Rare gas systematics: formation of the atmosphere, evolution and structure of the Earth's mantle

Earth and Planetary Science Letters, 81 (1986/87) 127-150

127

Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands [6]

Rare gas systematics" formation of the atmosphere, evolution and structure of the Earth's mantle C l a u d e J. All+gre, T h o m a s S t a u d a c h e r a n d P h i l i p p e S a r d a Laboratoire de G~ochimie et Cosmochimie, lnstitut de Physique du Globe et D~partement des Sciences de la Terre, Universit$s de Paris VI et VII, 4, Place Jussieu, 75252 Paris Cedex 05 (France)

Received June 27, 1985; revised version received April 30, 1986 To explain the rare gas content and isotopic composition measured in modern terrestrial materials we explore in this paper an Earth model based on four reservoirs: atmosphere, continental crust, upper mantle and lower mantle. This exploration employs three tools: mass balance equations, the concept of mean age of outgassing and the systematic use of all of the rare gases involving both absolute amount and isotopic composition. The results obtained are as follows: half of the Earth's mantle is 99% outgassed. Outgassing occurred in an early very intense stage within the first 50 Ma of Earth history and a slow continuous stage which continues to the present day. The mean age of the atmosphere is 4.4 Ga. Our model with four main reservoirs explains quantitatively both isotopic and chemical ratios, assuming that He migrates from the lower to the upper mantle whereas the heavy rare gases did not. Noble gas fluxes for He, Ar and Xe from different reservoirs have been estimated. The results constrain the K content in the earth to 278 ppm. Several geodynamic consequences are discussed.

1. Introduction The idea of using the n o b l e gases as geochemical tracers to c o n s t r a i n the history a n d structure of the Earth is not a new one. It has been invoked in several papers, for instance by T u r e k i a n [1], D a m o n a n d K u l p [2], Ozima a n d A l e x a n d e r [3], K a n e o k a a n d T a k a o k a (e.g. [4]), Hart a n d H o g a n (e.g. [5]), M a n u e l a n d Sabu (e.g. [6]) a n d Fisher (e.g. [7]), a m o n g others. Here, we take a new approach to that complex p r o b l e m : that is, to use systematically all of the n o b l e gases together (see [8]), instead of only one at a time. F u r t h e r m o r e , we c o m p a r e the results with other geochemical tracers such as Nd, Sr a n d Pb, whose isotopic c o m p o s i t i o n has been measured in the same or adjacent samples. By treating these data in the context of the basic elements of plate tectonics, we place this n o b l e gas approach into the frame of c h e m i c a l g e o d y n a m i c s [12]. T o this aim, we measured all of the rare gases in carefully selected samples. I n the case of midocean ridge basalts (MORB), we used very fresh glasses a n d we performed stepwise heating measurements [8-11] in order to get rid of c o n t a m i n a 0012-821X/87/$03.50

© 1987 Elsevier Science Publishers B.V.

tion b y atmospheric n o b l e gases dissolved in seawater. W e also crushed the samples u n d e r high v a c u u m in order to measure the gases enclosed in the vesicules only ([14], a n d u n p u b l i s h e d data). In the case of granitoids, we analyzed whole rocks a n d separated minerals. I n some recent papers [8-11,14] on basalts we gave some p r e l i m i n a r y i n t e r p r e t a t i o n s of our resuits b u t n o t in a n as systematic a n d q u a n t i t a t i v e way as we will do here.

2. Rare gas systematics W e Will first summarize the experimental results for mid-ocean ridge basalts (MORB), ocean island basalts (OIB) a n d granitic r o c k s - - m o s t of which were o b t a i n e d in our l a b o r a t o r y - - a n d the relations which exist between them. Together they form the basic framework of our theoretical interpretations. 2.1. E x p e r i m e n t a l data

We have analyzed n o b l e gas isotopic compositions of He, Ar, K r a n d Xe a n d n o b l e gas con-

128

7.2

129Xe

134X~"~

~3OXe

6.8 2.6 a

6.4

I

I

10 "°Ar/

I

21

0 Ar

4He

~,e ~:~liments

oo

2.8

' 71.6

r-

134Xe

.

20/LpL

' 710

129Xe/130Xe

,,.,3 J, old oceanic crust ~v

614 '

xl03

a

,

,

,

b

d [w

10 4 0A r/36 A r

20

xi03

,

I

I

I

I

10 20 x103 40A r/36Ar

Fig. 1. Correlations of rare gas isotope ratios in MORB and OIB glasses: xenon-argon (a), helium-argon (b), fission xenon-l;gXe (c) and fission xenon-argon (d). Mixing lines for different values of parameter r are also shown. For mixing lines and mixing equations, see [53]. L and M represent the Loihi and MORB poles and correspond to the lower and the upper mantle reservoir. O = Loihi: • = Indian Ocean; ~ = Atlantic Ocean; Q = Pacific Ocean; ~ = dunites [14].

centrations of He, Ne, Ar, Kr and Xe [8-11,14] in a set of fresh MORB glasses collected along midoceanic ridges from different oceans. We found large variations in the isotopic ratios of argon and xenon: the 4°Ar/36Ar ratio varies from 6000 up to 25,000 [8,10] (stepwise heating results) and 129Xe/13°Xe ranges from 6.71 up to the highest value ever measured in terrestrial samples of 7.36 *; these 129Xe anomalies are systematically accompanied by fission-xenon excesses. Such variations in the isotopic compositions of different M O R B have been interpreted as the result of mixing of lower mantle material with the upper mantle under the mid-ocean ridges (e.g. [8]). The correlations between the isotopic composition of gases such as Xe and Ar or He and Ar (Fig. la, b) rule out simple contamination by atmospheric noble gases or by noble gases dissolved in seawater * A I I 96-18-1, Staudacher et al., unpublished.

[8,13]. This interpretation has led us to the conclusion that the sample with the highest 4°Ar/36Ar a n d 129Xe/13°Xe ratios (AII 96-18-1) best characterizes the upper mantle source of MORB [8,10]. We have also measured noble gases in a number of samples from the Loihi seamount, Hawaii [8,14]: the helium isotopic composition is among the most primitive signatures ever measured in terrestrial samples (26,000) and the 4 ° A r / 3 6 A r ratio is 390 _+ 25, that is quite low. The xenon isotopic composition is indistinguishable from atmospheric xenon. Such data should give us information on the lower mantle or the separate OIB reservoir. Recent measurements on gases from Yellowstone Park by the Berkeley group [15] are in agreement with our data on Loihi [14] and our general conclusions. The Loihi noble gas pattern shows that there is no contamination by seawater dissolved rare gases. Furthermore, we have measured a number of

TABLE 1 Noble gas signature of several terrestrial reservoirs 3He 4He (10-1°cm3g -1) 3He

2°Ne 36Ar 40Ar (10 l ° c m 3 g - 1 ) ( 1 0 l°cm3g -1) 3 6 A r

S4Kr 130Xe 129Xe (10-12cm3g-1)(10-14cm3g 1) 13°Xe

134Xe 13°Xe

136Xe 13°Xe

Atmosphere

0.00014

722,500

348

663

295.5

1370

740

6.48

2.56

2.17

Deep-sea water

0.00063

722,500

1740

12,700

295.5

52,600

45,100

6.48

2.56

2.17

MORB mean

1.1-4.2 2.66

49,500-109,000 81,500

0.8-3.9 1.68

0.38-1.0 0.74

13,000-25,250 16,700

1.6-4.4 3.2

4.1-8.9 6.9

6.71-7.36 2.60-2.81 2.25-2.55 6.95 2.69 2.38

Loihi mean

0.03-0.42 0.26

20,000-43,000 26,000

0.5-8.0 5.8

0.7 1 4 . 0 8.6

360-425 390

1.5-32.1 20.0

0.3-21.9 15.9

6.46-6.48 2.54-2.60 2.16 2.21 6.48 2.58 2.19

12.7-64.7 31.9

336-1060 516

39.7-224 164

191 1 5 7 7 738

6.48-6.51 2.57-2.58 2.18-2.20 6.49 2.58 2.19

188-360 269

317-428 374

848-3037 1549

1520 7 8 1 0 4310

6.40-6.50 2.47-2.62 2.17-2.21 6.47 2.56 2.19

3-37 12.7

1650-170,000 20,600

19-157 69

6.39-6.70 2.66-7.25 2.26-7.92 6.52 2.94 2.63

Old oceanic crust 0.0002-0.0024 mean 0.001 Sea floor sediment mean Continental crust 0.0003-0.06 mean 0.02

1.7-40×106 1.6 )<"107 -

106-108 2.5 ~ 107

0.4-1.8 1.0 (1.4-18) (10) 1-5 2.6

17 117 64

Atmosphere: atmospheric noble gases (Table 3) divided by the mass of the outgassed mantle (section 3.1.2). Deep-sea water: data from [13,49-52]. MORB: for Ar, Kr and Xe

only data with 4°Ar/36Ar ratios > 10,000 are used; data from [8-11] and unpublished data from Southwest Indian Ridge (12 analyses). Mid-Atlantic Ridge (4 analyses), East Pacific Rise (8 analyses), Reykjanes Ridge (2 analyses), Carlsberg Ridge (1 analysis). Loihi: data from [8,14]. Old oceanic crust: unpublished data from Ninety East Ridge (2 analyses), leg 52 Jurassic Holes 418A (1 analysis) and 417D (5 analyses). Sea floor sediment: unpublished data from leg 66, Hole 487 (Mexican trench) (4 analyses) and MD-34D2 sediments, Southwest Indian Ridge (2 analyses). Continental crust." data from [9] and unpublished data for granites from Tibet; He data from [9] are corrected for He concentration (see also [8]).

130 acidic rocks which give us an indication of the noble gas isotopic ratios in the continental crust. Without going into details (the data will be published elsewhere), we give a rough summary. The 4 H e / 3 H e ratios are extremely high and range from 10 6 to 1.2 × 10 8 (atmospheric ratio = 7.23 × 105). The 2aNe/22Ne ratios are systematically enriched (Wetherill effects [16]). The 4°Ar/36Ar ratio ranges from 1 . 5 × 1 0 3 to 1 . 7 × 1 0 5. The xenon shows 131Xe, 132Xe, 134Xe, 136Xe excesses. The a36xe/13°Xe ratio varies between 2.26 and 7.92. Table 1 shows the complete set of data that will be the basis of our further speculations and calculations. We include data for the atmosphere, seawater [13,49-52], altered oceanic crust and oceanic sediments, the latter being the possible contaminant for MORB as well as the upper mantle through reinjection processes.

