the closed-system approximation for evolution of argon and helium in the mantle, crust and...

Chemical Geology (Isotope Geoscience Section), 52 (1985) 45-73 Elsevier Science Publishers B.V., Amsterdam -Printed in The Netherlands

45

THE CLOSED-SYSTEM APPROXIMATION FOR EVOLUTION OF ARGON AND HELIUM IN THE MANTLE,

CRUST AND ATMOSPHERE

ROGER HART, LEWIS HOGAN and JACK DYMOND

College of Oceanogmphy, Oregon State University, Corvallie, OR 97331 (U.S.A.)

(Accepted for publication October 4,1984)

Abstract

Hart, R., Hogan, L. and Dymond, J., 1985. The closed-system approximation for evolution of argon and helium in the mantle, crust and atmosphere. In: F.A. Podosek (Guest-Editor), Terrestrial Noble Gases. Chem. Geol. (Isot. Geosci. Sect.), 52: 45-73.

The atmosphere formed by the outgassing of the depleted mantle, leaving a remnant of non-degassed mantle which forms the source of some ocean-island basalts such as Hawaii and Iceland. The ‘OAr in the atmosphere degassed from 50% to 90% of the mantle possibly synchronous with sea-floor spreading, ocean- ridge hydrothermal activity and continent formation. The bulk of the degassing ended 1.2-1.8 Ga ago. The similarity of the ‘OArla6Ar ratio between the atmosphere and non-degassed mantle suggests both have approximated closed systems. On the other hand, more than 99% of He outgassed from the mantle has been lost to space from the upper atmosphere. Portions of the oceanic crust and mantle contaminated by atmospheric noble gases are distinguished from non-degassed mantle by this He depletion.

1. Introduction

Heterogeneities in the isotopic composition of Sr, Pb, and Nd in oceanic basaIts have been reported for some time (Gast et al., 1964; Tatusumoto; 1966; S.R. Hart et al., 1973; O’Nions and Pankhurst, 1974; Sun et al., 1976; DePaolo and Wasserburg, 1976a, b; O’Nions et al., 1977); only recently has at- tention been focused on the significance of the isotopic heterogeneities of Ar and He in the oceanic crust. Heterogeneities in the noble-gas concentrations were first proposed by Bernatowicz and Podosek (1978) and R. Hart and Hogan (1978), based on the observation that the abundance of 4oAr, 4He and 136Xe in the atmosphere is small compared to the abundance of their parent nuclides in the

mantle. Both sets of authors suggested that the upper mantle may have degassed more ex- tensively than the deep mantle. In another study R. Hart et al. (1979) suggested that the atmosphere degassed from the upper-mantle mid-ocean ridge basalt (MORB) source and predicted that the nondegassed mantle should have a 40Ar/36Ar ratio of 450.

While the early measurements suggested uniform 3He/4He ratios in oceanic basaIts (Craig and Lupton, 1976; Kurz and Jenkins, 1981), high ratios have been reported recently from “plume” areas (Kaneoka and Takaoka, 1978, 1980; Poreda et al., 1980; Kurz et al., 1981; 1982a, b; Rison and Craig, 1981; Kyser and Rison, 1982; AIIegre et al., 1983a, b).

Combined studies of *‘Sr/s%r and 3He/4He

0168-9622/85/$03.30 0 1985 Elsevier Science Publishers B.V.

46

variations along the Mid-Atlantic Ridge indicated mixing of a “plume” source, a MORB component, and a third component at first suggested to be subducted continental crust (Kurz et al., 1982a). Later Kurz et al. (1982b) suggested 3He/4He-87Sr/86Sr systematics cannot distinguish magma mixed with continental crust from that mixed with oceanic crust, oceanic sediments or seawater. The three- component model is also suggested by combined 87Sr/8aSr and 143Nd/144Nd studies (White and Hofmann, 1982). These authors suggested that, in addition to “plume” and MORB sources, a third component of subducted oceanic sediments is required to explain the low ( 143Nd/144Nd)/( 87Sr/86Sr) ratios measured in regions such as Samoa. Most recently up to five components have been used to explain the systematics of the solid- state isotopes in. the oceanic crust (White, 1985).

In this paper we establish a logical and mathematical foundation for threecompo- nent mixing of Ar and He in the oceanic crust and suggest that data currently available are consistent with a model which provides for mixing between a nondegassed “plume” source, a MORB source that has been ex- tensively degassed in 36Ar and 3He, and an atmospheric component which may be: (1) contamination, (2) assimilation of altered oceanic crust or sediments, or (3) recycled oceanic crust and sediments. In this model the Ar that has been degassed from the upper mantle is now partitioned between the sialic crust and the atmosphere. Indeed, the atmosphere resulted from the upper-mantle degassing event.

In Section 2.1 of this paper we present new Ar and He measurements from 38 submarine glassy basalts. In Section 2.2 we calculate the 40Ar/36Ar ratio of the nondegassed mantle by adding the Ar in the sialic crust and the atmosphere to that of the upper mantle. In Section 2.3 we calculate the 4He/40Ar ratio of the nondegassed mantle from the Th, U and K contents of oceanic basalt8 and compute the 3He/36Ar and 4He/36Ar ratio for non-de-

gassed mantle. In Section 2.4, we present calculations of curves for mixing of atmospheric, MORB and plume (non-degassed) sources. In Section 2.5 we estimate the amount of fractionation of c(* = (40K/36Ar) and pn = ( U/3He) between the MORB and plume source, and in Section 2.6 we calculated the mean age of cessation of degassing of the MORB source to the atmosphere to be between 1.2 and 1.8 Ga ago.

2. Three-component mixing of Ar and He in the oceanic crust

2.1. The Ar and He data from glassy submarine basal ts

The 3He/4He ratios were determined independently from splits of the same samples at either Woods Hole Oceanographic Institute or Scripps Institute of Oceanography and the reader is referred to papers by Craig and Lup- ton (1976) and Kurz and Jenkins (1981) for a discussion of the procedure used to deter- mine the He isotopic composition. The results for the heavy raregas measurements, major- element chemistry and detailed sample de- scriptions are presented in Hogan and Hart (1985).

Samples were hand-picked under a binocular microscope to eliminate alteration products and phenocrysts, rough-crushed and sieved to 0.84-6.mm size, and ultrasonically cleaned in double-distilled water. The samples were loaded into a F’yrex@ furnace and baked for 15 hr. at 2OO’C. A molybdenum crucible was outgassed at 1400°C for 20 min. and the sample baked for another 15 hr. at 2UO’C. A final lo-min. o of the crucible at 1400°C was done tely prior to run- ning either blank or sample. Kyser and Rison (1982) demonstrated crucible contamination, especially for Ne and He when samples were fused one after the other in the same crucible. As a precaution st this ef&&, only clean and outgaseed crucibles w@re used. The back- ground was determined for each individual sample by mimicking the heating steps and

47

temperature of the sample extractions. Back- ground w,as minimized by use of the large samples, u;sually in the range l-5 g. The back- ground comections for 4He range from 0.15% to 16%, for 36Ar they range from 9% to 51% and for 4”Ar they range from 2% to 26%. After introduction of 3He and 38Ar spikes, the gases wer’e extracted from the sample at 1400°C and cleaned on a titanium getter operating at 950°C. After cooling of the getter, the gas sample was released into an ultra-clean portion of the extraction line and cleaned once again on hot titanium. The heavy noble gases, Ar, Kr and Xe, were collected on charcoal at liquid-nitrogen temperature, and He and Ne were expanded into a Reynolds- type mass spectrometer for 3 min. before beginning the analysis. During the He and Ne analysis, the extraction line was pumped out for 5 min. while heating the getters to 400°C. After analysis, the spectrometer tube was pumped until the pressure reaches its back- ground (a 2 l 10-l’ Torr). The heavy noble gases were released from the charcoal by heating to 300°C for 0.5 hr. The gas was in- troduced to the mass spectrometer for 6 min. and Kr and Xe were measured. After pumping of the spectrometer tube, the remaining gas in the extraction line was admitted to the spectrometer and analyzed for its Ar isotopic composition. The precision determined on duplicate runs in our laboratory is 18% for 4He, 8% for 36Ar and 2% for 40Ar.

Duplicate analyses made in our laboratory are compared with analyses made at Scripps, Berkeley, U.S. Geological Survey, Menlo Park, and Woods Hole in Table I. There is some discrepancy in the 4He concentration between our laboratory and the Berkeley analysis (sample 1742). In general, however, the agreement among noble-gas laboratories demonstrates that the wide variations in 40Ar/36Ar, 4He/40Ar and 4He/36Ar ratios that we measure in glassy basalts, given in Table II, are significant.

2.2. The estimation of the 4oArf6Ar, 4oK/ 36Ar and UPHe ratios of the nondegassed mantle

Recent measurements of the 40Ar/36Ar ratio in phenocrysts and glassy margins of basaIt,s sampled from plume areas suggest that the 40Ar/36Ar ratio of the nondegassed mantle is similar to that of the atmosphere in con- trast to the high ratios measured in MORB (R. Hart et al., 1979,1983; Saito et al., 1978; Kaneoka and Takaoka, 1980; Kyser and Rison, 1982; All&e et al., 1983a). The similarity is of interest in Earth degassing models, and four explanations have been suggested:

(1) The Ar isotopic composition of the atmosphere is primordial (Manuel, 1978; Ozima and Zashu, 1983a).

(2) Atmospheric Ar has recycled through the deep mantle (Manuel and Sabu, 1981).

(3) The atmosphere has degassed in recent time from the lower mantle with a high degassing rate (Fisher, 1982).

(4) Atmospheric Ar has degassed only from the upper mantle, leaving a remnant of noble gases in the lower mantle (R. Hart et al., 1979,1983; Allegre et al., 1983a).

