquid silicates, F Time dependent 6u m ,o c

Retention coef. for rare gases and N, L Time dependent 7u m ,o cN Ž .Nitrogen recycling L 0.06, 4.55 0.0410 8a h ,u mAr Ž .Argon recycling L 0.06, 4.55 0.0003 9a h ,u mi

) Ž .Apparent solidrmelt partition coef. D 0.06, 0.15 0.2 10u mŽ .Continental crust growth and degassing 0.15, 4.55

Apparent fractionation coefficient, K 80 11u m ,c ci y1Crustal degassing L , Ga 0.9 12c c ,a h

Ž . Ž . Ž1, 2 The maximum amount is derived from the present-day terrestrial inventory Table 3 and the solar abundances Anders and Grevesse,. 36 Ž .1989 : ArrSis0.084 is the solar ratio of the species, Sis15.1% is the Si abundance in the bulk Earth Morgan and Anders, 1980 ; these

36 24 Ž .two values give a maximal Ar s2.7P10 mol which is approximately 10,000 times the present-day atmospheric abundance Table 3 .p m

Solar 22 Ner 36Ars2.7, hence 22 Ne -7.5P1024 mol. Similarly solar 14 NrSis3.12 and 14 N -1P1026 mol. In this model the initialp m p mŽ . Ž . Ž .abundances are controlled by: a the present-day abundances in the lower mantle estimated from steady-state models Table 3 ; b the rate

Ž . 36of rare gas dissipation which allows atmospheric compositions Section 4.1.1 . The calculated initial Ar is ;400 times higher than theŽ .present-day terrestrial inventory Table 3 .

Ž . Ž .2 This value is within the range typical of E-chondrites Section 2 .Ž . Ž . Ž .3 Generally 0-L bulk F1; the value is inferred for Xe from Pu–U–I–Xe systematics Azbel and Tolstikhin, 1993 and used herep m ,u m

for all rare gases.Ž .4 See Section 4.2.1 for discussion.Ž .5 See Section 3.2.5.Ž . Ž . Ž . Ž . w6 This parameter is decreasing through time from values typical for komatiite melts 0.5 to tholeiitic basalt melts 0.1 F t s timeu m ,o c

x w xw xw xw xGa, value s 0,0.5 0.16,0.5 0.6,0.2 4.55,0.1 , and intermediate values are found by linear interpolation.Ž . Ž . Ž .7 The retention coefficients for each rare gas and nitrogen are calculated using Spasennykh and Tolstikhin 1993 ’s approach: a Eq. 9,

Ž . Xe w x w xw xw xw xSection 3.2.5; b retention coefficients for Xe, L s time,value s 0.0,0.9 0.16,0.9 0.2,0.01 4.55,0.01 .u m ,o cŽ . Ž . Ž . w x w xw xw xw xc Solubility coefficients from Table 1, and d vesicularity coefficient y t s time,value s 0,0 0.16,0 0.2,0.001 4.55,0.001 , whereŽ . XŽ . XŽ .y t sy t rRT , and y t is the volume gasrmelt ratio, R is the gas constant and T is the temperature in K.

Ž . N Ž .8 L )0. Recycled N is enriched in 15N by 5 parts per mil relative to surface nitrogen see Section 2 .a h ,u mŽ . Ar 40 36 Ž .9 L )0. The recycling rate of argon is obtained by comparing the highest Arr Ar ratio observed in the upper mantle 40,000a h ,u m

Ž40 36 .with that computed without recycling Arr Ar s110,000 .u mŽ . i10 For incompatible elements D -1; the apparent value shown is discussed under Section 4.1.2.u mŽ .11 K )1. The value has been adjusted to get the present-day abundances of U and K in the upper mantle and crustal reservoirs.u m ,c cŽ . i 40

)12 L )0. The value corresponds to the mean K–Ar age of the continents at 1.5 Ga reflecting loss of radiogenic Ar from crustalc c ,a hŽ . 40

)rocks Hamono and Ozima, 1978 . This is not an important parameter because the abundance of Ar is low in the continental crust incomparison to the atmospheric inventory.


Ž .flux of proto-terrestrial material f bulk frompm ,u m

the terrestrial feeding zone pm into the Earth’smantle um, during an interval of time between tin

Ž .and t , and with and f bulk s0 if tG tb e pm ,u m b eŽduring accretion only one mantle reservoir is con-sidered, which for simplicity is termed as the upper

.mantle um, see Appendix A . The related flux oftrace elements i

w directed to the mantle is:pm ,umii iw s C f bulk L 1Ž . Ž .pm ,umpm ,um pm pm ,um

i Ž . i iwhere L bulk ' C r C is the retentionpm ,um u m pm

coefficient, iL '1 for the parent elements, andpm ,umiL F1 for volatile species, taking into accountpm ,um

impact degassing. The complementary part 1yi Ž Ž .L is released into the atmosphere Eq. A2.13 ,pm ,um

.Appendix BiC f bulk 1yiL 2Ž . Ž .pm ,u m Ž .pm pm ,um

The segregation of the core is assumed to haveŽoccurred during accretion e.g., Jones and Drake,

.1986 and its modelling is adapted from Azbel et al.Ž . Ž .1993 . Appendix B presents the relevant Eqs. A2.3 ,Ž . Ž . 182 182A2.5 and A2.6 . Hf– W isotopic systematicsfurther constrain the timing of metal segregation

Ž .Harper and Jacobsen, 1995; Lee and Halliday, 1995 .Ž .Recently, Kramers 1997 developed a model of core

formation taking into account 182 Hf– 182 W isotopicsystematics and suggested 60 Ma as a reasonabletime scale for the major stage of core segregation aswell as for the Earth accretion; this constraint, t sb e

60 Ma, is used hereafter.

3.2.3. Isolation of lower mantle and lower–upper( )mantle interactions t , tb e f i n

During the major stage of core formation, therelease of energy in the deep Earth was orders ofmagnitude higher than the total present-day heatflow, and a vigorous whole-mantle convection drivenby both gravity contrasts and heat took placeŽ .Vityazev, 1980; Davis, 1990 . Therefore an isola-tion of the lower mantle could have been effectiveonly at the very end of accretion, at t f60 Ma, orb e

later on. Modelling Pu–U–I–Xe isotopic variationssuggests that this isolation should have taken placenot later than the time when the atmosphere became

Žretentive to Xe, t s150 Ma Tolstikhin anda h.O’Nions, 1998 . From these considerations, we as-

Ž .Fig. 4. Mass fluxes through time. The shape of the accreting flux f is adapted from Vityazev et al. 1990 , the flux to the core fp m ,u m u m ,c rŽ . Ž .is from Azbel et al. 1993 , and the accretionrcore segregation time scale is from Kramers 1997 . The post-accretion degassing flux

Ž .f and the recycling flux f not labelled are from the present simulation with the present-day value of this flux being fromu m ,o c o c ,u mŽ . Ž . ŽReymer and Schubert 1984 . Fluxes between mantle reservoirs f not labelled and f f sf since end ofu m ,l m l m ,u m l m ,u m u m ,l m

. Ž .accretion, tf60 Ma are from this work. The crustal growth flux f is from Kramers and Tolstikhin 1997 .u m ,c c


sume that the lower mantle was isolated at t;60Ma. The isolation process is described as a mass fluxŽ .f ss from the upper mantle and the relatedum ,lm

flux of species is:ii i )w s C f ss D r FŽ . um ,lmum ,lm um um u m ,o c

i )q D 1yF 3Ž . Ž .um um ,o c

where the melt fraction F is decreasing withum ,o cŽ . i

)time Table 2 , and D is the effective partitionum

coefficient for incompatible trace elements. This co-efficient allows re-distribution of K, U and Th be-tween the two mantle reservoir in order to obtain thepresent-day 40Ar ) inventory in the upper mantle–

Žcrust–atmosphere reservoirs O’Nions and Tol-.stikhin, 1996 .