2.2. Identification of the observed isotopic ratios The natural variation in 4 H e / 3 H e ratios is obviously due to the balance between primordial helium and radiogenic 4He generated by radioactive decay of 232Th, 235U, and 238U; the 4He/3 He reflects the (U + T h ) / 3 H e ratio history. Similarly, 4°Ar is the product of 4°K decay and the 4°Ar/36Ar ratio reflects the 4°K/36Ar ratio history. The isotopic composition of xenon varies due to several processes. A first process is radioactive decay of now extinct 129I producing 129Xe. Secondly, spontaneous fission of 238U produces 131Xe, 132Xe, 134Xe and 136Xe. The same Xe isotopes are produced by now-extinct 244pu. Both processes produce 83Kr, 84Kr and 86Kr as well; however, the fission yield is lower than for Xe and Kr is natu-

rally more abundant so that the isotopic variations produced are much smaller. Therefore, the isotopic composition of krypton can hardly be distinguished from atmospheric krypton and is not used in this approach. It is not always easy to decide from the data whether the variations of fissiogenic xenon isotopes are due to spontaneous fission of 238U or 24a'pu, because the analytical errors are generally too large to distinguish between the two isotopic fission patterns that are only slightly different from each other. If we take into account the fact that 2~pu was already extinct when the continental crust formed, then the observed fissiogenic xenon variations in granites should always be due to spontaneous fission of 238U, as shown by Butler et al. [17] and subsequently confirmed by Staudacher and All~gre [9]. The situation is more confusing for MORB. Staudacher and All6gre [9], in a first approach, concluded that spontaneous fission of 244pu was responsible for the fissiogenic xenon anomalies in MORB samples. A more detailed study, however, showed that spontaneous fission of 238U should be the main cause of fissiogenic xenon excesses in the upper mantle: notwithstanding large analytical errors, the xenon isotopic composition of a gas-rich glass sample from the Indian Ocean is in reasonable agreement with the fissiogenic pattern due to spontaneous fission of 238U(Table 2). Let us now estimate the 238U/13°Xe ratio (/~) for Bulk Earth and the MORB source. Using a U concentration of 18-22 ppb for Bulk Earth [18,19] and redistributing the atmospheric xenon in the whole mantle, we get ~Bulk Earth ~ 5.3 × 10 5. With such a /~ value, we cannot expect measurable variations in the 136Xe/13°Xe ratio, even over a

TABLE 2 Fission xenon in a 1300°C fraction of MD34-D3, a MORB glass from the Southwest Indian Ridge, compared to 238U- and Z44pu-derived fission xenon

MD34-D3 1300° C fraction 238U-derived fission Xe 244Pu-derived fission Xe

136Xe (10-14 cm3 g l)

131Xe 136Xe

132Xe 136Xe

134Xe 136Xe

80 + 1

0.152 + 0.10

0.57 + 0.18

0.77 ± 0.14

-

0.083

0.576

0.816

-

0.251

0.876

0.921

131 time span of several billion years [9]. This # value is a maximum because only a part of the mantle has been outgassed. Therefore the 13°Xe content in the Earth was certainly higher than the present 130Xe in the atmosphere alone. To estimate/~ ~aORB we assume that the upper mantle has lost 5 / 6 of its uranium by continental extraction [19], and 99% of its xenon by degassing [10]; the derived value is /~MoRB= 8.8 × 10 6. With such a /~ value we can show that the 136Xe excesses in MORB glasses relative to atmosphere may be explained by spontaneous fission of 238U alone during geological time. Therefore, we suppose that spontaneous fission of 244pu is not the major component for the xenon excesses in MORB samples. The contribution of 238U spontaneous fission seems to be essential. Further studies may elucidate this point. 2.3. The noble gases as specific geochemical tracers

The extent of isotopic variations observed at the present time for 4 H e / 3 H e , 4°Ar/36Ar, 129Xe/13°Xe and 134, 136Xe/130Xe depends on the variations with time of the chemical ratios /~ = (U + T h ) / 3 H e , 4°K/36Ar, a291/13°Xe and 238U/13°Xe respectively. Two rather different processes govern these ~ values, besides radioactive decay. One is outgassing, which decreases the gas concentration in the mantle reservoir, thus increasing the /a value. This outgassing occurs at the ridge crest, through hot spots, hydrothermal activity and volcanism in general. It is clear that the outgassing of the mantle is a process directed upwards and that any outgassed reservoir is a superficial one or has had a superficial connection in its history. The other way to change /~ is the mantle depletion of K, U and Th due to continental crustal growth, which decreases the ~t value. Both processes, outgassing of the mantle and formation of the continents, have occurred on completely different time scales [9,10,12]. Using noble gases as geochemical tracers may allow us to trace these two geochemical phenomena and to derive their time dependence. The different parent isotopes which cause the isotopic variations of noble gases have very different half-lives. In the case of very short half-lives, such as for 129I and 244pu (17 and 82 Ma, respec-

tively) the parent-daughter systems are only sensitive to processes occurring in the very early history of the Earth. Other systems have long halfqives, such as 4°K-4°Ar (1.250 Ga) or 238U-4He (4.469 Ga) or 232Th-4He (14.0 Ga) and they allow a better record of the entire and late history. Finally, radioactive decay or the spontaneous fission of the above mentioned parent isotopes also produces heat within the Earth. When comparing heat flux, noble gas flux and noble gas concentrations, as pioneered for He by O'Nions and Oxburgh [20] it should be possible to constrain heat transfer within the Earth. 2.4. The model for the Earth's mantle

In a previous paper, All+gre et al. [8] published positive correlations between the following isotopic ratios: 4°Ar/36Ar, 129Xe/13°Xe, X34Xe/13°Xe (Fig. la, c, d) and 4 H e / 3 H e (Fig. lb), the last one being more complex. Considering the fact that the upper mantle is certainly an active convective reservoir, a simple way to explain the positive correlation of 129Xe (daughter of the short-lived 129I) and 4°Ar or 134'136Xe (daughters of long-lived parents) is the recent mixing of two distinct reservoirs. The first one should be a reservoir which was highly outgassed before 129I was extinct, and which is today characterized by 129Xe, 4°Ar and fission-xenon excesses. The second one should be a non- or poorly outgassed reservoir in which the excesses of radiogenic isotopes are small due to the high concentration of primitive noble gases. These correlations between radiogenic products of parents with very different decay constants is difficult to reconcile with a model in which the mantle forms a single cell, continuously stirred over 4.5 × 10 9 years. The mixing in such case will not preserve any correlation between early created anomalies like 129Xe and continuously formed ones like 4°Ar or fission Xe. Recent mixing under the ridge is the most likely explanation for these correlations. In addition, rare gas isotope ratios in MORB vary coherently with 87Sr/86Sr (Fig. 2) and 2°rpb/Z°4pb. The recognition that ridges are polluted by blobs leads to the use of so-called extreme MORB values rather than mean values in mass balance equations for Sr, Nd and Pb [31]. We assume, according to the inverse calculations

132 xlO 3

3. Mass balance for the different reservoirs, degree of outgassing and structure of the Earth's mantle

30

4°Ar 36Ar

'0r

20

I

.702

.703

I

•

.704 .705 87Sr/86Sr

Fig. 2. Correlation between argon and strontium isotopic ratios in glasses. © = Loihi; • = Indian Ocean; ~ = Atlantic Ocean; ®= Pacific Ocean; ® = Bulk Earth.

by All+gre et al. [18], that the depleted mantle is 1 / 3 of the whole mantle. Such balance does not automatically constrain the geometrical form of the two reservoirs [18]. Two possibilities were discussed: the two-layered mantle and the so-called inclusion model. One of the important constraints is the fact that we need to produce the two types of basalts (MORB and OIB) in both cases. In the two-layer model, MORB comes from the upper reservoir contaminated only by minute amounts of lower mantle material under the ridges while OIB is a mixture between the two reservoirs in various proportions. In the inclusion model OIB comes mainly from the pristine domains and MORB is a mixture between the two reservoirs. But as has been argued before, such mixing would erase the isotopic anomalies of rare gases in MORB, because the non-outgassed mantle has a more than 200 times higher noble gas concentration than the outgassed one. The preservation of 129Xe, 4°Ar and fissionxenon anomalies in the MORB source and the correlation with isotopic ratios of lithophile elements such as Sr, Nd and Pb leads to the conclusion that the two-layered mantle is the most likely model for the structure of the Earth's mantle today. We will use this model as the starting point. Following a previous approach we will use the present-day data, the mass balance equation and the mean age calculation.

We perform our calculations for argon first, and extend them to helium and xenon because the isotopic composition of argon and its variations with time are well known [10]. Complications arise for helium, which escapes from the atmosphere to s p a c e - - a process which will nevertheless be an advantage when we estimate the noble gas flux from the mantle to the atmosphere or from the lower to the upper m a n t l e - - a n d for xenon, whose initial isotopic composition is not well known (e.g. [21]).

3.1. Equation of mass balance for argon In this section we will consider h priori five different noble gas reservoirs in the Earth (Fig. 3), and assume that they are internally homogeneous: (a) atmosphere, (b) continental crust, (c) an upper mantle both outgassed by the formation of the atmosphere and depleted by the growth of the continents, (d) a part of the mantle that is outgassed but not depleted, and (e) a virgin mantle, neither degassed nor depleted. Note that a priori, we distinguish between outgassed and depleted mantle: extensive outgassing of the mantle is an early phenomenon which occurred long before the formation of continents (e.g. [9,10,18]) and does not necessarily involve the same part of the mantle as the one from which the continental crust has been extracted throughout geological time.

