Development of the early continental crust. Part III. Depletion of incompatible elements in the mantle

Precambrian Research, 10 (1980) 281--299

281

© Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

DEVELOPMENT OF THE EARLY CONTINENTAL CRUST. PART III. DEPLETION OF INCOMPATIBLE ELEMENTS IN THE MANTLE*

DENIS M. SHAW

Department of Geology, McMaster University, Hamilton, Ont. L8S 4MI (Canada) (Received and accepted September 6, 1979)

ABSTRACT Shaw, D.M., 1980. Development of the early continental crust. Part III. Depletion of incompatible elements in the mantle. Preeambrian Res., 10: 281--299. New analyses and critical re-evaluation of older data permit another estimate of the abundances of some 42 elements in the silicate shells of the Earth, excluding the core. These data and estimations of volcanic rock production lead to a series of estimates of the mass-fractions of depleted and undepleted mantle. Most likely estimates of the latter lie in the range 0.2---0.4. The best estimates are obtained for the most incompatible elements K, Rb, Sr, Ba, Nb, Th, U. The development of the continental crust and the change in tectonic processes over time is consistent with these interpretations.

INTRODUCTION

Previous papers in this series (Shaw, 1972, 1976) used trace element abundance studies to apply chemical constraints to early Earth evolution. New data on terrestrial crustal rocks (Shaw et al., 1976) and new estimates of terrestrial and lunar elemental abundances (Ringwood and Kesson, 1976; Smith, 1977; Sun and Nesbitt, 1977; O'Nions et al., 1978) have made it desirable to revise and extend the previous work. The aim of the present paper is to establish the abundances of 42 minor and trace elements in the mantle and crust of the Earth (i.e., excluding the core), using constraints imposed by: (a) rock analyses; (b) well-established elemental ratios; (c) isotopic ratios; (d) basalt compositional types. This approach leads to inferences about mantle heterogeneity which permit development of a qualitative model of crustal evolution.

*Contribution No. 103 of the McMaster Isotopic, Nuclear and Geochemical Studies Group.

282 DATA REVIEW -- FIRST ESTIMATES An a t t e m p t will first be made to revise the abundances, in the crust and in the mantle, of m a n y elements, including those reported in our recent paper (Shaw et al., 1976) on the composition of Canadian Precambrian composite samples (Table I, column a). Following the lines of an earlier discussion (Shaw, 1972, p. 1578), it will be taken that most elements have a similar abundance in the lower continental crust (LCC) to the upper levels (UCC), so that the mean continental crust (CC) average (Table I, column c) is the same as given for the UCC. For K, Rb, Sr, Th, U, however, there is evidence that the LCC abundances are different and since the values accepted in 1972 still appear valid t h e y are brought to column b of Table I (the depletion of Rb in the lower crust is likely to apply equally to T1, which has been arbitrarily assigned one half of its UCC value): for these elements the CC values in column c are the averages of UCC and LCC. It is possible that Li is also depleted in the LCC (see Sighinolfi and Gorgoni. 1978) but there are few available data yet for granulite facies rocks, so this has not been allowed for. Other recent studies indicating depletion of incompatible elements in granulite facies rocks (Drury, 1973; Jayawardena and Caswell, 1976) support the approach adopted for these elements. In column e of Table I are presented abundances for the oceanic crust (OC), using values obtained on ocean ridge basalts (see references in Table II): the value accepted for T1 (9.2 ppb) represents analyses of fresh glass (R.R. Keays, pers. comm.). The abundances of m a n y elements in alkalic basalts are much less constant than in mid-ocean ridge basalts (MORB), depending on how alkalic and how undersaturated a particular rock may be: the values chosen (Table I, column f; Table II) are appropriate to basalts rather than nephelinite etc. J.V. Smith has recently (1977) made a thorough compilation of abundances for all the elements in different Earth shells. His CC values are given in column d of Table I and may be compared with column c. Agreement is adequate, within a factor of 2, for m a n y elements, but is less satisfactory for Sc, V, Cr, Mn, Co, Ni, Cu, Ba, Au (he gives no values for Tb, Ho, Tm, Yb, Ir). The question of which estimates are " b e s t " can be side-stepped, since crustal abundances have little effect on the combined crust-plus-mantle abundances for m a n y elements, owing to the small crustal mass relative to the mantle. It is symptomatic of the difficulty of controlled speculation in this field that the best-known numbers are the least critical. Columns g--] of Table I show mantle (M) abundances, estimated in various ways. Although there is reasonable agreement among most estimates, there are differences for some elements, particularly F, P, T1, Pb, which are higher in Smith's estimates in column h. The estimates by Sun and Nesbitt (1977) in column i are generally similar to column h except for lower abundances of P, K, Rb, Ba. Ringwood and Kesson (1976) show abundances (column ]) for F, P, S, Cl below those of column h,

283 TABLE

I

Element

abundance

estimates

for

crust and mantle

( P P m ; K i n % , I r , A u , T I in p p b )

Crust

Mant~

UCC' a Li F P S C1 K Sc

LCC 2 b

22 500 660 600

-----

1 0 0

--

2.57 7

CC 2 c

2,0 --

CC 3 d

OC 4 e

AB s f

M2 g

9.5 -3000

---

--

22 500 660 600 100 2.3 7

20 620 1000 400 180 1.3 36

8.3 300 400 800 190 0.13 50

380 1.0 26

M3 h

M6 i

M7 ]

---

--

--

2 290 300

--

1 2 0

--

--

92

2 3

0.005 --

--

0.0 6

0,024 17

V

53

--

53

130

300

250

--

Cr

35

--

35

I00

300

280

--

3100

3000

2524

530 12 19 14

-----

530 12 19 14

1200 25 75 55

1500 32 100 75

1400 50 300 91

--1500 --

900 90 2400 10

1160 100 2000 --

1095 98 1694 34

80

Mn Co Ni Cu Zn

Rb Sr Y Zr N b

Ba La Ce Pr Nd Sm Eu

52

.