The lower mantle–upper mantle flux started tooperate during and after isolation of the lower man-

Ž . Ž . Žtle. The equality f ss sf bulk validum ,lm lm ,um.since ts65 Ma conserves the masses of the two

Ž .mantle reservoirs. f bulk is treated as a fluxlm ,umŽ Ž .of unfractionated material see Eq. A2.8 , Appendix

.B . To approximate the decrease of heat productionin the Earth, these fluxes are expressed as functions

Ž .smoothly decreasing with time see Fig. 4 .

( )3.2.4. Degassing of the upper mantle t ,tin f i n

Degassing of the upper mantle is described as aprocess related to a mass flux of liquid silicatesŽ .f ls from the upper mantle um into a smallu m ,o c

Ž .auxiliary short-lived sub surface reservoir, analogueŽ .to the present-day oceanic crust oc Fig. 3 . The

present-day expression of this process is degassing atMid-Ocean Ridges. The mass of this reservoir isassumed to be constant throughout Earth’s history,so that arriving and departing mass fluxes are equal,Ž . Ž .f ls sf bulk . These mass fluxes oper-um ,o c o c ,um

ate since t) t until present. The correspondingb e

fluxes of species are:ii i iw s C f ls K L 4Ž . Ž .u m ,o cum ,o c um um ,o c um ,o c

into the oceanic crust and:ii iC f ls K 1y L 5Ž . Ž .Ž .um ,o cum um ,o c um ,o c

Ž Ž .into the atmosphere see Eq. A2.13 in Appendix. Ž . Ž . i wB . In Eqs. 4 and 5 K s1r F qu m ,o c u m ,o c

i Ž .x iD 1yF , D is the solidrmelt parti-u m ,o c u m ,o c u m ,o ci .tion coefficient, and L is the retention coeffi-u m ,o c

cient, iL '1 for parent radioactive species andu m ,o cŽ .-1 for volatiles Table 2 .

The early degassing of the upper mantle is treatedas a process controlled by solubility iS of volatilespecies in silicate melts, which allows sequentialoutgassing of volatiles. Such degassing and simulta-neous gas loss from the atmosphere accompanied by

Žspecific isotopic and elemental fractionation Section.3.2.5 can explain the present-day characteristics of

Žatmospheric rare gases see Tolstikhin and O’Nions,.1994, for a more detailed discussion . We acknowl-

edge that the physico-chemical environment respon-sible for the solubility-controlled degassing is poorlyunderstood. In this contribution the fractional de-

Žgassing is described as Spasennykh and Tolstikhin,.1993 :

iL sXeL�w Xe Sqy Ž t .xrw i Sqy Ž t .x4 6Ž .um ,o c um ,o c

where the retention of each gas iL is scaled toum ,o cŽ .the retention of Xe and y t is a function of vesicu-

Ž .larity of melts see note 7 to Table 2 .The geological degassing of the upper mantleŽ .f ls is additionally investigated using an expo-u m ,o c

nential approximation:

f ls,t ,t sf ls,tŽ . Ž .a h fin finu m ,o c u m ,o c

qf ls,t exp yXt 7Ž . Ž . Ž .ah um ,o c

Ž . 16 y1where the present-day f ls,t s6P10 g afin um ,o cŽ .is considered as known Reymer and Schubert, 1984 ,

Ž .f ls,t is to be estimated by modelling of theah um ,o c

previous degassing–dissipation interval, t variesŽ .within t ,t , and X is constrained by the pre-a h fin

Ž . Ž .sent-day ratio Xe Pu rXe U in the upper mantle.The upper mantle was treated in this particular caseas a reservoir which was undergoing degassing onlyŽ iw sw s0, and L s0 for all volatileum ,lm lm ,um a h ,u m

.species .

( )3.2.5. Atmospheric escape t , tb e a h

The present-day elemental and isotopic abun-dances of non-radiogenic atmospheric gases are as-sumed to be the result of two simultaneous processes

Ž .operating after accretion t and before the timeb eŽ i .t of atmosphere closure for a given volatilea h

Ž .element: 1 fractional degassing of silicate meltsŽ . Ž . ŽSection 3.2.4 and 2 fractional elements and iso-


Table 3Comparison between model results and known or estimated values

Ž .Parameters and dimensions Known range value Rating Computedradjusted value Notes

Lower mantle lm238 U , ppb 13–22 model 13.5 1l m3 y13 y1 Ž .He P10 mol g 0.7–2.8 model 3–10 2l m4 3Her He F20,000 meas 5,500 3l m36 3Arr He F1.2 model 0.33 4l m40 36Arr Ar 300–10,000 model-meas 5,300 5l m22 3 22 3Ner He s Ner He 0.22–0.45 model 0.18 6l m u m20 22Ner Ne 13.7 model 13.7 7l m21 22Ner Ne 0.035–0.038 model 0.034 8l m14 21N 10 mol – – 1.8 9l m

15d N‰ – – y30 10Upper mantle um238 U ppb 5–8 model 7.5 11u m3 y15 y1 Ž .He P10 mol g 0.5–2.4 model 4.0 12u m4 3Her He , P1000 89"8 meas 90 13u m4 40 )Her Ar 3.3 model 2.5 14u m40 36Arr Ar f40,000 meas 39,000 15u m21 22Ner Ne 0.06"0.01 meas 0.06 16u m20 22Ner Ne 13.5 meas 13.7 17u m14 40Nr Ar 160"40 meas 160 18u m

15d N , ‰ y5"1 meas y5 19u m

Continental crust cc238 U , ppm 0.7–1.8 model 1.6 20c c40

) 17 Ž .Ar , 1.2P10 mol 3.9–10 model 5.4 21c c

Atmosphere ah36 15Ar , P10 mol 5.55 meas 5.55 22a h22 Ne , 1014 mol 2.96 meas 2.96a h14 20N , 10 mol 2.74 meas 2.74 23a h

Ž 27 .The present-day masses of the main reservoirs in 10 g are: core 1.9, lower mantle 3, upper mantle 1, continental crust 0.023.Ž .1 ThrUs3.9, KrUs12500; this abundance corresponds to a 0.7 depletion of incompatible parent elements, U, Th, and K, by a factor of

40) Ž .f0.7 which satisfies the Ar inventory of upper mantle–crust–atmosphere system O’Nions and Tolstikhin, 1996 .

