Statistical analysis of isotopic ratios in MORB: the mantle blob cluster model and the convective regime of the mantle

Earth and Planetary Science Letters, 71 (1984) 71-84

71

Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands [61

Statistical analysis of isotopic ratios in MORB" the mantle blob cluster model and the convective regime of the mantle Claude J. All6gre, Bruno Hamelin and Bernard Dupr6 Laboratoire de G~ochimie et Cosmochimie (LA 196), Institut de Physique du Globe et D~partement des Sciences de la Terre, Universitk de Paris VI et VII, 4, Place Jussieu, 75230 Paris Cedex 05 (France)

Received March 12, 1984 Revised version received July 27, 1984

A statistical examination of isotopic distributions for MORB from various ocean ridges leads to the "blob cluster model", in which the oceanic crust accreting at ridges results from the mixing of two components within the ascending mantle. These are (1) upper mantle material and (2) discrete rising blobs of more radiogenic material. The blobs are fractionated to a variable degree and are distributed in the upper mantle circulation in a manner that is related to the spreading rate. (1) The mean values of the isotopic distributions allow us to calculate the probabilities of the two types of material within the mantle. The results show that the proportion of asthenospheric material in the mixture increases with the spreading rate, in agreement with the hypothesis of blob dilution within the upper mantle convection. Mass fluxes can be estimated for the rising blobs from these probabilities, which depend on the respective concentrations in the sources of the two types of material. If the blobs originate in the lower mantle, this flux estimation would suggest that a significant part of the lower mantle has been injected into the upper mantle during earth history. (2) The standard deviations of the distributions depend on the "efficiency" of the mixing process: the more imbricated are the asthenospheric and blob materials in the mixture, the smaller is the isotopic spread. This efficiency parameter is shown to increase with the spreading rate, as already suggested by previous comparisons between the East Pacific Rise and the Mid-Atlantic Ridge. Moreover, this feature may also be correlated with other data such as ridge bathymetric variations.

1. Introduction T h e m e a s u r e m e n t of Sr, N d a n d Pb isotopes in m i d - o c e a n ridge basalts ( M O R B ) has revealed imp o r t a n t m a n t l e chemical heterogeneities [1-6]. K n o w l e d g e of the exact m e c h a n i s m which operates at spreading centers is crucial to the i n t e r p r e t a t i o n of these heterogeneities. Indeed, if the isotopic d i s t r i b u t i o n s observed in m i d - o c e a n ridge basalts ( M O R B ) reflect the actual heterogeneity of the u p p e r m a n t l e (intrinsic variability), the M O R B a v e r a g e v a l u e s are representative of the u p p e r m a n t l e a n d must be used in a n y box-model b u d g e t calculation. Moreover, in this case, the M O R B isotopic dispersion is also representative of the u p p e r mantle, a n d m u s t be explained directly b y 0012-821X/84/$03.00

© 1984 Elsevier Science Publishers B.V.

convection processes. If, alternatively, the variability is a t t r i b u t e d to p r e s e n t - d a y m i x i n g occurring at spreading centers b e t w e e n a material c o m i n g from the asthenosphere a n d " b l o b s " (or hot spot material) c o m i n g from b e n e a t h (extrinsic variability), the best estimate for the representative value of the isotopic c o m p o s i t i o n for the u p p e r m a n t l e is n o t given b y the m e a n s of the M O R B distributions [7,8], b u t b y t h e i r e x t r e m e values (or near extreme values). T h e M O R B variability is then n o t simply t r a n s l a t i n g the heterogeneity of the u p p e r mantle, a n d the latter can be studied only after "filtering o u t " the influence of the blobs. If the ridge material reflects the intrinsic isotopic heterogeneity of the u p p e r mantle, that is k n o w n to have been created over billions of years,

72 this implies that convection is not sufficiently strong to chemically homogenize the upper mantle. On the other hand, if the observed heterogeneities are extrinsic and created mainly by present-day mixing, and if the upper mantle is in fact isotopically quite homogeneous, this implies an efficient stirring process in a vigorous upper mantle convective regime. Such an efficient mixing regime could indicate a turbulence in the upper mantle or the existence of two-scale convection [9,55]. In addition, the injection of blobs under ocean ridges implies the existence of a deeper distinct isotopic reservoir which generates plumes that rise into the upper mantle. As we can see, deciphering the exact mechanism which creates the isotopic heterogeneity of MORB yields strong constraints on the mantle convection regime. In this paper, we will try to constrain the parameters for mantle dynamics by examining the ridge isotopic heterogeneities from a statisticalpoint of view. In the first part we will review the geochemical variations at spreading centers and will conclude that they strongly support the existence of blob injection at ocean ridges. This observational evidence will lead us to the concept of blob clusters which will constitute the basis of the model developed in the second part.