Tb

.

1

--

.

0.4 2 5 .

---

2.8

--

2.8

5.4

4

7

--

0.7

I.I

--

--

0.48

--

0.62

--

--

1.5 0.23

Hf

5.8 --

1.8

--

--

.

2.8

.

--

1.5

--

--

0.23

--

--

4

5.5

--

1.0

.

2.5

--

5.8

.

.

.

.

-0.64 --

----

--

--

--

--

--

--

.

0.12

.

.

2

2.0

0.5

0.3

--

0.02

--

--

3

2

4.0

--

0.5

--

--

1.0

--

0.3

--

--

--

6

--

--

3

--

--

0.15 0.05

1.8

4

0.33

1

0.5

0.4

--

--

.

0.30 .

.

--

---

0.5

1.5

-0.024

.

50

----

.

0.48

.

3

0.68 23 5.0 11 0.62 7.1 0,64 --

1.6 0.29 0.09

0.5

1 0.8

--

--

0.024

3

0.62

--

.

--

.

--

--

0.3 27 0.9 4.6 1.4 5.6 1 2.9

----

.

97

42

0.2 25

45 8 2.6

Yb

U

.

87

45 820 50 200 72 600 45 95

10 3 0.7

.

T1 Pb Th

2 120 40 100 3 10 3 10

28 6 1.2

T m

Au

.

70

52 380 33 160 20 250 22 60

26 4.5 0.94

--

Ir

--

52

80 430 21 240 26 1070 32 66

----

Er

W

--

0.48

Ho

Lu

50 550 -----

26 4.5 0.94

Gd

Dy

--

110 316 21 240 26 1070 32 66

35

68 102 317 59 ---

--

0.42

--

2

4

520 17 10

260 -2

390 17 6

330 12 3.9

9.2 0.5 0.2

45 2.4 4.0

1.3 0.05 0.05

10 0.2 0.064

----

----

2.5

0.4

1.5

1.3

0.I

1.0

0.02

0.028

--

--

UCC, upper continental crust; LCC, lower continental crust; CC, continental crust: mass 1.888.102s g; O C , o c e a n i c c r u s t : m a s s 0 . 4 7 9 " 1 0 2 s g ; A B , a l k a l i c b a s a l t ; M , m a n t l e : m a s s 4 0 7 . 2 " 1 0 2 s g, c o r e : m a s s ] g 7 . 6 " 1 0 2 s g. I S h a w e t al. ( 1 9 6 7 , 1 9 7 6 ) . 2 S h a w ( 1 9 7 2 , 1 9 7 6 ) ; S h a w e t a l. ( 1 9 7 6 ) . 3 S m i t h ( 1 9 7 7 , t a b l e 2 ) . M a n t l e a b u n d a n c e s f o r S , C1, K , R b , B a , T I , P b , T h , U a r e t a k e n h e r e a s 1 / 1 0 o f t h e v a l u e s g i v e n b y S m i t h ( 1 9 7 7 ) , in a c c o r d w i t h t h e f o o t n o t e to his t a b l e 2. 4 A b u n d a n c e s c h o s e n f r o m t h e a n a l y s e s o f f r e s h o c e a n r i d g e b a s a l t s l i s t e d i n T a b l e II. s V a l u e s c h o s e n f r o m r e f e r e n c e s in T a b l e I I . 6 Sun and Nesbitt (1977, table 2A) (Archean mantle). 7 Ringwood and Kesson (1976, table 3) (pyrolite).

284 TABLE II References for basaltic element abundances Mid-ocean ridge (MORB)

Alkalic (AB)

Anderson (1974) Albuquerque et al. (1972) Ayuso et al. (1976) Blanchard et al. (1976) Bryan et al. (1976) Crocket and Teruta (1977) Engel et al. (1965) Fleet et al. (1976) Frey et al. (1974) Haskin et al. {1966) Helsen et al. (1978) Kay and Hubbard (1978) Kay et al. (1970) Mazzulo and Bence (1976) O'Nions and Pankhurst (1976) Pearce and Cann (1973) Ringwood and Kesson (1977) Schilling et al. (1978) Shaw et al. (1974) Shaw and Muysson (1977) Shaw et al. {1977)

Frey and Prinz (1978) Engel et al. (1965) Gunn et al. (1970) Gunn et al. (1971) Gunn and Watkins (1976) Helsen et al. (1978) Kay and Gast (1973) Ka~ and Hubbard (1978) Miyashiro (1978) Pearce and Cann (1973) Schilling and Unni (1978) Schilling et al. (1978) Shaw et al. (1974a, b) Sun and Hanson (1975a, b)