3.1.1. Degree of outgassing of the mantle We will use the following notation (see also Fig. 3): a = 4 ° A r / 3 6 A r ; A = a t m o s p h e r e ; M = mantle; C = continent; D = depleted and outgassed mantle; VO = undepleted but outgassed mantle; V = undepleted and non-outgassed mant l e = v i r g i n mantle; O = D + V O = w h o l e outgassed mantle; T = C + M = C + D + V O + V = total silicate Earth; L = Loihi. Since 36Ar content in C is negligible and its concentrations in V and T are the same, we can write: d = 36ArA/(36Aro + 36ArA) = present degree of outgassing

(1)

The present isotopic budget for A and O is then

133

I

L

atmosphere

3.1.2. Chemical ratio budget A d d i t i o n a l n o t a t i o n s used here are: 4°K

t

depleted

degossed mantle

I

D

upper mantle

undepleted lower mantle undegassed mantle

1 Fig. 3. Schematic representation of the five terrestrial reservoirs.

( 40K t

( n o t e that all 4°K (and /~) values are p r e s e n t - d a y values), m T = mass of total m a n t l e = 4.1 x 10 27 g, m c = mass of c o n t i n e n t a l crust = 2.0 × 10 25 g, r o D = m a s s of d e p l e t e d mantle, m v = m a s s of n o n - o u t g a s s e d mantle, m o = mass of outgassed mantle, CcK = K c o n c e n t r a t i o n in c o n t i n e n t a l crust, C ~ = K c o n c e n t r a t i o n in the virgin mantle. All a, ix values are c a l c u l a t e d using units of m o l / m o l ; 36ArA = 5.58 × 10 is moles. Let us now write: /z* = 4° K c / ( 3 6 A r c + 3 6 A r A ) ~ 4° K c / 3 6 A r A

(6)

and: b --- 36ArD/a6Aro = m D / m 0 written: a T = d a A + (1 -- d ) a o

(2)

It is clear that a D ~< a o b e c a u s e of the higher K c o n c e n t r a t i o n in O t h a n in D. Then, we can derive d:

O/O -- a A

d,=(

aD-aT ~D

~A

A s s u m i n g that the c o n c e n t r a t i o n of 36Ar is the s a m e in D a n d VO, the chemical b u d g e t for A, D, a n d VO is written: /z T = d/l* + [~D + (1 -- b ) / t v o ] (1 - d )

(8)

where: ~D

W e can also define d ' by:

(7)

~ 36Ar ]o a n d ~ v o =

3-~Ar vo

(9)

F o l l o w i n g All~gre et al. [18], we define:

) (4)

and we have d >~ d'. F o r a D we use the highest M O R B value [8,10], a n d for a T the best value of Loihi glasses [8,14]: a D = 25,000; a A = 295.5; a T = a L = 390. N o t e that the value chosen for a T m u s t be c o n s i d e r e d as an u p p e r limit: a c c o r d i n g to o u r box m o d e l b u d g e t (see later) the Loihi reservoir m u s t n o t strictly r e p r e s e n t the virgin m a n t l e b u t includes a d e g a s s e d u n d e p l e t e d zone a n d thus has a slightly higher i s o t o p i c ratio t h a n the virgin m a n tle alone. U s i n g the values a b o v e we get d ' -- 0.996, which is thus a lower limit. This result indicates that the m a n t l e source of M O R B has lost at least 99.6% of its initial gas, c o n f i r m i n g previous estimates [10].

CcKmc ) w= C(mD + me) =

4°Kc 'OK

(10)

Tm T T h e n we have:

and: /*vo

t~v 1- d

(12)

a n d we can derive the d e p l e t e d p r o p o r t i o n of the o u t g a s s e d mantle: b

d /** ..~ 1 /**

W ~T

(13)

W /.Z~F,,,-

/*T will be d e d u c e d f r o m 4°Ar/36Ar ratios m e a -

134 sured in the Loihi seamount glasses (Table 1), assuming a closed-system evolution of the Loihi reservoir. However, a complication may arise due to the fact that the present-day undepleted (lower?) mantle is a mixture of virgin mantle (V) and virgin outgassed mantle (VO); see Fig. 3. Let us denote/2 as the chemical ratio of the lower mantle; then we have:

where X ¢ = 0 . 5 8 1 × 1 0 lo a 1, X = 5 . 5 4 3 × 1 0 a - 1 0 = 4 . 5 × 1 0 9 a, and:

lo

and upper mantle is at least 200. Therefore we emphasize that any reasonably proportioned mass mixing between upper and lower mantle will be dominated by the characteristics of the lower mantle. In terms of degree of outgassing of the earth, half of the mantle is almost completely outgassed to give the atmosphere.

3.1.3. Estimation of the potassium concentration in the primitive mantle The K concentration in the primitive mantle can be estimated in two different ways. If we know/a T , then we can use the relation:

GK= /2=

1

3°1-5 v+vo

(15)

and finally:

G Ar

(17)

As the degree of degassing of the outgassed mantle is close to 100%, we have: 36Aro + 36ArA ~-- 36ArA

=

-

mT

= + -/~ mT

(16)

To estimate /~* we must know CK. The best value derived from inversion calculations of Sr, Nd, U, Th, Pb data [19] and K / U = 12,700 [23] is CK = 1.7wt.%, which yields (equation 6): /~* = 182. With ¢xL = 390 [14] we get /2 = 337 (equation

14).

As we know that K and U have the same geochemical behavior on a global scale [23], we use for W the same value as the one deduced from U-Th-Pb systematics [19], that is, W = 0.85; i.e. 85% of the initial potassium content of D is now in the continents. The depleted proportion of the mantle itself is constrained from Sr-Nd systematics [18] to be:

Using the values above, we get (equation 16): b = 0.76 and m o l t o T

We derive: cK=

=

36ArA 1 mo /aT7

(19)

where f = 4 0 K / K at present time = 1.167 × 1 0 - 4 [24]. On the other hand, we may calculate the 4°Ar produced in the outgassed mantle in 4.5 Ga. If we assume that all of this 4°Ar is now in the atmosphere (complete outgassing approximation), we have: 4°Ar = ~ ( e x° - 1)4°K = 1.164°K

(20)

where 0 is the age of the Earth. Thus: cK~

m D / m T = 0.35

(l 8)

4°ArA 1 1 1.16 m o f

(21)

If these two estimates are equal we get:

0.46

Finally, from equations (11) and (15) we also get ~T 280 and /1D = 10,500. The above result means that 46 % of the mantle was involved in otTtgassing. Only about 3 / 4 of this outgassed mantle is also depleted today. Of course the 1 / 4 of the outgassed mantle is today mixed with the non-outgassed lower mantle and cannot be physically distinguished. Therefore, if the upper mantle is at least 99.6% outgassed, the presentday lower mantle has been outgassed t o - - 1 7 % . The rare gas concentration ratio between lower

/~T

136A~ A l ' i 6 = 2 5 5

(22)

=

which is close to the value we got in the previous section. F r o m equations (15) and (7) we can derive:

b=

mD/mT

.T( 1 - mD) 1-~ /z

(23)

my

and get b = 0.70, which is lower by only 8% than the value as previously derived.

135 In fact, the previous complete outgassing approximation is too crude for at least two reasons: first, the 4°Ar degree of degassing should be significantly lower than 100%; second, the extraction of potassium from the mantle has been neglected. The degassing model that we propose in section 4 suggests that 4°Ar is about 75% outgassed; the model also allows the estimation ~T = 300,.which is in good agreement with the values calculated above. Then, we can calculate the Bulk Earth potassium concentration (relation (19)): with/~T = 255, C~ = 253 p p m with/~T = 280, C~ = 278 p p m The latter value will be our preferred one, a value quite close to the potassium content of most of the carbonaceous chondrites. Taking U = 22 ppb [19], we get (K/U)BuJk = 12,600 which is in good agreement with other estimates [23].

3.2. Mass balance equation for xenon and helium 3.2. I. Isotopic ratios In principle we can use the same line of reasoning for Xe and He as for Ar. However, some complications arise. Xenon. For Xe we have to consider four mass balance equations: one for 129Xe and three for fissiogenic 132'134'136Xe. AS for Ar we will write: d'=

aP - a~r

al,

-

/

the escape velocity of the Earth and leaks from the atmosphere into space. Therefore, the mass balance equation cannot be written directly. However, we can use the mass balance to estimate what the atmospheric 4 H e / 3 H e ratio would be if He did not escape into space. Let us write: aA =

a T - (1 - d ) a D d

where a = 4 H e / 3 H e , a x = 2 5 , 0 0 0 [14], and, for mean MORB a D = 86,000 (e.g. [27]). Taking as a working hypothesis the same degree of outgassing ( d ) as for argon, we get a A = 24,800. In contrast, the actual value for atmosphere is 722,500.

3.2.2. The ratio of radiogenic isotopes 4He/4°Ar The K / U ratio is rather constant for the different mantle reservoirs [23]. We can calculate the corresponding (4 He */4°Ar *) ratio of radiogenic daughters produced in 4.5 Ga in a closed system. The theoretical value for the lower mantle with 278 p p m K, 22 ppb 238U, 238u/Z35u = 137.88 and T h / U = 4.2 (Fig. 4) is 1.79. The measured values for Hawaiian samples range between 1.1 and 3.3 [8,14] with a mean value of 2.15. This slightly higher ratio for the lower mantle could be due to the existence of a primitive 4He component. Using to advantage the fact that the initial 4°Ar can be neglected compared to the radiogenic part, we can calculate the ( 4 H e / 3 H e ) o at the formation of the Earth:

4"e' l n°Ar

(24)

where a i = i X e / ~ 3 ° X e ; i = 129, 132, 134, 136. As shown by All~gre et al. [8] and Staudacher et al. [14] no significant difference exists between the isotopic composition of xenon in the atmosphere and in samples from the Loihi seamount, assumed to represent lower mantle material. Therefore, a v = a A and d ' = 1. This value is close to what we had for Ar. We can check it by taking the value for d derived from Ar and calculate the ratio (129Xe/a3°Xe)T. We get a T = 6.484 which is experimentally indistinguishable from the atmospheric value of 6.48.

Helium. Important problems arise for helium. Due to its light mass, He has a thermal velocity close to

(25)

3He

4°Ar JLoihi - ~ } ] ~ = 5200

3He ]Loihi (26)

where the asterisk (*) indicates radiogenic isotope, (4He/4°Ar)Loi~ = 2.15, and (40Ar/3He)Loihi = 14,500 [141. The calculated ratio ( 4 H e / 3 H e ) 0 is in agreement with the value of 6670 for planetary gas measured in gas-rich meteorites [29,30], but significantly higher than the value of 2500 for solar helium [28]. The situation is quite different for MORB glasses. The measured (4He/4°Ar) ratio in these samples of 15.4 is much higher (data from [8]) than the calculated radiogenic one of 1.79 and cannot be explained by any pristine component. We will see in section 5.3 that helium has quite a

136 where we use (36Ar/3He)v = 35.5 from Loihi data [8,14]. Note that 238U and 4°K are present-day values. Another way is to consider the Loihi reservoir as a closed system and use the following chronometer equation:

/\ K=42

ppm

U=3.3

ppb

Th/U

=

2.5 UPPER MANTLE

3He ] Loihi

K=278 0=22

v

3He 0

where F is the radioactive 4He production from 238U, 235U and 232Th in the virgin mantle (see Appendix 1). We get:

ppm

/ZHe, V = 1060

T h / U = 4.2

ppb

Both ratios are in excellent agreement. As before, we can also perform this calculation for the MORB reservoir using:

LOWER MANTLE

Fig. 4. Inventory of radioactive elements in the upper mantle, lower mantle and the continental crust (sections 3.1.3 and 6.3).