The first three mechanisms fail to account for the high 40Ar/36Ar in the MORB source, while mechanisms (2) and (3) require an exchange process between the deep mantle and the atmosphere that does not involve the upper mantle. In addition the 4He/40Ar, 3He/ 36Ar, 2oNe/36Ar and 12gXe/130Xe ratios of non- degassed mantle are different from that of the atmosphere (All&e et al., 1983a; R. Hart et al., 1983). The closed-system approximation (4) not only predicts a 40Ar/36Ar ratio in the range of 350-500 for the lower mantle but also predicts a high 4oAr/36Ar ratio and low

3He’4He ratio 3pAr relative to 40K and 3He r the upper mantle by the

depletion of relative to U-Th during degassing to the atmosphere in the Archaean.

TABL

E1

Dupl

lcate

ansly

saso

fhel

ium

an

darg

onins

ubma

rineb

asnlt

glass

Samp

le NO

. %s

e "A

r %

Ar

*"Ar/"

Ar

'HeP

Ar

%Ie

lXAr

An

alys

t (lo

-'cm3

g-1)

(10-'c

m3

g-q

(lo-9

cm

3 g-

11

TRlO

l-ID

TRlO

l-ZD

TRlO

l-27D

DGM

17

42

ALV

736-

l

ALV

519-

2-2b

ALV

714-

1 th

oWta

fro

m

Galkp

agos

Ri

se

(Van

And

id

and

Balla

rd.

1079

) AL

V 71

4-4

thole

llte

from

Gal&

asoo

Ri

se

th0leW

efrom

82~4

O'No

n Re

rkiam

Ri

be.

dept

h 8O

Om(so

bilun

&197

8)

thol

eLtte

fro

m

62’3

O’N

on

Be

Wan

es

lUd5

s.

dept

h 86

Om(S

chUi

ing.19

73)

thok$

itefro

m61°

40'on

R

eYLh

nes

Ridg

e.

dept

h 10

06m(

S~19

73)

thole

&tep

ulow

fragm

ent

kom

Gp#m

#os

rpra

dtal

cante

r 0

4@NN

,depth

2760

m (V

ra

Ande

l an

d Be

Bard

. 19

79)

de&i

t%dth

okdtt

efxom

Fb

sfQVS

am

a on

Mi

d-

Aith

wit:

l%i&

ze

<ss"4

8'W.

d$&2

7OOm

(Br~

anet&

4.34

4.82

4.76

3.20

2.86

- 1.30

0.95

- 1.

09

- 0.43

0.30

- 0.25

6.30

- -

a.47

1.63

0.4

6 7.1

1 1.2

8 0.3

6

0.00

2 9.3

3 3.0

3 -

13.3

0 4.1

7 0.7

8 11

.76

3.45

21.1

7.92

0.24

81.7

3 9.3

3 0.3

2 11

1.20

-

-

57.0

0 51

.00

12.4

0 11

.62

11.2

0 11

.14

- - - -

- - - -

- -

302

3.71

31

7 6.

01

- -

436

2.64

- 340

337

306

310

341

3.30

0 2,

916 -

- 6.52

6.62

0.00

02

- 0.07

2.66

8.76

-

- - - -

- 1,22

9 1.

646

- 1,

167

1,89

6 1.

864

0.07

-

23

8,79

2 25

.482

-

Pore

& et

al

. (1

980)

th

is stu

dy

this

study

Pore

da

et

al.

(198

0)

this

study

Pore

da

et

al.

(198

0)

this

study

th

is stu

dy

Kyse

r an

d Ri

sen

(198

2)

Dalry

mpl

e an

d M

oore

(1

968)

th

is stu

dy

Kyse

r an

d Ri

son

(198

2)

this

study

Ku

rz

and

Jenk

ins

(198

1)

Kurz

an

d Je

nkins

(1

981)

th

is stu

dy

Kurz

an

d Je

nkins

(1

981)

th

is stu

dy

Kurz

an

d Je

nkins

(1

981)

th

is stu

dy

TABL

E11

Samp

le No

. De

aced

ption

'H

e 'H

e 'O

Ar

=Ar

'He/'

He

4oAr

/MAr

4Hefo

Ar

'Hels

bAr

(lOA

cm'(')

(lo

-" all

ag-')

(lO

d crn

'g-')

(lo+

cm3

g-l)

(X

10-Y

Atlo

ntlc

Ocea

n:

TRlO

l-2D

thole

itteEo

m62*

~'Non

~e

~ortu

r#Ri

dmde

~th8

OOm

(Sch

pliniL

.1073

)

TRlO

l-27D

tho

l&&e

frora

81

Q8'N

on

Re~b

$~Ri

dge.d

e~thl

OOOm

(S

~197

Q)

ALV

619-

2-16

de

pleta

dtbo

k&e

from

FAMO

US

am8

on

Lad-

AN

Ridg

e 38

*48'N

,dqxth

27OO

m (B

ryalla

ndMo

oxe.1

977)

AL

V620

-2B

thole

itte&o

mFAM

OUSa

rwon

Mi

d-At

lanti~

It~.88

~48'N

.

ALV

526-

S-l

ALV

626-

l A

ALV

627-

1-1

ALV-

528-

l

ALV6

29-4

C

AH

77-6

7-61

CH98

-DFt

78

CHSB

-DRS

A

thole

iitefzo

mFAl

llOUS

uuon

lU

id-At

lantic

Bidg

e,38

a48'N

(B

rsw1m

dMoo

re,19

77)

thole

iitefro

mFAM

oUsa

m8on

Mi

d-At

laatic

ltk&a

,38°4

8'N

(Brya

nand

Moor

e,197

7)

thole&

tefko

mP'A

MOUS

aeao

n M

M-A

tlaaf

b &i

&e,

&4&N

(B

rY8a

aadM

ooro

,l977

)

thole

lite

horn

FA

MOU

S am

a on

bU

i?-At

?~tia

~e.88

~48'N

, de

pth27

02m(

Brmn

andM

oore

, 19

77)

thoIe#

tsfxo

mFAM

OVSa

teaon

Mi

d-At

batia

~.88

"48'N

(B

ryul8B

IdMwz

e,1@

77)

tholeW

efroe

r.FAM

UUSu

waon

~-

A~~.a

8*~'N

t3&

Yua~

Mwml

s77)

thu

aewd

zaz#

idfro

ma0~

on

Mid

-Atlm

ib

Ridg

e (B

owau

k uk

dTra

u&1@

lIoD)

thole

iited~

edfro

m30°

Non

Mid-

A~tic

Ridg

e(Bo

ugau

lt an

dTre

ll&1@

80)

0.48

O-82

*' 0.1

1 0.3

8 18

.9*'

317

4.38

1.38

8

0.29

0.82

0.11

0.25

19.2*

' 44

2 2.8

4 1.

188

0.78

1.4s*

' 0.1

4 0.4

2 23

.0*'

339

5.54

1.88

0

4.85

8.16*

= 0.7

1 0.3

7 10

.8*'

1.92

3 8.8

0 13

.088

5.82

-

4.07

-

2.39

-

5.81

-

7.08

-

5.88

-

1.51

-

7.58

-

2.52

-

1.47

0.64

0.81

1.02

1.14

0.87

0.05

0.88

0.44

2.12

0.60

1.91

0.68

-

0.50

1.06

0.08

0.79

0.88

- 89

4 3.8

1 2.

846

-

1,09

2 7.5

0 8.

191

422

2.98

1.24

8

1,82

8 5.5

2 10

,088

2.30

9 6.1

9 14

.399

835

8.51

6.40

9

808

29.7

0 18

.000

825

11.6

7 9,

548

842

5.78

3,89

7

TABL

EII(c

ontin

ued)

fkulw

la De

dcri~

tlon

No.

z

'He

3-k

46Ar

=A

r 'I-I

efHe

40Ar

/36Ar

4Hep

Ar

%el"

Ar

(lo-6

cm

3g-')

(lo-"

cm3

6-1)

(10-

6 cm

fg-')

(lo-9

cm

3 6-1

) (X

10

-6)

Atla

ntic

ocea

n (c

ont.)

:

CH

#a-D

Rll

thoW

i%

&ed#

ed

from

SO

oN

on

11.0

6 2.

50%

’ o.

ai 0.

28

11.9

*’ w#

d-m

sM

8e

Wou

auR

&iTr

eu&l

em)

CH98

-DRI

P th

ol&W

dxe&

&hPm

80%

0n

11.2

2 -

0.97

0.08

-

plks

&hm

qe

n)dr

te

(Boo

st al

l Tr

aaa

ISPO

)

TRIE

STE-

II su

bnW

dbks

m&efr

ammi

d-

46.5

0 -

1.9a

1.28

- Rk

se.lS

"8'N

,d~th

(Tho

mpon

ett.19

80)

Tw4-

16

thdm

&fro

mM

id~~

Ri

dge.

10

.95

9.76

*’ 0.

57

0.74

11

.9*”

*ls’N

, de

#b

es40

11

1 ah

aooa

rnrd

1~~(

11~.

197a

)

TWQ-

35

15.9

6 10

.128

3 0.

81

0.93

12.4

*3

Peclf

fc

ocea

n:

Y74-

1-1-

34

Y74-

l-3-4

1

Y74-

l-4-1

5

Y74-

I-1-7

Y74-

3-33

GAL

714-

Gl

GAL

735G

l

GAL

714-

G4

th

fxotnJ

ucnd

e Fu

caRi

dge.

!xlQ@

lo

(Wak

e-

th +m

Juan

deFu

~Ridm

.&

#%l25

om(W

&e-

arbb

. 19

77) dept

h a7

w m

(V

an

bd6d

~3

~4

md.

19

79)

th~fco

tnp8h

oeho

eflow

oon

14.7

0

11.6

0

12.2

1

14.0

6

10.1

8

8.17

12

.58:

’ 0.

93

0.32

11

.2*’

2.90

9 8.

76

25,4

83

10.8

1 12

.66*

= 1.1

9 0.1

6 ll.a

*z

7,56

2 9.