p o i n t i n g u p t h e difficulties in c o r r e c t l y assigning a b u n d a n c e s to these v e r y volatile e l e m e n t s . In t h e light o f A n d e r s o n ' s ( 1 9 7 4 ) analyses o f fresh M O R B glasses, it a p p e a r s u n l i k e l y t h a t the m a n t l e c o u l d c o n t a i n m o r e C1 t h a n basalt, so for these f o u r e l e m e n t s R i n g w o o d a n d K e s s o n ' s values are p r e f e r r e d . In spite o f these p r o b l e m s a first a t t e m p t can be m a d e t o e s t i m a t e elem e n t a l a b u n d a n c e s in the w h o l e silicate p a r t o f t h e Earth. C o l u m n a o f Table I I I s h o w s s u c h an e s t i m a t e , based on t h e c o n t i n e n t a l crust, o c e a n i c crust and m a n t l e a b u n d a n c e s given in c o l u m n s c, e, h ( c o l u m n j for F, P, S, C1) o f T a b l e I, w e i g h t e d b y their r e s p e c t i v e masses. In c o l u m n b, Table III, is an estim a t e c a l c u l a t e d f r o m S m i t h ' s a b u n d a n c e s ( c o l u m n s c, d o f his table 2, 1977), also w e i g h t e d a p p r o p r i a t e l y : his m a n t l e a b u n d a n c e s ( c o l u m n d of his table 2) are the s a m e as in c o l u m n h o f T a b l e I here. In the light o f the i d e n t i t y o f t h e m a n t l e a b u n d a n c e s in e a c h case, and o f t h e n e a r l y negligible masses o f lithophile e l e m e n t s c o n t r i b u t e d b y the c o n t i n e n t a l crust a n d o c e a n i c c r u s t relative to t h e m a n t l e , e s t i m a t e s a a n d b o f T a b l e I I I are v i r t u a l l y identical ( e x c e p t for F, P, S, C1). REVISED ESTIMATES T h e t r a c e - e l e m e n t a b u n d a n c e s in the E a r t h ' s silicate m a t e r i a l , in T a b l e III {columns a, b) s h o w d i s a g r e e m e n t w i t h s o m e e s t i m a t e s b y O ' N i o n s et al.

285 TABLE

III

Terrestrial

abundance

a Li F P S C1

2.1 70.3 105 319 59.3 207 6.1 35 .~1 n 0 900 90 2390 10 42 0.73 29 1.0 5.8 1.5 10.5 1.15 3.2

K

Sc V Cr Mn Co Ni Cu Zn Rb Sr Y Zr Nb Ba La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

Hf W Ir

.

Au

Tl Pb Th U

.

1.7 0.31 0.095 0.49 . 0.32 . 0.14 . 0.41 0.022 0.53 0.31 6

. *2 . *2 . .a

*~

estimates

the

core

b

c

d

2.1 290 305 122 24 192 6.2 36 3100 900 90 2380 10 42 0.73 30 1.1 5.7 1.5 7.3 1.15 3.3 . 1.8 0.33 0.098 0.52 . 0.32 . 0.14 . _ 0.023 0.51 0.31 >6

------

------

3

12 0.28 0.092 0.035

excluding

3

12 0.28 0.091 0.037

462 --------1.31 41 -------

(ppm;

K in %, It, Au, Tl in ppb) e 3.9 77 _,1 _,l 37 248 18 150

--

------------

_,l __,1 --*~ ,1 83 140 0.85 27 4.8 29 1.5 7.5 0.70 1.9 0.24 1.3 0.38 0.15 0.54 0.10 0.66 0.15 0.42 0.064 0.42 0.072 0.42 0.37

15 -12 0.42 1.40

. 0.93 0.29 ---

--0.12 0.53

--

0.49

--

0.31

. . . 0.33 ----

-0.051 ----

--

--

--

__,i

--

-0 . 0 0 5 *4 0.18 0.046

13 0.24 *s ---

7.2 0 . 0 0 2 9 *4 0.095 0.026

a Estimate using columns c, e, h o f T a b l e I ( e x c e p t F , P , S , C1) w e i g h t e d by masses as given in Table I. b Estimate calculated from Smith (1977, table 2, columns c, d) using mass fractions 0.00711 and 0.9929. c O'Nions et al. (1978). d Values amended from column a (see text), e Calculated from Ganapathy and Anders (1974, table 4, column 3) by multiplication by 1.461, assuming elements absent from the Earth's core. *] O m i t t e d because present in the core. ,2 CC abundance taken from column d , T a b l e I. ,3 Mantle abundance taken from column i , T a b l e I. *4 2 o 4 p b ' ,s Primordial

abundance.

( 1 9 7 8 ) s h o w n in c o l u m n c. T h o s e e s t i m a t e s w e r e b a s e d on a c o h e r e n t series o f assumptions dependent on observations that: (a) K / U = 104 f o r terrestrial m a t e r i a l s ; (b) the m e a n global h e a t f l o w is 1 . 9 5 ucal c m - 2 s - ' ;

