All?gre Claude J. Isotope Geology

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In conclusion,whenweobservethe (Sr, Pb)isotope diagramwhich seeks tounify thetwo

series ofcorrelations (Sr^N d^Hf) on the onehandand (

206

Pb^

207

Pb^

208

Pb) ontheoth er,

it can ¢rst of all be seen th ere are not two completely separate domains for OIBs and

MORBs. On the contrary, there is no gap, even in region s in whichplumes are injected into

ocean ridges (Schill inge¡ect), wherethetwo domains overlap.Thistopologydoesnotsug-

gestamodelwherebyOIBscomefromaseparateandrelativelyhomogeneouslower mantle.

The sec ond observation, which is broughtoutby the (Sr, Pb) isotope diagram, is that regio-

nalization occurs.Therearegenuineisotopicp rovinces.

The most general division, as said, is between basalts from the Indian Ocean and South

Atlantic on oneside andthose ofthe Paci¢c andthe North Atlantic on theotherside.This is

marked byhigher

Sr/

Sr ratios than for the North Atlantic^Paci¢c province, for a same

206

Pb/

204

Pb ratio and therefore occupies the top part of the (Sr, Pb) isotope di agram.This

distinction is particularlytruefor OIBsbutis alsofoundfor MORBs.

Moreover, this ‘‘Indian’’ isotope signature is very old, as it is found inTibetan ophiolites

(135 Ma pi eces of oceanic crust trapped in the India^Asia collision zone inTibet) (Go

pel

etal., 1984).Howcanthisbeaccountedfor?Whatreadilydistinguishesrocksfrom conti nen-

tal crust and rocks from the mantle is their much higher

Sr/

Sr ratio while the

206

Pb/

204

Pb ratios are similar. If a piece of continental crust is swallowed up by the mantle

and mixes with it, the

206

Pb/

204

Pb ratio increases little while the

Sr/

Sr i ncreasesgreatly.

The di¡erence with sedim ent recycling is that sedim ents contain a large amount of lim e-

stone whose isotope ratios are close to 0.707^0.709 and are very rich in Sr (1000 ppm).

Theythereforebu¡er the Sr isotope ratios.When continental crustas sociatedwith its litho-

sphereisdelaminated, thereisno‘‘limestone e¡ect.’’Now,theprovincewheretheIndiansig -

nature is found is the province where continents existed (Gondwana) in the past and broke

up, probablyleading to delamination.The overall conclusion from examin ing the (Sr, Pb)

isotope diagram is that OIBs comefrom an isotopically veryheterogeneous sourcebut hav-

inga⁄nitieswiththeMORBsource ofthe sameregion.

Thus, we began bydrawing a clear distinction between MORB and OIB and now we are

saying there is no gap between them. How can this be explained? How can rare gas es be

worked into the sch ema since we have seen an extremely clear distinction in their isotopic

ratiosbetween OIBsand MORBs? This is anas-yet-unan sweredquestion.

6.5.5 The

187

Re

187

Os system and (Os, Pb) isotope diagrams

We have already come across the

187

Re

187

Os system for which the decay constant is

l ¼1.6 4 10

11

1

. Howdoes the

187

Os/

188

Os ratio evolve in the Earth’s mantle? By exam-

ining osmiridiums, that is, osmium- rich minerals containing no rhenium, as sociated with

ultrabasic rocks, Alle

greand Lu ck (1980) were ableto show theisotope evolution of mantle

osmium correspon ded toachondritic mantlewith

187

Re/

186

Os 1.This isb ecauseosmium

is an element that remains in the mantle when partial melting g ives rise to oceanic crust. It

is more‘‘co mpatible’’ than either nickel or chromium.The Os concentration of ultrabasic

rocksis close to6 ppm andis 0.06 ppm inthe continentalcr ust.Ifwewritethe crust^mantle

balance equation:



¼ 

þ 

1  W



309 Isotope geology of lead

thevalue of W

is:



 0:15 

0:06

¼ 1:5  10

4

Therefore:



 

ð1  WÞ

 

This is what we actually obs erve: extraction of continental crust has no e¡ect on the iso-

tope evolution of Os of the upper mantle. However, what we do notice is that Re is fractio-

nated a little like lutetium during magmatic processes. It concentrates in the liquid, but

weakly. According ly the Re/Os ratios ofbasalts are extraordinarilyhigh.Values of 50 or100

are commonplacefor the

187

Re/

188

Osratio, whereasthe m antlehasratios closeto0.1.