2. Evidence for injection of blobs at ocean ridges The idea of hot spot injection under ocean ridges originated in the studies of the North Atlantic Ocean by Schilling [10]. His original arguments, based on trace element data, were soon confirmed by Sr and Pb isotopic measurements [11,12], the results of which are not subject to magmatic fractionation during the formation of oceanic crust at ridges [13]. However, the understanding we have of the composition and dynamics of hot spot sources has evolved since these early studies. In the model developed by Morgan [14], following the initial ideas of Wilson [15], hot spots appeared as fixed, more or less continuous flows ascending from the lower mantle. However, as we will see, hot spots are more readily considered as blobs coming from a source which is extremely heterogeneous in its

chemical and isotopic characteristics. Mixing phenomena under ridges thus appear more and more as a multipolar interaction instead of a simple bipolar mixing [16,17]. Several recent studies have indeed contributed to give new evidence of hot spot influence on ridges and constraints on the origin of blobs.

2.1. Relation between bathymetry and isotopic composition at ridges The first evidence for a relation between bathymetry and isotopic composition at ocean ridges was given by Hart et al. [11] and later by White and Schilling [18]. Le Douaran and Francheteau [19] have documented this relation with a detailed study of the Mid-Atlantic Ridge zero age bathymetry. However, the study of the same zone by Dupr6 and All~gre [20] showed that no correlation was observed between the raw data for isotopic compositions and bathymetric depths. More recently, however, Hamelin et al. [21] have resolved this dilemma, showing a good correspondence between the geochemical and geophysical parameters when the short wavelengths of the Fourier series decomposition are filtered out. The second observation made by Hamelin et al. [21] was that for fast-spreading ridges, variations of both the bathymetry and isotopic compositions are much smaller than for slow-spreading ridges. This link between spreading rate, topography and chemical heterogeneity will be the basis of the model discussed in this paper.

2.2. Local scale isotopic variations Several isotopic studies for limited segments of ridge have been published recently. These studies have shown that important local isotopic heterogeneities can be observed in areas corresponding to isotopic and bathymetric swells of the ridge [21-24]. For some other areas, a relative homogeneity is observed [25,26]. This will be interpreted in our model as the result of mixing between blobs and asthenosphere at different depths in the upper mantle: good mixing at depth and during magma genesis gives relatively good surface homogeneity, whereas poor mixing at depth and localized near

73 surface mixing yields sharp local isotopic and chemical variations (cf. below). 2.3. The Indian Ocean case

The Indian Ocean is characterized by the very peculiar isotopic composition of its islands [27], clearly distinct from that observed in the islands of the East Pacific and North Atlantic Oceans [28,29]. Thus, it was important to check whether this "abnormal" isotopic signature is also found on the Indian ridges. Indeed, this has been shown, first by Dupr6 and Allrgre [17] for the Carlsberg Ridge, and more recently for the South West Indian Ridge by Hamelin and Allrgre [30]. 2.4. Rare gas systematics

Recent work of All~gre et al. [31] on the rare gas isotopic composition of ocean ridges has demonstrated correlations between 4°Ar/36Ar, 129Xe/ 13°Xe and 134Xe/13°Xe. The 4°Ar/36Ar and 134Xe/13°Xe isotopic variations result from the long decay period of 4°K and 238U, whereas those of 129Xe/13°Xe have been created by the extinct radioactivity of 1291. The correlation between the two types of isotopic ratios gives additional evidence for recent mixing under ridges between a primitive reservoir (with respect to rare gases) and another strongly outgassed reservoir [31]. 2.5. The isotopic heterogeneity of the blobs and their internal structure

Although it is widely agreed that ocean island basalts (OIB) come from deep-seated reservoirs in the mantle, it is well known from Pb-Pb or Pb-Sr isotopic results that their isotopic signatures are very variable from one island to another. However, as argued recently by Dupr6 and All~gre [17] and Hart [32], a regional grouping can be defined which permits mapping of the whole Earth. Detailed study of archipelagoes like Hawaii or Azores [33-35] has permitted examination of the isotopic structure of blobs at a smaller scale. It has been demonstrated that (1) islands of one archipelago may give different isotopic values from those of others (within the regional isotopic group-

ing defined above), and (2) the chronology of formation of volcanic islands on slow spreading plates (like the Azores archipelago) does not define orientated regularities as on the fast-spreading Pacific plate (Hawaiian archipelago). These observations suggest that plumes should be considered as clusters of discontinuous blobs, the surface distribution of which is governed by structural factors such as spreading rate and fault distribution [36-38] resulting from "regional stress and local mantle regime. 2.6. The ridge model

The set of observations discussed above can be synthesized in a model where ridges result froln the mixing between asthenospheric and blob materials. In a given region, the asthenospheric material seems to be more homogeneous than the blob material. Blobs reach the surface as clusters more or less efficiently intermingled with the asthenospheric material. Thus, the isotopic heterogeneity observed for the different ridges of the world reflects blob heterogeneity, the proportions of asthenosphere and blobs in the mixture as well as the quality of the mixing process. The first parameter seems to be a regional characteristic, whereas the second depends mainly on the spreading rate. We will develop below a quantitative model based on these ideas, to interpret the observed distributions of isotopic values for the various ocean ridges.