03

68,2

67

16.1

7*’

1.84

12.7

6*’

1.92

21.8

9*’

0.74

13.4

3*’

1.31

15.4

7*’

2.16

13.9

2*’

0.69

0.58

3,

201

7.98

26

,549

0.92

1.46

0.66

- 2.

081

6.05

12

,586

507

27.0

0 13

.104

2.01

3 9.

31

18,1

40

0.28

-

7,86

3 6.

52

51,2

12

0.45

1.

12*2

1.

539

14.7

7 22

,733

1.09

7

4,91

2

1.61

0 773

872

35.7

8

30.5

1

23.6

2

19.2

4

19.7

9

39,2

78

149.

924

35.6

69

14,8

77

17,2

61

GAL

731-

64

thol

eiite

ba

salt

from

GU

pago

s 9.

91

- IP

retd

ing

cent

ex.

0°49

’ (V

an

Andt

l en

d Bt

llud,

19

79)

K78-

12-I

1-78

th

olei

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dred

ged

from

Gp

lipag

os

14.6

0 -

spre

edln

~ ce

nter

; 2%

9’N,

9&

3O’W

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pth

2440

m

(C

hrist

ie an

d Si

nton

, 19

81)

K78-

17-l

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eU:e

dr

edge

d fro

m

Gala

$ago

s 9.

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-

spne

dlng

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9S

%O’

W.

dept

h 24

40

m

Whr

ittie

en

d Sl

nton

. 19

81)

K78-

12-1

240

thol

eiitt

dr

edge

d fro

m

Gal&

agos

12

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-

rpmu

ttnSc

enter

,2°88

'N,

96%

0'W,de

pth28

60mU

%ris

tit en

d Sl

nton

, 19

81)

K78-

12-1

2-11

8 th

olei

ite

dred

ged

from

G&

pago

s sp

r&iuS

cente

r.2°8

8'N,

96%

O’W

, de

pth

2660

m

Kk

lstit

K78-

12-1

6-3

Y73-

4-30

-s

Y 73

-4-3

0-s

DGM

17

42

DGM

17

12

DGM

end s

into

n, 1

981)

thol

eiite

dr

edge

d fro

m

Gal&

agos

rp

redn

~cea

ter,2~

89'N

. 96

’17’

W.

dept

h 28

76

m

(wie

an

d Si

nton

. 19

81)

bult

dred

ged

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52

In the closed-system approximation discussed here, the lower mantle is defined as closed system I. The upper mantle, sialic crust and atmosphere make up closed system II that has the Ar partitioned between its parts (Fig. 1). Although most of the He has escaped from the atmosphere, Ar has been retained so that mass conservation leads to:

[40Ar]p = [40Ar], + (40Ar, + 40Ars)/(Xm) (1)

where [40Ar]P = concentration of 4oAr in the lower mantle; [40Ar]M = concentration of 40Ar in the upper mantle; 40Ar, = total amount of 40Ar in the atmosphere; 4oAr, = total amount of 4oAr in the sialic crust; and Xm = mass of the degassed mantle (X = frac-

He Leak 0 \\

A.=396 Ar. He

H,=1.4XlO-0

Closed System I

-24,600 ~12.6X10-6

:kY

Ap=400 Hp=62X10-’

Fig. 1. Schematic representation for the closed-system evolution of Ar and He in the mantle, crust and atmosphere. AS = ‘OArla4Ar ratio for the atmosphere; Ho = ‘He/ ‘He ratio for the atmosphere; AM = +OAr/s6Ar ratio for the upper-mantle MORB source; Ap = 40Ar/s”Ar and Hp = ‘He/‘He, ratios for the non-degassed lower- mantle plume source represented as closed system I. The degassed upper mantle, sialic crust and atmosphere comprise closed system II, and Ar and He are now partitioned among them, due to degaasing and different&ion of the upper mantle. Closed system II is not closed for He which is lost by escape mechanisms from the upper atmosphere. The 3He is lost preferentially to ‘He, so that Ha is lower than either HM or Hp. Ar, because of its lower thermal velocity, has not escaped. Since the “Ar content of the upper mantle and sialic crust is insignificant compared to the amount in the atmosphere, the difference between A, and Ap is due to the ‘OAr in the upper mantle and sialic crust. AM and Hw are both more radiogenic than the lower-mantle ratios because j6Ar and pHe have been depleted much more than K or U, and ‘OAr and ‘He have built up by radioactive decay from their parent nucleii.

tion of mantle degassed and m = mass of the mantle). From this equation it is possible to estimate the concentrations of 40Ar, 36Ar, and hence, the 40Ar/36Ar ratio of the lower mantle.

First, we will use this equation to compute the 40Ar concentration of the lower mantle. The 40Ar content of the atmosphere is well known to be 36.78 - 10” cm3 (Verniani, 1966). The 40Ar content of the sialic crust, assuming the average age of the sialic crust is 2 Ga (Hurley and Rand, 1969) and the K content ranges from 1% to 3%, is in the range from 4.6 - 102’ to 14 * 102’ cm3 (R. Hart and Hogan, 1978). The atmosphere and sialic crust values are combined to give a range from 41 * 1021 to 51 . 1021 cm3 for the total amount of 40Ar removed from the mantle. Estimations of [40Ar], range from 1.7 l lob6 to 3.2 . low6 cm3 g-’ (Dymond and Hogan, 1978; R. Hart et al., 1979; Takaoka and Nagao, 1980; Fisher, 1983). We will use the upper-limit value of 3.2 * 10d6 cm3 g-’ that we previously adopted (R. Hart et al., 1979). Fig. 2 shows the calculated values of the 40Ar concentration of non-degassed mantle as a function of the portion of mantle degassed for the lower- and upper-limit values of 40Ar,.

Eq. 1 is also applicable to [ 36Ar]p, the 36Ar content of non-degassed mantle but in this case it is more reliable because the 36Ar contents of the upper mantle and sialic crust are negligible compared to the 36Ar content of the atmosphere. For example, choosing 3.2 l low6 cm3 8-l for [40Ar] M as used above and 14,500 for 40Ar/36Ar ratio for the upper mantle (Fisher, 1975; Allegre et al., 1983a; R. Hart et al., 1983), then [36Ar]M is 1.3 l

10-l’ cm3 g-l. This value is similar to the one adopted by R. Hart and Hogan (1978) and Fisher (1983). The 36Ar content of the atmosphere, 12.46 . 1019 cm3 (Verni- ani, 1966), divided by the total mass of the mantle gives a minimum of 2.9 l lo+ cm3 g-l for the 36Ar concentration for the non- degassed mantle, about two orders of magnitude higher than that of [36Ar]M. A similar argument can be made for the contribution

53

from the sialic crust. The maximum 36Ar concentration in crustal rocks is 3 l 10-s cm3 g’ (Dalrymple and Lanphere, 1969), so the maximum total 36Ar in the crust is between

0.16

t \

(K/U=l-1.27X10’)

0.12

Ot-- 1 I I I

20 40 60 60

Percent Mantle Depleted (xl

Fig. 2. 4oAr, K and U concentrations in the non- degassed mantle as a function of the fraction of the mantle depleted or degassed. The 4aAr content is derived from eq. 1 by combining the 4oAr in the atmosphere, sialic crust and degassed mantle. The K content of the non-depleted mantle was derived from the 40Ar using eq. 3 and assuming a closed system for 4.5 Ga. The U content was derived assuming a K/U ratio in the range from 1.0 l lo4 to 1.27 l lo4 (from Jochum et al., 1983). The maximum values correspond to a sialic crust that has been closed to Ar for 2.0 Ga, a K content of 3% and 4oAr content for MORB of 3.2 l 10e6 cm’ g’. The minimum values correspond to a sialic crust having 1% K and an 40Ar concentration for MORB of 1.17 l

lo-’ cm’ g’, The arrows refer to recent estimates of the K and U concentrations of the mantle as discussed in the text.

1 l 10” and 4 l 10” cm3, once again two orders of magnitude lower than the atmospheric contribution to the 36Ar inventory of the atmosphere of 12.46 l 1019 cm’. Thus, the two most uncertain variables in eq. 1 may be neglected, and the equation can be simplified to:

[ 3%r] p = 36Ara/xm (2)

The result of this calculation is shown in Fig. 3, a plot of [ 36Ar] r vs. the fraction of the mantle outgassed. Dividing [ 40Ar] r by [ 36Ar] r gives the (40Ar/36Ar)p ratio in the range from 350 to 500 as shown in Fig. 4.