The continental crust has Os isotope ratios similar to basalts.This means there is a high

level of fractionation at the mid-ocean ridges but that it is neutral at the subduction zones.

The diagram of isotope evolutionthereforelookslikethati n Figure6.58.

Perhaps the most spectacular illustration of this di¡erence in concentration between

cru st and mantle is the (Nd, Os) isotope diagram for the Stillwater Complex i n Montana,

which is an ultrabasic massif. The magma is known to have been contaminated by the

cru st. The mixing curve is spectacular and ne eds no comment (Lambert et al., 1989)

(Figure6.59).

Whi l ethe

187

Re

187

Os system does notprovide manyresourcesfor studyingthe di¡eren -

tiation of continental crust and mantle, it is an excellent tracer for studying the reinjection

187

Os/

186

187

Os/

186

187

Os/

188

187

Os/

188

1.1

0.9

0.111

0.0987

0.1234

2.468

1.851

1.234

0.617

0.8

2 3

Time (Ga)

4 4.55

Continental

crust

Mantle

1 2 3

Time (Ga)

4 4.55

Witwatersrand

Tasmania

Waratah

Urals

Columbia

Meteorite

initial

ratio

a b

Figure 6.58 (a) Evolution of the

187

Os/

186

Os ratio of the mantle from osmiridiums associated with

ultrabasic rocks. (b) Isotope evolution of the continental crust and mantle. The mantle slope

corresponds to a chondritic Re/Os ratio as shown by Alle

gre and Luck (1980).

310 Radiogenic isotope geochemistry

ofoceanic crustorcontinental materialsi ntotheEarth’smantle.Withthisobjectivein mind,

weshall examinethe (Os, Pb)isotope correlation diagrams obtained forbasaltsbycompar-

ing the (Pb, Sr) diagrams (Figure 6.60). Letus examine the (

187

Os/

188

Os,

206

Pb/

204

Pb) dia-

gram for basalts.We consider only bas alts whose Os content is greater than 45 ppt (the

others are suspected of being either victims of an alytical error or of secondary contamina-

tion during theirgenesis).

This diagram brings out something very di¡erent from the corresponding (Sr, Pb) dia-

gram.There is no sample in the bottom right.This is because the mantle is very rich in Os

and the mixtures are shown by very curved paths. Math ie u Roy Barman and the present

–2

–4

1 2 3 4 5

0.1233 0.616

187

Os/

186

Primitive

magma

Continental

crust

Stillwater

187

Os/

188

Figure 6.59 Isotope diagram for (Os, Nd) in the Stillwater Complex, a mixture of ultra-basic magma and

contaminating continental crust. The Nd/Os ratio is 400 for the ultrabasic magma and 400 000 for the

continental crust. After Lambert

.(1989).

1.8

18.0

Pelagic sediment

Terrigenous sediment

Oceanic

sediment

Oceanic crust

with sediment

60%

20%

19.0 20.0 21.0 22.0

22.0

1.6

1.4

1.2

0.120

0.140

0.160

0.180

0.200

0.220

Depleted

mantle

0.150

0.144

1.20

1.10

1.0

0.138

0.132

0.126

1918 2120

187

Os/

188

187

Os/

188

187

Os/

186

187

Os/

186

206

Pb/

204

206

Pb/

204

DMM

Hawaii

Kerguélen

Pitcairn

Rarotonga

Iceland

Comors

Canaries

St.Helena

Basalts > 45 ppt Os

Samoa

Society islanda

Azores

Macdonald

hot spot

Figure 6.60 Isotope correlation diagram for (Os, Pb) and theoretical mixing models. (a) Theoretical

mixing models between the mantle and the various components swallowed up by the mantle. The

boxed part corresponds to (b). (b) Isotope correlation diagram for (Os, Pb) for basalts. DMM, depleted

upper mantle. After Hauri and Hart (1993); Roy Barman and Alle

gre (1994).