3. Statistical mixing model for ocean ridges 3.1. Theoretical principle of the mixing model

Considering the histogram of isotopic ratios measured on a given ridge segment, the statistical distribution D ( i , j ) associates a number j with each class of isotopic ratio i. Suppose this distribution is approximately normal. The model must then quantitatively explain both the mean value and the variance of this distribution. For this purpose, we have postulated that the materials sampled on a ridge are elements of the population resulting from a mixing of two components, one

74

coming from the asthenosphere (A), and the other associated with a hotspot (H). This mixing is described by the binomial distribution which is taken as a reference model for our statistical description. If each reservoir is composed of a number of volume units of rocks of isotopic ratios R A and R H, then the isotopic ratio of a given basalt RM resulting from mixing is given by the relation:

RM=RAX+Rw(1 -x)

(1)

with x, the mixing coefficient, depending on the proportion of mixed mass units m A and mn, and on the concentration of the reference isotope in

P = 0.5

no n~ixing

(~= 1

each reservoir, CA and

CH:

CAm A

x - CAmA + CnmH

(2)

The analogy with the classical statistical model for mixing is helpful to explain quantitatively the observed variability of this mixing coefficient. When red and white bails are put together in a box, the perception one has of this "mixing" depends on the number of balls sampled from the box: if only one ball is drawn at a time, it will be either white or red, and the distribution of N samples ( N being the total number of balls) will be divided into two piles, the height of which will be proportional to the "probabilities" p and 1 - p of red and white balls. Alternatively, if all N balls are drawn together, the distribution will consist of one pile with a corresponding proportion p of red balls (Fig. 1). Of course p is actually a frequency and not a probability in a strict sense. More generally, the binomial distribution is described by the well known expression:

D(k,n,p)

n! k!(n-k)!

pk(1

_p),-~

(3)

which gives the probability for k red balls being found in a n ball drawing. If p is known, the histogram of the distribution can be calculated with this formula, where n is fixed and k varies from 1 to n. It can be demonstrated that the mean of this distribution is p and that its variance 02 is given by: 02 = p ( 1 - p ) / n (4)

~--0.I

When each type of ball is segregated, the distribution corresponds to n = 1 and:

complete i mixing 0

0=0

o2 = p ( 1 - p )

1

Fig. 1. Binomial distnbution schematic illustration: If all the balls are drawn at one time, the mixing is complete, and only one possibility exists. If only one ball is drawn at a time, two possibilities exist. If ten balls are drawn together, the probabilities of the eleven possibilities are given by the binomial law [3].

(5)

When the balls are completely mixed, this corresponds to n ~ oo and o0 = 0. A "segregation coefficient" can then be defined by the ratio

q, = 02/0o2 = 1 / n

(6)

which is equal to 1 when each type of ball is segregated and equal to 0 (n ---, oo) when the mixing is perfect. In the case of ocean ridges, mixing between

75 blobs and asthenospheric material can occur in two different ways: either by solid state mechanical mixing, or by magmatic mixing combining diffusion and turbulence. These two processes are superimposed on each other, and the isotopic heterogeneity in MORB results from this combination. Mechanical mixing takes place during the ascent of blobs through the mantle. If blobs remain voluminous, massive and far apart from each other, the upper mantle will consist of large-scale domains, each of well-defined isotopic composition. The transition zones resulting from the mechanical intrusion of blobs will be narrow and restricted to the edges of the blobs, not affecting the bulk mass. On the contrary, if blobs are numerous, small and scattered, the upper mantle will be structurally more homogeneous, but the wavelength of isotopically homogeneous zones will be shorter. Edge interactions will have a greater influence on little blobs, which will already be partially mixed with asthenosphere during ascent. Partial melting under the ridges will then act on this solid "plum-pudding" upper mantle. This process involves large domains of the mantle, from which liquids are extracted and collected to generate the erupted magma. Since advection, chemical diffusion and isotopic exchange are much more efficient in liquid phases, homogeneization will then be favored over the geographical domain affected by this magma genesis. Once they are extracted, magmas stay in magma chambers in which a further homogeneization can occur. Since magma chambers are probably larger under fast-spreading ridges, and also because the rate of successive feedings of the chambers by magma injections is also probably more rapid, the tendency for lateral homogenization will be increased under a fast-spreading center compared to a slow ridge. Coming back to the geochemical problem, the isotopic histogram can be converted to a probability histogram if the chemical concentrations of each reservoir (A and H) are known. The probability (frequency) in the sense of statistical mixing of "blobs" (mantle domains) can be defined as: Pm

mA m A + m H

(7)

On the other hand, we have the mixing parameter x obtained from the measured isotopic ratios in relations (1) and (2). The relationship between p and x is given by:

Kx Pm = 1 "}-(g - 1)x

(8)

where K is the ratio of the concentration of the chemical species in the two reservoirs: K = C H / C A. This ratio will depend on whether mixing occurs in the magmatic or solid state or in some combination of the two. The important question is now to relate this mixing parameterp to the physical processes which occur at ridge crests. If M A and M H are the total amount of asthenospheric and hotspot material which are extruded at a ridge per unit of time and unit of length, then: M A + M H = 2~hp

(9)

where T is the half-spreading rate, p the density, and h the lithospheric plate thickness. If the mixing observed at the surface in basalts is representative of the whole lithosphere, that is if the mixing between blobs and asthenospheric material occurs beneath the ridge before the accretionary processes (partial melting, segregation and formation of oceanic crust and residual lithosphere), one can write:

1 -p

Mr~ MA + M H

MH 2"chp

(10)

or: M n = (1 -p)2"rhp

(11)