We now proceed with a calculation of the K and U content of nondegassed mantle. This calculation enables several useful cross-checks on the assumptions of the closed-system model as we develop it in the following pages. The first question to consider is this: If we assume the 4oAr in the atmosphere and sialic crust was produced from the decay of the 40K originally in the MORB source, do we get reasonable values for the K content of the Earth? The answer is derived from the following simple decay equation: 4oAr = 4oAro + (40KXe/h)[exp(AT)-l] (3) where 40Ar = present-day concentration of Ar; 40ho = concentration of 4oAr 4.5 Ga ago; 40K = present-day concentration of 40K; XE = decay constant for decay of 40K to 4oAr (0.581 l 10-l’ a-‘; Steiger and Jiiger, 1977); and X = total decay constant for decay of 40K to 40Ca and 40Ar (0.5543 l 10m9; Steiger and Jeer, 1977). Using the 40K/K ratio of 1.17 . 10V4 (Steiger and Jziger, 1977) and the constants given above, eq. 3 may be simplified for 7 = 4.5 Ga as: 40Ar = 40Ar,, + 1.39 l 10s4K (4)

Since the 40Ar content of the mantle has already been derived from mass conservation (eq. l), the K content as a function of Xm (portion of the mantle outgassed) is easily calculated and is shown in Fig. 2. First it is necessary, however, to demonstrate that 40Aro is negligible compared to 4oAr. As

54

20

-i m 1s

“E 0 12

m ‘0 P a

a’ c CT 4

-

0

000 r

So0 # 400 I 1600 r 1400

I” o- 1000 5 ‘-

1000 /

F 800 I , I I I

0 20 40 60 80


Fig. 3. “Ar content and 4oK/86Ar and U/3He ratios for the non-degawed mantle as a function of the fraction of the mantle depleted--degassed. The ‘6Ar content was calculated from eq. 2, assuming the 16Ar contents of the sialic crust and MORB source are small compared to the a6Ar content of the atmosphere. The maximum and minimum values of the 4oKP6Ar and UPHe ratios are for the same cases as those in Fig. 2. The ‘He content was calculated from the arAr concentration assuming a sHe/a6Ar ratio for the bulk Earth of 0.03 (see Fig. 6). The arrows refer to independent e&mates of 4oK/s6Ar and U/SHe derived by the fitting of decay curves (see Fig. 13).

shown in Fig. 2, 40Ar is in the range from 2 l lo-’ to 10 l lo-’ cm3 g’. As mentioned above j6Ar of the nondegassed mantle is of the order of 2.9 l 10-s cm3 g-l. The initial 40Ar/36Ar ratio of the mantle was probably not as high as the solar wind value of 1 and may have been as low as the value of 10e4 for carbonaceous chondrites (Ozima and

Percent Mantle Degaseed (x)

Fig. 4. 40Ar/36Ar ratio (Ap) for the non-degasaed mantle plume source as a function of the fraction of the mantIe degassed to the atmosphere as derived from eqs. 1 and 2 (see Figs. 2 and 3).

Kudo, 1972). Thus, 40Aro must have been at least lo2 times lower than present-day 4oAr and can be neglected in eq. 4. We have also derived the U concentration as a function of the fraction of the mantle outgassed by assuming a K/U ratio of between 1.00 l lo4 and 1.27 l lo4 (Sun et al., 1975; Jochum et al., 1983). The solutions for K and U in the mantle decrease as the degassed portion of the mantle increases. Recent estimates of the K concentration of the mantle based upon measurements in ultramafic xenoliths are in the range from 180 to 300 ppm (Jagoutz et al., 1979; Sun, 1982). Recent ‘estimates of the U concentration of the mantle are in the range from 15 to 31 pbb (Jagoutz et al., 1979; AllGgre et al., 198313). These recent estimates of K and U are consistent with our model of 4oAr o ng from the mantle

ater than 50% of the

We close this of the paper with calculations of oK/3aAr and pnr =

mantle. The values calculated here -are derived solely by mass- conservation equations (1) and (2) presented in this section plus the MK decay equation (4). The results shown in Fig. 3 are for pnP in the range from 370 to 550 and pw in the range

65

from 900 to 1350. In Section 2.6, we will derive PAP and c(~ by an independent method, the fitting of the growth curves for 4oAr and 4He to the initial and present-day 40Ar/36Ar and 3He/4He ratios for the nondegassed mantle. These values, indicated by the arrows in Fig. 3, are respectively 425 and 1060 for PAP and pnp. Although there is latitude in these estimates good agreement exists between both methods.

2.3. Estimation of the 4He/40Ar, 3He/36Ar and 4He/36,4r mtios of the non-degassed mantle

The 4He/40Ar, 3He/36Ar and 4He/36Ar ratios measured in glassy submarine basalts are im-

portant tracers for mantle evolutionary processes. Low He/Ar ratios are indicative of the atmosphere because He has been lost from the upper atmosphere but Ar has not (Kock- arts 1973; Buhler et al., 1976). In addition, the 4He/40Ar ratio for the closed-system decay is remarkably well constrained over a wide range of decay intervals, because of a fortui- tous combination of decay constants and K/U ratios (Gamlich and Naughton, 1972; Fisher, 1975, 1983; Schwartzman, 1978). Because the 4He/40Ar ratio is important for delineating mantle noble-gas processes we briefly repeat this calculation.

Well-known U-He and K-Ar decay equations can be used to compute the 4He/40Ar ratio for a system closed for 4.5 Ga. The

K/U (10’)

Fig. 5. Variation of the ‘He/“Ar ratio calculated from eq. 3 and 5 for time intervals equal to 4.5 and 1.0 Ga and with the K/U ratio for oceanic basalta. The bottom line for each group represents Th/U = 2, the top line, Th/U = 4. This figure suggests that bulk-Earth ‘He/‘OAr ratios below 1 are unlikely, that the most probable ratio ‘is in the range from 1.4 to 1.7.

56

MORB Plume Back Arc R.Hart et al.(this work) A a

Allhgre et al.(ig83a) l 0

Ozima and Zashu(lQ83a) m 0

Kyser and Rison(lQ82) l Kaneoka and Takaokat 1 Q80) I3

Saito et al.(lQ78) b .a

10 -

Cosmic

lo-'-

lo-* s Planetary

3He14He= (10-13)10-s I

lo-3 -

2 ti

$ lO-'-

0

IO-5 t

ORB

Ie/*He= (8-10)10-s

I fi IO-'

z cn 0

@ Seawater s 3He/ 4He -l.40°10-6 5

IO-81 1 I I 1 I 1 10-4 IO-3 IO-2 10-l IO0 10 102

4 He/40Ar

57

decay equation for He is as follows:

4He = 4He,-, + 8238U[exp(X2387-l)] + 7235U[eX&#-l)] + 6232Th [~?~p(h2327-l)] (5)

where 4He = concentration at present; 4He0 = initial concentration of 4He; 238U = present concentration of 23sU; X238 = the decay constant for ‘138U (1.55125 l lo-lo a-‘; Steiger and JQer, 1977); T = age of Earth, 4.5 Ga; 235~ = present-day concentration of 235U; x 235 = deca.y constant for 235U (9.8485 l 10-l’ a-‘; Steiger and Jeer, 1977); “‘Th = present concentrat:ion of 232Th; and X232 = decay constant of 23?Th (4.9475 l 10-l a-‘; Steiger and J&er, 1977).

The equation can be simplified by using the following relationships: 232Th/Ur =: 2 to 4 (R. Hart, 1976;

Tatsumoto, 1978) and

23*U/23sU =: 137.88 (Steiger and Jiiger, 1977)

where UT = total present-day U concentration. The 4He concentration can be determined for a given decay time, 7. For example, if 7 = 4.5 Ga, the concentration 4He is given by: 4He = 4Heo + 16.64Ur

A similar treatment can be applied to 4oAr as was done following eq. 3 and the 4He/40Ar ratio formed as:

4Heo + 16.64Ur ~- 4He/40Ar = 40Aro + 1.36 . 104K

As demonstrated in the previous section the 40Ar and 4He content of the Earth 4.5 Ga ago was negligible, consequently: 4He/40Ar = 1.2 2 l 10s(Ur/K) (6)

The U/K ratio of oceanic basalts falls in the range of 1.0 l lo4 to 1.27 l lo4 (Sun et al., 1975; Jochum et al., 1983). The time evolution of the 4He/40Ar ratio is shown in Fig. 5 for a range of U/K and Th/U ratios. The calculations indicate the 4He/40Ar ratio of a closed mantle system, hereafter referred to as the “bulk-Earth” value, should range between 1.40 and 1.73. This result is similar to that of other workers (Gamlich and Naughton, 1972; Fisher, 1975,1983; Schwartzman, 1978). The 3He/36Ar ratio corresponding to the bulk- Earth 4He/40Ar ratio can be estimated to be between 0.03 and 0.06 from Fig. 6. This is lo5 times higher than the atmosphere ratio and suggests greater than 99% of the 3He outgassed from the mantle has been lost to space.

As shown in Fig. 6, the 4He/40Ar ratios measured in glassy submarine basalts vary from 0.01 to 123 and 3He/36Ar ratios from 0.00015 to 3.85. Ozima and Zashu (1983a)

Fig. 6. Plot of aHe/36Ar vs. *He/*OAr for submarine glassy basalts. The term MGRB (solid symbols) stands for mid-ocean ridge basalt, thought to represent degassed-depleted mantle. The term plume (open symbols) refers to basalt samples for oceanic islands (OIB’s) represented by Hawaii, Reykjanes Ridge, Sala y G6mez Ridge and Revilla Gigedos Islands. The bulk-Earth field was determined by projecting the bulk-Earth closed-system ‘He/‘OAr ratio of from 1.4 to 1.7 to the plume field. The estimated sHe/86Ar ratio for the bulk-Earth ls in the range from 0.03 to 0.06, intermediate between the cosmic ratio of 1.89 (Jeffrey and Anders, 1970) and the planetary value of 0.009 (Mazor et al., 1970). The value for seawater is modified from Kyser and Rison (1982). The durkeut fieZd encloses samples having ‘He/‘He ratios in the range from 6 * 10q6 to 10 a 10m6 and indicates samples contaminated by atmospheric He having aHe/4He = 1.4 . 10W6. The light-gray field refers to samples with aHe/4He ratios from 16 l 1O-6 to 52 l 10V6 representative of the non-degassed mantle. The intermediate-gray field encloses samples having sHe/‘He ratios equal to the MORB value of between 10 l 10V6 to 13 * 10s6. The samples with the highest ‘HerOAr and ‘He/=Ar ratios do not have the highest SHe/4He ratios as would be expected from the mixing of primordial and atmospheric He as suggested by Manuel and Sabu (1981). Our interpretation is that the samples with below the bulk-Earth values have mixed with atmospheric noble gases and the samples above the bulk-Earth value have had their ‘Hela6Ar and ‘He/‘OAr ratios enhanced by volatile exsolution during the degassing of MORB.