=/2380] ~n~,D

=/23801/4°K

~ 3He }D

I

/36Ar]

~ 4-~K ]~ 36Ar ]o~ 3He ]D

(29) different behavior from the other rare gases. He in the upper mantle is not simply a remnant of an initial state after outgassing, but it diffuses from the lower mantle to the upper mantle, thus increasing the (4He/4°Ar) ratio. 3.2.3. Chemical ratios In this section we will calculate different chemical ratios of the mantle reservoirs, using elemental ratios for Loihi and MORB glasses. J.LHe"

"Ho,V =

3H

)v =

- K) 36ArJvk3H-- Jv

= 1100

(27)

TABLE 3 Theoretical noble gas contents in the closed atmosphere (CA) derived from the estimation of the initial 3He content in the outgassed mantle and the elemental noble gas ratios for Loihi seamount

Loihi

3He 1 2°Ne 26 36Ar 35 84Kr 0.85 13°Xe 0.007

(mole) 1.57×1014 4.08×1025 5,50×1025 1.33×1024 1.10×1012

Taking (36Ar/3He)D = 0.32 and (4°K/36Ar)D = 10,500 (section 3.1.2), we get: (Z38U/SHe)o = 372 This value is smaller than that for the closed system. Obviously, the chemical ratios/~Ar in virgin and depleted mantle (280 and 10,500 respectively) have a completely different behavior from the corresponding chemical ratios /~He. We will come back to this problem later. We can also use the chemical ratio to estimate the 3He lost to space through geological time. As for argon we define: /X~e

= (238Uc 1 k 3neA ] = b W / x r t e ' V = 7 1 0

/X~te =

7,5×10 6 0.72 1.01 0.86 0.57

(31)

If we suppose a closed atmosphere (noted CA) for both Ar and He we get:

(mole) 1.17×109 2.93×1015 5.58×1015 1.i5×1014 6.23×1012

(238U I i 36Ar \ 4--~-K ]C ~ H3 - ~ )AP,~r

(30)

3HecA

[ 238U \ / = 36Ar [ - ~ / P',~,r A / 4oK ]c~/~--~ = 1.57 >( 1014 moles

) (32)

and 4HecA =3 HecA × 25,000 = 3.93 × 10 is moles. Actually, the Earth's atmosphere only contains

137 1.2 × 109 moles of 3He. This is in agreement with the classical observation of He escape to space and consequently the relatively small residence time of helium in the atmosphere.

I~xe: To calculate the ratio 238U/13°Xe we use the measured (36Ar/13°Xe) ratio in Loihi and MORB glasses which are = 5500 and 1300, respectively ([8,14], and unpublished data). Thus, we get: /~xe.v = ,130Xe]v=(-- ~ ) , 3 6 A r ] v , ~ 3 - ~ X e ] v - = 1.70 × 10 5

(33)

As pointed out by Staudacher and All+gre [9], it is not possible to change significantly the isotopic composition of xenon in 4.5 × 10 9 years with such a low # value. Therefore, the isotopic composition of xenon measured in Loihi samples and the isotopic composition of the terrestrial atmosphere can be considered as representative of the initial terrestrial xenon. For the depleted reservoir we get:

238U ] = 1.4 × 10 6

( 238U ] 4°K

36AE (34)

This value, however, is a lower limit, due to the fact that, for the calculation of /~Ar, we used d = 0 . 9 9 6 . For example, if we use a degree of outgassing of 99.9%, then /~Ar would be 4.2 × 10 4 and consequently ~xe = 5.6 × 106. This is close to the value we estimated in section 2.2 and allows us to produce the fissiogenic excesses in MORB glasses by spontaneous fission of 238U alone. However, some small contribution from spontaneous fission of 244pu cannot be excluded.

3.3. Conclusions From this first approach, based on mass balance equations in a simple five-box model we obtained a quite c o h e r e n t - - e v e n if s i m p l e - - m o d e l of the Earth's mantle. If we accept a two-layer model for the present structure of the Earth's mantle, with a separated upper and lower mantle, we can deduce the following: The gas loss of the outgassed mantle is extremely high ( > 99.6%). The isotopic signature of the lower mantle is entirely controlled by the

undegassed part of the mantle, even if the mantle proportions of upper and lower mantle have changed with time (46-54% 4.5 G a ago; 35-65% today), as already proposed by All6gre et al. [8]. 17% of the present-day undepleted mantle (VO) has been outgassed before. Gas concentrations in the lower mantle (V + VO) and upper mantle (D) differ by a factor of 200 or more. This large difference shows that the mass exchanges between upper and lower reservoirs are minute. If not, mixing with lower mantle material would have diluted all the isotopic excesses of the upper mantle. 4. M e a n age and relation between c~, p, and time

To describe the isotopic evolution of a geochemical reservoir taking into account the transfer of both gas and radioactive parent we are led to some complex calculations. As shown for the case of Sr and Nd [18], and more recently for Th, U, Pb [19], the problem can be more easily tackled, and the solution is less model dependent, when using the concept of mean age. Direct use of model ages by calculating the ratios between a and /~ is not useful because of the drastically different geochemical behavior of the parent elements compared with the gaseous daughter elements in the process which generated MORB. Various processes affect the rare gases during magma generation, migration, and eruption before they are trapped in the glass, precluding derivation of chemical ratios applicable to the mantle from absolute concentrations in the MORB. Among those processes are liquid-solid fractionation during partial melting, gas-liquid fractionation during magma migration and residence in the m a g m a chamber, and, of particular importance, gas loss before and during eruption (e.g. [10,461). Therefore, we base our calculations on measured isotopic ratios, as proposed by Staudacher and All+gre [9]. The mean age of the atmosphere is defined by: 1

0

(Ta) = O - -~A fo tJ( t )dt

(35)

where 8 = age of the Earth; J(t) = gas flux from the mantle traced by the stable isotope denoted as

138 S (3He, 36Ar or 13°Xe), SA = p r e s e n t mass of the i s o t o p e S in the a t m o s p h e r e , a n d S O = initial mass of i s o t o p e s in the mantle. S a r d a et al. [10] p r o p o s e d a linear c o m b i n a t i o n o f two e x p o n e n t i a l functions to explain the o b s e r v e d A r a n d Xe d a t a in the a t m o s p h e r e a n d the m a n t l e by a two-stage outgassing:

I0 '° 10'

3%r

10 a

10 ~

flux ga 1

10 6

P'+be -v']

J(t)=KSo[(1-b)e I

t

I

I

1

4

3

2

1

0

(36)

and: (37)

d = d 1 + d 2 = SA/S o

A r e a s o n a b l e solution w o u l d be: b = 10 -3 4He flux 102°g a

fl=2.8×10

1

7a

1

y = 1.8 >( 10 -9 a -1

.5

T h e resulting m e a n age of the a t m o s p h e r e is:

1


.1 I

i

i

I

4

3

2

1

4-

T h e outgassing history of the earth is then d i v i d e d into two episodes. The first " h o t " e p i s o d e m u s t have been shorter than = 50 M a ; it is foll o w e d b y a long c o n t i n u o u s stage p r o b a b l y related to g e o d y n a m i c a l c o n d i t i o n s closer to the p r e s e n t ones, i.e. seafloor spreading. This m o d e l is in q u a l i t a t i v e a g r e e m e n t with the two-stage m o d e l of H a m a n o a n d O z i m a [45] a n d one of H a r t a n d H o g a n ' s [5] m o d e l s b u t is m o r e explicit a n d m o r e c o n s t r a i n e d . T h e degrees of degassing of stable i s o t o p e s are in the following range:

4-

3-

34°Ar flux

2-

101° ga -t

1

i

d 1 = 8 0 - 8 5 % (fast outgassing) 4

2

3

2

1

0

d 2 = 2 0 - 1 5 % (slow outgassing) T o c o m p a r e the degassing of stable a n d r a d i o genic isotopes, we can calculate a degree of degassing for r a d i o g e n i c isotopes, d e n o t e d d * , for b o t h the early (dx*) a n d the late process (d~'). W e find the following values:

radiogenic gas

12g Xe~'flux

for

1

4°mr, d * = 75% d~* = 1.5%

105ga 1

20

d~" = 73.5%

for 129Xe we give the values for the radiogenic p a r t of the flux, i.e. the flux o b t a i n e d when s u b t r a c t i n g

40

0

age (Ga)

Fig. 5. Evolution of the '*He, 36Ar, 4°Ar, and radiogenic 129Xe (129Xe *) fluxes into the atmosphere. Notice log scale for 4He and 36At. The very high peak of 4He flux in the first = 50 Ma

is due to the large primordial 4He component combined with the fast initial outgassing rate. Peaks for 4°Ar and 129Xe * are due to production of 4°Ar and 129Xe and the very fast initial outgassing rate.

139 the part due to the degassing of the amount of 129Xe initially present within the Earth (negligible in the case of 4°Ar): d* = 92% dt*=52%

d~'=40%

the discrepancy previously found using a simple exponential function. We now have a reasonable description of the kinetics of mantle degassing, and we can use it in order to: derive the input of the noble gases into the atmosphere throughout geological time, the outgassing fluxes for 4He, 4°Ar and 129Xe as il-

Such proportions reflect the very different decay constants of 1291 and 4°Ar, which is the reason for

4He

4He

3He

3He

-

11,000-

O0;j

c osEo

10,000-

407,000 307,000

9,000-

207,000 8,000IOZO00 ZOO0

7000-

i

~

J

r

4

3

2

1

4

0

4°Ar

4°Ar 36Ar 20,000

DEGASSING

f

r

T

q

2

1

0

50

I~0

1

0

ATMOSPHERE

36Ar 200

10,000

T

3

100

/

5

/ 0

i

4

0

i

i

1

3

2

1

0

129Xe 13°Xe

4

,

3

2

129X e

7.0 13°Xe 6.40645 ~ A T M O S P H E R E DEGASSING

6.75

MANTLE

6.5--

6.34

,

,

4

3

:;

, I

age (Ga)

0

6.34

~,

:3

~

~I

0

age (Ga)

Fig. 6. Evolution with time of the noble gas isotopic ratios of He, Ar and Xe in the upper mantle and the atmosphere. The atmosphere is considered to be a closed system and no continentaldegassingis envisioned.For mantle He, no flux of gas from the lower mantle is taken into account.