However, blob injection could be a shallow phenomenon involving only the upper part of the lithosphere, or even only the crust. Defining w as the proportion of lithosphere created by the mixing (w varies from 0 to 1): M H = (1 -p)2"rwhp

(12)

The product (1 - p ) . ~"is then directly proportional to the total mass of blobs injected under a ridge per unit time. The second, more delicate question is the interpretation of the parameter ~, which measures the "quality" of mixing, between the blobs and

76 size of the b l o b s will be given by:

a s t h e n o s p h e r e units in the m a t e r i a l from which the b a s a l t s originated. This p a r a m e t e r is related to n which is the ratio of the size of s a m p l i n g relative to the size of the smallest heterogeneity. T h e size of s a m p l i n g is the size o f m a n t l e involved in the genesis of a basaltic unit (defined b y its h o m o g e n e o u s isotopic character). This size m a y vary f r o m one ridge to another. T h e size o f the smallest h e t e r o g e n e i t y is the size at which the b l o b s have been segmented. If the b l o b s were infinitely segmented a n d evenly d i s t r i b u t e d along the ridge a n d i n t i m a t e l y m i x e d with a s t h e n o s p h e r i c material, ~ w o u l d be equal to zero. A t the o p p o s i t e extreme, if the ridge were c o m p o s e d of a sequence of zones with large b l o b s a n d p u r e l y a s t h e n o s p h e r i c zones, ff w o u l d be equal to unity. This p a r a m e t e r thus d e p e n d s u p o n two factors, n a m e l y the geographical dispersion of the b l o b s a n d the efficiency of mixing. These two factors are correlated, since the mixing is easier with n u m e r o u s d r o p l e t s than with large blobs. If M is the mass of m a n t l e involved in the p a r t i a l melting process which generates the b a s a l t for one m a g m a c h a m b e r a n d m is the mass of b l o b arriving in the s a m e area, the mixing is efficient if M >> m, but, o n the contrary, if M ~< m, the mixing is n o t as good. In o t h e r words, the ratio M / m gives an e s t i m a t e of the p a r a m e t e r n o f the ball model. Moreover, s u p p o s i n g that the degree of p a r t i a l melting a n d the q u a n t i t y of m a g m a e r u p t e d are c o m p a r a b l e for each ridge, a m e a n M can be evaluated, a n d the c o r r e s p o n d i n g evaluation of the

m~Mq

(13)

3.2. Mixing parameter estimation 3.2.1. Choice of parameters I n o r d e r to derive the p r o b a b i l i t y p from the d i s t r i b u t i o n of each isotopic tracer a n d each ridge p o r t i o n , one first needs k n o w l e d g e of two a d d i tional p a r a m e t e r s : - - t h e isotopic ratios of the " e n d - m e m b e r s " involved in the mixing, RH a n d R A. - - t h e c o n c e n t r a t i o n ratio of the chemical elem e n t in the two e n d m e m b e r s of the mixture,

K = C H / C A. F o r the isotopic c o m p o s i t i o n of c o m p o n e n t A, the lowest Sr a n d Pb isotopic c o m p o s i t i o n m e a sured on M O R B of the c o r r e s p o n d i n g ridge will be taken, whereas for c o m p o n e n t H the highest values of the oceanic islands of the c o r r e s p o n d i n g a r e a will be taken. Indeed, it has been e m p h a s i z e d that N o r t h A t l a n t i c a n d East Pacific M O R B a n d isl a n d s b e l o n g to the same isotopic trend, interp r e t e d as a mixing line [21,39]. T h e I n d i a n O c e a n seems m o r e complicated, since the islands define a different isotopic group a n d are m o r e scattered t h a n in the A t l a n t i c a n d Pacific [17,30]. However, the hypothesis of mixing u n d e r the ridges r e m a i n s valid [17,24,30] in this case too. The selected values for the isotopic c o m p o s i t i o n s of the end m e m bers for the different provinces are r e p o r t e d in

TABLE 1 Strontium data Ridge

~"

Number

RM

OM

of data

EPR Galapagos Carlsberg MAR SWlR

5.62 + 2 3.4 2.87 + 0.9 1.76 + 0.3 0.8 +0.1

10 36 7 91 18

0.70249 0.70281 0.70286 0.70295 0.70313

0.00014 0.00015 0.00022 0.00033 0.00034

End-members asth

OIB

0.702 0.702 0.702 0.702 0.702

0.704 0.704 0.704 0.704 0.704

Xsr

Pl.s + o

~l.s

a

0.755 0.595 0.570 0.525 0.435

0.820+ 0.05 0.688+ 0.068 0.659+ 0.11 0.616+ 0.16 0.522+0.18

0.017 0.022 0.054 0.108 0.130

1.01 + 0.36 1.06 + 0.06 0.98 + 0.31 0.69 + 0.11 0.38+0.05

~"is the spreading rate (cm/yr) [42,53,54]. R M is the mean Sr isotopic value of the ridge, and o u the standard deviation of the isotopic distribution. References for the data are: EPR (East Pacific Ridge), [21,39,49]; Galapagos (Galapagos spreading center), [50]; Carlsberg (Carlsberg Ridge), [17,51,39]; MAR (Mid-Atlantic Ridge), [18,20,51,52]; SWIR (South West Indian Ridge), [24,30]. Xsr is the proportion of Sr coming from the upper reservoir (A), calculated from relation (1), Pl.5 is the mean of probabilities for the upper reservoir elements calculated from (8) with Ks, = 1.5 [40]. ~, is the mixing quality factor, calculated from (5) and (6). a is the product ~. ( 1 - p), which is proportional to the total mass of blobs M H injected into the upper reservoir per year.