58

suggest that the mantle has a low He/Ar ratio and that the high He/Ar ratios are the result of fractionation processes during petrogenesis. As first suggested by Ozima and Alexander (1976) He may be retained in the melt pref- erential to Ar because of its higher solubility. Manuel and Sabu (1981) suggest that He has diffused into parent basaltic melts from an unspecified mantle source to account for high He/Ar ratios. There are however, a number of problems with this “modified atmospheric pattern model”. First of all the theoretical closed-system 4He/40Ar ratio for the bulk- Earth is distinctly non-atmospheric. Further- more, as pointed out by R. Hart et al. (1983), mantle noble gases in MORB samples have non-atmospheric 20Ne/36Ar, 12gXe/‘30Xe, 40Ar/ 36Ar and 3He/4He ratios. Finally, as also indicated in Fig. 6, the 3He/4He ratios for the samples do not vary as expected by simple enhancement of He with a single 3He/4He ratio. The samples with the lowest 4He/40Ar ratios have atmosphere-like 3He/4He ratios. Samples with 4He/40Ar ratios in the range from 0.1 to 6 have the highest 3He/4He ratios of any submarine basalts measured. On the other hand, MORB samples which have the highest 4He/40Ar ratios, well above the bulk- Earth value, have intermediate 3He/4He ratios. If the high 4He/40Ar ratios are a result of simple enhancement of He, samples with the highest 4He/40Ar ratios should have the highest 3He/4He ratios; this is not the case.

Our interpretation of Fig. 6 is more consistent with the data. We assume that the samples having 4He/40Ar ratios similar to the theoretical bulk-Earth value represent samples in which the noble gases are relatively unfractionated by mantle processes. This assumption is supported by the observation that these samples are from areas of deep- mantle plumes and have the highest 3He/4He ratios that have been measured in submarine basalts (Fig. 6). The samples with low 4He/ 40Ar ratios have been contaminated by atmospheric noble gases. This concept is attractive because samples with the lowest 4He/40Ar ratios also have low 3He/4He and 40Ar/36Ar

ratios as would be expected from atmospheric contamination. In fact, as pointed out by Ozima and Zashu (1983a) and Hogan and Hart (1985), some of these samples also have high Kr and Xe concentrations as would be predicted from the assimilation of altered oceanic crust.

Submarine basalts having 4He/40Ar ratios greater than the closed-system value also appear in Fig. 6. These are all samples of MORB with 3He/4He ratios in the range from 1.0 . lo-’ to 1.3 l lo-‘. At first thought, it seems that degassing should decrease the 4He/ 40Ar ratio because of the greater diffusivity of He out of silicate melts. However, the diffu- sional effects on the 4He/40Ar ratio depend on the degassing process. As discussed by Schwartzman (1978) and Batiza et al. (1979), if the degassing process is one in which a volatile phase such as dominantly CO2 bubbles exsolves from the silicate melt, the noble gases will partition into the volatile phase inversely proportional to their solubility in the silicate melts. The exact degree of the partitioning depends upon the volume of

Silicate Melt

Bubble

Fig. 7. Diagrammatic representation of the volatile exsdution process described by eq. 7. As silicate melt ascends from the mantle a volatile phase exsolves from the melt as represented by the bubble in the figure. The noble gases partition into the volatile phase inversely proportional to their soluhility in the silicate melt. Because He is more soluble than Ar the He/Ar ratio is increased in the melt. NT stands for total number of noble-gas atoms in the system and VT is the total volume of the syatem. 6N represents the number of atoms partitioned into the volatile phase with volume 6 V.

59

the exsolved volatile phase relative to the silicate melt.

The effect of differential solubilities can be demonstrated mathematically using Henry’s law: n = PK(T)

where n = iatomic concentration in the silicate melt; P = partial pressure, of the gas species in the volatile phase; and K(T) = Henry’s law constant, a function of the absolute temperature T.

As shown in Fig. 7, the total number of atoms in the melt-volatile system is given by: N,=N, +SN where No q I total number of atoms in the system; N1 = number of atoms in the silicate melt; and l; N = number of atoms in the volatile phase. If we consider some arbitrary volume V, then the concentrations in the melt and the volatile phase are related by: no=nl +612(6V/V)

where 6 V := volume of the volatile phase, and V = volume of the total system. Applying Henry’s law to 6 n, and using the ideal-gas law expression for the number of atoms in the volatile plnase to eliminate the pressure dependence, one derives the following expression:

where k q I Boltzmann’s constant; and T = absolute te.mperature.

The ratilo of two noble-gas species can be expressed as:

nll no1 1 + (6 V/V)[K,(T)kT]-’ -=- - n12 no2 1+ (6 V/V)[K,(T)kT]-’

(7)

The solubility of noble gases in basaltic melts has recently been studied by Hayatsu and Waboso (1982, 1985 in this issue) and found to decrease with atomic mass and in- crease with temperature and pressure following Henry’s law. The solubility is less in tholeiitic basalt melts than in basaltic ande-

site. At 1200°C the Henry’s law constant for He in tholeiitic basalt melt is 64.6 l lo-‘l cm’ g-l dyn-’ and that of Ar is 2.23 l 10-l’ cm5 g-l dyn-’ a d n gives a maximum enrichment factor of 24 for the He/Ar ratio during volatile exsolution. As shown later in this paper (p. 64) the enrichment factor D defined as:

and calculated by several techniques is 20 f 5. Some MORB samples show an enrichment by as much as a factor of 100 indicative of either volatile exsolution at higher temperatures and pressures, or of multi-stage exsolution process in which the volatile phase is released from an ascending melt in a series of distillations. Con- sequently,-it is expected that the most differentiated melts will have the highest 4He/40Ar ratios, an effect that has been observed by Hart et al. (1982) in samples from the Juan de Fuca Ridge.

The preceding development is an approximation. At mantle temperatures and pressures the equation of state must be of the Van der Waals’ type. The above discussion is only to demonstrate the effects of the differential solubilities on the raregas concentrations in basaltic melts.

Combining the 4He/40Ar ratio for the bulk- Earth and our computed 40Ar/36Ar ratio (Fig. 4), the 4He/36Ar ratio for the nondegassed portions of the mantle is between 490 and 865. As shown in Fig. 8, a plot of 4He/40Ar

, 4He/36Ar, six of our samples and one i:orn Allegre et al. (1983a) have 4He/36Ar ratios close to that predicted for the closed- system nondegassed mantle. The measurement of Allegre et al. (1983a) was made on a sample from Loihi Seamount, ours were from the East Rift Zone of Kilauea, the Salay y Gomez Ridge, Revilla Gigedo Island and the Reykjanes Ridge. Of these, the samples from the Loihi Seamount, Reykjanes Ridge and some from the Kilauea East Rift zone have 3He/4He ratios greater than MORB. The other samples have not yet been analyzed for

60

R-Hart et al.(this work) MORE Plume Back Arc

. 4 Allsgre et al.(lQS3a) s 0

Orima and Zashu(lQS3a) . 0 Kyser and Rison(lQS2) + 0

Kaneoka and Takaokat 1980) B Saito et al.(lQ’lS) +

Fisher(1975) 0

,ypg BulkEarth

0 Seawat er r%

2

; 0.01 1 100

4He/40Ar

106

Fig. 8. Plot of 4He/40Ar as a function of ‘He/“Ar for glaaay submarine basalts. The symbols are the same as for Fig. 6. The bulk-Earth value, corresponding to non-degaesed mantle, is determined from the closed-system ‘OAr/ JsAr ratio between 300 and 460 (Fii. 4) and the closed-system ‘He/*“Ar ratio between 1.4 and 1.7 (Fig. 5). Samples below this field have been contaminated by seawater noble gases. The samplea above this field have had their ‘He/‘OAr and ‘Hels6Ar ratios enhanced by vola&le exsolution during the degawing of MOREas described in Fig. 7.

61

3He. This supports the concept that these samples are from the nondegassed mantle and that the lo,w 4oAr/36Ar ratios are not a result of the addition of atmospheric Ar. It must be pointed out, however, that a number of samples from the Kilauea East Rift Zone form a mixing trend toward seawater Ar in Fig. 6.

2.4. Mixing of Ar and He Isotopes in the oceanic crust, estimation of D by the mixing curve method

As discussed in Section 2.2 the MORB

22 -.

20 ..

18 --

18 -.

12 -.

10 -.

8-

8 -’

MORB I I I’ I

/*I

1; I

D=20

source appears to have been depleted in 36Ar compared to the “plume source”. The MORB samples (Fig. 9) have lower 3He/4He ratios than the plume samples, suggesting that ‘He has also been depleted in the MORB source. The uniformity of the ‘He14He ratio in MORB suggests either that the degree of depletion of 3He and the time at which degassing stopped is relatively uniform or the upper mantle is well mixed with a turnover time small compared to the rate of radiogenic production of 4He. In this section we derive the equations for the mixing curves shown in Fig.

MORB Plume Back Arc R.Hart et al.(thio work) . A

Alligre et aL(lg83a) . 0 Ozima and Zaehu(1983a) n 0 Kyser and Ryrondg82) + 0

Kaneoka and Tekaoka dg80) 0 Saito et al. (1973) It

Oceanic Basalts

D= (3He/3dAr)M (SHeWAr) P

Plume8

0’ 4 I 8 I 12 I 18 I 20 , 24 I 28 I 32 I 38 I 40 I 44 1 48 I 52 1

SHe/4He(X lo-9

Fig. 9. Plot of 40Ar/s6Ar as a function of ‘He/*He for oceanic basal& The mixing lines were calculated from eq. 13 using a D’ = (sHe~/s*Ar~)/(sHe~/s6Arp) = 20 for MORB-plume mixing having end-member components as discussed in the text.

62

9 and suggest that the array of isotopic ratios of Ar and He measured in the oceanic crust can be explained by mixing of the MORB source and of the plume source magmas with each other and with an atmospheric component.