311 Isotope geology of lead

author (1994), and also EricHauri and Sta n Hart (1993)oftheWoods Hole Oceanographic

Institution,c alculatedatheoretical mixing modelwithvarious components.Itstrajectories

p rovide quite good explanations for the observations.The important point here is that the

recycled mate ri als mustbe in quitelarge proportions for them tobe detected. Nonetheless,

th is model gives quite a good explan ation of the Os isotope diversity in o ceanic basalts in

the contextofthe H^Wmo del.

6.5.6 Conclusions

After these ¢rst ¢ve dense and often di⁄cult sections, it is probably worthwhile (or essen-

tial?) to review these matters. Our method has been to use isotope correlation diagrams

two by two, to extract the useful information from them and then to combine the results

crosswiseto con¢rmthem,refutethem, clar ify them, or develop them:



Examination of the S r^Nd^Hf isotope systems established thatextraction of continen -

tal crust from the mantle left an upper mantle that was‘‘depleted’’ in some elements (and

soin so me isotope ratios)andwasofalower massthanthetotal mantle.



Thisideaofatwo-layerstructureofthemantlewascon¢rmedbyexamin ationoftherare-

gas isotope composition, the upper mantle being both ‘‘depl eted’’and ‘‘degassed.’’ The

upper mantle is the MORB source.The c omplementary reservoirs of these transfers are

the continental crust and the atmosph ere where the elements exp elled from the mantle

haveaccumulated.



However, since the mass of the depleted mantle is greater than thatof the uppe r mantle,

wehavetoaccep t mass exchangesbetweentheupperand lower mantle (theupper mantle

beingde¢nedaseverythingabove670km).



The conti nentalcru stisstructuredintotectonicsegments,representing the episodes dur-

ing which continental crust formed atthe expense ofthe m antle. However, the continen-

tal crust is composed of ‘‘young’’materials from the mantle and also reworked materials

that are older continental mate rials which have been eroded, deposited as s ediment,

metamorphosed, and granitize d.The wholeprocess seems tobe well understood and, of

course, to¢tinwiththe schem as developed bygeologists.



Studies oflead isotopes con¢rmedthat a large partofthe continentalcrustwas extracted

from the mantle before 3 Ga, as best evidenced by the

207

Pb/

204

Pb isotope signature

comparedwith ratios for the mantle.



The atmosphereseemstohavebeen sealed forargon, krypton, and xenonbut permeable

for helium, which escapes into space, and‘‘se mipermeable’’ for neon.The age offorma-

tion oftheatmosphere is veryancient andgreater than 3 Ga, and, so itsseems, older than

the mean age ofthe continents. But we have saidthatthis questionwas n ot settled andwe

shall return toit.



Di⁄cultiesarosewhenitcametothegenesisofOIBs.Initially, itwasconsideredthatthey

stemmed fromthe lower mantle, which isboth more primitive and less degass edthanthe

upper mantle.This was what was termed th e standard model. Study of the lead isotope

composition overthrew this simple model. Either the OIBs do not come from the lower

mantle, or the lower mantle is not primitive.This brings in the subsidiary question: why

do OIBshave rare-gas isotope signaturessome ofwhich se emvery primitive?

312 Radiogenic isotope geochemistry



At this point in the discussion we introduced the Hofmann^White hypothesis by which

OIBs arerelatedtorecyclingofoceanic crust.But where doesthisrecyclingoccur? Inthe

upper mantle? Then how can the rare-gas measurements from Hawaii or Iceland be

interpreted? Or in the lower m antle? But how can the upper mantle me chanism and its

formationbe explained?

All told, then, two majorquestions remain unanswere d: theorigin of OIBand thenature of

the lower m antle (which questions are connected). Th is uncertainty notwithstanding, we

can develop an overview of the physical and chemical processes related to the geodynamic

cycle.