140 lustrated in Fig. 5, and the evolution of the corresponding isotopic ratios in mantle and atmosphere (Fig. 6); - - derive the input of H20, N 2, CO 2, ..., into the atmosphere and constrain the history of the hydrosphere (which will be done elsewhere).

where G is the degree of gas loss during transfer and eruption of basalts *. Thus, we can write: Xl

__

]J'glass- gglass

XD

~D

(40)

gD(1 - - G ) -- 1 ~

and: G = 1 - lllD/~glass

(4])

5. N o b l e g a s transfer b e t w e e n reservoirs

The arguments developed here have led us to a rather coherent history of the Earth's mantle. The structure of the mantle is quite simple. We have two layers the relative dimensions of which have changed with time: as suggested previously [8], the boundary has migrated upwards. The lower reservoir has been progressively mixed with parts of the shallower one. Before explaining the whole process we will examine the mode of gas transfer between different reservoirs, namely:

For /~D we take the ratios calculated in sections 3.1.2, 3.2.3. /%la~ and the corresponding K, U and noble gas concentrations are listed in Table 4. The gas loss, G, calculated for the different noble gases is: He, 98.1%; Ar, 98.3%; Xe, 98.2%. These calculations rule out any attempt to use simple parent~gas ratios measured in M O R B glasses to deduce directly the composition of the mantle or concentrations of noble gases therein. Even worse, these ratios cannot be used to calculate from these values any mantle model ages as attempted in [35].

upper mantle ~ atmosphere 5.2. Elemental ratios of noble gases

lower mantle ~ upper mantle Such analyses have already been attempted, but we will use here the relative systematics of the different noble gases. 5.1. Outgassing processes during eruption of M O R B The exact process by which MORB degas on the seafloor is not yet very well known. We will try to assess this phenomenon qualitatively. For this we again use the chemical ratio t~ = X / g . All the radioactive isotopes ( X ) are incompatible elements and generate noble gases (g). Then we can write: X~ = X D / f

(38)

where Xj, X D are the concentrations of X in the liquid phase and in the mantle source of MORB respectively, and f is the degree of partial melting. The noble gases undergo two processes, namely, partial melting with partitioning between liquid and solid phases (as for X above) and partitioning between liquid and gaseous phases during transfer of the basalts to the surface. A part of this gas is lost at eruption on the seafloor. Thus we write: gD (1 -- G) gglass- f

(39)

Before looking at elemental ratios of H e / A r , A r / X e . . . . , we have to mention that these ratios are based on the measurement of absolute gas amounts and are, in contrast to isotopic ratios of one noble gas, less precise. There are several reasons for this: (1) We do not use noble gas spikes and rely on a calibrated volume of atmospheric noble gas [9,10] that we measure separately. Therefore the conditions for the atmospheric standard and the sample gas are never the same and the precision of the spectrometer as a pressure gauge is estimated to be within only 5-10%. (2) Usually MORB glasses have very low noble gas concentrations of 3He, Ne, 36Ar, Kr and Xe; thus contamination with atmospheric gases via atmosphere or seawater may be possible [10,37]. To get reliable data we use the techniques of stepwise heating and crushing under high vacuum. In the following, we calculate the concentrations for Bulk Earth by taking the noble gas inventories of the atmosphere and diluting them * Note that the degree of outgassing (G) of the basaltic magmas at the seafloor is a completely different concept than the degree of outgassing of the mantle in the preceding sections.

141 TABLE 4 Mean concentrations of noble gases and radioactive elements in normal MORB glasses and corresponding /z values ~glass

Concentration

the values versus atomic mass (Fig. 7). Taking R = l / h where l and h stand for "light" and " h e a v y " isotope respectively, we find for masses higher than neon:

(tool g l) 4oK a 23~U b 3He c 36Ar ~" 130Xe c

1.5X10 1.7X10 8.1X10 2.4)<10 2.2×10

RA ~-" RLoihi > RMORB

9 10 15 15 18

2.0)<10 4 =238U/3He 6.2×105=40K/36Ar 7.5x107=238U/130Xe

" From Sarda et al. [10]. b Using K / U = 1 2 , 7 0 0 [23]. c From All~gre et al. [8] and Staudacher and AllOgre ([11], and unpublished data).

to the volume of the outgassed mantle (m o -- 0.46 mT). For 3He, which is lost into space, we take the earlier calculated value of 1.57 x 1014 moles 3He (section 3.2.3). Now, we normalize the measured concentrations in MORB and OIB glasses to the calculated Bulk Earth concentrations and report

(42)

This results is easy to explain by distillation if we assume that (a) light gases are more easily released than heavy gases, and (b) outgassing is a cumulative phenomenon. Therefore, the upper reservoir is more depleted in light noble gases than in heavy ones. We can elucidate this phenomenon by a simple model. Let D be the "effective partition coefficient" between the gaseous phase to be released and the mantle: D = Cgasphase/fmantle

(43)

We then use Rayleigh's law: R = Rof(D1

D2)

(44)

ic

where R =36Ar/84Kr or 84Kr/t3°Xe in MORB, R 0 = corresponding initial ratio, and f = residual gas in the mantle being 0.004 when taking 99.6% gas loss. We get:

aC A

D36Ar -- D~,Kr =

0.11

D~,w - D,3oxe = 0.16

o. 1 |

LOIHI

0.01

MORB

0.001 I

L,

~Hd°Ne~r

I

"'Kr

I

,~OXe

mass

number

Fig. 7. Noble gas concentrations pattern for MORB glasses ([8 11], and unpublished data) and glasses from Loihi seamount [8,14] normalized to the atmosphere: CA is the calculated concentration obtained when diluting the atmosphere noble gas content in the outgassed part of the mantle, i,e. rn o =

mT/2.

which exactly explains the phenomenon of distillation between Ar, Kr and Xe. There is, however, an important contradiction when taking R = 3 H e / 3 6 A r (or 3He/13°Xe). For the lower mantle we get for example R = 3 H e / 3 6 A r = 0.028, whereas we get R = 3.13 for MORB. Distillation, however, should favor the outgassing of 3He in MORB compared to 36Ar and RMORB < RLo~ should be measured. The opposite is observed. This discrepancy may be explained both by a He flux from the lower mantle to the upper mantle [271, which, however, is not accompanied by an equivalent Ar, Kr, or Xe flux, and by a thorough He enrichment in the melt during the process of partial melting under the ridges. We should point out here that the global He flux from the lower to the upper mantle is not identical with the gas flux coming from the lower mantle with the plumes. The latter is a local flux in which all gases are involved, while the He flux is a global phenomenon due to He diffusion

142 through the boundary layer between upper and lower mantle. From Fig. 7 we also find a small neon enrichment in MORB glasses compared to the Loihi glasses. We cannot decide here whether this enrichment is due to some neon diffusion from the lower to the upper mantle, or to an enrichment in the liquid during partial melting under the ridges. Staudacher et al. [14] recently analyzed the noble gases in Hawaiian glasses. From these data, we have calculated (see Table 3) the elemental ratios of the noble gases relative to 3He and considered them as representative of the primitive Earth (virgin mantle). Such ratios, along with the 3He amount in the hypothetical closed atmosphere (CA) as derived above (section 3.2.3), allow us to calculate the amounts of 2°Ne, 36Ar, 84Kr and 13°Xe in the closed atmosphere, which can be compared to the actual atmospheric inventory (Table 3). We can see that all the values A / C A are close to 1, as should be the case if all the outgassed noble gases are now in the atmosphere, even if this is a crude approximation. However, there are some interesting differences between different noble gases. The best agreement exists for argon. The small deficit in Kr (14%) and Xe (43%) can be explained by adsorption of these noble gases on sediments, especially on shales, as already proposed by Canalas et al. [32] to explain the so called "missing xenon" (see also [34]). However, the amount of this missing xenon does not have to be 22 times the atmospheric xenon inventory, but only ~ 0.7 times Xea (see also [14]). These considerations clearly show that it is difficult to justify an initial composition for the Earth based on any meteorite type, especially for rare gases. This has already been claimed by Wetherill [33] in 1981. A further deficit exists for neon (28%). This cannot be accounted for by adsorption. Therefore it is possible that a part of the neon was lost from the atmosphere to space, possibly during the early days of the Earth.

5.3. Noble gas flux from the mantle and continents and mass balance Helium fluxes. Until now we have not used He as an argument in the mass balance calculation, because of its limited residence time in the atmo-

sphere. However, if we want to estimate the gas flux from the Earth's mantle, the fact that He escapes into space is an advantage. Due to the relatively short residence time of helium in the atmosphere ( ~ 106 years) compared to the geological time scale we can assume that the Earth's mantle outgasses as much He as is lost from the atmosphere to space and that we have a steady state. The present flux of He is:

d(4-et=I 4-e (4.e 1 3H--~ [~HeHe]M --

d~

3He ]A] Q~

[laHel (4Hel ] + [~ 3-~e ] c -

~T~He]A]Q2

(45)

where Q t = 3 H e flux from m a n t l e / 3 H e in the atmosphere, and Q2 =3 He flux from c o n t i n e n t / 3He in the atmosphere. Having a steady state and no important mass fractionation for He isotopes when escaping to space [38] we can write: (4He/3He)M - (4He/3He)A 3Fc =3FM ~ ~

(46)

where 3Fc = 3 He flux from the continents, 3FM = 3He flux from the mantle, (4He/3He)A = 7.22 x 105, ( 4 H e / 3 H e ) c = 2 - 3 x 107 (Table 1), and (4He/3He)M = 86,000 [27]. We find that the 3He flux from the continents, 3Fo is about 2 3% of the 3He flux from the mid-oceanic ridges. The 3He flux from the mantle is estimated to be 1100 mol a -1 [39]. Then the 3He flux from continents is 3Fc --- 28 mol a 1 As already suggested by O'Nions and Oxburgh [20], a part of the 3He outgassed from the continents comes from the underlying mantle; let us try to estimate the relative amounts of each. We will use a continental mean age of 2 Ga and U and Th concentrations of 1.3 and 6.0 ppm respectively (Fig. 4): thus 6.8 x 1017 moles of 4He are generated within the continents (mass = 2 x 1025 g). We will assume now that all 4He produced in the continents is outgassed. Taking a mean 4 H e / 3 H e ratio of 2.5 x 107 for the continents, we may outgass a total of 2.7 x 10 l° moles of 3He together with 4He, i.e. a mean 3He degassing rate of 13.7 mol a - 1. The complement of -~ 14 mol a - 1 of 3He, should come from the mantle via the continents.

143 Thus we get the following fluxes:

ATMOSPHERE 4He (__)

3FM = 1114 mol a -1 = 1100 (at ridges)

= 7.23 10 5

%

+ = 14 (through continents) 3FC • 13.7 mol a 1 H 4FM= ( 43H-~ e ) ,. 3 F M = 9 . 6 X l 0 7 m o l a / 4He ] 3F, 4Fc = ~3--~e ]c c = 3 . 4 x 108 mol a -1

argon flux from mantle and continent to the

109 moles

4F m = 9 ! 6

a -I

3F m :

a- 1

moles

I

CONTINENT ~He/3He

Argon fluxes. Let us now calculate the present-day

1015 m o l e s

= 1.17

~F E : 3.4 108 moles 3F C = l & .

time of about one million years can be calculated for 3He in the atmosphere.