Mixing equations for the mixing of magma having varying isotopic ratios can be generated from the following general equation expressed in terms of 36Ar: 36Ar,, = fM36ArM + fp36Arp

where 36Armx = concentration of 36Ar in the mixture; fM = fraction of the mass in the mixture from the MORB source; 36Ari,, = 36Ar concentrations in the MORB source; fp = fraction of the mixture from the plume source; and 36Arp = concentrations of 36Ar in the plume source. An expression for @‘Ar takes the same form but can be converted to an expression using 40Ar/36Ar ratios: A mx 36hmx = fr,.,AM36ArM + fpAp36Arp (9) where Amx = 40Ar/36Ar ratio of the mixture; ANI = 40Ar/36Ar ratio of the MORB source; and AP = 4oAr/36Ar ratio of the plume source.

By substituting 36Armx from eq. 8 into eq. 9, we may write for the ratio fM/fp for Ar :

f AM (Amx-Ap)36Arp -=

fAP (AM-Amx)36ArM (10)

In a like manner an expression is derived from the 3He/4He ratios of the mantle sources:

f m4 Wmx-W4Hep -= fm (hrHmx)4HeM

(11)

where Hmx = 3He/4He ratio in the mixture; HP = 3He/4He ratio in the plume source; 4Hep = concentration of He in the plume source; H% = concentration of He in the MORB source; and HM = 3He/4He ratio in the MORB source.

It is useful now to define ideal mixing as a process in which the noble gases are not fractionated by degassing. The conservation of mass then requires:

fAM/fAP = f?iM/fHP

permitting eqs. 10 and 11 to be equated. However, He may be enriched up to a factor of 100 over Ar so we now define an enrichment factor E such that:

fAM/fAP = E(fHm/fm) so that taking enrichment into account we have from eqs. 10 and 11:

H mx -HP = E (Amx -ApI

HM-Hmx

t4Heh (36Ar)p c12J

(AM-Amx) (36Arh t4Wp

For the purposes of simplication, the 4He/ 36Ar ratio of the MORB source divided by the 4He/36Ar ratio of the plume source will be expressed by R. Eq. 12 can be solved for Hmx and written:

H mx = HAAM-Amx) +H,(Amx - Ap)RE

(Amx -APW + (AM-Am* 1 (13)

This equation expresses the 3He/4He ratio of the mixture as a function of the 40Ar/36Ar ratio of the mixture in terms of the isotopic composition of the end-member components and the values of R and E. The form of this equation is similar to that of Volmer (1976) for Sr-Pb systematics and that of Kurz et al. (198213) for the He-& mixing except for our introduction of E, the enrichment factor, to account for possible fractionation of the 4He/36Ar ratio.

The value of H,, the 3He/4He ratio of the MORB source, is perhaps the best known of the input parameters. As shown in Fig. 6, the 3He/4He ratio in most MORB’s has an average value of 12.6 * 10s6 but varies from 10 * 10C6 to 13 . 10v6 (Lupton, 1983). The 4oAr/36Ar ratio of MORB varies greatly; the highest value we have measured in our laboratory is 7740 on a glassy basalt sample from the Galapagos spreading center. Fisher (1975) reported a value of 15,800 for the 40Ar/36Ar ratio for glassy basalts from 10% on the East Pacific Rise and AIl&gre et al. (1983a) report a value of 24,460 on a glassy basalt from 23% on the Mid-Atlantic Ridge. It seems likely that the highest 40Ar/36Ar ratios are the most representative for the unmixed MORB

63

source, and for this reason we will adopt a value of 24,,600 for AM, the 40Ar/36Ar ratio of degassed mantle.

The value of HP, the 3He/4He ratio of. the plume source, is also difficult to evaluate because of the high variability of the 3He/4He ratio in samples representative of the deep mantle. The highest 3He/4He ratio that has been measured in glassy submarine basalts that also have 4He/40Ar and 4He/36Ar ratios high enough to indicate the lack of atmospheric contamination (see Fig. 6) is 27.9 l

10e6 reported on sample 27D from the Reyk- janes Ridge (Poreda et al., 1980; R. Hart et al., 1983). The highest 3He/4He ratio measured on submarine glassy basalts from oceanic island is 44.7 l 10m6 measured in a sample dredged from Loihi Seamount by Kurz et al. (1982a), however, Ar has not been measured on this sample so atmospheric contamination cannot be evaluated. These high 3He/4He ratios for the Hawaii basaltic glass have been confirmed by other workers (Rison and Craig, 1981; Kyser and Rison, 1982; All&e et al., 1983a). The latter report a 3He/4He ratio of 31.78 l UY6 and a 40Ar/36Ar ratio of 392 on sample KK-29-20 from Loihi Seamount. The 4He/40Ar ratio is 2.50, the 4He/36Ar is 980 and 3He/3”Ar is 0.03, indicating that this sample is relatively uncontaminated by atmospheric Ar and may be representative of a closed-system nondegassed mantle as defined in the previous section. Two other samples reported by Allegre et al. (1983a) from Hawaii, KK-24-7 from Loih:i and KK-9-14 from Hualalai have 3He/4He ratios of 23.33 l lO-‘j and 26.17 l

10m6 respectively. The 4He/40Ar ratios for these samples are low, 0.042 and 0.036 respectively, indicative of significant contamination by atmospheric Ar. Sample 1706 from the East Kilauea Rift having a 3He/4He ratio of 35.0 l 1.0e6 as reported by Kyser and Rison (1982) has low 4He/40Ar and 3He/36Ar ratios, suggesting it also has exchanged rare gases with the atmosphere. These data indicate that the o:riginal 3He/4He ratio of the Hawaii plume source may be higher than the values measured iin these samples. The highest 3He/

4He ratio yet measured in oceanic island basalt is 51.1 l 10s6 by Kaneoka and Takaoka (1980), from an olivine phenocryst extracted from a basalt from Haleakala. The 4He/40Ar ratio is 0.1011 and 4He/36Ar ratio is 31.3, suggesting some contamination by atmospheric Ar. A more recent analysis (Rison and Craig, 1983) of the same sample gave a 3He/4He ratio of 44.24. Recently, Ozima and Zashu (1983b) reported a 3He/4He ratio of 316 l loo6 measured in a diamond from South Africa. This value is higher than the planetary 3He/4He ratio of 142 l

low6 measured in carbonaceous chondrites (Reynolds et al., 1978). It seems probable that plume source samples with the highest ‘He14He ratios measured are the least likely to have exchanged with the atmosphere, but it is also possible that the unde- gassed mantle is heterogeneous. For the purposes of demonstrating the application of mixing curves to the array of He and Ar isotopic data from the oceanic crust, we will adopt the value of 52 l 10s6 for the 3He/4He ratio in the non-degassed mantle because it is similar to the highest ratios yet measured in oceanic basalt. With further data, it may be necessary to adopt an even higher value as suggested by the measurements on carbonaceous chondrites (Reynolds et al., 1978) and diamonds (Ozima and Zashu, 1983b).

Regarding A,, the 40Ar/3”Ar ratio of non- degassed mantle, we will limit our discussion to the seven samples having 4He/40Ar and 4He/36Ar ratios indicative of minimal exchange with the atmosphere (Fig. 8). These are: samples from the Reykjanes Ridge with 40Ar/36Ar ratios of 317, 442 and 339, one from the Sala y Gbmez Ridge having a “Ar/ 36Ar ratio of 899, one from the East Rift Zone of Kilauea having a 40Ar/36Ar ratio of 817, one from Revilla Gigedo Island exhibit- ing a 40Ar/36Ar ratio of 757, and the Loihi Seamount sample reported by All&re et al. (1983a) with a 40Ar/36Ar ratio of 392. The possibility that these samples have exchanged with the atmosphere and that the deep mantle has both a high 40Ar/36Ar ratio and a high

64

3He/4He ratio cannot be completely ruled out, but at present there is no known source in the solar system having both high 3He/4He and 40Ar/36Ar ratios that could have mixed with atmospheric Ar to produce the atmospheric-like 40Ar/36Ar ratios in non-degassed oceanic-island basalts (OIB’s). If atmospheric Ar has been added without He then the OIB’s would have low He/Ar ratios and they do not. We propose that these samples are representa- tives from the non-degassed mantle having a 40Ar/36Ar ratio AP = 400 f 50. The higher 40Ar/36Ar ratios measured in some Sala y Gomez, Kilauea and Revilla Gigedo samples indicate a small MORB component in these samples.

We now turn to an evaluation of R, the 4He/36Ar ratio of the MORB source divided by that of the plume source, and E the factor that expresses the alteration of the 4He/3aAr ratio during degassing of the MORB source. It will be more convenient, to combine R and E into a single factor and convert the 4He/36Ar ratios into 3He/36Ar ratios by multiplying by the 3He/4He ratios for MORB and the plume source. Thus we define the factor D:

D = E[ ( 3He/36Ar)M /( 3He/36Ar), ] Using the values of 52 l low6 and 12.6 l 10m6 respectively for the 3He/4He ratio in the plume source and MORB, we may write: ( 3He/4He)p = 4.13 (3He/4He)M (14) It follows then that D = RE/4.13. The value of D will, of course, be in error by an amount corresponding to any error associated with the estimates of the 3He/4He ratios.

In the sections that follow we will deter- mine D by three independent methods and compare them as an internal check of our model. The methods are:

(1) The fit of mixing curves to Fig. 9 (this section).

(2) The change of PA = 40K/36Ar and PH = U/3He estimated from the mass-conservation equation that describes the formation of the atmosphere and sialic crust from the upper mantle (Section 2.5).

(3) The differences in the p-values estimated by the fit of closed-system growth curves to 40Ar/36Ar and 3He/4He ratios (Sec- tion 2.6).

We now examine our first method for the determination of D. Fig. 10 shows the result of mixing-curve calculations for HM = 12.6 * 10-6, AM = 16,000, HP = 52 l 10-6, AP = 400, and D-values of 0.1, 1 and 20. It is apparent that the curve generated with D = 20 fits the actual data considerably better than those generated with lower D-values. However, at values greater than 10, the precision of the fit decreases rapidly so the error on the fit is 20 + 6. In addition, the mixing line between the MORB source and a seawater source is shown in Fig. 9. The seawater mixing line was calculated using an atmospheric 40Ar/36Ar ratio of 295, a 3He/4He ratio of 1.4 l 10T6 and a D-value of 20. This atmospheric mixing curve best simulates the case of assimilation of altered oceanic crust and sediments that

Fig. 10. Plot of 40Ar/s6Ar vs. *He/‘He POWS the effect of D cm the shape of the mixing curves, D = (s6Arp/s6~M)/(SHep/‘HeM).