286 (c) the global heat loss equals heat generated by radioactive decay of U, Th, K; (d) the Earth contains 0.046 ppm U (modified after Tera et al., 1974); (e) the covariation of 87Sr/S6Sr and 143Nd/~44Nd in oceanic basalts may be extrapolated to the whole Eartb, leading to conclusions that Rb/Sr = 0.032, 87Sr/86Sr =- 0.705 and ~43Nd/144Nd = 0.5126; (f) the observed isotopic ratios of Pb, U, Th lead to the conclusion that ~38U/~°4Pb = 9.0; (g) terrestrial ratios of refractory elements (Sr/U, Sr/Nd, Sm/Nd) are chondritic. The values in Table III, column c, will be provisionally accepted as revisions to column a. In addition, the adjustments to Nd and Sm necessitate proportional adjustments to the other REE, which thus were made using the chondritic ratios La/Nd, Ce/Nd, etc., taking the chondritic abundances given by Smith (1977, table 2, column 1). These revised REE values are shown in Table III, in column d. The abundance estimate of Ba (Table III, column a) may also be questioned. Since Ba is a refractory early-condensing element, like Sr and the REE, a good estimate for Ba should be obtained as the product of the terrestrial abundance of Sr (41 ppm) and the chondritic Ba/Sr ratio, which is 0.29 (Smith, table 2, column 1), giving 12 ppm. This value, included in column d, yields a K/Ba ratio of 39, which accords with the ratios in the UCC and OC (21 and 130, respectively, Table I). Another adjustment required is for Zr. Since Sr, Zr, Hf are refractory early condensates their ratios in the Earth should be close to chondritic; i.e., Sr/Zr = 2.771 Zr/Hf = 28.2 {Smith, 1977, table 2). The Zr abundance was consequently adjusted (using Sr = 41 ppm) to obtain 15 ppm, while Hf needs no change. The value for T1 (Table III, column a) also needs to be checked. In most terrestrial samples the ratio R b f r l is within the limits 1000 and 82 (Shaw et al., 1974): taking a median value of 100, with a Rb abundance of 1.31 ppm (Table III, column c), gives T1 = 13 ppb which is also included in column d. The value of 2°4Pb given by O'Nions et al. (1978a) corresponds to a primordial total Pb of a b o u t 0.24 ppm, also included in column d. With these various adjustments in mind a comparison may be made with the estimates (column e) made by Ganapathy and Anders (1974) for the whole Earth, scaled as indicated in Table III on the presumption that the elements shown are not present in the core (obviously siderophile elements were omitted). This is a rather considerable, assumption for some elements (e.g. Cu, Zn, W, Pb) but, excepting these, the agreement is fairly close except for Sc, V which differ by factors of 1/3, 1/4, respectively: no obvious reason for these differences is apparent. In summary, a first revision has now been made to some of the terrestrial (silicate) abundances in Table III, column a: the preferred values {columns c, d) are now carried to Table IV, column a. From these revised values it is possible to recompute mantle abundances (Table IV, column b), assuming the CC and OC abundances in Table I.

287

TABLE IV R e v i s i o n s t o a b u n d a n c e s in T a b l e I I I , c o l u m n a ( p p m ; Tl in p p b )

K Rb Sr Zr Ba La

Ce Nd Sm Eu Gd Dy Er Yb Lu T1 Pb Th U

First revision

Second revision

Co

Cm

Co

Cm

a

b

c

d

462 1.31 41 15 12 0.42 1.40 0.93 0.29 0.12 0.53 0.49 0.31 0.33 0.051 13 0.24* 0.18 0.046

357 0.945 39 13.9 7.1 0.27 1.1 0.80 0.27 0.12 0.52 0.47 0.30 0.32 0.050 11 2 0.15 0.039

-----

----

--

--

1.36 4.53 3.01 0.938 0.388 1.72 1.59 1.00 1.068 0.165 -----

1.22 4.24 2.89 0.919 0.385 1.71 1.58 0.99 1.065 0.164 -----

--

Co, a b u n d a n c e in silicate p a r t s o f t h e E a r t h ; Cm, m a n t l e a b u n d a n c e c a l c u l a t e d f r o m Co, ass u m i n g CC a n d O C a b u n d a n c e s in T a b l e I. *Primordial.

CONCEPT OF PRIMORDIAL MANTLE

Recent discussions of mantle geochemistry frequently refer to " d e p l e t e d " and " u n d e p l e t e d " material. Depleted mantle rocks have lost, through partial melting or some other process, some proportion of their incompatible element complement. In addition to emphasising the heterogeneity of the mantle, these concepts imply the existence at some time in the past of mantle material which had suffered no depletion at all, and was therefore pristine or primordial. The simplest meaning to attach to "primordial mantle" would be material prior to separation of any crustal components whatsoever. This outer Earth shell had a mass Wo and has later developed a continental crust Wc, oceanic crust Woe and mantle Win. So: Wo = W m + W c + Woc ,

and if we define mass-fractions x relative to Wo (e.g. Xm =Wm/Wo), then: 1 =x m +x c +Xoc

.

288 Using masses given in T a b l e I these fractions are c a l c u l a t e d to be: Xm -- 0 . 9 9 4 2

Xc = 0 . 0 0 4 6

Xoc = 0 . 0 0 1 2

Using c to d e n o t e c o n c e n t r a t i o n o f a n y e l e m e n t p r e s e n t in these d i f f e r e n t bodies, then: Co = X m C m

+ X c C c 4- X o c C o c

(1)

If n o w the m a n t l e be s u p p o s e d to consist o f a d e p l e t e d f r a c t i o n (Xd =

Wd/Wo) and an u n d e p l e t e d f r a c t i o n (Xu), then: (2)

Xm = X d + Xu

and XmC m

= XdC d + XuC u

(3)

T h e q u e s t i o n m a y n o w be f r a m e d - - can a n y p r i m o r d i a l m a n t l e still exist, or has t h e s e p a r a t i o n o f the p r e s e n t - d a y c o n t i n e n t a l a n d o c e a n i c crusts used u p irr e v o c a b l y the initial s t o a k o f one or m o r e e l e m e n t s ? L e t us s u p p o s e t h a t the a n s w e r is " y e s " , i.e., b y the s u p p o s i t i o n t h a t p r e s e n t - d a y u n d e p l e t e d m a n t l e d o e s in f a c t have the p r i m o r d i a l c o m p o s i t i o n , so t h a t Cu = Co. T h e n , f r o m eq. 3: XmCm

= XdCd

+ XuCo

w h e n c e , using eq. 2 Xm

Cd = Co +

Xd

(era - Co)

(4)