Ž . Ž y1 3 y1. Ž . Ž .2 Abundances in 10 mol g computed previously are 0.7 Allegre et al., 1986r87 , 0.9 O’Nions and Tolstikhin, 1994, 1996 , 1.1`Ž . Ž .Porcelli and Wasserburg, 1995b and 2.8 Azbel and Tolstikhin, 1990 .Ž . Ž3 Observed plume-related rocks and fluids appear to be formed after severe mixing of uprising plumes with upper mantle material Kurz et

. 4 3al., 1983, 1987; Farley et al., 1992; Poreda et al., 1993; Marty and Tolstikhin, 1998 . Therefore the lowest observed Her He ratios inŽ .plumes Kurz et al., 1983; Staudacher et al., 1986; Honda et al., 1993 should be considered as the upper limit for this ratio in plume source,

i.e., in the lower mantle.Ž . Ž . Ž .4 Previous steady-state models give: 0.7–1.2 O’Nions and Tolstikhin, 1994, 1996 and F0.9 Porcelli and Wasserburg, 1995b .Ž . Ž . Ž . Ž .5 From: a analysis of rocks and minerals related to hot-spot magmatism, G5,000 Poreda and Farley, 1992 ; b He–Ar mantle

Ž . Ž . Ž .relationship, 6,000 Ozima and Zahnle, 1993 ; c steady-state models of layered mantle, 5000–5800 O’Nions and Tolstikhin, 1994, 1996 ,Ž .and G9400 Porcelli and Wasserburg, 1995b .

Ž . Ž .6 From steady-state models, 0.22–0.45 O’Nions and Tolstikhin, 1994; Porcelli and Wasserburg, 1995b . This value is also valid for theupper mantle.Ž . Ž .7 Same as initial Table 1 .Ž . Ž .8 From steady-state models of layered mantle, 0.035–0.038 O’Nions and Tolstikhin, 1994; Porcelli and Wasserburg, 1995b .Ž .9 This is the first estimate for the abundance of nitrogen in the lower mantle.Ž .10 Same as initial, Section 2.Ž . Ž . Ž . Ž .11 From Jochum et al. 1983 , Galer et al. 1989 , Kramers and Tolstikhin 1997 .Ž . Ž y1 5 y1. Ž . Ž . Ž12 Previous models give in 10 mol g : 1.2 Allegre et al., 1986r87 ; 1.5 Kellogg and Wasserburg, 1990 , 2.4 Azbel and`

. Ž . Ž .Tolstikhin, 1990 ; 1.0 O’Nions and Tolstikhin, 1994 ; 0.51 Porcelli and Wasserburg, 1995b .Ž . w3 x Ž . 4 3 4 21 ) 8 Ž13 The calculated values of He above , Her He and the production ratio Her Ne s1.8P10 Mamyrin and Tolstikhin,u m u m

. w21 ) x y1 7 y11984 give Ne s1.9P10 mol g .u m


.topes escape of volatiles. In this contribution, therate of escape of each isotope i is controlled by the

i Ždissipation parameter L see the last term in Eq.a hŽ . .A2.13 , Appendix B which value is adjusted tomatch the observed atmospheric abundance. Thisparameter is assumed to operate after the major

Ž .phase of accretion t s60 Ma until the time ofb eŽ i .atmosphere closure t for a given isotope.a h

The time of atmosphere closure can be only in-ferred for Xe from modelling of Pu–U–I–Xe sys-

Xe Žtematics, t s 150 " 50 Ma Tolstikhin anda h.O’Nions, 1998 . In the absence of short-life radioac-

tivity, it is not possible to constrain the respectivetime scales for the lighter gases and we simplyassume that the dissipation process for all speciesŽ .except helium had ceased at 230 Ma, which corre-sponds to the time scale of decay of a high UV flux

Ž .from young stars Pepin, 1992 .

( )3.3. Geological eÕolution t , ta h f i n

Modelling of lower mantle–upper mantle interac-tions and post-atmosphere closure degassing of theupper mantle has already been discussed in Sections3.2.3 and 3.2.4. Another continuous process, thegrowth of the continental crust, is described as amass flux of liquid silicates from the upper mantle

Ž .into the crust d M rd tsf ls . According toc c um ,c c

U–Th–Pb modelling, a linear growth of the conti-nents since atmosphere closure for Xe until now,

Ž0.15- t-4.55 Ga, is a good approximation see

Kramers and Tolstikhin, 1997, for a detailed discus-. Ž .sion . Therefore f ls sConstant, which is de-u m ,c c

Žtermined by the present-day mass of the crust see.Fig. 4 . The crustal inventory of species is expressed

as:

di N rd tsiC Pf ls PiKŽ . u m ,c cc c um u m ,c c

yiL Pi N qS

il i N 8Ž .c c ,a h c c c c

where iK and iL are the fractionation andum ,c c c c ,a h

degassing parameters, respectively. These two appar-ent parameters are adjusted to obtain the acceptablepresent-day U, Th and K in the upper mantle and themean K–Ar age of the continents. The last term in

Ž .Eq. 8 relates to decay of radioactive species.Ž .Volatile recycling from sub surface reservoirs

into the mantle is adopted from Azbel and TolstikhinŽ .1990, 1993 . This process is controlled by the recy-

i Ž Ž . Ž .cling parameter L Eqs. A2.4 and A2.13 ,a h ,um.Appendix B constrained by observed isotopic com-

positions of volatile species in the upper mantle.

3.4. Summary of equations, input and obserÕationalparameters

The parameters used by the model are of twotypes. Some of these are estimated from measure-ments or other models which are widely acceptedand are listed in Table 1. Others have been adjustedusing the model in order to match observational data

Žand are listed in Table 2. A set of parameters Tables

Notes continued to Table 3:Ž . Ž .14 The calculated value, 2.5, is slightly lower than a steady-state estimate of 3.3 using KrUs12,500 Jochum et al., 1983 , ThrUs2.6Ž . Ž .O’Nions and McKenzie, 1993 and the mean residence time of Ar in the upper mantle of 1 Ga Galer and O’Nions, 1985 . This is because

238 40 w3 x 4 3 4 40 ) w40 ) x y1 0the Ur K ratio was lower in the past. He , Her He and Her Ar shown in col. 4 give Ar s1.4P10 molu m u m u m u m

gy1.Ž . 40 36 Ž . w40 ) x15 Arr Ar s40,000 has been derived from Ne–Ar isotopic relationships Allegre and Moreira, 1996 . The product of Arù m u mŽ . w36 x y1 5 y1the note above and this ratio gives Ar s3.7P10 mol g .u mŽ . Ž . 21

) Ž .16 0.06 is typical of the least contaminated MORB glass samples; see Porcelli and Wasserburg 1995b . Ne note 13 and the initialu m21 22 Ž . 22 y16 y1Ner Nes0.0327 Table 1 give Ne s7P10 mol g .u mŽ . Ž .17 The highest observed ratio which is quite similar to the initial ratio Table 1 .Ž . Ž .18 From N–Ar correlation in MORB Marty, 1995 .Ž . Ž . Ž .19 From analyses of mantle materials: diamonds e.g., Boyd and Pillinger, 1994 , and MORB glasses Marty, 1995 .Ž . Ž . Ž . Ž . Ž .20 From: Wedepohl 1995 – 1.7 ppb; Yaroshevsky 1985 – 1.8; Lambert and Heier 1968 – 0.7; Weaver and Tarney 1984 – 1.3;Ž Ž .Taylor and McLennan 1981, 1985 – 1.25 and 0.91, respectively.Ž .21 Corresponds to the mean KrAr crustal age at 1.5 Ga.Ž . Ž .22 Ozima and Podosek 1983 and references therein.Ž . Ž .23 Pepin 1991 .


.1 and 2 which allows to reconcile results of calcula-Ž .tions with observational data Table 3 is termed as a

reference solution.