= 0,85

3He

A

1

We see immediately that the situation for 4He and 3He is quite different. Presently, 22% of 4He and 99% of 3He come from the mantle while 78% of 4He but only 1% of 3He come from the continental crust (Fig. 8). Let us examine now the relation between production rate of 4He and outgassing in the upper mantle. The production rate of 4He in the depleted mantle is 4.1 x 107 mol a 1 (3.3 ppb U, 8.3 ppb Th). However, the 4He loss through the mid-ocean ridge is 9.6 x 107 mol a -1 and therefore larger than the production rate. To compensate for the difference we need 5.5 x 10 7 mol a -1 ( = 60% of 4He loss) of 4He coming from the undepleted mantle. Along with this 4He, the upper mantle gets 2200 moles of 3He per year (with (4 H e / 3 He)v = 25,000), which is within a factor of two of the value estimated for the global 3He loss from the upper mantle. Consequently, He in the upper mantle is close to a steady state with outgassing to the atmosphere balancing 3He and 4He gain from the lower mantle and 4 He production in the upper mantle. Finally, we comment on He escape from the atmosphere to space. The total outgassing of 4He from mantle and continent is 4.4 x 108 mol a -1. Integrated over the last 4.5 x 10 9 years that yields a total of 2.0 × 1018 moles. On the other hand, we estimated that the total 4He loss from the atmosphere to space was 3.9 × 1018 moles (section 3.2.3). This result is in agreement with the idea that the atmosphere is in a steady state, the discrepancy being due to the greater He degassing flux in the early history of the Earth. A residence

4He

I

= 2.5 10 7

238o = 1.1 io 17 moles 232Th : 5 . 2

I

107 moles a - 1

]

1114 moles a - 1

10 17 m o l e s UPPER

MANTLE

~Pc = 3.0 10 8 moles a-I

3Me

: 1.2

4He

= 9 . 9 10 17 motes

23~j

= 2 . 0 10 16 moles

t

10 13 moles

3He

J+He --= 3He

86 000

= 1 . 6 10 - 5

238U

= 3 , 3 ppb

~p urn

= 4.0 107 moles

l

a-I

~Flm = 5.5 107 moles a -1 Ftm

2200

LOWER

3He = 2,1

10 14 moles 10 TM moles

cc/q

232Th = R,3 pob

232Th = 5.1 10 16 moles

4He = 5.3

= 1 . 8 10 - 1 0 cc/q

4He

~Me = 25 000

moles a - 1 MANTLE

3He

= 1,R

10 - 9 c c / q

4He

= 4,5

10 - 5 cc/q

3He 2380 = 22 ppb

238U = 2.5 10 17 moles

232Th = 92 ppb

232Th = 1.1 10 18 moles 4p ~n

= 6,3

108 moles a- 1

Fig. 8. Amounts and concentrations of helium and corresponding radioactive elements in the main terrestrial reservoirs, and helium fluxes between the different reservoirs. Detailed calculations of He concentrations will be given in [55].

atmosphere, based on our estimates for helium (Fig. 9). The 4He/4°Ar ratio in MORB is about 15.4 ([8], and unpublished data). Taking the 4He flux from the mantle we get: 4°FM =4FM/(4He/4°Ar)MOR B = 6.2 × 10 6 mol a -1, 36FM = 4OFM/(4OAr~ 36Ar)M = =250mola

40

Fr4/25,000

1.

In a review article Wasserburg et al. [40] estimate the (4He/4OAr) of gas escaping from the continental crust to be -- 10. Consequently, we get 4oFc = 3.4 x 10 7 mol a - l , or 6.8 × 1016 moles within the 2 Ga mean age of the continents. On

144

the other hand, we produce about 2.2 × 1017 moles of 4°Ar (K c = 1.7wt.%) during the same time interval. Thus, we have: = lost 4°Ar/produced 4°Ar = 0.31. This means that only 31% of the 4°Ar produced in the continental crust has been lost during geological time. This is certainly an upper limit because

Let us again examine the relation between production and outgassing for the mantle. The production rate of 4°Ar in the upper mantle (representing 1 / 3 of the total mantle) is 1.0 × 107 mol a i (42 ppm K; Fig. 4). This is about 2 times more than the amount of 4°Ar which is lost by outgassing through the mid-ocean ridges. Thus, t h e 4°Ar concentration in the upper mantle is growing again.

w e a s s u m e d a 4 H e l o s s o f 100%.

An interesting point is the observation that the flux of 36Ar escaping from the continents today is greater than the flux escaping from the mantle. Such a paradox reflects the fact that continents have incorporated a large amount of atmospheric material (adsorbed on shale buried with metamorphic fluids, etc.). On the other hand, the depleted upper mantle has been almost completely outgassed and as we will see in section 6.1.3., gas recycling due to subduction of oceanic crust or sediments into the upper mantle must be minute.

Xe flux from the mantle. In an analogous way to He and Ar we can calculate the present Xe flux through the mid-ocean ridge (Fig. 10): 13°FM =3FM/(3He/13°Xe)MoR B = 0.3 reel a 1 using a mean (3He/I30Xe)MORB = 3400 [8]. The amount of 13°Xe in the atmosphere is AIMOSPHFRF L2~Xe

13~XR

6.48

t3~Xe

: 2.56

13oxe

129X~ : 4 . 0

In 12 m o l e s

l~0×e

IO 11 m o l e s

- (;.2

t3h×e : 1.(; 1012 moles

ATMOSPHERE 4OAr

129F m : 2 • 2 mol~s a-"

3OAr = 5.58

10 15 moles

: 1165

10 18 moles

hOAr

13°Fm :

.3 moles a- [

134Fm :

.8 moles a- I

A 40F C : 3.4 107 moles

40F m =~6.2 106 moles a - 1

a -1

129Xe = 1.1

36F C ~ 103 moles a -I

36F m : 250 moles a -I

CONTINENT ~OK

I

1.0

10 18 moles

~OAr = 1.5

10 17 moles

:

23811 = 1.1 10 L7 mrlles

40P C : 5.9 107 moles

4.8 ~0 I t moles

134Xe

1.2 1012 mole

I

129Xe : 1.} 10 11 moles

UPPER

a -I

MANTLE

t~°Xe : 1.7 10 l ° moles

36AT : 1,7 1013 moles

J

4°1<

36Ar : 2,7 10 -10 c c / q

4OAr

~r

= 25 000

~°Ar

= 1.8 10 17 moles

6.7 10 . 6

: 2.0 10 16 moles

um

R

R A N 1 L

[29Xe = 2.q 10 -12 ec/o

130Xe

13°Xe = 2.7 10 - [ 3 ce!n

134Xe

13~Xe : 7.5 10 - t o cc!q

130Xe : 2.01 : O,l

134p

238U

~.~ ppb

mole a -1

um

42 ppm 40

= 1.0 107 moles a- I K LOWER LOWER

36Ar : 7.7 10 15 moles

MANTLF

36Ar = 6.5

10 - 8 c c / q

4OAr : 2.5

10 - 5 c c / q

~0Ar 4OAr = 3.0 10 18 moles

2380

cc/~l

U P P

L29Xe : 7.}6

]

134×8 : 4.8 10 1° moles

4OAr : 4 . 3 10 17 moles

1012 m o l e s

130Xe

:

390

WOK : 2.2 10 18 moles

CK ~OP~m = 1.3 10 8 m o l e s

= 270 ppm

a-1

MANII

129Xe = 9.6 10 12 moles

129Xe

130Xe = 1.5 10 12 moles

13°Xe

134Xe : 3.8 1012 moles

134Xe

238U

130 ×e

F 129Xe = ft.1

10 - I t

ce/q

1 3 ° × e = 1.2

10 - i l

cc/q

134Xe -

10 - i i

ec/q

= 6.48

5.2

= 2.5(; = 2.4

10 17 moles

134p

:

1.1 m o l e

238U

- 22 ppb

a-I

lm

Fig. 9. Amounts and concentrations of argon and corresponding radioactive elements in the main terrestrial reservoirs, and argon fluxes between the different reservoirs.

Fig. 10. Amounts and concentrations of xenon, and corresponding radioactive elements in the main terrestrial reservoirs, and xenon fluxes between the different reservoirs.

145 TABLE 5 Relative amounts of radioactive elements and noble gases in the four main terrestrial reservoirs

K U Th 3He 4He 36Ar 4°Ar 129Xe t3°Xe

Lower mantle

Upper mantle

Continental crust

Atmosphere

0.65 0.65 0.65 - 0.946 0.842 0.58

0.05 0.05 0.03 0.054 0.157 0.001

0.30 0.30 0.32 0 - 0 - 0

0 0 0 - 0 - 0.0001 0.42

0.57 0.58 0.58

0.08 0.01 0.01

0.03 - 0 - 0

0.32 0.41 a 0.41 a

a 0.24 in the atmosphere+0.17 in sediments.

6.23 × 1011 moles. In fact, this quantity only represents = 57% of the 1 3 ° X e that has been outgassed from the mantle (see section 5.2). The remaining 43% is probably trapped in sediments as indicated in Fig. 10. The 13°Xe lost through the slow continuous outgassing represents about 20% of the atmospheric 13°Xe (see section 4). If we integrate the present 1 3 ° X e flux from the mantle over 4.5 G a we get 1.4 × 1 0 9 moles, that is only about 1% of the xenon lost by the slow continuous outgassing. This is again an indication that gas loss through the mid-ocean ridges was much more important in the past than today. In the sections above it has been possible to calculate the noble gas content of the different terrestrial reservoirs and the present-day fluxes between them. In Table 5 we give the fraction of noble gas isotopes and parent elements in the four main reservoirs we have considered here. There are large differences between radiogenic and nonradiogenic primitive isotopes and of course between noble gases and lithophile elements.

6. Geodynamical consequences 6.1. Structure and behavior of the mantle The calculations we have developed in this study of the two-layer mantle are quite coherent. The upper mantle is now rather well documented. The situation is different for the lower mantle.

Thus far, glass samples from the Loihi seamount provide us with the only rare gas data for the lower mantle. More work has to be done to find other suitable glass samples from hot spots coming from the lower mantle. One of the most important results is the difference in gas concentration between outgassed and non-outgassed mantle and the existence of large rare gas anomalies in the outgassed upper mantle reservoir.

6.1.1. Exchange between upper and lower mantle Except for He (and maybe Ne) the exchange between upper depleted and lower mantle seems to occur exclusively through hot spots or blobs. Hot spots or blobs transfer their gases directly to the atmosphere while the lithophile elements are incorporated into the oceanic crust and involved in the cycle of reinjection-mantle mixing-crust formation, etc. Any other significant gas transfer between lower and upper mantle would have wiped out the special signature of the highly outgassed upper mantle with its particular noble gas anomalies. The fact that there seems to be a continuous transfer only of helium from the lower to the upper mantle indicates a boundary between the two types of mantle which obviously can only be overcome by the rare gas with the highest diffusion rate. At ridge crests a special mechanism occurs. Blobs are injected under the ridges [31]. Part of their rare gas inventory is mixed with the upper reservoir from which the MORB are formed. Such a process explains the correlation observed in MORB between 1 2 9 X e / 1 3 ° X e , 4°Ar/36Ar, 87Sr/ 8 6 8 r and 4 H e / 3 H e as already pointed out. 6.1.2. Origin of OIB In our model, oceanic island basalts show the rare gas signature of only slightly outgassed mantle, i.e. the lower mantle. All6gre and Turcotte [44] proposed a boundary layer model in which OIB no longer have a pure lower mantle source. The boundary layer is a mixture of upper mantle and reinjected oceanic and continental crust a n d / o r sediments. Large blobs rising from such a boundary layer drag lower mantle material with them. Due to the high rare gas concentration in the lower mantle, the lower mantle material will impose its signature on the rare gases but not on lead isotopes.