77 TABLE 2 Lead data Ridge

N u m b e r of

RM

°M

data EPR JFGR Carlsberg MAR SWlR

17 14 11 38 8

18.29 18.47 18.10 18.57 18.02

0.21 0.15 0.36 0.50 0.32

End-members asth

OIB

17.3 17.3 17.3 17.3 17.3

20.5 20.5 19.5 20.5 19

xpb

Ksr/Kpb

0.691 0.634 0.636 0.603 0.575

1.38 0.86 0.73 0.57

References for the data are: EPR, [21,33,51]; J F G R (Juan de Fuca and Gorda Ridges), [41]; Carlsberg [17,51,33]; MAR, [20,51,21]; SWIR, [30]. K s r / K a b represents a comparison between the concentration ratios of Sr and Pb in the two reservoirs, it can be calculated from [11]: Ksr = Xsr 1--Xeb Kpb 1 -- Xsr " Xpb

Table 1 for Sr and Table 2 for Pb. The question of the concentration in tile reservoirs involved in the mixture is more difficult. If the mixing process takes place before any melting event by purely mechanical processes, the concentrations of the two end-members is that of the peridotites in the asthenosphere and in the blob reservoirs respectively, and their concentrations are probably not different by more than a factor of 2 or 3 [40]. If the mixing occurs between asthenosphere and partially molten blobs or if both sources are partially molten and the mixing occurs in magma chambers, the difference may rise to 5 or even 20 because blob material probably corresponds to a small degree of partial melting while magma derived from the asthenosphere corresponds to a larger degree of partial melting. A combination of the two processes will thus give intermediate values. We are then faced with the questions: how do "blobs" interact with asthenosphere, and how much of the oceanic lithosphere is involved in the mixing? Conversely, geochemistry can yield some important constraints on these questions, and thus important information about the convection regime of the mantle.

3. 2.2. Results: mean values and probabilities p The calculations were carried out with the histograms of isotopic composition given in Fig. 2. Duplicates or sets of samples coming from restricted areas less than 10 km wide [25,41] must be averaged to obtain a homogeneous sampling net-

work and to avoid overweighting the locations where detailed studies have been performed. Except for the Mid-Atlantic Ridge, the isotopic data remain rather scarce, and in several cases, the statistical significance of the distribution is questionable. The following results must then be considered as preliminary comments, illustrating the line of reasoning, and should be tested by future studies. --First, the results obtained from Sr data for all the ridges show that the corresponding values of x clearly depend on the spreading rate: the proportion of Sr coming from the asthenosphere

87 s /

ge Sr

2o6 pb/204 Pb East Pacific Rise

i rl

Galapagos

F1

I

I

R

~

[]

I

Juan de Fuca Gorda Ridges I

I

Carlsberg

"=~-Atlantic

N~nn 0.702

Ridge

Southwest-indian Ridge ~ , , [] ,,. 0.704 17

,,m

, 2'0

Fig. 2. Histograms of the Sr and Pb isotopic distributions of different ridges. References for data are in Tables 1 a n d 2 .

78

X Sr

(a)

t

K Sr/K

!

I EAST PACIFIC RISE

,,~ j "

I_

'

'

L

,

Pb I

'

'

'

'

6

EAST PACIFIC

6

5

5 4

E

-

4

(cm/y)

(era/y)

1

1

I~$OUTH WEST INDIAN J

[

I

1

05

0.6

0.7

0.8

I

I

I

~

I

0.5

J

i

I

I

1

1.5

Fig. 4. Ksr/Kpb versus spreading rate.

X Pb (b)

2

NORTH ATLANTIC

2

0.4

3

CARLSBERG

3

CARLSBERG

I

i / EAST PACIFIC RISE

Ksr :# Kpb. The K s r / K p b ratio varies from 1.38 to 0.56 and this variation is clearly related to the spreading rate (Fig. 4).

E (cm/y)

3.2.3. Study of variances and epparameters NORTH ATLANTIC

./oo;.s.,. 0.5

0.6

....

0.7

Fig. 3. Proportions of blob material under the different ridges. (a) Proportions calculated from Sr data. (b) Proportions calculated from Pb data. End-member isotopic compositions are indicated in Tables 1 and 2. The more rapid the spreading, the more diluted the blobs become within asthenospheric material.

increases with the spreading rate (Table 1, Fig. 3a). - - I n the case of Pb data, a similar decreasing trend as for Sr is obtained, taking for the Indian ridges less radiogenic end members than for those of the Atlantic and Pacific (Table 2, Fig. 3b). As already stressed above, this may correspond to the fact that the ocean island lead characteristics are very scattered, but do define regional groupings. This then justifies the proposed selection of endmember lead values, insofar as the chosen values remain on the observed Pb-Pb and Pb-Sr correlations, and correspond to ocean island values observed in the regions of the ridges considered. Transforming x values to frequency p is a difficult exercise since we do not know the value for K. The relationships between XSr and Xpb versus ~and XST versus xpb (not shown) demonstrate that

The standard deviations of the isotopic distributions show a clear decreasing function with the spreading rate (Tables 1 and 2). Variances and parameters can be calculated directly from the probability histograms deduced from the isotopic histograms through relation (7) (Tables 1 and 2). It is immediately apparent that ~ and ~"are inversely correlated, i.e., that the spreading rate and the mixing quality are directly related (Fig. 5): the more rapid the spreading, the more efficient is the mixing between blobs and asthenospheric material.