6.6 Chemical geodynamics

This mo del, which the present author formalized ¢rst in 1980 and then in 1982 (see

Alle

gre,1987), is the result of a long evolution of ideas.The ¢rst attempts to relate isotope

variations and major geological phenomena concerne d the interpretation of variations

in the isotopic composition of galenas. For example, studies by Paul Damon at

Columbia University, New York (Damon, 1954)andDon Rus sell at the University of

Toronto (Russell, 1972) sought to go beyond the age of the Earth and to look at the work-

ing of the pl anet as a whol e.The decisive step s that followed were made by Patterson and

Tat s u m o t o (1964) studying the formation of continental crust with lead isotopes and

Patrick Hurley’s team at the Massachusetts Institute of Technology u sing strontium iso-

topes (1962).

The next stage was by Paul Gast in the 1960s with two signi¢cant papers, one on the

limitation of mantle composition (1960) while the other, writ ten with Til ton and Hedge

(196 4), showed for the ¢rst time that the mantle was not isotopically homog eneous

(Patterson, 1963). Wa s s e r b u r g (196 4) sought to tie in the development of continental

cru st and the complementary evolution of the mantle using a quantitative model. Other

important contributions con ¢rming the isotopicheterogeneityofthe mantle were madeby

Tat s u m o t o (Tatsumoto et al., 1965; Tatsumoto, 1966) for lead and Ha rt et al.(1973)for

strontium.

The chemicalgeodynamic approach cameab out after the discoveryof Nd isotopevaria-

tions, which began with the (Sr, Nd) correlation, an d gave some coherence to the various

isotopic measurements.The approach involved combining observed variations in isotopi c

composition into a logical and coherent scheme within the framework of plate tectonic s

(Alle

gre, 1982;Alle

gre et al., 1982; Hart and Zindler, 1986; Zindler and Hart, 1986; Hart,

1988;Hofmann,1988).

6.6.1 The foundations of the model

Inthis approach, it wasproposedto construct a coherent model ofthe Earthbased onthree

fundamental features:

(1) The Earth’s structure, ¢rst of all, as determined by seismology: a continental crust

and an oceanic crust, a marked p- and s-wave seismic discontinuity at 670 km, and a

mantle^core discontinuity.

313 Chemical geodynamics

(2)Platetectonics,next,withcyclesofspreadingofocean£oorsbasedontheformationof

lithosphereatthemid-oceanridgesanditsrecyclingatsubductionzones.Onthiscycle

issuperimposedtheinjectionofmagmasfromdeeper-lyinghotspots.Thecontinents

breakup,driftaround,andcollidebutremainattheEarth’ssurface.Theuseofthis

modelfortheentiregeologicaltimescaleresultsfromtheapplicationtogeochemistry

ofafoundingprincipleofgeology,uniformitarianism.

Nocallismadeon‘‘extraordin-

ary’’phenomenatoexplainthepast.Yet,nothingshowsitistrue.Perhapstheworkings

oftheEarthinthepastwerequitedi¡erentfromwhatwehavereconstitutedforthelast

fewmillionyears.Thesuppositioninthechemicalgeodynamicmodelisthatifitwas

thecase,thevariationsremainedwithinacontextsimilartotheonewe¢ndnowadays.

(3)Thedataofisotopegeochemistry,lastly,andtobeginwiththoseforSrandNd.Inthis

model,itisassumedthatthecontinentsarethe‘‘scum’’oftheEarth,andresultfromdif-

ferentiationofthemantlewhichhasextractedfromthemantleelementslikepotassium,

rubidium,andtherareearthsaswellasuraniumandthorium.Geologicalmapping

suggeststhattheextractionofcontinentalmaterialfromthemantleoccurredoverthe

courseofgeologicaltime,givingrisetoanewtectonicprovinceeachtime(seePlate4).

This conve ction process divided the Earth’s mantle little byl ittle into two reservoirs: the

upper reservoir, the MORB source, depleted in some chemical elements by extraction

of the continents, and the lower mantle less depleted (but not primitive!). This division

also a¡ects the rare gases which have degassed from the (consequently depleted) upper

mantlebut remain more concentrated in the lower m antle, the escaped heavygases having

collected inthe atmosphere.

