All?gre Claude J. Isotope Geology

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comes from the d epleted upper mantle, and let us calculate the composition of the‘‘recon-

structed’’primitive mantle (Table 6. 1 0) before extraction ofthe continental crustby mixing

ofcontinental crustwith depleted mantle:

½A

primitive

¼½peridotite0:99 þ½granite0:01:

This composition is almostidenticaltothatofthe peridotite analyzed.The on lyelement for

whichadi ¡erence canbe clearlyseen is potass ium, which isnot a major element! T hose dif-

ferencein composition cannotbe distinguishedbyanygeophysical,seismological, orgravi-

metric m easurements.

Remark

Remember this warning in chemical geodynamics: minor elements mean major problems. Whereas

in petrology, major elements mean key problems!

We have translated this in Figure 6.67, remembering we have calculated factorsW.Itwill

berecalledthat:

where m

is the mass of continental crust, and m

is the mass of the primary mantle

before depletion; we can take it to be equal to the upper mantle, such that m

¼0.015;

Table 6.9 Composition of granite and of peridotite of the mantle

Oxide Element Peridotite Gran ite

percentweightof

oxide

percentweight

ofmajor

element

perc ent weight

ofoxide

percentweight

ofmajor

element

O43.36 50.38

SiO

Si 41.8 2 0.80 19.51 72.30 0.50 3 3 . 1 3

Al 3.50 0.10 1.26 14.15 0. 10 5 . 094

Fe 9.06 0. 15 6.33 1 .91 0.02 1 .3 3

MgO Mg 37.9 9 0.5 22.86 0.040 0.008 0.03

MnO Mn 0.17 0.01 0.1 4 0.370 0.001 0.22

CaO C a 3.02 0.06 2. 15 1 .3 3 0.01 0.949

ONa 0.820. 1 0.6 3.49 0.03 2.589

OK 0.030.006 0.0250 2.55 0.06 2. 1 2

Table 6.10 Composition of the primitive mantle

OSiAlFeMgMnCaNaK

‘‘Reconstructe d’’prim itive

mantle(%)

43.4219.641.2986.2822.6030.13892.1370.61980.4595

Depletedmantle 43.36 19.51 1.26 6.33 22.86 0.14 2.15 0.6 0.025

329 Chemical geodynamics

is the concentration of element i in the continental crust, C

is the concentration of

element i in the primitive mantle, and W is the proportion of the element concentrated

in the continental crust.

It is possible to calculateW fora few majorand minorelements.The scale (in log

) is sepa-

rated in two by the values  ¼0.015; an element that does not fractionate between crust and

mantlehas this value. Above this value the element is enriched in continental crust; below, it

is depleted. It shall be seen that while silicon and manganese are not very di¡erent from it,

below  the elements are enriched in the mantle, while above they are enriched in the crust.

Tab l e 6. 1 1givesthevalues ofthe various isotope ratios that canbeus ed for studying the conti-

nental crust^mantlesystem.

Hofmann’s two-stagemodel

Hofmann (1988) develope d a simple model that gives a p rettygood accountofthe chemical

composition of the continental crust, th e oceanic crust, and the upper mantle. Although

u nsophisticated, it does allow us to g et our thinking straight. It assumes, as already estab-

lished, that the continental crust became di¡erentiate d from the p rim itive mantle through

1.0

0.4

0.15

0.06

0.045

0.015

0.0004

Th, Rb, K, U, Pb

1.0

0.8

0.9

K, U

Enriched elements

in the crust

Enriched elements

in the mantle

Figure 6.67 The

scale for some elements.

is the fraction of an element contained in the

continental crust relative to the sum total (crust þupper mantle), and  is the proportion by mass of

the lower mantle–upper mantle. It separates the elements enriched in the crust from those enriched in

the mantle.

We know it is an approximation because the mass of the depleted mantle is greater than that of the

upper mantle. However, it helps to get our ideas straight.