We c a n n o w c o m p u t e m a x i m u m possible values o f Xd, say X d , such t h a t the e l e m e n t in q u e s t i o n is n o w at zero c o n c e n t r a t i o n in the d e p l e t e d zones, i.e., c d = 0. Such a t e s t will o f course o n l y be r e l e v a n t f o r e l e m e n t s w h i c h are exp e c t e d to a c c u m u l a t e in t h e c r u s t o f t h e e a r t h (e.g. K), a n d n o t f o r e l e m e n t s such as Ni w h i c h p r e f e r e n t i a l l y r e m a i n in the m a n t l e . T h e n eq. (4) gives: Cm Z d =x m

-

__ Co

F o r e x a m p l e in t h e case o f K, f o r w h i c h Co = 0 . 0 4 6 0 and c m = 0 . 0 3 5 7 % (Table IV), t h e n Xd = 0.221 a n d Xu = 0.773. This m e a n s t h a t all t h e K in t h e p r e s e n t oceanic a n d c o n t i n e n t a l c r u s t c o u l d be a c c o u n t e d f o r b y t a k i n g all the K in 22.7% o f p r i m o r d i a l m a n t l e , leaving 77.3% u n d e p l e t e d . O f c o u r s e this is a simplistic solution, to a s s u m e t h a t t h e m a n t l e consists o n l y o f t w o materials, primordial and totally-depleted, Nevertheless, f o r t h e e l e m e n t s listed in T a b l e IV, values of Xd range f r o m 0.02 (Lu) to 0.41 (Ba). The answer t o the q u e s t i o n p h r a s e d a b o v e is t h u s as follows: t h e s e p a r a t i o n of the p r e s e n t - d a y c o n t i n e n t a l a n d oceanic crusts has

289

n o t used up irrevocably the stock of any of the incompatible elements.

It is therefore not impossible that more continental and/or oceanic crust could continue to separate from the present-day mantle. PROPORTIONS OF DEPLETED AND UNDEPLETED MANTLE

Retaining from the last section the binary concept of undepleted and depleted mantle, it follows from eq. 3 that: Cm = Cd(1 - p ) +PCu

(5)

where p = X u / X m , i.e., the fraction of the mantle which is undepleted. Of course this would imply that, if the CC has changed in mass and composition over time, Xu and Xd will be variable, and consequently the concentrations also: this will be disregarded for the present, considering only the present day. If c d and Cu can be estimated, then so can p. It can be assumed that depleted mantle is the parent material from which MORB is produced: it will be assumed that a fraction Fd melts and that i n c o m p a t i b l e e l e m e n t s will alm o s t e n t i r e l y g o i n t o t h e m e l t so that Cd = FdCoc, where Coc is the MORB abundance of such an element, taken as representative of the oceanic crust. It may also be accepted that undepleted mantle is the source of alkalic basalt (Ca) so that we can similarly approximate and write Cu = F u c a . Substituting these values in eq. 5 we obtain: Cm = FdCoc(1 - p ) + PFuCa

(6)

or

p (Fuca/C m - FdCoc/C m ) = 1 - FdCoc/C m

(7)

which can be written, for element i, in the linear form, P Y i = zi

(8)

In order to test this equation we will accept that MORB forms by 25% melting of depleted mantle (Gast, 1968; Kay and Hubbard, 1968) and that alkali basalt forms by 5% melting of undepleted mantle (Sun and Hanson, 1975a, b; Kay and Gast, 1973, suggest a lower figure), so that F d = 0.25, F u = 0.05. This t h e o r y should only apply to incompatible elements, i.e. those for which the bulk solid-liquid partition coefficients are very small, say < 0.1. The following elements were tested, using the data in Tables 1 and IV: Li, P, C1, K, Rb, Y, Zr, Nb, Ba, Sr, La, Ce, Nd, Sin, Hf, T1, Th, U. The results are shown in Fig. I and indicate that the assumptions break down in several ways. Thus some elements fall in the region of the diagram where Cu < Cd, and some fall in the region where Cm < Cd: both these cases violate the assumptions and indicate that for these elements other important factors have been neglected, or the abundances used are erroneous, or the melting assumptions do not hold, or the elements can not be accepted as in-

290 .~--Cm
~ ~Cm>C d

+100

/ ce

RbO°/ I /

o .&;

....

S mI

Cu>Cd

IITh

5~[~L:L____ Lil I

Cu

Cd

t

-50 -50

0

"

+50

zi

~Ennchment in MORB vs. M0ntle

Fig. 1. Relationship expressed by eqs. 7 and 8 for some incompatible and related elements. Elements which fall outside the upper righthand sector violate one or more assumptions embodied in the equations. Any element conforming to the assumptions for an earth in which 41% of the mantle remains undepleted would fall on the line p = 0.41.

c o m p a t i b l e . Nevertheless the a s s u m p t i o n s h o l d a p p r o x i m a t e l y f o r the elem e n t s in the u p p e r r i g h t h a n d q u a d r a n t o f Fig. 1, i.e. Ba, Nb, Rb, Th, U, K, Sr. F o r these e l e m e n t s t h e m e a n value o f p , o b t a i n e d b y solving eq. 7 in each case and averaging (0.41), is s h o w n b y a straight line t h r o u g h the origin. T o test these e l e m e n t s a little f u r t h e r , and t o c h e c k w h e t h e r o t h e r values o f Fu and Fd w o u l d fit the data, eq. 6 was solved as t h r e e s i m u l t a n e o u s equations in t h e u n k n o w n s p , Fu, F d , a c c e p t i n g the values o f Cm, Ca, Coc for K, R b and Ba. This yielded the values Fu = 0.036, Fd = 0.274, p = 0.23. These results were t h e n p u t b a c k into eq. (6), using c a a n d Coc for Nb, U, T h to solve f o r Cm, giving t h e following results (in p p m ) :