The cycleofoceanic crust which is extracted fromthe mantle andthen returnedtoitafter

atime ofspreading atthe surface acts as the extractor of mantle elements.The magmaph ile

elements (potassium, rubidium, cesium, uranium, thorium, etc.) were enriched for the ¢rst

time in liquid during the magmatic processes offormation ofoceanic crust. (The partition

coe⁄cient D ¼C

solid

magma

ofth ese elements is ver ylowfor solid^magmapartitionphe-

nomena.) Then, they were enriched a second time during subduction processes, which

transfer elements from the oceanic crust to the continentsvia more complex fractionation,

butwhosepartition coe⁄cientsaresomewhatdi¡erentfrom thoseofthe mid-ocean ridges.

If we term the processes occurring along the mid-ocean ridges the R- proces s (ridge) and

the processes occurring during subduction the S-process (subduction), the extraction of

elements from the mantle to the continental crust corresponds to the sum (R þS).We can

writesymbolically:

continental crust ¼ SðR  mantle Þ;

withRoperatingonthe mantleand S on theproductofthis¢rstoperation.

The oceanic crust modi¢ed by the S-process plunges back into the mantle and is mixed

me chanically with itby mantle co nvec t io n. In this way, an increasingly ‘‘depleted’’ m antle

is formed.The raregases areoutgassedby the R-processbut S- processvolcanism alsoleads

to outgassing, p reventing theraregasesfromb eing recycled into themantle.

This dates back to one of the founders of geology, Charles Lyell, and underpins the development of this

discipline on a scientiﬁc basis.

Not to be confused with the notation for the r- and s-processes in nucleosynthesis!

314 Radiogenic isotope geochemistry

The mantle is therefore madeup ofan upp e r mantl e, which is‘‘deplete d’’ in elements such

as potassium, uranium, thorium, and r ubidiu m, and degasse d of most of its rare gases and

of a lower mantle, whi ch, while not pristine, is less depleted in potassium, uranium, thor-

ium, andrubidium, andisricher in raregases.

If, as some investigators as serton thebasis of seismic tomography, the downgoing plates

were recycled in thelower mantleth roughoutgeological history, thelower mantlewouldbe

depleted because it is the downgoing plates that convey the depletion (the extraction ofele-

ments concentrated in the continental crust). It is essential, therefore, that the plates have

been reinjected fort h e mos t par tintheupper mantle. Likewise, ifallthe mantleweretotally

outgassed, there would not be any marked di¡erence in the isotope ratios of the rare gases

like helium and neon contained in MORB and OIB. The mantle is therefore necessarily

composedoftwoseparate (but notisolated)reservoirs.

6.6.2 The internal geochemical cycle

Two funda mentalgeochemicalprocesses thatarean integralpart ofgeodynamic processes

occur in the upper mantle.The oceanic lithosphere is formed atthe mid-ocean ridges and

separates abasaltic ocean crust enriched in certain elements (relativetothe mantle) suchas

potassiu m, rubidium, uranium, the rare earths, etc. and an u nderlying, ultrabasic residual

lithosphere depl eted in these elements and whose remelting cannot create much basalt

because the essential elements mak ing up certain basalt minerals (feldspars, clinopyrox-

enes) such as calcium and aluminum havebeen extracted to manufacture oceanic crust. It

isoften said inpetrologists’jargonthatthe deep ocean lithosphereis infertile becauseitcan

nolonger producebasaltby fusion.Thisoceaniclithosphere(crustandresiduallithosphere)

is reinje cted into the mantle where it mixes back with the upper mantle (McKenzie, 1979;

Alle

greetal.,1980;Whiteand Hofmann,1982).