330 Radiogenic isotope geochemistry

partial meltingwithadegreeofmeltingF

andthatthisextractionleftadepletedmantle. The

depleted mantle then underwent a second stage of partial m elting i n much more recent

times with a degree of melting F

. For example, the di¡erentiation of the continental crust

may have a mean age of about 2 Ga.The di¡erentiation of ocean crust is far more recent,

less than100 Ma.

Theequationswithwhichto computesucha modelarestraightforward.Webeginwiththe

formulaforthe creationofmeltbypartial meltingatequilibrium,assumingthatth e compo-

sitionofthis meltrepres entsthe average composition ofthe continentalcrust:

0:s

þ F 1  D



where C

is the concentration of element (i)inthemelt,C

0:s

is the concentration in th e

initial solid, D

is the fractionation factor between the magmatic melt and the residual

solid , and F is the degree of partial melting.

After the ¢rst melting episode producing the continental crust with a degree of melting

), the concentration foran element (i) ofthe residual mantle is:

 C

0:s

þ F

1  D



If the residual solid is subj ected to a new melting episode, the concentration of the melt

(magma) foran element (i) iswritten:

 C

0:s

þ F

1  D



 D

þ F

1  D



Table 6.11 Average isotope ratios of the three reservoirs of the silicate

Earth

Continental crust Depletedmantle Primitive mantle

Rb/

Sr 0.35 0.0014 0.087

Sr/

Sr 0.7123 0.7021 0.70475

147

Sm/

144

Nd 0. 1 1 0.252 0. 1975

143

Nd/

144

Nd 0.51155 0.51330 0.51265

176

Lu/

17 7

Hf 0.0073 0.0459 0.0333

176

Hf/

177

Hf 0.281 69 0.28343 0.28287

187

Re/

188

Os 3 7 .54 0.3622 0.3850

187

Re/

186

Os 312 3.01 3.20

187

Os/

188

Os 1.40 0.1251 0.1254

187

Os/

186

Os 11.7 1.040 1.0422

238

204

Pb 9.58 5.77 8.78

232

Th/

238

U 4.55 2.54 4.27

206

Pb/

204

Pb 18.59 17.43 18.34

207

Pb/

204

Pb 15.586 15.42 15.55

208

Pb/

204

Pb 39.56 37.13 39.05

331 Chemical geodynamics

The degree of melting needed to pro duce the continental crust may be estimate d

from the concentration of the most highly magmaphile elements (rubidiu m, barium,

thorium) in the crust. For such elements, the coe⁄cient D

is close to zero so that the

equation

þ F 1  D



reduc es to



Since the average concentration of these elements in the continental crust is

approximately

 100

weobtain a meltfraction of

 0:01:

We can then calculate empirical partition (fractionation) coe⁄cients for all the other ele-

ments fro m their estimated mean concentrations in the continental crust, C

,thevalueof

¼0.01, and the initial bu lk mantle composition C

, using the equilibrium melting equa-

tion. Finally, we can calculate the composition of the second melting event produc ing the

o ceanic crust using these formulae with the same partition coe⁄cients and letting F

vary

around 0.1.

This is the approach Al Hofmann took in 1988. Hofmann assumed, and this is his b ig

hypothesis, thatfractionation coe⁄cients are identical for the creation of both continental

cru st and oceanic crust.The model thereforegives an exclusive role to partial meltingofthe

mantle. Again, this hypothesis is debatable and even simplistic, but it does have the advan-

tageofbeing clearandofsettinglimits and providing abenchmark forother more elaborate

mo dels.

Because there aregood reasons to thinkthatthe processes forming the continental crust

are more complex thanjust simple, equilibrium partial melting, Hofmann et al.(1986)also

used an alternative method for determining solid^li quid fractionation factors. This

methodisbased entirelyon observationsfrom naturallyoc curringoceanicbasalts.