4. Results of modelling

4.1. Light rare gases

( )4.1.1. Initial abundances of rare gases t s0in

The initial abundances of the light rare gases areconstrained from two different considerations.Straightforward mass balance requires a loss of ra-diogenic 129Xe) from the accreting planetesimals–Earth–Atmosphere system by a factor of ;100,which is a minimum estimate for the loss of primor-

130 Ždial Xe and other primordial gases Wetherill,1975; Azbel and Tolstikhin, 1993; Tolstikhin and

.O’Nions, 1998 . To model considerable isotope frac-tionation of Ne during atmospheric escape, the

Xe Žamount of Ne in the upper mantle at ts t whena h.Ne had quantitatively been lost together with Xe

should be by a factor of G5 higher than that in theŽ .present-day atmosphere Pepin, 1991 . These two

estimates give a minimum abundance ratio22 Ž . 22 Ž .Ne t r Ne t of 500. The model-in pm fin ( l mH a h )

derived initial 22 Ne and 36Ar are ;2000 andpm pm

;400 times higher than the present-day inventory,Ž .respectively Table 2 and 3 . Given the uncertainties

on early degassing–dissipation processes, these esti-mates are valid probably within a factor of 10. Theseinitial abundances are high but still comparable with

Ž .those in some extraterrestrial reservoirs Section 5.1 .

( )4.1.2. Early mantle degassing 0,230 MaImpact degassing of proto-terrestrial materials

Ž .during accretion 0, 60 Ma is controlled in thismodel by the retention coefficient L , whichpm ,um

Ž .low value f0.04 has been inferred from Pu–I–XeŽ .systematics Azbel and Tolstikhin, 1993 and applied

Ž .Fig. 5. Evolution of the upper mantle rare gas abundances in the upper mantle relative to those in the present-day atmosphere during theearly fractional degassing–dissipation–fractionation episode. Vertical dotted lines show times of atmosphere closure for each gas. When Xehad been fractionated and set in the atmosphere, Xe t s150 Ma, its abundance in the upper mantle was ;0.1 of the present-daya h

atmospheric abundance. Therefore further post-atmosphere-closure degassing did not change substantially the abundance and fractionatedsignature of Xe . At that time, the lighter gases were expected to be lost from the atmosphere but their upper mantle abundances were stilla h

high and further degassing would have transferred unfractionated species into the atmosphere. This allows to process lighter gases through adissipation–fractionation event at later times and thus can explain contrasted fractionation for different gases.


for all rare gas species. Correspondingly, f96% ofvolatile elements were released into the early atmo-sphere. Such low retention is consistent with the lowrare gas content of the mantle compared to that ofextraterrestrial material.

During the following time interval, from the endŽ .of accretion t s60 Ma until atmospheric reten-b eŽ .tion of Xe c t s150 Ma , the lower mantle wasa h

effectively isolated and slightly depleted with U, Thand K by 30%, relative to the bulk mantle abun-dances. The complementary upper mantle was en-riched with these parent elements by a factor of f2,which allows to obtain the present-day 40Ar ) inven-tory in the upper mantle–crust–atmosphere reser-

Ž .voirs O’Nions and Tolstikhin, 1996 , The corre-i

) Ž .sponding partition coefficient D s0.2 Table 2um

allows such redistribution of species.Ž .During this interval 60, 150 Ma , the lower

mantle was also moderately outgassed. The massflux from the upper mantle to the lower mantleŽ .f ss contained little volatiles, and this fluxum ,lm

simply diluted lower mantle material. Indeed, theabundances of volatiles in the upper mantle weredecreasing with time as a function of their solubili-ties, with the least soluble gases being the most

Ž Ž ..depleted ones Section 3.2.4, Eq. 6 . The requireddegree of solubility-controlled degassing and rare

Ž .gas fractionation in the upper mantle Fig. 5 and theabundances of all gases in the atmosphere can beaccommodated using values of parameters presented

Ž . Žin Table 1 solubilities and Table 2 upper mantle.degassing and fractionation . A high retention of rare

Ž .gases and a low vesicularity taken as zero ofdegassing melts both point to a very low residence

Ž . Ž .time of the melts in sub surface domain s wheredegassing could have occurred. Such a process couldbe a consequence of vigorous convection in theupper mantle if the time interval available for aportion of melt to pass through the low-pressure

Ž .zone nearby the Earth surface and undergo de-gassing would have been less than the mean nucle-ation rate of vesicles.

4.1.3. Gas loss and fractionation in the early atmo-( )sphere 60, 230 Ma

During the time scale 60–230 Ma, the dissipationparameter i

La , which controls the rate of gas lossa hŽin this model Section 3.2.5, see also last term in Eq.

Ž . .A2.13 , Appendix B , was computed iteratively tosatisfy the present-day atmospheric abundance of

Ž .each non-radiogenic isotope Table 3 . The calcu-lated values increase with decreasing atomic weightso that the lighter species have shorter residence timein the dissipating atmosphere. Such trend is expectedfor the loss of trace volatile species from a gravita-

Ž .tional field of a planet or planetesimal .i i Ž .The values of t and La Table 2 are highlya h a h

model-dependent. They only illustrate that the trans-port balance model allows a dissipation–fractiona-tion process to operate in an early atmosphere inde-pendently on the physical nature of this process, e.g.,

Žhydrogen hydrodynamic escape Pepin, 1991; Zahnle.et al., 1988, 1990 , or impact-related processes

Ž .Vityazev and Pechernikova, 1996 .

Fig. 6. Post-atmosphere-closure rate of upper mantle degassing.Ž .The mass flux f ls controlling degassing of the upperu m ,o c

mantle is approximated by an exponential function shown in thetop left inset. Left and right vertical axes are the calculatedpresent-day ratios in the upper mantle as a function of the flux

136 Ž . 136 Ž .decay parameter X. The Xe Pu r Xe Pu, U ratio is usedu m

as a index of degassing. This ratio should be 28 and 7 in areservoir with initial PurU as shown in Table 1 closed sincet s0 and Xe t s150 Ma, respectively, whereas the observedin a h

Žratio was found to be less than 0.2 Phinney et al., 1978; Caffee et.al., 1988 . It is interesting to note that a very high degree of upper

mantle degassing implies a calculated 40Arr 36Ar ratio in theupper mantle as high as ;106 in the absence of Ar recycling.


( )4.1.4. Geological eÕolution 230, 4560 MaŽ .O’Nions and Tolstikhin 1996 have investigated

the lower mantle–upper mantle and backwards massfluxes which were constant through almost all of thehistory of the Earth, from 4.35 Ga ago to present,and derived a low mean value for these fluxes,F2P1016 g ay1. Fig. 4 illustrates a more realisticcase with decreasing fluxes but the main conclusionis the same: during most of the Earth’s history, theinferred fluxes appear to be much lower than thepresent-day slab flux, ;1018 g ay1. A small massflux from the lower into upper mantle transferrednegligible amounts of the parent incompatible ele-ments and rare gases. However, because the upper

mantle was extremely degassed, the rare gas transferwas enough to sustain the upper mantle abundancesof these elements at a steady-state.