(•)Sr I

--

"C (cm/y)

I

~ T

PACIFIC

6

-

4 D*L*PAOOS

~'

CARLSSSRG .r,c

f 0

I SOUTHWESTINDIAN 0.1

2

0.2

Fig. 5. Mixing quality parameter (~) versus spreading rate: The intimacy of mixing is enhanced when the ridge spreading is faster.

79

3.2.4. Bathymetry This relation follows the correlation between morphology and isotopic ratios for different ridges, in the way proposed by Hamelin et al. [21]. The roughness of a ridge can be estimated by the variance of the distribution of its zero-age bathymetry, and the variability of the different ridge topographies can then be compared. This has been done, using the mean bathymetric values for 500 km averages given by Anderson et al. [42] (Fig. 6). Again roughness is inversely correlated with spreading rate, and this is interpreted as evidence for better mechanical mixing under fast-spreading ridges. Since the efficiency of mechanical mixing is related to the size and geographic distribution of blobs, it is suggested that the latter are smaller, more mixed and more randomly distributed along the fast-spreading ridges. Using the simple relation (13) m = M e as a rough approximation, the relative size of the blobs corresponding to the different types of ridges can be compared. First, if M does not depend on the spreading rate: marl m Pac

~Atl = (I)Pac

1.99

( ~ D(m)

(cm/y)

~

T PACIFIC RISE

6

~.TARCTIC

4

"--CARLSBERG N k ~ R T H

ATLANTIC

2

ARCTIC SOUTHWEST I Nrl I AN ( ~ ' ~ ~

200

400

600

Fig. 6. Ridge roughness comparison: Topographic standard deviations versus spreading rate confirm that both the geochemical and geophysical variations are smaller as the spreading rate increases.

and then blobs 500 km large in the Atlantic would imply blobs of 250 km in the Pacific. However, it is generally considered that under the fast-spreading ridges, M is larger than under the slow ones, because of larger active magma chambers and melting zones. If, for instance, M Mo'l'q then: =

mAtt = qbAt._1_~ TPa_._...~cq mPac @Pac I "rAil I If q = 1 the Pacific blobs may be reduced to 80 km large. If q = 2 they will be 20 km. Although these results are quite qualitative, the line of reasoning is useful and with more data may provide a way to distinguish mechanical mixing from magmatic mixing in the study of Ksr/Kpb.

3.2.5. Blob cluster model A simple model can be proposed to describe ridge processes, consistent with the above geochemical and morphological observations, and by analogy with simple fluid mechanical concepts. Suppose a series of oil drops are emitted from holes at the bottom of a convecting water container. The diameter of these drops will be fixed by the oil/water surface tension ratio, as long as the water is convecting with a low Rayleigh number. The drops will rise to the surface with approximately their initial spacing and their initial size. If, at the other extreme, the convective regime of the water is violently turbulent, the drops are fractionated into droplets by the strain they suffer a n d are randomly scattered in the water: their mean spacing will be smaller than the spacing of their emission holes and their size will be smaller. Except for the effect of surface tension, the analogy with mantle structure is then straightforward: supposing that blobs are emitted from the bottom of the upper mantle, these blobs remain quite voluminous in areas of weakly convecting mantle, i.e., under the slow spreading plates; conversely, in rapidly convecting zones of the mantle, the blobs are deformed and rapidly fractionated and clouds of droplets rise to the surface (Fig. 7). In ridge processes magma genesis will slightly complicate the mixing phenomenon. Small blobs are both mechanically and magmatically more

80

SLOW SPREADING REGIME

,~.

~

.~.

within the plates seems to favor this model. In the Atlantic, oceanic islands are clustered in circular archipelagoes or isolated large islands, whereas in the Pacific they are more scattered, as qualitatively predicted by the mantle blob cluster model. The statistical study of oceanic islands and seamounts, as undertaken by Jordan et al. [44], will be complementary to the ridge study. A comparison between the distributions of size and isotopic composition of seamounts will also clarify the mode of mixing. This work has still to be carried out.