For thispur pose, heuseda methodoriginally proposedbyMichel Treuil foranother use.

Supposethatthe partial meltingformula mightbeapproximatedby:

þ F

where C

is the concentration of element (i) in the liquid , and C

the concentration of ele-

ment(i) inthe initialsolid.

332 Radiogenic isotope geochemistry

This means consideringthatD

iss mallrelativetotheunitinthegeneral formula.We can

then write the ratio between two elements for which this approximation can be made,

whichwe note (i)and(j):

ðiÞ

ðjÞ

ðiÞ

 D

ðjÞ

ðiÞ

ðjÞ

Zr/Sm

Zr (ppm)

Hf (ppm)

MORB

OIB

80 120 160

R = 0.48

200 240 280

Hf/Sm

MORB

OIB

1.0

0.8

0.6

324567

R = 0.31

Hf (ppm)

Hf/Eu

MORB

OIB

2.4

2.8

2.0

1.6

324567

R = 0.78

Figure 6.68 Illustration of Hofmann’s second method for determining the fractionation factors of the

various magmaphile elements. The slope deﬁnes the relative value of the solid/magma fractionation

factors. It is seen here that

, and

333 Chemical geodynamics

Normalized concentration

Primitive mantle

= 0.016 Continental crust

Residual mantle

= 0.01

100

0.1

0.0010.0001

0.01 0.1 1 10

Figure 6.69 Hofmann’s calculation to explain the composition of continental crust and oceanic crust.

After Hofmann (1988).

Normalized concentration

Compatibility

(oceanic basalts)

MORB

Continental

crust

Rb Th

Rb Ce Pr Sr

Hf Ti

Gd Dy Y Tm Lu Al Sc Fe Co Ni

U K La Pb

(Ta)

Nd Sm Zr Eu Tb Ho Er Yb Na Ca Cu Si Mg

100

0.1

Figure 6.70 Actual distribution of the composition of continental crust and of MORBs. Notice the

anomalies for niobium, (tantalum), lead, strontium, and titanium. From Hofmann (1988).

334 Radiogenic isotope geochemistry

This equation, from whichthe melt fraction F hasbeen eliminated, gives the concentration

ratios of two elements in the melt as a function of their respective ratio in the source and of

their partition coe⁄cients.

Ina C

; C



diagram, th atis aratio ofelements asafunctionofthe concentration of

one element in the liquid (magma), the process is represented by a straight line whose

slope is proportional to D

D

.IfD

, the slope i s positive and vice versa. It c an

be seen then that by plotti ng the ratios between two elements as a function of the concen-

tration of one of them, it can be determined whether D

is g reater than or l ess than D

(Figure 6.68).

This approach of estimating the relative magnitudes of the partition coe⁄cients can

be used to test the above crust^mantle di¡erentiation model: if we plot abundances

on the y-axis and the sequence of chemical elements on the x-axis, ordered according

to their decreasing solid^liquid fractionation factors, there should be no major dis-

continuities for MORBs. Hofmann et al. (1986) also calculated theoretical m odels

(Figure 6.69).

When th e calculations are compared with actual ob servations, it can be seen that the

mo del does not re£ect the observations exactly although the di¡erence is not great

(Figure6.70).

(1) Elements with very low fractionation factors are more abundant in the real world

than in the model. Hofmann et al. (1986 ) overcame this di⁄culty by assuming that a

small partofthe melt is retained in the mantle.T his is an ad hoc hypothesisbutthereis

no reason to rule it out since, through erosion and subduction, this process certainly

occurred.

(2) Th e second di⁄culty concerns the elements Nb and Ta, Ce and Pb, S r and Ti, which

‘‘cause’’ peaks or valleys in the abundance diagram. Hofmann et al. (1986) ascribed

these‘‘anomalies’’ to the factthat the actual fractionation factors involved in the di¡er-

entiation of continental crust and those involved in the di ¡erentiation ofoceanic crust

arenot identical.This relatesbacktothe di¡e rencebetweenth e R- and the S-processes,

one without water, the other withwater.