Nb Th U

Cm (calculated)

Cm (Tables I I I and IV)

1.23 0.075 0.029

1.5 0.15 0.039

291

So for these elements (K, Rb, Sr, Nb, Ba, Th, U) a satisfactory model for the mantle, based on the premise that alkalic basalts represent 3--5% partial melting of undepleted mantle and that MORB represent 25--30% partial melting of depleted mantle, leads to the conclusion that 23--41% of the present mantle is undepleted material. This conclusion is n o t applicable to the REE, which fall in the wrong quadrants of Fig. 1. For example the abundances of La and Ce are (in ppm):

La Ce

Cu

Cd

Cm

2.3 4.8

0.75 2.5

0.27 1.1

i.e. the apparent mantle abundance is less than both Cu and Cd, which is impossible. These two elements behave incompatibly, although other REE may not. For La and Ce the abundances Ca, Cu, Coc, Cd all conform closely to the interpretations of REE behaviour in alkalic volcanics made by Kay and Gast (1973) based on more precise calculations using partition coefficients. Under these circumstances it is desirable to see whether a further revision of mantle abundances for the REE can help resolve this anomaly. If we accept that p ---- 0.3, then with the values just listed of Cu and Cd for La it follows from eq. 5 that Cm = 1.215 ppm, which would lead back through eq. 1 to obtain Co = 1.359 ppm. It will n o w the taken that although O'Nions et al. (1978a) were correct in their assumption that terrestrial REE abunTABLE V F i n a l e s t i m a t e s of terrestrial a b u n d a n c e s (Co), disregarding t h e core, a n d p e r c e n t a g e ( f ) l o c a t e d in t h e c o n t i n e n t a l c r u s t ( p p m : Ir, Au, TI in p p b ) Co

f

Co

Li F P

2.1 70.3 105

5 3 3

Rb Sr Y Zr Nb Ba La Ce

1.31 41 1.0 15 1.5 12 1.36 4.53

S Cl

319 59.3

1 1

K Sc V

462 6.1 35

23 1 1

Cr

3100

0

Pr

--

Mn Co Ni Cu Zn

900 90 2390 10 42

0 0 0 1 1

Nd Sm Eu Gd Tb

3.01 0.938 0.388 1.72 --

f

Co

f

1.59 -1.00

---

28 5 10 7

Dy Ho Er Tm

8

Yb

-1.07

41 11 7

Lu Hf W

0.165 0.53 0.31

1 5 --

Ir

6

0

3 13

0 14

--

--1

4 2

Au Tl

1

Pb

2.1

4

1 --

Th U

0.18 0.046

15 15

T h r e e digits are r e t a i n e d for r a t i o c a l c u l a t i o n s o n l y ; f is r o u n d e d t o t h e n e a r e s t p e r cent.

292

dances are chondritic, it is n o t necessary that other r e f r a c t o r y elements b e quite so tightly coupled. If we then abandon the necessity that the ratios Sr/La, Sr/Ce etc. be chondritic, and substitute t ha t Co for La be 1.359 ppm, we obtain abundances f or the other REE as listed in Table IV, columns c and d. The values in this second revision are appr oxi m at el y 3 X the first revised estimates, and all ex cep t Gd are within 3 X the G anapat hy and Anders' (1974) terrestrial estimates (Table III, column e). All the REE now have mantle abundances greater than either Cu or Cd, which is as it should be. With these revised values, the values of p can be calculated for REE ot her than La. For Ce the value o f p is 0.77, which is similar to Sr (p = 0.82) and reflects the fact tha t bot h elements are less depleted in ocean ridge basalts than, for example, Rb. The other REE give negative values of p, i n d i c a t i n g that t h e y are retained in the mantle and can n o t be treated as being incompatible. The final revised values o f Co are grouped together in Table V. Also included is the mass-fraction (f) in per cent of each element which is located in the continental crust. ADDITIONAL ESTIMATES OF DEPLETED MANTLE

In the last section it was shown that, if the mantle m ay be considered as containing two type~ of material (undepleted and depleted), than a plausible interpretation of incompatible element abundances le~ds to the conclusion that 0.23--0.41 of the mantle remains undepleted. Other ways of estimating this fraction will now be examined. Firstly, the depleted mantle must have at least sufficient mass that the present ocean crust can have been derived from it. Taking Woc = 0.4"/9. l 0 ss g and accepting that this represents approximately 25% melting of portions of a depleted mantle Wd, then Wd ~> 4- 0.479 • 10 ~s g = 1.92. l 0 ss g, which leads to p = 0.995. Secondly, the source of MORB is in the lithosphere, so another estimate of Wd is that depleted mantle occurs only in the lithosphere (e.g. n o t also in the mesosphere as proposed by Dickinson and Luth, 1971). Taking the earth radii to the to p and base of an averaged lithosphere as 6350 and 6275 km, and the density to be 3.293 (Smith, 1977, Fig. 2) the mass is 12.37 • 102s g. Consequently Wu = (407.2 - 12.37) • 102s g or 394.83" 102s g: the ratio of residual undepleted mantle to total mantle (p) will be 0.97. The proposition that volcanic activity has been proportional to the generation o f radioactive heat within the earth has been used by Dickinson 'and Luth (1971) and Schilling et al. (1978). The form er authors calculate that 32.5 • 1016 g yr -1 (= Rm) o f mantle have been converted to a depleted state and carried down to the mesosphere, by oceanic volcanism, during the last 10 s years. During earlier times, owing to a greater product i on rate of radioactive heat, the conversion rate could have been m uch greater. Schilling et al. (op. cit.) have calculated an integrated factor (R4. s6) of a b o u t 2.0 for this ef-