146

6.1.3. Reinjection of oceanic crust: the subduction barrier Here we briefly discuss reinjection of oceanic crust and oceanic sediments into the upper mantle through subduction zones because this has extremely important consequences. The upper part of this oceanic crust is certainly altered and thus contains large amounts of atmospheric noble gases ([37], and Table 1). In addition to the altered oceanic crust, oceanic sediments are also at least partly reinjected into the mantle. Based on such data some authors doubt that the upper mantle is characterized by such high rare gas isotopic ratios. However, two errors are usually made in such estimates: (a) noble gas concentrations of mantle derived samples are taken as mantle concentrations, and (b) usually all noble gases in the oceanic crust or sediments are presumed to be reinjected through subduction, without taking into account that a major part of

this gas .is lost back into the atmosphere through volcanic .activity in subduction zones. Let us~ try to represent this in a simple calculation. For that we will use a set of new data we have obtained on ophiolites, altered old oceanic crust and sediments which will be published elsewhere. We will give here only a summary of these results. Let us suppose a constant subduction rate within the last 4 Ga (which is certainly underestimated). Furthermore, we will assume that only the upper 500 m of oceanic crust are altered and that a 500 m layer of oceanic seafloor sediments are subducted together with the oceanic crust. We have to take into account that about 5 X 1 0 25 g of material are reinjected into the upper mantle within 4 Ga (about 2 times the mass of the present-day continental crust). If no gas loss from the reinjected material occurs through subduction volcanism, then together with oceanic crust and sediments 5 x 1 0 24 c m 3 of H 2 0 ; 8 X 1017 c m 3 of 36Ar and 1.3 X 10 as cm 3 of 13°Xe must also be carried along *. This, however, represents about 4 times the water amount of the world oceans, 2 times the 36Ar and 3 times the 13°Xe amount in the upper mantle. * Noble gas concentrations of old oceanic crust and sediments (see Table 1); noble gas content in the upper mantle (see Figs. 6 and 7); water content in old oceanic crust is = 0.86wt.% [47]; water content in seafloor sediments is > 20% [48]; volume of the oceans = 1.2 x 1024 cm 3.

atmosphere

//

~

"~

!K (

llJIIIII; I]IflIIIII\~Y,

.J

|

~ b" ~ '

,'~/]lllllllIIIJIIli]lll//~x~

......................... h ................................................. '............

~

" ~

. ,::.:: :

subduction volcanism

v;,;: L

a

y

er

Y

{,2"'";/ Fig. 11. Schematic representation of the gas fluxes in the mantle-atmosphere system. Note that the gas flux from the atmosphere to the oceanic crust and sediments must be as large as the flux from the subduction zones to the atmosphere.

It is obvious that reinjected material must be highly outgassed in subduction zones through the intense volcanic activity in such regions. In fact subduction volcanism is a barrier for volatiles (Fig. 11). Such an effect has many consequences as will be developed elsewhere.

6.2. Outgassing and geodynamics of the mantle In section 4 we estimated that the radiogenic isotopes, which are formed in the upper mantle are outgassed to the atmosphere to a very high degree. This requires strong convection in the upper mantle. The lower mantle which contains a higher concentration of radioactive elements and which is two times more voluminous is certainly convective too. On the other hand, very little of the radiogenic isotopes formed in the lower mantle are transferred to the upper mantle (hot spots transfer their gases directly to the atmosphere). Therefore, we have to admit an effective boundary between upper and lower mantle. Let us now describe the way the Earth was outgassed. The outgassing is a combination of two processes, namely, enrichment in gases by partial

147 melting in the upper mantle and an almost total gas loss during or after the eruption at the surface, involving creation of oceanic lithosphere at a ridge crest. Our calculations allow us to estimate the degree of partial melting at about 10% (section 6.3) and the gas loss of the erupting basalts at about 98% (section 5.1). The degree of mantle outgassing gives us a measure of the creation of oceanic crust. For instance, if we suppose that 46% of the mantle was totally outgassed within the first 100 Ma, then 1.9 x 1019 g a -1 must have been affected. Estimates show that today 7 x 1016 g a-1 of oceanic lithosphere are created and reinjected back into the mantle. Therefore, we have to admit that in the very early history of the Earth, the creation of oceanic crust was = 200 times more intense than today. This value is by no means unreasonable. In fact, we know from Sr isotopic systematics in limestones [36] that the amount of oceanic crust created was 5 times higher 3 G a ago than today. This estimate gives us an idea of the variation of the geodynamic regime of the Earth and the variation of convection with time. The fact that only 46% of the mantle is completely outgassed also constrains the early convective regime of the mantle. It seems that a central part of the Earth was protected from turnover. 6. 3. Heat production and degassing Following O'Nions and Oxburgh [20] we will compare heat transfer and degassing in the present-day mantle. Through the rare gas results we have a good idea of the concentrations of radiogenic elements in the Earth (Fig. 4). Bulk silicate earth contains K = 278 ppm, while the upper mantle should contain 42 p p m K (sections 3.1.2 and 3.1.3). Taking a present-day K / U ratio of 12,700 [23], we get 22 p p b U for the primitive mantle and 3.3 ppb U for the depleted mantle. The T h / U ratios for the primitive mantle and the upper mantle are 4.2 [19] and 2.5 [23,25] respectively. Thus, the Th concentrations are 92 ppb and 8.3 ppb for the primitive and depleted mantle respectively. Let us see whether these numbers are compatible with the data for MORB. The K content of

typical MORB is---500 p p m (e.g. [10]). If we assume that K is a completely incompatible element we can write the partial melting factor F as Cmantle//CMoRB ~ 10%. This estimate is in agreement with estimates derived from petrological arguments. We may complete this section about mass balance of radiogenic elements by calculating the concentrations of K, U, Th in the continents using: C T ~-. C c m c / m

D+ CD

(47)

and get CK = 1 . 7 % ; CU = l . 3 ppm; CcTh=6.0 ppm. Fig. 4 shows the present-day inventory of radiogenic elements in the three main reservoirs. The U and Th concentrations are in a very good agreement with completely independent estimates obtained on the basis of U-Th-Pb systematics [19]. The heat loss through the whole surface of the Earth amounts to 4.2 x 1013 W [22]. The heat production in the upper mantle (35% of mantle) can be calculated from the amounts of U, Th and K and is 9.9 x 10 xl W. The heat production in the lower mantle is 1.5 x 1013 W. The heat production in the continents is 6.4 x 1012 W. Obviously a large part of the heat flux at the surface is accounted for by heat coming from the lower mantle [20]. This confirms the results already claimed by several authors that the depleted upper mantle is heated from below and not from within. The difference between the heat loss of the Earth and the heat production in the mantle of 2 x 1013 W has been the subject of many recent papers: this difference seems to require a two-layered mantle, showing t w o different regimes of heat transmission, that is, a convective one within the convection cells and heat conduction within the boundary layer which separates upper and lower mantle (e.g. [41]). The boundary layer acts as a barrier which makes heat loss slower [54]. This picture agrees well with the noble gas results. We have shown that He, Ar and Xe isotopic results strongly favor the existence of a lower undegassed mantle and that a large part of the 4He lost at the surface originates in the deep mantle ( -- 60%), but that no deep argon nor xenon is required to explain the argon and xenon fluxes at the surface. These features are compatible with

148 TABLE 6 Noble gas concentrations in the pristine mantle

3He 2°Ne 36Ar S4Kr

13°Xe

Concentration (cm3 STP g l)

Normalized to 84Kr

1.895<10 4.92×10 6.63 × 10 1.60×10 1.33×10

1.18 30.7 41.4 ~1 0.0083

9 s 8 9 1l

a diffusion process through the b o u n d a r y between the u p p e r a n d lower reservoirs for both heat and, to a lesser extent, helium. Conversely, this b o u n d a r y prevents Ar, K r a n d Xe diffusion. These c o n s i d e r a t i o n s suggest that the efficiency of diffusion is larger for heat t h a n for helium, a n d larger for helium than for argon a n d xenon: the few available e x p e r i m e n t a l d a t a support this [42,43]. The b o u n d a r y layer, as envisioned by All~gre a n d T u r c o t t e [44], must exist at the b o t t o m of the u p p e r m a n t l e a n d be generated by the c o n t i n u o u s i n p u t of cold dense oceanic lithosphere. This b o u n d a r y layer, heated from below, gives b i r t h to thermal instabilities a n d rising blobs that are the origin of oceanic islands.

6.4. Inventory of the volatiles on the Earth Let us finally calculate the rare gas concentrations in the Earth, taking argon as the key element. As we have p o i n t e d out before, argon cann o t escape to space due to its high atomic weight n o r should it be adsorbed substantially o n shales. T a k i n g n o w the argon of the Earth's a t m o s p h e r e a n d diluting it i n t o 46% of the m a n t l e we get 6.6 × 10-8 cm 3 g 1 as initial 36Ar c o n c e n t r a t i o n in the Earth. All other gases are now calculated according to the Loihi rare gas p a t t e r n (Table 3) a n d are given in T a b l e 6. These c o n c e n t r a t i o n s represent the rare gas c o n c e n t r a t i o n s in the pristine Earth, before a strong convection in the u p p e r part of the Earth's m a n t l e was established, involving fast outgassing of the u p p e r m a n t l e a n d form a t i o n of the Earth's atmosphere.

Acknowledgements C. J a u p a r t provided valuable help c o n c e r n i n g the thermal aspects of this paper, K.K. T u r e k i a n a n d D.L. T u r c o t t e m a d e m a n y helpful c o m m e n t s .

S.H. R i c h a r d s o n c o n t r i b u t e d to critical discussions. M a n y thanks to Claude Mercier for such heavy word processing a n d her patience in the never e n d i n g changes that occurred in the text. I.P.G. C o n t r i b u t i o n No. 895.

Appendix 1 C a l c u l a t i o n of the a m o u n t of 4He p r o d u c e d d u r i n g the time 0: 4He = 4 H e 0 +238U • F F is a f u n c t i o n of the decay constants: F = 8(e ~ ° - 1) + 7Ra(e x,° - 1) + 6 R 2 ( e x2° - 1) where )`8, )`s, )'2 are the decay c o n s t a n t s for 238U, 235U, 232Th respectively; Ra =235 U / 2 3 8 U = 1 / 1 3 7 . 9 (in mole units); a n d R 2 = 2 3 2 T h / 2 3 8 U = 1.033 • T h / U , where T h / U is in weight units. T a k i n g T h / U = 4.2 a n d 0 = 4.5 G a (in section 3.2.3) we get F = 18.7.