Accordingly, Hofmann’s approach is interestingfor teaching p urpos es.Itshowsthatwith

a very simple model, the general relationship s between c ontinental and oc eanic crust can

be reasonably well modeled, butthat aprec ise description involves disti nguishingbetween

di¡erentiation of continental crust and partial melting occurring at the mid-ocean ridges.

It is agood exampleofmodeling tomeditateon.

6.6.8 The origin of MORB and OIB and the mantle structure

Letusturnback now tothequestionofthe originofoceanicbasalts. Letus examinethe pro-

blem of the origin of the two main types ofoceanic basalt, MORB and OIB, on the basis of

the statistical distribution of their isotope composition. Both types of basalt are the result

of a threefold process: partial melting of the mantle, col lection of magma, and transfer to

335 Chemical geodynamics

the surface.These three processes apply to a mantle source made up of the mixing of thin

folded layers of a basaltic component (eclogite) i n an ultrabasic matrix (peridotite). We

k now from petrological experiments (partial melting experiments in the laboratory in var-

iedconditionsofpres su reandtemperature) thattheMORBs correspondtoagreaterdegree

ofpartialmelting(5^10%)thantheOIBswhichareclose r to0.1^1%.Th ereforeOIBssample

a larger volume of mantle pe r cubic meter of magma than MORBs do. But on the other

hand,thevolumegiven outby the ocean ri dges (MORB) is so muchgreater thanthevolu me

from plumes (OIB) that a much greater volumetr ic proportion of the mantle is sampled by

the MORBsthanbythe OIBs.

Exercise

Calculate the volume of mantle sampled in 5 million years by the MORB. What proportion

does that correspond to for the upper mantle?

Answer

4  10

m(ridgelength) 4  10

2

(spreading)  6  10

(thickness)  3.2  10

(density) 

5  10

(duration)  10 ¼1.5  10

kg. Now, the mass of the mantle is 1  10

kg, there-

fore more than 100% is sampled in 500 Ma. If the sampling were random, all of it would

be sampled! (But in practice some domains are sampled several times because of

recycling.)

That said, the statistical distribution of

Sr/

Sr,

He/

He, or

206

Pb/

204

Pb isotope ratios

for MORB and OIB exhibits much greater dispersion for OIB than for MORB (White,

1985;Alle

gre, 1987).

This is particularly obvious if all the zones where the Schilling e¡ect is observed are

removed fromthe statistics.

Measu rementsofleadisotope compositionshaveshownthatthesignaturesofthevarious

OIBs are very varied (Figure 6.5 1 ). The accumulation of Sr and Nd isotope data have also

revealed the same phenomenon.The Sr and Nd isotope correlation is not a simple straight

line as earlystudieshadsuggested (Figure6.7 1 ).

The MORBs, then, haveveryhomogeneous isotopic compositions.This corresponds to

what weknowabouttheir source (theupper mantle), which iswell mixedbymantle convec-

tionprocess es.

In contrast, OIBs come from a much less well mixed zone of the mantle.The idea that

ha s developed, and which combines this last observation and the physical conditions

for manufacturing plumes, as in £uid mechanics experiments, is, as said, that OIBs

are generated in the bou ndary layers at the b ase of the convective systems (Figure 6. 7 2).