293

fect during a period of t = 4.56. 109 yr, so t hat the total m a s s (Wd) of depleted mantle would be RmR4.s6t or 2.96" 1027 g. Taking W m = 4.072 • 1027 g th e n p = 0.272. If, however, the process has only acted over the last 1 . 5 . 1 0 9 y r then the factor becomes R~.s = 1.2, f r o m which Wd = 5.85- 1026 g and p = 0.856: so p is sensitive to such uncertainties. A related approach uses estimates of recent rates of volcanic r o c k production, f r o m mid-ocean ridges and other volcanoes supplied directly f r o m the mantle (i.e. disregarding island arc volcanics, which introduce a possible complication o f co n t i ne nt a l recycling). T he major c o m p o n e n t is ocean ridge volcanism, for which Schilling et al. (op. cit.) accept the rate (estimated by W.S. F y f e) o f 4 . 1 0 ~3 kg y r - ~ : this is close to m y (1976) estimate of 8.3 km 3 y r -~ or (with a density o f 2.75 g c m - 3 ) "2. 3- 10 ~3 kg yr -1 . Schilling et al. also estimate " h o t - s p o t " or within-plate volcanism to contribute 4.35 • 10 ~2 kg yr -1 , making a total of 4 . 4 3 5 . 1 0 ~3 kg yr -~ . Over a period of t = 4.56- 109 y-r, with a f act or R4.s6 again of 2.0, this gives a mass of 4.045 • 1026 g (this a m ount s to 20 × the mass of the continental crust but this calculation would necessitate recycling). If it be assumed t h a t this represents 25% mantle melting t hen the depleted mantle residue is Wd = 1 . 6 1 8 . 1 0 2 7 g, which gives p = 0.60. For the shorter period o f 1.5- 109 yr, with the factor R~.s = 1.2, this gives Wd = 3.193 • 1026 g a n d p = 0.92. Results obtained f r o m these di f f er e nt estimates of p are presented in Table VI. The first two clearly are of little value and m ust be regarded as maxima. The n ex t f our values illustrate the uncbrtainties inherent in the necessity o f using integrated estimates o f volcanic activity t h r o u g h o u t geological time. The last estimates, using incompatible element abundances m ay be m ore acceptable and suggest t hat a b o u t one third of t he mantle remains u n d e )leted. TABLE VI Estimates of proportion (p) of undepleted material in the mantle Model

p

Source rock of present-day oceanic crust, assuming 25% melting Present-day 75 km lithosphere Integrated production rate of depleted mantle *~ proportional to heat production .2 (a) over 4.56.109 yr (b) over 1.5- 109 yr Integrated production rate of MOR and withinplate volcanics, proportional to heat productionS2, (a) over 4.56.109 yr (b) over 1.5" 109 yr Present-day abundances of K, Rb, Sr, Ba, P, Nb, Th, U

0.995

.1 Dickinson and Luth (1971). *~ Schilling et al. (1978).

0.97

0.27 0.86

0.60 0.92 0.2--0.4

294 ISOTOPIC EVIDENCE The study of radiogenic sons and daughters has contributed enormously to understanding Earth processes and the literature will n o t be reviewed again in detail. However, several conclusions are needed here. Numerous authors {e.g. O'Nions and Pankhurst, 1974; Sun and Hanson, 1975; Sun and Nesbitt, 1977; Hofmann and Hart, 1978) have established, on the basis of Pb and Sr isotopic ratios that ocean-ridge basalts and ocean-island alkalic basalts come from source regions which have remained isotopically separated for times in excess of 1--2- 109 yr. Also ocean-ridge basalts show considerable uniformity in isotopic ratios, as in other chemical features, suggesting a rather homogeneous world-wide source; b y contrast, ocean-island alkalic rocks show ratios which are rather uniform in each island, b u t otherwise widely variable, suggesting less homogeneous sources. These observations have been often interpreted as approximating to a two-stage evolution, with the two magma sources corresponding to what has here been identified respectively as depleted and undepleted mantle (see recent discussion b y Hofmann et al., 1978). The constraints from the Rb-Sr isotopic system can now be joined with the previous reasoning. Hofmann and Hart (1978) show that ocean-ridge basalts have rather constant 87Sr/86Sr ratios, close to 0.7027. If the primordial Earth ratio was 0.699, as appears probable, and if ocean-ridge basalts show the Sr isotopic ratio of their source material, then this material must have a Rb/Sr ratio of 0.015. As Hofmann and Hart point out, if Sr is an incompatible element during mantle melting, and if ocean-ridge basalts contain 120 ppm Sr (Table I) then their source material will contain a b o u t 30 ppm Sr, assuming 25% melting. With the Rb/Sr ratio above, the source material should then contain 0.45 p p m Rb (and if K / R b = 1000 then the K content will be 450 ppm). Let us n o w equate the source material to depleted mantle and apply eq. 5, Cm = Cd(1 - p ) +PCu, taking Cd = 0.45 ppm, cm = 0.945 ppm (Table III) and p = 0.3 (previous section). Then cu = 2.1 ppm. This value m a y be compared with the estimate of Cu that is obtained by dividing the Rb content of alkali basalt by 20, obtaining 2.25 ppm. Applying the same approach to St, we obtain from eq. 5 that Cu = 60 ppm, whereas from alkali basalt Cu = 41 ppm. The agreement in both cases is encouraging, suggesting that the method is sound and that p is approximately equal to 0.3.