The rate of upper mantle degassing is controlledŽ .in this model by flux f ls . Beside the refer-u m ,o c

ence trend shown in Fig. 4, this flux was additionallyinvestigated using the upper mantle ratio of136 Ž . 136 Ž . ŽXe Pu r Xe U F0.25 Phinney et al., 1978;

.Caffee et al., 1988 , which depends only on thereasonably well known initial 244 Pur 238Us0.0068Ž .Hudson et al., 1989 and the rate of Xe release fromthe upper mantle. Under assumptions presented in

ŽSection 3.2.4 no rare gas transfer into the upper.mantle this approach gives the minimal rate of

Ž . Ž .Fig. 7. Evolutionary trends for U–He a, b and U–Ne c, d isotopic systematics in the main terrestrial reservoirs. Open square, diamondand circle are initial abundances of He and Ne in the lower and upper mantle and atmospheric reservoirs, respectively; solid square,diamond and crossed circle show the present-day abundances. Because the upper mantle might have been severely degassed just after the

Ž .end of accretion, the abundances of primordial rare gases could have been lower than the present-day abundances, e.g., 4 Ga ago a, c . Atthat time, the production rate of radiogenic species was higher than at present, and the relative contribution of radiogenic gases in the uppermantle could have been higher than now, and the 4 Her 3He and 21 Ner 22 Ne ratios could have decreased through most part of the Earth’s

Ž . 21 22history. The inset in d illustrates major decreasing of Ner Ne during a dissipation–fractionation process in the early atmosphere,followed by a minor increasing of this ratio as a result of 21 Ne) degassing. In this model, the process of lower mantle individualisation istreated as a flux of partially degassed solid silicates; this explains the initial decrease 3He and 22 Ne abundances in the lower mantle at

Ž .t f60 Ma when it has been effectively separated a, c .l m


Ž . Ž .degassing Fig. 6 . The mass flux f ls,t s5a h u m ,o c

P1018 g ay1 inferred for ts t s230 Ma from thea h

reference solution is decreasing by a factor of 2during ts ln2rX;0.3 Ga for X taken from Fig. 6.The total calculated rate of post-atmosphere-closure

36 Ž . 36 Ž . y4degassing Ar t r Ar t f10 correspondsfin a h40 36 6 7 Ž .to Arr Ar f10 to 10 right axis , greatlyum

exceeding the bulk upper mantle ratio of 40,000Žinferred from Ar–Ne MORB correlation Allegre`

.and Moreira, 1996 and even the highest observedŽ .one, 60,000 Burnard and Turner, 1996 . This differ-

ence constraints the Ar transfer from the atmospheret to the upper mantle at L s0.0003 Ga y1.i a h ,u m

Fig. 7 illustrates 4 Her 3He and 21 Ner 22 Ne evo-lution trends obtained for the reference scenario with

Ža rather intense degassing flux after accretion Fig..4 . These trends show that a relative contribution of

radiogenic isotopes in the upper mantle between 4.35Ma and 3.5 Ga ago could be as high as 21 Ner 22 Ne

4 3 5 Ž .f0.09 and Her Hef2=10 Fig. 7 , exceedingthe present-day ratios.

The 4 Her 3He and 21 Ner 22 Ne ratios de-um um

pend on the lower mantle–upper mantle flux ofvolatile species, the rate of production of radiogenicspecies in the mantle reservoirs, and the mean resi-dence time of incompatible elements in the uppermantle. Fig. 8 illustrates that the input parameters

Ž .mentioned above Tables 1 and 2, Fig. 4 allow areasonable agreement between the calculated pre-sent-day upper mantle ratios and the observed ratiosshown as a shadowed ellipsoid. The absolute abun-dances of 3He and 22 Ne are quite similar to those

Žinferred from previous models Table 3 and refer-.ences therein .

4.2. Nitrogen

4.2.1. Initial abundanceThe initial ratio of 14 Nr 36Ar in proto-ter-pm

restrial material is constrained from two parameters.First, the argon–nitrogen isotopic correlation inMORB allows to estimate 14 Nr 36Ar f6P106,lm

Fig. 8. Isotopic ratios of 4 Her 3He and 21 Ner 22 Ne versus concentrations of stable species in mantle reservoirs: a link between evolutionaryand steady-state models. Solid and dashed lines show evolutionary trends for the upper and lower mantle reservoirs, respectively. Dottedlines show transfer of He and Ne from the lower into the upper mantle; dashed-dotted lines show addition of radiogenic species in the uppermantle during t s1 Ga. The shadowed ellipsoid corresponds to the observational mixing MORB–PLUME trend after correction foru m

atmospheric Ne. The open ellipsoid illustrates a possible position of this trend 3 Ga ago and thus a difference between steady state andevolutionary models. Other symbols are as in Fig. 7.


which may be considered as the post-accretion un-fractionated ratio. Second, N was retained in thegrowing Earth preferentially to Ar because of itshigh solubility in silicate melts under reduced condi-

Ž .tions Mulfinger, 1966; Humbert et al., 1997 asexpected during accretion and core formationŽ . 14 36Ringwood, 1984 . Very high Nr Ar ratios inchondrites and iron meteorites, 104 to 106 times the

Ž .solar value e.g., Pepin, 1991 , reflect preferentialretention of N. The retention of N is expressed asŽ .L Nit s1, 25 times that of Ar. Then the initialpm ,um

abundance of nitrogen is determined as:

1414 36 36N f Ar Nr Ar L Ar rL NitŽ . Ž .Ž . pm ,umpm pm lm

f4.9P1023 mol

The value obtained above is close to the upper limitof E-chondrites abundances.

4.2.2. EÕolution of nitrogen in mantle reserÕoirsDuring accretion, the nitrogen content of the up-

Ž .per mantle was increasing Fig. 9 , reflecting growthŽof the Earth and the high retention of N Section

.4.2.1 . After accretion and lower mantle isolation, avigorous degassing decreased N abundance in the

Ž .upper mantle 60–230 Ma . The occurrence of suchdegassing implies significant increase of the oxygenfugacity in order to allow nitrogen degassing. In-deed, recent experiments shows that the N solubilityin basaltic melt decreases drastically with increasingf and stabilises for a f range between IW toO O2 2

Ž .QFM buffers Humbert et al., 1997 . Such f in-O 2

crease might have been related to the progressivedepletion of iron in the mantle and therefore related

Ž .to segregation of the core. Later on t)230 Ma , theN abundance in the upper mantle was maintained by

Ž . Ž .three processes: 1 lower mantle flux; 2 surfaceŽ .nitrogen recycling; 3 upper mantle degassing. Con-

trary to the upper mantle reservoir, the lower mantleexperienced only a small decrease in its N contentduring moderate early degassing of this reservoirŽ .Fig. 9 .

4.2.3. EÕolution of nitrogen in the atmosphereThe abundance and isotopic composition of nitro-

Ž .gen in the early atmosphere 4.5–4.3 Ga ago weregoverned by mantle degassing and atmospheric dissi-

Ž .pation Fig. 10 . From comparison with rare gases, it

Fig. 9. Nitrogen evolutionary trends for two mantle reservoirs.The computed initial abundance of nitrogen is within the rangeobserved in E-chondrites. The evolutionary trend for the upper

Ž .mantle corresponds to the reference version Fig. 4 ; a sharpminimum of 14 N and an increase of d 15 N during 0.2 - t-1u m u m

Ga reflects an early intense degassing.

follows that N could have been dissipating at a fasterrate and during a longer time interval than Ne, andits isotope composition in the post-closure atmo-

Ž 15 .sphere was slightly heavier d Nsq2.5‰ thanŽ .that at present 0‰ .