References 1 K.K. Turekian, The terrestrial economy of helium and argon, Geochim. Cosmochim. Acta 17, 37, 1959. 2 P.E. Damon and J.L. Kulp, Inert gases and the evolution of the atmosphere, Geochim. Cosmochim. Acta 13, 280, 1958. 3 M. Ozima and E.C. Alexander, Jr., Rare gas fractionation patterns in terrestrial samples and the Earth Atmosphere evolution model, Rev. Geophys. Space Phys. 14, 385, 1976. 4 I. Kaneoka and N. Takaoka, Rare gas isotopes in Hawaiian ultramafic nodules and volcanic rocks: constraints on genesis relationships, Science 208, 1366, 1980. 5 R. Hart and L. Hogan, Earth degassing models and the heterogeneous versus homogeneous mantle, in: Terrestrial Rare Gases, E.C. Alexander, Jr. and M. Ozima, eds., Japan Scientific Societies Press, Tokyo, 1978. 6 O.K. Manuel and D.D. Sabu, The noble gas record of the terrestrial planets, Geochem. J. 15, 245, 1981. 7 D.E. Fisher, Implications of terrestrial 4°Ar/36Ar for atmospheric and mantle evolutionary models, Phys. Earth Planet. Inter. 29, 242, 1982. 8 C.J. All6gre, Th. Staudacher, Ph. Sarda and M. Kurz, Constraints on evolution of Earth's mantle from rare gas systematics, Nature 303, 762, 1983. 9 Th. Staudacher and C.J. All~gre,Terrestrial xenology, Earth Planet. Sci. Lett. 60, 389, 1982. 10 Ph. Sarda, Th. Staudacher and CJ. All+gre, 4°Ar/36Ar in MORB glasses: constraints on atmosphere and mantle evolution, Earth Planet. Sci. Lett. 72, 357, 1985. 11 Th. Staudacher and C.J. All~gre, Noble gases in MORB from the Indian Ocean, Terra Cognita, Spring Issue, p. 42, 1984. 12 C.J. All6gre, Chemical geodynamics, Tectonophysics 81, 109, 1982.

149 13 M.S. Quinby-Hunt and K.K. Turekian, Distribution of the elements in sea water, EOS 64, 14, 130, 1983. 14 Th. Staudacher, M.D. Kurz and C.J. All~gre, New noble gas data in glass samples from Loihi seamount and Hualalaii, and in dunite samples from Loihi and Reunion islands, Chem. Geol., 56, 193-205, 1986. 15 B.M. Kennedy, M.A. Lynch, ,l.H. Reynolds and S.P. Smith, Intensive sampling of noble gases in fluids at Yellowstone, I. Early overview of the data; regional patterns, Geochim. Cosmochim. Acta 49, 1251-1261, 1985. 16 G.W. Wetherill, Variations in the isotopic abundances of neon and argon extracted from radioactive minerals, Phys. Rev. 96, 679, 1954. 17 W.A. Butler, P.M. Jeffery, J.H. Reynolds and G.J. Wasserburg, Isotopic variations in terrestrial xenon, J. Geophys. Res. 68, 3283, 1963. 18 C.J. All~gre, S.R. Hart and J.F. Minster, Chemical structure and evolution of the mantle and continents determined by inversion of Nd and Sr isotopic data, II. Numcrical experiments and discussion, Earth Planet. Sci. Lett. 66, 191, 1983. 19 C.J. All+gre, E. Lewin and B. Dupr~, Systematics in thorium-uranium-lead geochemistry, submitted to Chem. Geol., 1986. 20 R.K. O'Nions and E.R. Oxburgh, Heat and helium in the Earth, Nature 306, 429, 1983. 21 T.J. Bernatowicz and F.A. Podozek, Nuclear components in the atmosphere, in: Terrestrial Rare Gases, E.C. Alexander, Jr. and M. Ozima, eds., Japan Scientific Societies Press, Tokyo, 1978. 22 J.G. Sclater, C. Jaupart and D. Galson, The heat flow through the oceanic crust and the heat loss of the Earth, Rev. Geophys. Space Phys. 18, 269, 1980. 23 K.P. ,lochum, A.W. Hofmann, E. Ito, H.M. Seufert and W.M. White, K, U and Th in mid-ocean ridge basalt glasses and heat production, K / U and K / R b in the mantle, Nature 306, 431, 1983. 24 R.H. Steiger and E..lager, Subcommission in Geochronology: Convention on the use of decay constants in geo- and cosmochronology, Earth Planet. Sei. Lett. 36, 359, 1984. 25 M. Condomines, P. Morand and C.J. All~gre, 23°Th-238U radioactive disequilibria in tholeiites from the FAMOUS zone (Mid-Atlantic Ridge, 36°50'N): Th and Sr isotopic geochemistry, Earth Planet. Sci. Lett. 55,247, 1981. 26 R.K. O'Nions, S.R. Carter, N.M. Evensen and P.J. Hamilton, Upper mantle geochemistry, in: The Sea, Vol. VII, C. Emiliani, ed., Interscience, New York, N.Y., 1981. 27 M.D. Kurz, Helium isotope geochemistry of oceanic volcanic rocks: implications for mantle heterogeneity and degassing, Ph.D. Thesis, MIT-Woods Hole Oceanographic Institution, WHOI 82-32, 1982. 28 D.C. Black, On the origin of trapped helium, neon and argon isotopic variations in meteorites, I. Gas rich meteorites, lunar soils and breccia, Geochim. Cosmochim. Acta 36, 347, 1972. 29 P.M. Jeffery and E~ Anders, Primordial noble gases in separated meteoritic minerals, I, Geochim. Cosmochim. Acta 34, 1175, 1970. 30 D.C. Black, On the origin of trapped helium, neon and argon isotopic variations in meteorites, II. Carbonaceous

meteorites, Geochim. Cosmochim. Acta 36, 377, 1972. 31 C.J. All+gre, B. Hamelin and B. Dupr~, Statistical analysis of isotopic ratios in MORB: the mantle blob cluster model and the convective regime of the mantle, Earth Planet. Sci. Lett. 71, 71, 1984. 32 R.A. Canalas, E.C. Alexander, Jr. and O.K. Manuel, Terrestrial abundance of noble gases, J. Geophys. Res. 73, 3331, 1969. 33 G.W. Wetherill, Solar-wind origin of 36Ar on Venus, Icarus 46, 70-80, 1981. 34 T.J. Bernatowicz, F.A. Podosek, M. Honda and F.E. Kramer, The atmospheric inventory of xenon and noble gases in shales: the plastic bag experiment, ,l. Geophys. Res. 89, 4597, 1984. 35 D.E. Fisher, Radiogenic rare gases and the evolutionary history of the depleted mantle, J. Geophys. Res. 90, 1801, 1985. 36 O. Brrvart and C.J. All+gre, Strontium isotopic ratios in limestones through geological time as a memory of geodynamic regimes, Bull. Soc. Geol. Fr. 7, XIX, 6, 1253, 1977. 37 J. Dymond and L. Hogan, Factors controlling the noble gas abundance patterns of deep sea basalts, Earth Planet. Sci. Lett. 38, 117, 1978. 38 B.A. Mamyrin and I.N. Tolstikhin, Helium isotopes in the Earth's atmosphere, in: Helium Isotopes in Nature, 203 pp., Elsevier, Amsterdam, 1984. 39 H. Craig, W.B. Clarke and M.A. Beg, Excess 3He in deep sea water on the East Pacific Rise, Earth Planet. Sci. Lett. 26, 125, 1975. 40 G.J. Wasserburg, E. Mazor and R.E. Zartman, Isotopic and chemical composition of some terrestrial natural gases, in: Earth Sciences and Meteorites, pp. 219-240, North-Holland, Amsterdam, 1963. 41 D. McKenzie and F.M. Richter, Parameterized convection in a layered region and the thermal history of the Earth, ,l. Geophys. Res. 86, 11667, 1981. 42 W.G. Perkins and D.R. Begeal, Diffusion and permeation of He, Ne, Ar, Kr and D 2 through silicon oxide films, J. Chem. Phys. 54, 4, 1683, 1971. 43 M.D. Kurz and W.J. Jenkins, The distribution of helium in oceanic basalt glasses, Earth Planet. Sci. Lett. 53, 41, 1981. 44 C.J. All~gre and D.L. Turcotte, Geodynamic mixing in the mesosphere boundary layer and the origin of oceanic islands, Geophys. Res. Lett. 12, 207-210, 1985. 45 Y. Hamano and M. Ozima, Earth-atmosphere evolution models based on Ar isotopic data, in: Terrestrial Rare Gases, E.C. Alexander, Jr. and M. Ozima, eds., Japan Scientific Societies Press, Tokyo, 1978. 46 Th. Staudacher and Ph. Sarda, Comment on Fisher's "Radiogenic rare gases and the evolutionary history of the depleted mantle", submitted to J. Geophys. Res., 1985. 47 T. Donnelly, J. Francheteau, W. Bryan, P, Robinson, M. Flower and M. Salisbury, Initial Reports of the Deep Sea Drilling Project, Vols. 51-53, U.S. Government Printing Office, Washington, D.C., 1978. 48 T.C. Moore, P.D. Rabinowitz et al., Initial Reports of the Deep Sea Drilling Project, Vol. 74, U.S. Government Printing Office, Washington, D.C., 1984. 49 R.H. Bieri, M. Koide and E.D. Goldberg, The noble gas contents of Pacific sea water, J. Geophys. Res. 71, 5243, 1966.

150 50 H. Craig, R.F. Weiss and W.B. Clarke, Dissolved gases in the equatorial and south Pacific Ocean, J. Geophys. Res. 72, 6165, 1.967. 51 R.H. Bieri and M. Koide, Dissolved noble gases in the east equatorial and southeast Pacific, J. Geophys. Res. 77, 1667-1676, 1972. 52 E. Mazor, J.G. Wasserburg and H. Craig, Rare gases in Pacific Ocean water, Deep Sea Res. 11,929-932, 1964. 53 C.H. Langmuir, R.D. Vocke, Jr. and G.N. Hanson, A

general mixing equation with applications to Icelandic basalts, Earth Planet. Sci. Lett. 37, 380, 1978. 54 S.P. Clark and K.K. Turekian, Thermal constraints about distribution of long-lived radioactive elements in the earth, Philos. Trans. R Soc. London Ser. A 291, 219-275, 1979. 55 Th. Staudacher, Ph. Sarda, S.H. Richardson, C.J. All~gre and J. Sagna, Noble gases in basalt glasses from a topographic high on the MAR at 14°N (in preparation).