295 DISCUSSION The values of p obtained by considering incompatible element abundances, and the consistent results obtained from the Rb-Sr isotopic system, are small (0.2--0.4) compared with some of the other estimates in Table VI. If however we accept that depleted mantle has been accumulating over the whole age of the Earth, then the agreement is better. This is in fact a reasonable argument to accept, since there is;much evidence (Shaw, 1972, 1976; Hargraves, 1976; Lowman, 1978) t h a t the primary Earth differentiation produced a thin worldwide crust of intermediate composition, which would of course imply an equivalent proportion Of depleted mantle. Moreover there is no necessity that the estimates of p derived from elements such as K, Rb, Ba, etc. should be as great as estimates based on bulk volcanic rock production. It is in fact to be expected that the incompatible elements would give l o w e r values of p, since evidence has been presented by m a n y authors (e.g. Moorbath, 1977; Burke and Kidd, 1978} t h a t such elements have increased in abundance in the continental crust over the course of time. Two factors so far omitted from the discussion are the effects of recycling of lithospheric plates, and the stability of continental shields. It is clear that, if the Earth is not expanding, conservation of surface areas requires t h a t s o m e proportion of the oceanic crust and possibly also of the continental crust, returns to the mantle. If all the oceanic crust so behaves then there is little point in trying to estimate the role of mid-ocean ridge volcanism in mantle differentiation except for the ultra-volatile elements such as C1, Br and the rare gases. The relatively small volume of ophiolite complexes (fossil ocean crust) in the continental crust suggests that most ocean-crust basalt is in fact returned to the mantle. In this case the main sources of continental crustal growth would be the continental plateau basalt effusions, which m a y be estimated at 50% of all hot-spot activity, or 2.17.1012 kg yr -1 (from Schilling et al., 1978), and island arc volcanism (including plutonism), estimated as 5.1012 kg y r - ' (Anderson, 1974). It is also clear that much of the continental crust produced from the mantle has survived any recycling processes. The surface area of, continental shields, of Precambrian age, was estimated by Poldervaart (1955) as 1.05.1018 cm 2 . This represents 0.206 of the Earth's surface and 0.546 of the mass of the whole continental crust. The question of why, over the last 0.5--1.0.109 yr, more than half the continental crust has been preserved although nearly all the ocean crust has been consumed, is perplexing. Since the question more correctly should be phrased in terms of (much thicker) lithospheric plates, the difference in continental and oceanic crustal densities is of little significance. T.H. Jordan has recently (1978) proposed a mechanism which may in part provide the answer. According to this view, based on thermal reasoning, the continental masses possess roots extending to depths as great as 400 km, consisting of

296 mantle material which has suffered "irreversible basaltic depletion" (op. cit., p. 546). This material has lower density than undepleted mantle, is at lower temperatures, has higher viscosity and has a more elevated solidus than at equivalent depths beneath the oceans. This depleted mantle, with overlying continental crust, constitutes the tectosphere, and the whole behaves as a rigid plate in response to global tectonics. The inertial response of a 400-km thick continental tectosphere to a converging 50--75 km thick oceanic lithosphere will be minor and the wholesale destruction of oceanic crust is to be expected. According to Jordan the continental roots have accumulated throughout geological time and are thickest beneath the stable continental nuclei. Taking the area of continental shields given above, and assuming a depth of 400 km at the present day, the volume of such roots is 3.95- 102s cm 3. If the depleted mantle density is 3.30 (Boyd and McCallister, 1976) then the mass is 1.30.1026 g ( o r p = 0.97), and if we take Dickinson and Luth's (op. cit.) estimate that depleted mantle is being now produced by ocean ridge volcanism at a rate of 32.5- 1016 g yr -1 , then these roots could have been produced during the last 0.4" 109- yr. This is of course a very uncertain estimate because (a) the present production rate of depleted mantle was higher in the past, as discussed above, which would tend to shorten the time required, (b) not all depleted mantle need have been plated on to the continents, thereby increasing the estimated time required, and (c) thinner roots wilt also exist beneath other parts of the continental masses (phanerozoic fold-belts and continental margins). The conclusion of Jordan's discussion of tectospheric growth proposes that the interval 2.8--2.0 • 109 yr BP marks the beginning of development of thick root-zones and that this " m a y be responsible for the fundamental transition from Katarchean permobility to Proterozoic linear (geosynclinal) and mobile belt tectonics" (op. cit. p. 548). A recent study of Sr and Nd isotopic ratios in ancient crustal rocks (McCulloch and Wasserburg, 1978) from the Canadian shield suggests that "the period 2.5 to 2.7 Ca was a major epoch of formation of new continental crust" (p. 1007), and that this new crust comes from the "emplacement of magmatic rocks derived from a uniform mantle reservoir" (p. 1010). Similar results have also been obtained from Norway (Jacobsen and Wasserburg, 1978). The reason for this major epoch of crustal formation remains obscure, but a catastrophist might find the capture of the Moon an attractive speculation. A possible model for crustal evolution to fit the ideas expressed in this paper is presented in Shaw (in press). ACKNOWLEDGEMENTS Discussions with faculty and student colleagues at McMaster and elsewhere have helped greatly in developing ideas expressed here. Financial support of the Canadian National Research Council through Grant No. AO155 is acknowl-

297

edged. I am grateful to Helen EUiott for preparing typescript from a succession of messy manuscripts. I am obliged to Chen-Lin Chou and J.V. Smith for pointing out an error in an earlier version.

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