Mixing is mechanical. P iec es of the lithosphere are caught up in the convective move-

ments of the mantle. In this process, rock is stretched, folded, an d pi nched. Rock from the

ocean crust, generally basaltic, is transformed mineralogically by metamorphism during

subduction into rockssuchas eclogite(assemblyofgarnetandpyroxene).Theupper m antle

lookslike a marbled cake (Alle

gre and Turcotte,1986) withabasic pe ridotite (pyroxeneand

olivine)compositioninterspersedwithstrandsofeclogites, drawnoutandstretchedtovary-

ing degrees.These strands are shreds of ancient oceanic crust which has been laminated,

pinched, and folded by mantle movements. After some time, these ever-thinner stran ds

will end up reacting mineralogically with the peridotite mantle and will disappear

(Hofmann and Hart,1978;Alle

gre and Turcotte, 1985), while the mantle will b e fertilized

by this abso rption, that is, made capable of basalt extraction by melting again. But these

slivers of continental crust are not uniform. So me have dragg ed layers of sediments down

with them. These sediments carried by the downgoing plate are dehydrated, compacted,

and then metamorphosed. They are also stretched, thinned, pinched, and folded

(Figure6.6 1).

Some of the pieces of oceanic crust reinjected into the mantle are very peculiar as they

havelostthe chemical elements that will give risetovolcanism in the subduction zones and

through that to continental crust.These are the materials which e¡ect the depletion of the

mantle in some elements (rubidium, uranium, etc.) and wh ich is re£ected in isotope ratios,

315 Chemical geodynamics

becauseallofthemateri alsswallowedupbytheupper mantlehavevariedisotope ratiosand

chemicalratios.

Isthis marbled mantle apurely theoretical model dreamtup bygeochemistsand geophy-

sicists? Not a bit of it! It is real enough. It can be seen cropping out in a few special places

where tectonic processes have brought pieces of mantle to th e surface. This is the case in

southern Spain near the little town of Ronda (the temple of bull¢ghti ng), in northern

Morocco near the village of Beni-Bousera (Figure 6.62), at Lhez (France) in the Pyrenees,

and at LanzonearTurin (Italy).

These massifs are often made up ofperidotite, often depleted in aluminum and calcium,

with isotope s ignatures of the upper mantle. They contain strands of eclogites which have

been shown to come from ancient oceanic crust.They also contain ancient sediments and

even diamond transformed into graphite, that is, old limestones rich in organic material

that has been re duced and changed into diamonds.The upper mantle is indeed made up of

a thorough mixture of peridotite an d eclogite. By c ontrast, the lower mantle contains far

fewer strands andis much moreuniform.

Atmosphere

(S)

MORB

(S)(R)

melting

zone

melting

zone

melting

zone

MIXING

UPPER

MANTLE

LOWER

MANTLE

Figure 6.61 Fractionation of the geodynamic cycle. The internal geodynamic cycle exhibits mixing,

differentiation, and removal phenomena, mostly in the upper mantle.

316 Radiogenic isotope geochemistry

6.6.3 Statistical geochemistry

Sofarwehavespoken agreatdealofreservoirs exchanging material,considering thatconti-

nental crustis segmented into age provinc es andthereforeheterogeneousbut thatthe man-

tle is homogeneous (at least at regional scale).The upshotofthis is that we have considered

an ave rage value to characterize each reservoir. Without relinquishing such modeling,

which is straightforward and extrem ely useful, we have to supplement it with another

description, which is statistical. Each reservoir is described not by a single average value

butbyadistr ibution ofvalues, isotope ratios,orchemic al concentrations.

When an oceanic plate dips into the mantle it is chemically and isotopically heteroge-

neous. Admittedly, when oceanic crust forms at the mid-ocean ridges it is isotopically

homogeneous (by melting) but chemicallyheterogeneous, with the crustbeing enriched in

rubidium compared with strontium, the lithospherebeing depleted in Rb/Sr, and the sedi-

ments rich in Rb/Sr when detrital and poor when they are limestone.These chemical het-

erogeneities are re£ected by isotopic heterogeneities during the ridge^subduction zone

journey, byradioactive decay.Then,ofc ourse,the sam ehappensinthe mantlewith radioac-

tivitycontinuing itsinexorable decayand its creation ofnewisotopes.

The upper mantle, then, is not isotopically or chemically homogeneous, but hetero -

gen e ou s. It is not characterized by a single average isotope ratio, as in the ‘‘box’’ model

we dealt with when examining the earlier crust^mantle system, but by a spread of

isotope ratios,withanaverage, variance (standard deviation), and a degree of asym -

metry for each type of ratio. This statistical distribution also has, of course, a geographi-

cal distribution.