4. Consequences and speculations about mantle processes 4.1. Geochemical consequences

FAST SPREADING REGIME Fig. 7. The blob cluster model.

easily mixed than large blobs. In addition, in fast-spreading ridges large magma chambers will increase the mixing efficiency while in slowspreading ridges local heterogeneities will be more easily preserved because of the offset between small magma chambers. This also explains the observations of ridge topography: the accretionary zones act as chimneys sucking large proportions of the blobs upward to the surface. Huge blobs rising under slow ridges will be imprinted in the topography, whereas disseminated small blobs under fast-spreading ridges will remain undetected. The same type of contrast will be found in gravimetric data [42,43]: fast-spreading ridges with their small well mixed blobs are compensated, whereas slow-spreading ridges with their badly assimilated blobs show gravimetric anomalies. It should be possible to calculate a dynamic model of blobs on this principle, but this is beyond the scope of this paper. Another qualitative topographic observation about the mode of distribution of oceanic islands

4.1.1. Geochemical characteristics of mantle reservoirs As suggested in the introduction, a corollary of the ridge mixing model involving extrinsic character of the isotopic heterogeneity is the way we estimate the representative values for the geodynamic reservoirs in box model calculations. Indeed, if the existence of reservoir mixing under the ridges is accepted, it is clear that the mean isotopic value measured on a ridge is not representative of the upper reservoir. At the other extreme, the "tails" of the isotopic distributions must be chosen, and moreover, these extreme values are really representative only in the case of the poorly mixed slow-spreading ridges. As a sort of paradox, the best estimate of isotopic and chemical values for asthenospheric material, called N-MORB, is not from those of fast-spreading ridges but from the tail of the distribution of slow-spreading ridges where, on the average, the proportion of this material is the smallest! This is what we actually observe: the lowest 87Sr/86Sr and the highest 4°mr/36Ar, 129Xe//13°Xe, 143Nd//la4Nd are found on the North Atlantic Ridge! If we want to study the intrinsic chemical and isotopic characteristics of the upper mantle created by continental crust extraction or subduction injection processes, we have to "filter out" the effect of blob injection. Such "filtering" can be done by working on slow-spreading ridges in the areas of

81 deep bathymetry. Preliminary examination of such cases, seems to indicate that such heterogeneities are far smaller than those created by blob injection. Such observation, if not invalidated by future work, justifies our simplification in considering that the upper reservoir is homogeneous. 4.1.2. Trace element distributions The proposed model can be applied to every trace element concentration or trace element ratio involving hygromagmaphile elements, which have been strongly depleted in the asthenosphere, compared to the primitive mantle, by continental crust extraction [45]. The difference in concentration between the asthenospheric material and the blob material will be larger for more hygromagmaphile elements, and the variance observed in the concentrations or concentration ratios in MORB will be smaller for a fast-spreading ridge than for a slow one. The additional complexities due to melting and crystallization processes are certainly secondary, especially when element ratios are considered, moreover they reinforce the previous phenomenon by increasing the tendency for homogenization. The observations of a correlation between trace element variance and degree of incompatibility, as emphasized by Hofmann et al. [46], should be re-examined in the present context.

are strikingly homogeneous all over the world. Recent studies of the Indian Ocean ridges suggest however that this ocean may have slightly different values for its asthenospheric reservoir especially in lead isotopes [30]. More work will be needed to elucidate this point which is beyond the scope of the present paper. In fact two processes are competing: (1) the injection and mixing discussed above, and (2) the homogenization of differences created by this process within the upper convecting reservoir. A combination of differences in the contaminating end-member and different rates of homogenization can probably generate the observed differences between the MORB endmembers in different oceans. However, these slight differences are of second order compared to the OIB heterogeneities and to the MORB scatter created by mixing with OIB and do not strongly affect the results of the calculations. 4.1.4 Flux of blobs We can estimate the total flux of blobs at ridge crests: Frt = M H L (where L is the total ridge length). Using relauons (8) and (12), we obtain: FH =

4.1.3 Reservoir homogeneity Starting from the principles discussed above, the question of the internal isotopic homogeneity of each mantle reservoir remains to be solved. The blob reservoir is clearly heterogeneous. Even though geographical provinces can be defined (such as for the North Atlantic OIB, or for the Indian OIB), significant heterogeneities are found even within these provinces. It is, however, probable that these heterogeneities are averaged within the "sucking zone" under the ridge. This effect, which has been clearly demonstrated in the case of the Azores by Dupr6 [35], justifies the adoption of a common value for the H reservoir under each segment of ridge as a first approximation. But it is only an approximation and future work will certainly need to accommodate further complexities. For the MORB reservoir the problem is more complex: the extreme values of the MORB trend

1-x ) 1 +(-/£---1)x 2TwhpL

As a world average ~ = 4 c m / y r , h = 102 km, L = 6 x 10 4 knl and XSr can be taken as about 0.7 (Table 1). Therefore, the extreme possible values of the flux can be calculated: (1) If mixing takes place only in the liquid state, blobs being mixed to generate the oceanic crust only, K = 1 0 and w = 0 . 1 , then F H = 1 . 9 7 km3/yr or 6 x 1015 g/yr. (2) Alternatively, for mixing between peridotite reservoirs, K = 3 and w = 1, then F n = 60 km3/yr or 1.8 x 1017 g/yr. Given that ridges influence only one third of the earth's surface ( - 2000 km on each side of the ridge), if the blob rate is uniform, Y.Fn is between 18 × 1015 g / y r and 5.4 × 1017 g/yr. In the hypothesis in which blobs are coming from reservoirs different from the upper mantle, integrating these fluxes over 4.5 x 10 9 yr yields 8 × 10 25 g and

82 2.4 × 1027 g respectively. With an upper mantle of 1 × 10 27 g, the first case corresponds to 10%, the second to 200%! If this latter flux existed, it would have ruled out any fundamental difference between the two reservoirs (3He or ]29Xe being the most counterindicative in this respect!). On the other hand, hypothesis (1) is of the order of magnitude expected from global budget models [40]. Therefore, this could suggest that blobs mix with asthenosphere mainly during magma generation or in relation to magma generation.