65

have picked up the atmospheric rare-gas signa- ture. Keeping this approximation in mind, the mixing curves indicate that the array of 40Ar/36Ar and 3He/4He ratios measured to date in rocks from the oceanic crust can be attributed to a three-component mixing between a degassed MORB source, a closed-system plume source, and an atmospheric source that may be a result of assimilation, subduc- tion, or contamination.

The sim.plest conclusion that can be drawn from the mixing-line best fit of D = 20 is that silicate melts generated in the MORB source have undergone enrichment of the 3He/36Ar ratio by volatile exsolution as described by eq. 7 in Section 2.3. However, before such a conclusion can be made, it must be pointed out that the hyperbolic curvature of the data array may reflect mixing of the atmospheric component rather than a high D-value. Lf so, as more samples having little or no atmospheric component are analyzed, the best-fitting line may begin to approach the case of D = 1.

Finally, we would like to point out that the high 4oAr/36Ar ratios and low ‘He14He ratios in MORB have been attributed to the enrichment of K. and U in the upper mantle (Kyser and Rison, 1982). Pb and Sr isotopic studies of MORB suggest that the MORB source has been depleted in U and Rb and, therefore, probably in K (Tatsumoto, 1966; S.R. Hart et al., 1973; Sun et al., 1975). Consequently, the high 4oAr/36Ar and low 3He/4He ratios measured fin MORB are most likely a result of the degassing of 36Ar and 3He in the past rather than an enrichment of K and U.

2.5. Estimation of the 40K/36Ar ratio in MORB and D by the mass conservation method

In the closed-system model presented in this paper, the high 40Ar/36Ar and low 3He/ 4He ratios in MORB are attributed to an in- crease in the 40K/36Ar and U/3He ratios by degassing of ‘“Ar and 3He sometime in the past.

It is possible to estimate the K content of the depleted upper mantle by assuming that all the K removed from the upper mantle is coherently transferred to the sialic crust during the outgassing process (Schwartzman, 1973). This model, that advocates outward degassing of the upper-mantle gases to the atmosphere, is consistent with upward migra- tion of K to the sialic crust. It has been pointed out that the amount of 40Ar in the atmosphere roughly corresponds to the amount to be expected from the decay of the K in the sialic crust during the first 2.5 Ga of the Earth’s history (Schwartzman, 1973), an observation that supports the assumption that the K removed from the upper mantle is now present in the sialic crust (Schwartzman, 1973; R. Hart et al., 1979).

The K content of the upper mantle is related to that of the lower mantle by the equation:

[KIM= WI p--WXm (15)

where [K] M = K concentration of the MORB source; [K] p = K concentration of the plume source; KS = K content of the sialic crust; and Xm = the mass of mantle that has been depleted to produce the sialic crust. Taking the mass of the sialic crust as 1.02 l 1O25 g (Arm- strong, 1968) and the K content to be in the range from 1% to 3%, then KS is in the range from 1.02 l 1O23 to 3.06 l 1O23 g. The value of [K] p as a function of X already has been calculated, so that eq. 14 can be used to cal- cultate [K] M as a function of X as shown in Fig. 11. The KM/KP ratio, the depletion factor for potassium in the MORB source ranges from 0.5 to 0.92 (Fig. 11C).

We now consider the depletion factors for 36Ar and 3He. In Section 2.2 of this work we adopted an 4oAr concentration for MORB in the range from 1.7 l 10m6 to 3.2 l 10m6 cm3 g-‘. In Section 2.4 we adopted All&gre et al’s (1983a) value of 24,450 for the 4oAr/36Ar ratio for MORB (see Fig. 9). These two estimates place the 36Ar concentration for the MORB source between 0.49 l lo-l0 and 1.3 l 10-l’ cm3 g-l. We have estimated the 36Ar

66

concentration for the non-degassed mantle to be in the range from 3.3 l 10-s to 5.9 l lo-* cm3 g-’ (see Fig. 3). The ratio [36Ar] P/ [36Ar]M, the concentration of 36Ar in non- degassed mantle divided by that of degassed mantle, is in the range from 252 to 1142. It

1800 t

200 t

0.18 -

0.12 -

0.08 -

0.04 -

0

L ?

@ IK,IK,JIU,/Upl

3 0.0 - II

f 0. F 0.7 -

!2 0.5 - 11

I I I I 0 20 40 00 80


Fig. 11. A. K content of the upper depleted mantle (MORB source) determined from eq. 16 as a function of the fraction of the depleted mantle, muming that all the K that was removed from the mantle is now in the sialic crust. Curve ZZ is for a sialic crust of 3% K and curve Z is for a sialic crust of 1% K. B. U content determined for a K/U ratio of 1.27 l

lo4 (Jochum et al., 1983) as a function of the fraction of the mantle that hae been degaseed. Curves Z and ZZ correspond to the same K concentrations for the sialic crust aa indicated in (A). C. Ratios K~llKp and iJ~/ZJp of the K and U contents in the upper mantle to that of the lower mantle aa a function of the fraction of the mantle that not only degassed to produce the atmosphere, but at the mme tie also coherently differentiated to produce the sialic crust. Curves Z and ZZ are as in (A).

follows that ~~~~~~~~ the ratio of 40K/36Ar in degassed mantle to that of non-degassed mantle, is in the range from 126 to 1051.

The 3He content of the MORB source can be computed from the 40Ar concentration, the 4He/40Ar ratio and the 3He/4He ratio of degassed mantle to be between 2.1 * 10-l’ and 7.0 l lo-” cm3 g-‘. It follows that the calculated 3He/36Ar ratio of degassed mantle is between 0.16 and 1.4. The 3He/36Ar of nondegassed mantle is from 0.03 to 0.06 (Fig. 6), and D is in the range from 3 to 47. This range overlaps the value of 20 f 6 determined by the fit of mixing lines.

2.6. Mean time of cessation of degassing, estimate of D by fit of growth curues method

In this section we will estimate the mean time for the cessation of degassing to under- score the concept that degassing of the atmosphere from the MORB source must have stopped long enough ago to allow enough time for the buildup of the 4He/3He and 40Ar/ 36Ar ratios in MORB by the production of 4He and 40Ar from the radioisotopes of U, Th and K.

To obtain a solution we will assume that there is a time, 7, at which 4oAr not only ceased to degas to the atmosphere, but also began to accumulate in the MORB source. This assumption is a reasonable approximation for three reasons:

(1) As shown in the previous section the degassed mantle is more than 99% depleted in 36Ar and therefore was 99% depleted in 4oAr before it stopped degassing.

(2) Although some 40Ar has obviously escaped from the MORB source after T, the rate of degassing of 4He from the mantle is 20 times less than its production rate (Manuel and Sabu, 1981).

(3) The uniform 3He/4He ratio of MORB suggests the cessation of degassing of 3He could have taken place over a relatively short time span. With this assumption we can solve for two values of 7, one from the 40Ar content

67

of the atmosphere and one from the 4oAr concentration of the MORB source mantle.

We will define the term “convergent solutions” to describe the following set of calculations: (1) the K content of the Earth as a function of 7 is calculated using eq. 3 and a value of 2l.87 - 10”’ cm3 for the 4oAr content of the atmosphere (Verniani, 1966) for vari- ous fractions (Xm) outgassed; (2) the K content of the MORB source as a function of 7 is calculated using eq. 3 with 40Ar concentrations between 1.7 l 10m6 and 3.2 l lO-‘j cm3 g-’ (Dymond and Hogan, 1978; R. Hart et al., 1’979; Takoaka and Nagao, 1980; Fisher, 1983).

One ex’ample of a successful solution to a convergent calculation is shown in Fig. 12. Concordant times, 7, are in the range from 1.2 to 1.8 Ga and concordant K concentrations are in the range from 280 to 440 ppm.

Other convergent solutions are possible. 4 Solutions for

I Cloned System Age

for MC)RE

Fig. 12. Convergent solutions for 7, the mean time for the cessation of degassing, as a function of the K content of the Earth. The curves were derived using eq. 3. Solutions for the time of cessation of degassing of the atmosphere assume the .“Ar content of 21.79 l lo*’ cm’ to have degasaed from 90% of the mantle (x = 0.9). Solutions for beginning of the retention of ‘OAr in MORB assume an “Ar concentration for MORB of 1.7 l low6 cm’ g’. AK symbolizes the difference in the K concentration between the degassed and non-degassed mantle. The top of the shaded ared corresponds to 90% of the mantle degassed while the bottom represents 50%.

The K concentration increases as the 4oAr in MORB increases, and as the fraction of the mantle degassed decreases. The symbol AK in Fig. 12 stands for the difference in the K content between the nondegassed and the degassed mantle and increases with the fraction of the mantle outgassed. The fact that solutions are possible supports the model and assumptions presented in this paper.