2-3 cm 1-2 cm

3 m

2-10 cm

5 cm

30 cm

5 m

2 m

15cm

10 cm

50cm

10 cm

12 cm

15 cm

60cm

Figure 6.62 Garnet pyroxenite (eclogite) bed structures in the peridotites of Beni-Bousera massif,

Morocco. Pyroxenite in blue, peridotite in white. (a) Series of pyroxenite beds of different sizes in the

peridotite; (b) pinching and swelling; (c, d) folding. After Alle

gre and Turcotte (1986).

317 Chemical geodynamics

For example, the 

and 

parameters are each replacedbyadistribution notated as:





¼ 

m;;dðÞ



and 



¼ 

m;;dðÞ



where

m isth e mean of 

or 

,  the standarddeviation, and d theasymmetry.

Naturallyenough, the morethe systemis subjectedtoconvectionthe moreitis mixedand

the morehomogeneous itis, andthe smaller is.Twoantagonisticphenomena aretherefore

in action: chemical fractionation near the Earth’s surface, whichtendstoincrease chemical

(and so isotopic) h eterogeneity, and convective mixing phenomena within the mantle,

whichtend toreduce them. Itis acontestofch emical d i ¡erent iat io nversus mixing.

Partial melting and volcanism (at the ridges and hot spots) of the heterogeneous mantle

yield samples ofthe mantle, whichare more or less random, fromwhichwe can measurethe

Sr/

Sr,

143

Nd/

144

Nd,

Rb/

Sr, and

147

Sm/

14 4

Nd ratios, etc., for which we can also

de¢ne distributions and with them a mean, a standard deviation, and an asymmetry. (We

notate these distributions by { }: 



¼ 

m;;dðÞ



and similarly for





¼ 

m;;dðÞ



An importantstepin our projectis,ofcourse, todeterminetheactualdistributionsofiso-

tope ratios in the mantle from th e distributions sampled and measured at the surface. A

p riori, it might be thoughtthat the larger the sample, the closer 

is to 

.We take as a

working hypothesis that 

¼K 

,thatis,the distr ibution measu red from su rface sam -

ple s is propo r t ional tot he d ist r ib ut ion oft he mantle atdept h.Whenthe distributions mea-

sured on various samples of a same type of basalt are more dispersed than those measured

on another type, itis legitimate to supposethatthe sources ofthe formerare more heteroge-

n eous than the sources of the latteror that the phenomena g iving rise to the basalts did not

homogenize th em as much (bec ause we are mindful, of course, that the phenomena of par-

tialmeltingofthemantle, thenofpoolingoftheliqu idsgivingrisetomagmas,ten dtohomo-

genize the isotope ratios).They therefore e¡ect a sort of natural average of the zone where

partial melting o ccurred (statistical sampling). As it is accepted that isotope homogeniza-

tion o ccurs at such temperatures, basalt sampling provides a representative average of the

samplespace. Studyofthebasaltpopulation is therefore a sample ofthe mantle onthescale

of a few kilometers. But at the same time, these phenomena of magmatogenesis erase any

small erlocal heterogeneities, as the magma averages them out. Now, when we speakofh et-

erogeneityofthe m antle, we mustbe clear whatwe m eanbyit.T here arevarioustypesofhet-

erogeneity, as Figure 6.63 shows.

6.6.4 Geochemical fractionation

Since the beginning ofthis chapter, we have spoken of che mical fractionationwhich modi-

¢esthe Rb/Sr,Sm/Nd, U/Pb chemicalratios,etc., modi¢cationsthat arere£ectedbyisoto-

pic changes.The variations in isotope ratios are the re£ection, with a time lag, of chemical

fractionation. It is customary to say that radiogenic isotope ratios are chem ical fos sils.We

shouldthereforelooka little more closelyatgeochemical fractionation.

The essential fractionation s in chemi cal geodynamics are those related to the formation

of magma, at the mid-ocean ridges to manufacture oceanic cru st, at th e subduction zones

to produce arcvolcanism and extract continental crust, andin the deep continental crustto

yieldgranites. All arerelated tothe partial melting process (Gast,1968).

318 Radiogenic isotope geochemistry