4.1.5 Homogenization in magma chambers It has been suggested that the smaller variations associated with fast-spreading ridges could result mainly from the larger size of active magma chambers [39]. Mixing and isotopic homogenization certainly occur between the liquid phases within the chambers; this can explain for instance the larger isotopic spread observed on the seamounts near the Juan de Fuca, Gorda and East Pacific Rises, compared to the MORB of these ridges [41,47]. For seamounts, only mechanical mixing is efficient and therefore the heterogeneity is larger than that observed for MORB. However, this process alone is not sufficient to explain the whole ridge pattern. If regional statistical variations with a wavelength of the order of 500 km, as for those of the MidAtlantic Ridge, do exist under the East Pacific Rise, it seems unlikely that magma chambers can homogenize on this scale. Other hypotheses about the distribution of heterogeneities must then be added anyway. The blob cluster model is intended as a solution to this problem. It incorporates homogenization in magma chambers but adds another mechanism to explain complete homogenization. 4.2. Convective regime of the mantle 4.2.1. Dynamic role of blobs The total amount of blob material is proportional to ( 1 - p ) z . When plotting this parameter versus spreading rate, we can show that it increases less rapidly than spreading rate (Fig. 8). An important consequence of the results obtained with this model is that blob injections, or hot spots, are not responsible for plate motions or for

(cm/y) ,

( 1 - P ) ~;

tAT'ANr.~I~/~

t/ so I

j

1.5

1.0 EAST PACIFIC

0.5

I

0

3 5 Fig. 8. ( 1 - p ) r versus ~- diagram, a = ( 1 - p ) r is directly proportional to the mass of blobs injected under the ridge per unit of time.

differences in spreading rate, since their flux does not increase in proportion to spreading rate. The blobs appear to be passively swept into the upper reservoir convection, in which they are more or less diluted according to the spreading rate. These blobs are probably not permanent plumes as in Morgan's classical model, but rather drops originating from a common blob emission. Such a pattern of multiple emission from a single point in a single event gives the impression of a semi-permanent pseudo-fixed reference frame for hot spots. If the blobs are not the dominant forces in seafloor spreading, this does not mean, however, that blobs are not able to induce continental fracture or rift propagation either by mechanical or thermal effects [14]. On the contrary, it is possible that large blobs in slow-spreading areas may generate sufficient stresses for such processes, but in this case rift initiation and the plate motion driving mechanisms must be distinguished. This is in agreement with the idea of ridges being largely passive features in plate tectonics.

4.2.2 Mantle structure and dynamics The fact that blob dispersion is proportional to spreading rate also means that the upper mantle is made of separate regional boxes with different convection regimes (Fig. 9). The idea that such

83 continent

Mantle

Fig. 9. Schematic picture of mantle dynamics.

cells m u s t h a v e b e e n i s o l a t e d f r o m e a c h o t h e r for h u n d r e d s o f m i l l i o n s o f y e a r s has b e e n i l l u s t r a t e d b y r e c e n t studies o f I n d i a n M O R B [17,30]. T h e e x i s t e n c e o f t w o d i s t i n c t r e s e r v o i r s for isot o p i c c o m p o s i t i o n , a n d e s p e c i a l l y for r a r e gases, is in a g r e e m e n t w i t h t w o - l a y e r m a n t l e c o n v e c t i o n a n d w e will d i s c u s s the m a n t l e d y n a m i c s f o r this case. T h e a b o v e c o n s i d e r a t i o n s suggest t h a t the blobs originate from melting processes around or b e l o w the 700 k m d i s c o n t i n u i t y as a r g u e d b y A l l 6 g r e a n d T u r c o t t e [48]. A c c o r d i n g to t h e s e a u t h o r s , b l o b g e n e r a t i o n m a y o c c u r j u s t a b o v e this discontinuity, and blobs may drag up material f r o m u n d e r l y i n g l o w e r m a n t l e , d u r i n g their ascent. If this m e c h a n i s m exists, it c o u l d also e x p l a i n w h y in s o m e a r e a s (like the I n d i a n O c e a n ) , r e i n j e c t e d s e d i m e n t s b l a n k e t i n g t h e b o u n d a r y l a y e r at t h e b o t t o m o f the u p p e r m a n t l e c o u l d c o n t a m i n a t e the blobs, especially for lead isotopic composition.

Acknowledgements W e g r a t e f u l l y a c k n o w l e d g e C. J a u p a r t , D . T u r c o t t e , J.L. L e M o u e l , V. C o u r t i l l o t a n d J.-P. P o i r i e r for f r u i t f u l d i s c u s s i o n s a n d S. R i c h a r d s o n for c l e a n i n g u p t h e m a n u s c r i p t . T h i s is I . P . G . P . C o n t r i b u t i o n N o . 763.

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