Plumes arise from the instability of the boundary layers, like tho se that give rise to hot

spots. These boundary l aye rs are relatively st agnant zones located at the frontier

between convecting systems. T hey are stagnant layers which receive surface material

(oceanic crust, oceanic crust and sediment, continental lithosp here).They are therefore

poorly mixed and so heterogeneous. The dispersion observed in the various isotopic

diagrams is interpreted as the result of mixing bet ween a mantle that is analogous to

that which generated the MORBs (depleted mantle) and various extraneous compon-

ents (e.g., sediments, re cycled oceanic crust, or del aminated lithosph ere). In the

336 Radiogenic isotope geochemistry

atm

702

703

704

705

São

Miguel

São Miguel

St.Helena

Hawaii

St.Helena

Kerguélen

Tristan

Tristan da Cunha

Kerguélen

MORB

0.702 0.703 0.704 0.705

206

Pb/

204

208

Pb/

204

Sr/

0.702 0.703 0.704 0.705

18 18 19 20 2119 20 21

Tristan da Cunha

Gough

Kerguélen

Figure 6.71 With the increased number of measurements, multiple correlations, which were simple

when chemical geodynamics began, have become more complicated. This diagram (after Alle

gre and

Turcotte, 1985) shows the comparative dispersion of MORB and OIB measurements in various

correlation diagrams but also the continuity between their domains.

670 km

OIB

MORB

Mesosphere

boundary

layer

LOWER MANTLE

Figure 6.72 Diagram showing how one can think of the upper mantle convecting separately from the

lower mantle but exchanging matter with the lower mantle. After Alle

gre and Turcotte (1985).

337 Chemical geodynamics

Dupal zone, these zon es receive pieces of continents delaminated by continental colli-

sion phenom ena. Elsewhere, they receive recycled oceanic crust with o r without

sediments.

Thequestionis:whereis (are)thebou ndarylayer(s) fromwhichtheOIBtaketheirsource?

Twozones ofthe mantle aretobe con sidered: the 670-kmboundarylayerabove the seismic

dis continuityand the core^mantle interfaceboundarylayer.

The present author still believes most ob servations can be explained by OIB originating

at a depth of 670 km (mesosphere boundary layer) as proposed by Alle

gre and Turcotte

(1985).

(1) In the contextof a two-reservoir mantle as required by the isotope geochemistryof rare

gas es and as is consistent with the isotopic mass balances of Sr, Nd, and Hf, the idea of

OIB rising fro m the 670- km boundary provides a natural explanation ofthe continuity

observed between MORB and OIB in the various isotope diagrams if they come from

the same reservoirs.This includes th e fact that th e Dupal signature exists for both OIB

and MORB(Figure6. 71 ).

(2) The du ality observed in the isotopic composition of rare gases and not in the isotopic

composition ofthe elements Sr, Nd, Hf, or Pb canbe accounted forby the entrainment

phenomenon proposed by O’Nions and Oxburgh (1983).When an instability gives rise

to a plume in a boundarylayer, the process entrai ns a fraction of the lower layer of less

than2^5%.

The concentration ratio ofraregasesbetweenthelower mantleand theupper mantle

is 100 to 500, as can be extracted from the mass balance of various rare gases.When

plu mes form, the mixture so created is dominated by the signature of the lower layer,

but to variable degrees depending on the proportion of entrainment. Large plumes

entrain a greater p roportion of the lower layers compared with small plumes.This is

indeed what is observed: the big hot spots (Hawaii, Iceland) have more‘‘primitive’’ He

or Ne signatures than small hot spots. However, such entrainment phenomena do not

leave traces in the Sr and Nd isotope signatures because, for these elements the di¡er-

ence in concentration between lower and upper mantle is a factorof 2 or 3 and not100

or 500(Alle

gre, 1987;Alle

gre and Moreiva, 20 04).

Exercise

Imagine a plume starting from the boundary layer and entraining 5% by mass of material

from the lower mantle. Suppose that "

plume source

¼þ5, "

¼þ2, and the concentration ratio



¼ 2. Calculate the plume’s "

value.

Answer

plume

¼þ4.7, which is difﬁcult to distinguish from values like þ5orþ6, which are usual for

OIB.

The outcome is that we have no direct information about Sr, Nd, Hf, or Pb for the

lower mantle. It is a hidden reservoi r and its properties can only be determined

di¡erentially.

338 Radiogenic isotope geochemistry