This result is also encouraging because it agrees with other related geologic events. In our model, as first presented by R. Hart et al. (1979), the continents (sialic crust) are formed from the upper-mantle MORB source by the processes of partial melting that are associated with sea-floor spreading and subduc- tion. As first suggested by Hamano and Ozima (1978) degassing of 4oAr was synchronous with continent formation. Thus a mean age for the cessation of degassing of between 1.2 and 1.8 Ga ago is compatible with the mean age of 2.0 Ga ago for continent formation as proposed by Hurley and Rand (1969) and the more recent estimate of 2.3 Ga ago calculated by Allegre et al. (1983b) assuming degassing continued for a short time after continent formation. Furthermore, mantle isochrons may have been set by the cessation of the removal of continental material from the MORB source. Our estimate for T to be between 1.2 and 1.8 Ga ago agrees with mantle isochron ages as presented by Brooks et al. (1977). Lastly, we suggested that degassing and continental formation were synchronous with hydrothermal activity at mid-ocean ridges. Veizer and Compston (1976) and Perry et al. (1978) both suggest authigenic minerals reflect the hydrothermal contribution to seawater. Their data show a marked decrease of hydrothermal activity 2.0 Ga ago. About this time stream supply from the continents apparently became dominant over hydrothermal activity as the main control on seawater chemistry. Thus a rather consistent pic- ture of a cessation of degassing, hydrothermal activity and continental formation shortly after 2.0 Ga age is emerging from the analysis of recent data.

68

We now address the question whether simple two-stage growth curves for 4oAr and 4He from the radioactive decay of 40K, U and Th can explain the isotopic composition of MORB’s and OIB’s within the time and data constraints already established.

First, we consider the nondegassed mantle, and adopt the diamond ratio of 316 . 10m6 as the initial 3He/4He ratio (Ozima and Zashu, 1983a) and 10e4 as the initial 4oAr/36Ar ratio (Ozima and Kudo, 1972). As the value for the present-day isotopic ratios of 3He/4He and 40Ar/36Ar for the non-degassed mantle we

40Ar/36Ar

D= PHe/“Ar) M = 14.5 (*~elS~Ar) P

100, T=O A Solar

10-a lo-’ 10-s

3He/4He

Fig. 13. Two-stage growth curves for the production of ‘“Ar/36Ar and *He/‘He ratios in non-degaseed mantle and MORB. It is assumed that the MORB source degassed up until 1.8 Ga ago and then was virtually closed to Ar and He. This assumption is supported by the obeervation that 96% of ‘He production is currently retained in the mantle and the uniform SHe/4He ratio of MORB (see text). The value for D = 14.5, derived from the ratio (I~A//LH)M(~A/~H)P, assumes no change of the K/U ratio during the depletion.

will adopt those from Fig. 9, i.e. 3He/4He = 52 * 10e6 and 40Ar/36Ar = 400. Our results for these input parameters give p(A = 425 and pn = 1060 and as shown in Fig. 13 falls within the range of p-values calculated independently from mass-conservation equations. Thus, the data that are presently available are consistent with the closed-system approximation for the non-degassed mantle.

We will now turn our consideration to MORB. As previously shown in this section the mean time for the cessation of degassing, T, is in the range from 1.2 to 1.8 Ga, and the convergent solution approach suggests that the MORB source was approximately an open system before T and a closed system after- wards. We can, therefore, apply the same closed-system criterion to the data for MORB after 7. We will present a demonstration calculation using 7 = 1.8 Ga ago. We use a value of 12.6 l low6 for the 3He/4He ratio and 24,450 for the 40Ar/36Ar ratio for MORB. The results of this calculation are PA = 133,500 and pn = 55,600.

We are now able to calculate a value for D. This follows from the following relationship:

If we assume that the K/U ratio was not fractionated by the depletion event then:

B = t3Heh

/

t3WP - P = D

IIHMPAP (36WM (36Arh

This assumption may not be strictly true because the K/U ratio in OIB’s is slightly different than that for MORB (Sun et al., 1975). However, they do not differ by more than a factor of 2. The value of D calculated from the ratio of the p’s is 14.5 and in agreement with the previous two estimates of D as well as the ratio of Henry’s law constants for fractionation of the 3He/36Ar ratio during volatile exsolution. For T less than 1.8 Ga, the solution of D would be correspondingty higher.

69

TABLE III

Summary of model

ASSUMPTION: All of the Ar in the atmosphere degassed from some portion of the mantle of initially homogeneous noble-gas composition

Data input: J6Ar of atmosphere 40Ar of atmosphere 40Ar in sialic crust *OAr in MORB source mantle

Output: 40Ar/“Ar ratio of non-degassed mantle “Ar concentrations of non-degassed mantle 56Ar concentration of non-degassed mantle

12.46 * 1919 cm’ (Verniani, 1966) 36.78 * 101’ cm) (Verniani, 1966) (4.6-14) l 10” cm3 (R. Hart and Hogan, 1978) (1.7-3.2) * lob6 cm’ g’ (R. Hart et aI., 1979)

350-500 (2-10) l 10-s cm3 g’ (3.3-20) - lo-* cm’ g-l

ASSUMPTION: Non-degassed mantle has approximated a closed system for 4.5 Ga Output:

Fraction of mantle outgassed 90% (180 ppm K) 50% (300 ppm K)

4oK/36Ar ratio of non-degassed mantle (drip) Data input:

K/U Output:

370-550

(l-1.27) * 10e4 (Jochum et al., 1983)

U concentration of non-degassed mantle 15 ppb (90% outgassed) 38 ppb (50% outgassed)

U/jHe ratio of non-degassed mantle (C(W) ‘He/‘OAr ratio of non-degassed mantle 4He/*6Ar ratio of non-degassed mantle 4He concentrations of non-degassed mantle

Data input: ‘He/‘OAr as a function of JHe/36Ar

Output: SHe/36Ar of non-degassed mantle ‘He of non-degassed mantle

Data input: 40Ar/36Ar ratio of degassed mantle 3He/4He ratio of degassed mantle 40Ar/S6Ar as a function of ‘He/‘He

output:

900-1,350 1.4-1.7 490-865 (2.8-17) . lo-’ cm3 g-l

Fig. 6

0.03-0.06 (l-3.6) . lOme cm3 g’

24,450 (AIlBgre et ai., 1983a) 12.6 l 10v6 (Lupton, 1982) Fig. 9

ratio of 3He/36Ar in degassed to non-degassed mantle, D = (3He/36Ar)M/(3He/36Ar)p 20 t 6 (see Fig. 9)

concentration of 36Ar in degassed mantle (0.49-1.3) * lo-lo cm3 g-’ concentration of 3He in degassed mantle (0.21-0.70) * lo-*’ cm3 g’

ASSUMPTION: There is a time, T, the mean time of the cessation of degassing at which ‘OAr stopped degassing to atmosphere and the degassed mantle became retentive

Output: mean tie of cessation of degassing 1.2-1.8 Ga 4oK/36Ar ratio of degassed mantle 133,500 (forr = 1.8 Ga) UPHe ratio of degassed mantle 55,600 (for T = 1.8 Ga) K concentration of mantle 280-440 ppm

70

TABLE III (continued)

ASSUMPTION: The K/U ratio was not fractionated by the degassing event

output: ratio of 3He/S6Ar in degassed to non-degassed mantle,

D _ (40K/36 Ar)M(U/3He)p 14.5 (for r = 1.8 Ga)

(U/3He),(40K/3sAr)p

3. Conclusions

Variations in the isotopic heterogeneities in submarine glassy basalts are best explained as a mixing of three components: (1) non- degassed mantle; (2) mantle that was degassed and depleted until 1.2-1.8 Ga ago; and (3) recycled and assimilated altered oceanic crust.

The noble-gas parameters for the non-degassed mantle can be approximated by closed- system modeling. This model is summarized in Table III. The 4He/40Ar ratio for the non- degassed mantle with a K/U ratio of 1.27 l

lo4 should be in the range from 1.40 to 1.73. Corresponding to this value, the 3He/36Ar ratio for the bulk Earth is between 0.03 and 0.060 (intermediate between planetary and solar). A mass-conservation treatment of Ar in the atmosphere, sialic crust and degassed mantle predicts that the 40Ar/36Ar ratio for the non-degassed mantle is in the range from 350 to 500. The 4He/36Ar ratio for the non- degassed mantle can be calculated to be in the range from 490 to 870. These values are at least a thousand times higher than the 4He/ 36Ar ratio for the Earth’s atmosphere. Thus, the 4He/36Ar ratio can be used to distinguish samples of nondegassed mantle from samples contaminated by the Earth’s atmosphere. In- deed a number of ocean-island basalts (OIB’s) from Hawaii and the Reykjanes Ridge have 40Ar/36Ar, 4He/36Ar and 4He/40Ar ratios predicted for closed-system nondegassed mantle. In addition, these samples have the highest 3He/4He ratios yet measured in the oceanic crust. Mass-conservation considerations pre- dict PAP = (40K/36Ar) for the nondegassed mantle to be in the range from 370 to 550, and c(m = (U/3He) for the nondegassed mantle to be in the range from 900 to 1400.

The degassed mantle (the MORB source)

has been depleted in 36Ar by a factor of at least 100 and 3He by a factor at least 5 times the nondegassed mantle. The U and K contents of the MORB source were depleted by a factor of 1.1-2.0 times that of the non- depleted mantle. Therefore /JAM = (40K/36Ar) was enriched by a factor of at least 50 and pnu = (U/3He) by a factor of at least 2.5 by the degassing-depletion event. Convergent solutions for 7, the mean time at which degassing of Ar from the upper mantle to atmosphere stopped, are in the range from 1.2 to 1.8 Ga ago for K contents of the bulk Earth in the range from 280 to 440 ppm.

A plot of 3He/4He vs. 40Ar/36Ar suggests that the 40Ar/36Ar ratio of MORB is - 24,500 and 3He/4He ratio is - 12.6 l 10w6. The fit of mixing curves to this plot requires that the 3He/36Ar ratio for MORB is 20 + 6 times that of the bulk Earth. The fit of two-stage decay curves to the data compels a similar conclusion. Such curves suggest PAM is in the range from 85,000 to 132,500 and /gnu is in the range from 11,000 to 16,000. Assuming no fractionation of the K/U ratio by the depletion event, the 3He/36Ar ratio of MORB is calculated to be 14.5 times that of the non- degassed mantle. We propose the 3He/36Ar ratio of MORB was enhanced during volatile exsolution from silicate melts.

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the closed-system approximation for evolution of argon and helium in the mantle, crust and...

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