It must be noted here that this scenario mayevolve in the future, as the addition of nitrogen fromlate impacting bodies at the surface of the Earthmight not have been negligible. The cratering recordof the Moon shows the reality of such process, andall meteorites show Nrrare gas ratios higher by oneto three orders of magnitude than the atmosphericratio. Therefore, it appears feasible to add nitrogen tothe surface inventory from late impacting bodiesŽ .e.g., comets without changing significantly the rare

Ž .gas isotope composition e.g., Xe of the atmosphere.This possibility, which will be developed in anothercontribution, does not change significantly the pre-


Fig. 10. Nitrogen evolutionary trends for atmospheric reservoir.Ž .Post-accretion 60–230 Ma evolution of N in the atmosphere

Ž . Ž .reflects three processes: 1 mantle degassing, 2 loss of N fromŽ . Ž .the atmosphere upper panel , and 3 N fractionation in the

Ž .atmosphere related to this loss lower panel . After N was set inŽ .the atmosphere at f230 Ma or f4.32 Ga ago , degassing and

recycling fluxes slightly varied N abundance in this reservoir and15 Ž .decreased d N by f2‰ insets .a h

sent modelling in that it still requires two reservoirs,the surface and the mantle, having contrasted Nisotopic composition before or around 4 Ga.

The atmospheric 15Nr 14 N ratio decreased withtime towards its present-day value as a result ofmantle degassing, with nitrogen depleted in 15N andrecycling of surface N enriched in this isotope.

4.2.4. Nitrogen recyclingThis evolutionary model predicts small changes of

nitrogen and rare gas abundances in the mantle andŽ .atmospheric reservoirs since ;4 Ga ago Fig. 11 .

Because the residence time of these species in theupper mantle appears to be shorter, ;1 Ga, asteady-state assumption can be applied to this reser-

Žvoir. Then, by analogy with rare gases Kellogg andWasserburg, 1990; O’Nions and Tolstikhin, 1994,

.1996; Porcelli and Wasserburg, 1995a,b , nitrogen inthe upper mantle could originate from fluxes oflower mantle materials and crustal rocks.

The nitrogen abundance in a steady-state uppermantle is computed from the mean MORB14 40 ) Ž . 40

)Nr Ar s160 Marty, 1995 and Ar s1.4Pum umy10 y1 Ž .10 mol g Table 3 ; the product of the two

values above gives 14 N s2.2P10y8 mol gy1 withum15 Ž .d N sy5‰ Marty, 1995 .um

Nitrogen from the lower mantle is most probablytransferred without isotopic and elemental fractiona-tion, e.g., by bulk entrainment, having d 15 N slm

y30‰. In contrast, nitrogen recycled from thecrust–atmosphere reservoirs is characterised by

15 Žd N sq5‰ Bebout and Fogel, 1992; Boyd anda h.Pillinger, 1994 . These compositions allow to com-

pute a mixing 14 N r 14 N ratio for the uppera h lm

mantle reservoir at 0.4, which, together with thew14 x w14 x y8 y1N , gives N s1.6P10 mol g orum a h um

Fig. 11. Argon–nitrogen relationship. To reconcile computed and15 Žobserved d N sy5‰, the atmospheric recycled N withu m

15 .d N sq5‰, Fig. 1 should constitute f2r3 of the Na h ,u mŽbudget in the upper mantle and the remaining N f1r3, with

15 .d N sy30‰ is transferred from the lower mantle togetheru m

with primordial rare gases. The two fluxes together with the uppermantle degassing flux allow the observed Ar–N relationships tobe reproduced.


Ž14 . 19N s1.6P10 mol. This amount has beena h u mŽ .accumulated in the upper mantle during t N f1um

Ga, so the recycling flux of surface 14 N is estimatedat 1.6P1010 mol ay1. The corresponding concentra-tion of nitrogen in subducted material would be

y7 y1 Ž .2.7P10 mol g 3.8 ppm . It is interesting tocompare this concentration with those observed insubducted rocks. According to Bebout and FogelŽ .1992 the high-grade metamorphic rocks from the

Ž .subduction zone Section 2 contained f140 ppmof N with the lowest concentration measured in anindividual sample at 30 ppm. This minimum value isstill an order of magnitude higher than the computedconcentration in the subducting slab, which mixingwithin the upper mantle is able to maintain the uppermantle abundance of nitrogen.

5. Discussion

5.1. Initial and lower mantle abundances

Ž .Fig. 12 displays rare gas abundances 1 calcu-lated in proto-terrestrial material and in the present-

Ž .day lower mantle, 2 measured in the Earth’s atmo-Ž .sphere, as well as 3 those in several extra-terrestrial

reservoirs. Implanted solar wind rare gas abundancesand calculated for proto-terrestrial materials show a

Ž . Žremarkable similarity. Pepin 1991, 1992 see refer-.ences on original contributions therein discussed the

solar wind source for rare gases on terrestrial planetswith the following conclusion: ‘‘ . . . the possibility ofsolar-wind source for rare gases on Venus and Earthmust be taken seriously.’’ Off-disc penetration ofancient solar wind into a post-nebular environmentŽ .Sasaki, 1991 could be a mechanism which allowed

Ž .this contribution. Recently, Ozima et al. 1996pointed out that the Q-type rare gas component

Ž .common in meteorites Wieler et al., 1991, 1992could also originate from fractionation of initiallysolar-like gases, suggesting ‘‘a prominent role forsolar outflow in the rare gas budgets of planetaryobjects’’. The similarity of initial and solar im-planted gases derived from this model re-enforcesthe above considerations.

Concerning the computed high abundances of rareŽ .gases in proto-terrestrial material Fig. 12 , it should

be emphasised that these are poorly constrained. Forexample, another scenario envisaging a short episode

Fig. 12. A comparison of rare gas abundances in terrestrialreservoirs with those observed in extra-terrestrial materials. Therelative rare gas abundances in the lower mantle inferred from

Žsteady state models O’Nions and Tolstikhin, 1994; Porcelli and.Wasserburg, 1995a,b; Tolstikhin and O’Nions, 1996 are similar

Žto those obtained in evolutionary ones Allegre et al., 1986r87;Àzbel and Tolstikhin, 1990, 1993; O’Nions and Tolstikhin, 1996;

.this work . Both resemble patterns typical of solar implanted raregases. Relative abundances in proto-terrestrial material are con-trolled in this model by those in the lower mantle and thereforeare essentially the same as those of the implanted gases. Theabsolute initial abundances depend on the early degassing–dis-sipation–fractionation processes and are poorly constrained, prob-ably within an order of magnitude.

of gas loss and fractionation in the early atmosphereŽ .e.g., as a consequence of a giant impact could

Ž .result in lower by a factor of ;10 initial rare gasabundances. However, modelling of Pu–U–I–Xesystematic suggests a ;50-fold loss at least of gasspecies from proto-terrestrial materials orrand fromthe early Earth–Atmosphere system.

Steady-state modelling of rare gases in a layeredmantle results in solar-wind-like relative abundances

Žof rare gases O’Nions and Tolstikhin, 1994; Porcelli.and Wasserburg, 1995b . The relative initial and

lower mantle rare gas abundances obtained in thiscontribution are quite similar to those obtained from

Ž .steady-state modelling Fig. 12 reflecting a tightconnection between the evolutionary and steady-statemodels.


5.2. Rare gases in the Earth’s core?

Generally metallic phases of meteorites do notcontain substantial quantities of primordial rare gases.

Ž .However Takaoka et al. 1993 reported recently alarge abundance of trapped Q-type rare gases inmetal separates from the unique Yamato-74063 me-teorite, with 130 Xes1.4P10y14 mol gy1. This con-centration is higher than those inferred from mod-elling for the lower mantle reservoir, 10y16 to 10y17

y1 Žmol g Porcelli and Wasserburg, 1995a; Tolstikhin.and O’Nions, 1996, 1998 .

We estimated the maximum equilibrium concen-tration of rare gases in the Earth’s core, assumingequilibrium partitioning of rare gases between metal

Ž .and silicates Section 3.2.2 . Core growth and ele-ment partitioning was modelled in a way similar to

Ž .that adopted by Azbel et al. 1993 . This modelreproduces the depletion pattern of moderatelysiderophile elements in the Earth’s mantleŽRingwood, 1984; Jones and Drake, 1986; O’Neil,

.1991 as well as the isotopic composition of tungsten182 Že Wsq5.1 for the silicate Earth Lee and Halli-

.day, 1995 . In this contribution, Co was used as aspike for the metalrsilicate partitioning process. Thefinal depletion of Co in the upper mantle was com-puted to be 0.1, in agreement with the estimate of

Ž .O’Neil 1991 . A moderate value of metalrliquidsilicate partitioning of 0.01 was assumed for all raregases, corresponding to metalrsilicate rare gas parti-

Žtioning under a pressure of ;30 kbar Matsuda et.al., 1993 .

The results show that the rare gas concentration inthe metal phase could be a factor of 1.5 higher than

Žthat estimated for the present-day lower mantle Fig..12 . Partitioning of elements between metal and

silicates on the core–mantle boundary is poorly un-derstood at present, but the possibility of rather highrare gas abundances in the core should stimulatefurther investigations.

5.3. Recycling of atmospheric gases

At first glance there is some discrepancy betweenlight and heavy rare gas isotope signatures in theupper mantle: a substantial contribution of primor-dial solar-like components is indicated by the iso-topic compositions of He and Ne, whereas the non-radiogenic Xe and Kr are almost indistinguishable

from those in air. This discrepancy has led someauthors to the conclusion that ‘‘while some commonfractionation process gave rise to the present isotopiccomposition of Xe, Kr, and Ar, Ne underwent quite

Ža different fractionation process’’ Ozima and Zahnle,.1993 .

Alternatively, recycling of atmospheric speciescould produce this difference, provided that the sen-sitivity to air contamination was different for lightand heavy rare gases in the upper mantle. It isimportant to note that an extremely small flux ofatmospheric rare gases but helium into the uppermantle can dramatically influence their isotope com-position in this reservoir. Models developed by Az-

Ž .bel and Tolstikhin 1988, 1990, 1993 suggest that,even assuming atmospheric recycling to be the onlysource of non-radiogenic rare gases in the uppermantle, rather low concentrations of Ar and Xe in

w36 x y14 y1subducted slab, Ar ;2P10 mol g andw130 x y17 y1Xe ;10 mol g , can maintain the observedupper mantle compositions of these gases, e.g.,40Arr 36Ar f 20,000–40,000 and 136 Xer 130 Xe f2.5. This model predicts a similar concentration ofw36 x y14 y1Ar in the subducted slab of 3P10 mol g .These concentrations are orders of magnitude lowerthan those observed in altered basalts and sedimentsŽ .Allegre et al., 1986r87; Bernatowicz et al., 1984 .`Therefore atmospheric rare gas recycling can occureven in the presence of the subduction barrierŽ .Staudacher and Allegre, 1988 , and a substantial`portion of Xe and other rare gases but He can indeedbe accounted for by recycling of atmospheric gases,as discussed recently by Porcelli and WasserburgŽ .1995a,b within the frame of a steady-state approxi-mation.

To estimate the sensitivity of an individual stableŽ .rare gas iss to air contamination, it is worth to

compare its concentration in the most prominentw s xcontaminant, sea water N , with that in the uppersea

mantle concentration computed with this model,w s x Ž w s xN for this comparison, N were computedum um

s Ž Ž .in the absence of recycling, L s0 Eqs. A2.3a h ,umŽ . ..and A2.13 Appendix B . Substitution of the rele-

Žs . w s x w s xvant concentrations in R N s N r N givessea umthe following array:

3 13022 36 84Ž .R He R Ne R Ar R Kr R XeŽ .Ž . Ž .Ž .0.0008 1,300 60,000 80,000 100,000


These concentration ratios clearly show that thepossible contamination is negligibly small for He,and is much smaller for Ne than for heavier gases. Ahigh solar-like relative abundance of Ne in the man-

Ž .tle Section 5.1 and its low solubility in water resultin a f80-fold increase of the rate of contamina-tionrrecycling for Xe relative to Ne and thus canexplain their different isotopic signatures in the man-tle.

6. Conclusions

We have developed a model for light rare gasesand nitrogen evolution in the Earth–Atmosphere sys-tem from the Earth’s accretion to the present. Thismodel is able to reproduce the elemental and isotopiccompositions of these elements in the main terrestrialreservoirs. The processes and parameters envisionedin this model are the following.

Ž .1 Rare gases in the proto-terrestrial matter hadinitially a solar-like composition, whereas the iso-topic abundance of nitrogen was that of E-chondrites.

Ž .2 Impact degassing during Earth’s accretion al-lowed f95% of rare gases to be degassed fromaccreting matter and f5% to be retained in thegrowing Earth. Nitrogen was less efficiently releaseddue to possibly reducing conditions prevailing at thattime.

Ž . Ž .3 Towards the end of accretion 60, 230 Ma ,some upper mantle domains underwent partial melt-

Ž .ing e.g., by impacts accompanied by fractional

degassing. Efficient loss of volatiles from the uppermantle–atmosphere reservoirs during these episodesinduced elemental and isotopic fractionation. Thetiming of ‘atmospheric closure’ was different foreach species, allowing various degrees of fractiona-tion.

Ž . Ž4 After closure of the atmosphere at ;4.30.Ga , the flux of volatiles between the terrestrial

reservoirs decreased exponentially, and our planetacquired rapidly a present-day-like volatile regime.An important consequence of this view is that thenitrogen abundance of the early atmosphere wasclose to that presently observed, supplying nitrogennecessary for the development of organic matter.

Ž . Ž5 Nitrogen and, to a lesser extent, xenon kryp-.ton and argon were recycled back to the upper

mantle which was simultaneously fed by pristinevolatiles from the lower mantle through plume di-apirs. These two processes together with upper man-tle degassing kept rare gas and nitrogen isotopeabundances in this reservoir almost at a steady-stateduring the last ;4 Ga.

Acknowledgements

Both authors greatly thank an anonymous re-viewer and Prof. B.J. Wood for numerous construc-tive comments. I.N. Tolstikhin was supported bygrants from the French Ministry of Higher EducationŽ .Bourse de Haut Niveau and from the InstituteNational Polytechnique de Lorraine. CRPG contribu-tion 1283.

Appendix A. Parameters and definitions

MAIN RESERVOIRSpm Proto-terrestrial materialum Upper mantle of the Earth. Note that before the lower mantle isolation there was

one mantle reservoir which is also termed upper mantle in order to simplifyequations given in Appendix B.

cr Corelm Lower mantle of the Earthcc Continental crustoc Oceanic crustah Atmo–hydrosphere of the Earth


MATERIALSbulk Bulk materialmet Metal materialls Liquid silicatesss Solid silicates

TIMEw xt Time Ga, Ma

Ž 129 127 y4.t Fixed time, t s0 Ga start of accretion, when Ir Is10in in

t Accretion time scale; at t the core had been formed and the lower mantle wasb e b e

separated from the upper mantlet Time interval between start of accretion and closure of the atmospherea h

Ž .t Fixed time, t s4.56 Ga nowfin finŽ i .t N Mean residence time of an incompatible element i in a reservoir, i.e., in the upperum

mantlew xT Age Ga

ily Decay constant of radioactive isotope, Gay1

SPECIESi Isotope, iss, is r and isd stand for stable, radioactive and radiogenic isotopes,

respectivelyi w xN Amount of isotope i of element N in a reservoir, i.e., in the upper mantle molumi N ) Idem for radiogenic isotopeumi Ž .N P Idem for radiogenic isotope yielded by progenitor P shown in bracketsumi Ž .N t Idem at given time or time interval, e.g., in the upper mantle at ts ta h um a hŽ i .N Amount of isotope i of element N in a reservoir shown first transferred fromu m a h

reservoir shown second, e.g., amount of i N in the upper mantle transferred fromthe atmosphere

w i x i w y1 xN Concentration of isotope N in a reservoir, e.g., in the upper mantle mol gumiC Concentration of isotope i in a reservoir, i.e., in the upper mantleum

15 �wŽ15 14 . Ž15 14 . x 4d Ns Nr N r Nr N y1 =1000sample a h

MASSES, MASS FLUXES, AND FLUXES OF SPECIESw xM Mass of principle reservoir, i.e., the upper mantle gum

Ž .f bulk Mass flux of material of given sort from a reservoir shown first into a reservoirlm ,u mw y1 xshown second g a

iw Flux of species from a reservoir shown first into a reservoir shown second relatedlm ,u m

to a mass flux, e.g., flux of species i from the lower mantle into the upper mantleŽ . w y1 xrelated to mass flux f bulk mol alm ,um

TRANSPORT, FRACTIONATION and OTHER COEFFICIENTSiL Retention coefficient showing which portion of species has been preserved in aum ,o c

Ž .mass flux f ls and arrived into reservoir oc; a complementary portionu m ,o c

1yiL is that transferred into the atmosphereum ,o ciL Transport coefficient for flux of species i from reservoir ah into reservoir uma h ,u m

w y1 xwithout mass flux Gai w y1 xL Transport coefficient for flux of species i from reservoir ah Gaa h


iD Partition coefficient for species i between solid and liquid silicates in a givenu m ,o c

fractionation process, i.e., in the upper mantle–oceanic crust fractionation process.Ž .F ss Fraction of material of given sort in a fractionation process, i.e., fraction of solidum ,o c

silicates in the upper mantle–oceanic crust fractionation process; if not shownthen fraction of liquid silicates.

i Ž . i Ž . i wK ls ' K Fractionation factor related to liquid silicates , for example K s1r Fum ,o c um ,o c um ,o c um ,o ci Ž .x i Ž . i iq D 1yF and K ss ' D . Ku m ,o c um ,o c um ,o c um ,o c

i w xS Solubility of species i in liquid silicates molrgratm .y Vesicularity, i.e., the ratio of volume of vesicles to total volume of melt.

Appendix B. Equations

Ž .Whole set of equations see Appendix A for definitions and Tables 1 and 2 for input parameters

B.1. Proto terrestrial materials pm

d M rd tsyf bulk,t ,t A2.1Ž . Ž .pm ,u mpm in b e

d i N rd tsyiC Pf bulk,t ,t qSl Pi N A2.2Ž . Ž .pm ,umpm pm in b e r pm

B.2. Upper mantle um

d M rd tsf bulk,t ,t yf met,t ,t yf ls,t ,t yf ss,t ,tŽ . Ž . Ž . Ž .pm ,umum in b e in b e a h in b e finum ,c r um ,c c um ,lm

qf bulk,t ,t yf ls,t ,t qf bulk,t ,t A2.3Ž . Ž . Ž . Ž .b e fin b e fin b e finlm ,um um ,o c o c ,um

di N rd tsiC L bulk f bulk,t ,t yiC K met f met,t ,tŽ . Ž . Ž . Ž .pm ,um pm ,um um ,c rum pm in b e um in b e um ,c r

yiC K ls f ls,t ,t yiC K ss f ss,t ,tŽ . Ž . Ž . Ž .um ,c c um ,lmu m a h fin um b e finum ,c c um ,lm

qiC f bulk,t ,t qiC K ls L ls f ls,t ,tŽ . Ž . Ž . Ž .u m ,o c um ,o clm b e fin um b e finlm ,um um ,o c

ii i iq C f bulk,t ,t q L t ,t N qSl P N A2.4Ž . Ž . Ž .o c b e fin a h fin a h r umo c ,um a h ,u m

Ž . i Ž .m f w Ž .m f i Ž .m f Ž .m f i Ž .m f Ž .m f xwhere K met s D met r F ls q D ss F ss q D met F met mf is an upper mantle frac-u m ,c rŽ . Ž .tionation zone during core segregation process; K ls and K ss are defined in Appendix A.

B.3. Core cr

d M rd tsf met,t ,t A2.5Ž . Ž .c r in b e u m ,c r

di N rd tsiC K met f met,t ,t A2.6Ž . Ž . Ž .u m ,c rc r u m in b e u m ,c r

B.4. Lower mantle lm

d M rd tsf ss,t ,t yf bulk,t ,t A2.7Ž . Ž . Ž .lm b e fin b e finum ,lm lm ,um

di N rd tsiC K ss f ss,t ,t yiC f bulk,t ,t qSl Pi N A2.8Ž . Ž . Ž . Ž .um ,lmlm um b e fin lm b e fin r lmum ,lm lm ,um


Ž .Sub surface degassing reservoir, analogue of the oceanic crust, oc:

d M rd tsf ls,t ,t yf bulk,t ,t A2.9Ž . Ž . Ž .o c b e fin b e finum ,o c o c ,um

di N rd tsiC K ls F ls f ls,t ,t yiC f bulk,t ,t A2.10Ž . Ž . Ž . Ž . Ž .um ,o c u m ,o co c um b e fin o c b e finum ,o c o c ,um

B.5. Continental crust cc

d M rd tsf ls,t ,t A2.11Ž . Ž .c c a h fin um ,c c

ii i i id N rd ts C K ls f ls,t ,t yL t ,t N qSl P N A2.12Ž . Ž . Ž . Ž .um ,c cc c um a h fin a h fin c c r umum ,c c c c ,a h

B.6. Atmosphere ah

di N rd tsiC 1yF bulk f bulk,t ,t qiC K ls 1yF lsŽ . Ž . Ž . Ž .Ž .Ž .pm ,um pm ,um um ,o c u m ,o ca h pm in b e u m

=i ii i if ls,t ,t q L yL t ,t N qL t ,t NŽ . Ž . Ž .b e fin c c ,a h a h fin a h a h fin c cum ,o c a h ,um c c ,a h

iiyL t ,t N A2.13Ž . Ž .b e a h a ha h

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The evolution of terrestrial volatiles: a view from helium, neon, argon and nitrogen isotope modelling