All?gre Claude J. Isotope Geology

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The oppos ing model by which OIB stems from the core^mantle boundary at a depth of

2900 km is based primarily on seismic tomography. The method yields two essential

results:

(1) In various lo cations corresponding to subduction zones, slabs can be‘‘seen’’ plunging

intothe mantlebeyondthe 670-kmboundary (seeVan de r Hilstet al., 1991;Grandet al.,

1997).

(2) Fine-scale imageryse ems to showsome plumes arise from the core^mantleboundary

whileothers seemto originate at670 km (Montelli etal., 20 04).

This model is not suppor ted by any clear and di rect geochemical arguments. There are

manycounterargumentstotheinterpretations ofthese observations:

(1) If downgoing plateshadplunged intothe lower mantle completely throughout geolog i-

cal time, we would have a global mantle convection regim e. But, as we have seen, the

rare gases require a two-layer mantle. As these slabs are chemically ‘‘depleted struc-

tures’’ becaus e of the extraction of continental crust, it is the lower mantle that would

havean isotopic signature depleted in Srand Nd. Conversely itis the mid-ocean ridges,

whose surface origin is attested by the most reliable part of seismic tomography, that

havesuchasignature.

There are several ways ofovercoming this contradiction b etwe en s eismic tomogra-

phyand isotope geology.

The¢rstis toacceptthatthegeophysicalobservationsrelatetothe presentperiodalone. The

situation must havebeen di¡erent in the past.There must have been a two-layer mantle for

most of geological time, and this layering must have been destroyed only recently. In the

past, onlyas mall fractionofthe slabs mighthaveplunged into thelower mantle.This would

easilyexplainthe isotopic massbalancesof Nd and Sr.

The second is to accept that what the seismic tomography images show is not a down-

going plate but a cold current in the lower m antle convection pattern. A combination of

both interpretations is alsopossible.

Thethirdis to consider thatonlyapart, aboutone-third, ofthe plateis subducted intothe

lower mantle while most of the slabs p ile up in the uppe r mantle as observed by Fukao et al.

(1992).

(2) How, then, can the seismic images of plumes be interpreted? By accepting that the

regimesbetween uppe r and lower mantle are thermallyand not mechanically coupled.

Lower mantle plumes provide heat, whi ch triggers certain instabilities in the 670-km

boundarylayer. And this isprobably the general explanation.The lower mantle^uppe r

mantle coupling is largely the rmal. T his in n o way m eans there are no exchanges of

mas s between the upper mantle and the lower mantle. Such exchanges have been sub-

stantial and about one-third of the lower mantle is reinjected material from the upper

mantle according to th e Sr an d about Nd isotopic mass balance calculation.This pro-

vides a picture, then, of the mantle and of exchanges which have taken place between

thevarious reservoirs throughoutgeologicaltime (Figure6. 7 3).

But we have to distinguish between structure and texture. The stru ctu re consists of

two layers convecting independently but exchanging mass and energy c ontinuously. The

texture is the intimate mixture of pyroxenite strips which are elongated, folded, and

339 Chemical geodynamics

embedded into peridotite i n the upper mantle or ringwoodite (garnet plus spinel) in the

trans ition zone.

Since pyroxenite melts more readily than peridotite, the proportion of pyroxenites con-

tributing tothebasaltic meltis higher than theiractual presence in the mantle.Thispropor-

tion depends on the degree of partial melting and also th e proportion of pyroxenite in the

source. Recent work by Sobolev et al.(20 07) estimates thos e prop ortions in various types

ofbasalt at10% in MORB an d 70% in OIB. Remember that MORB corresponds to10% of

partial m eltingandOIB to 2%.

The MORB source is a well-stirred reservoir whe re pyroxenite has been partially

destroyed.OIBscamefrom asourcewherepyroxenitemakesup10^15%ofthemassbecause

theyareformedwhen subducted slabs pile up.

6.6.9 Comparison and limits of the model

We now have a coherent model of mantle structure and dynamics.While it should not

be taken as an eternal truth, it should not be abandoned either, until we have something

better.

Upper

mantle

Upper mantle

Atmosphere

Continent

OIBRidge

Ridge

Lower mantle

OIB

Figure 6.73 Two diagrams of geodynamic mechanisms. Top: using strontium, neodymium, and

hafnium isotopic tracers. Bottom: using rare gases.

340 Radiogenic isotope geochemistry

Direct comparison of geochemical models and geophysical observations

is a delicate

business, because, as pointed out, the fundamental processes do not involve th e major ele-

ments much.Yet it is the major elements that, through mineralogy and the physical proper-

ties of minerals, condition geophysics observations. A second reason is that geophysical

observations are made on the Earth as it is today, whereas isotopic g eoche mical observa-

tions cover the 4.5 billionyears of its history. And as we know, the Earth has evolved during

its history.

Onevery importantpointto makeis thatthe re is noguaranteethatthis cyclic process has

been constantthroughoutgeological times, either interms ofspeedor interms ofthe‘‘qual -

ity’’oftheprocess. Assaid, oneofthesources ofthe Earth’s energypower ingmantle convec-

tion is the radioactivity of uranium, potassium, and to a lesser extent thorium. This

radioactivityhas declinedovergeologicaltime.It maybe,then, thatconvectionwas stronger

inthe past, oreventhatits overallstructurewasdi ¡erentfromwhatweknow today.

Theformationofoceanic crustand the extraction ofcontinental crust mayhavebeen dif-

ferent in the past.What suggests this is that we ¢nd in the Archean submarine ultrabasic

lavas (komatiites), which are unknown nowadays and the continental crust contains acid

rocks that are unknown today such as the TTG association (tonalite, trondhjemite,

granodiorite).

Themodelwehavedeveloped,basedontheparadigmofplatetectonics,coversthe4.4bil-

lion years of the Earth’s history, provided the phenomena are qualitatively similar.

However, studies of ancient rocks have notshown any major contradiction.The agreement

obtained between a vision by extrapolation into the past of present-day Sr and Nd isotope

data and the study ofpast variations ofthese isotopes i n shales or komatiites shows theyare

con sistent.We therefore have no hard facts that currently require us to radically change our

mo del, but there is no guarantee this position will not change in the future if newstudies so

require. Meanwhile, let us work with it, without being dogmatic, but without qualms.

Science isneither anunchangeabledogmanoradomainwhere ‘‘anything goes.’’

6.7 The early history of th e Earth

Isotopegeologyhasachievedresultsofconsiderablescope concerningthe Earth’sstructure

and evolution.W hy not apply the s ame methodsofreasoning to extinct forms ofradioactiv-

ity, which would allow us a more precise vision of our planet’s early history? Why deprive

ourselvesofa clos e-up ofthe ¢rstdaysofthe Earth’shistory?

The initial idea is very straightforward, then. Before setting it out in a few examples ^

becausehereasthroughoutthistextbook,thefocusison method ^ itisuseful torecall alittle

vocabulary. It is generally considered thatthe solid material making up the telluric planets

conden s ed from a mostlygaseous primordial nebula toform soli d dust particles.This solid

material then accreted to form eve r larger bodies: grains formed beads, then balls, and

thenbodiesof1km,10 km,100 km in diameter, and so on.Thiswas thep rocessofacc ret ion

during which a fraction ofthe nebula’s gases weretrapped inside the solids. In this context,

therearetwo extreme scenarios fo r explainingtheformation ofthe Earth (Figure 6. 74).

Especially the wonderful pictures produced by seismic tomography.

341 The early history of the Earth

Inthehomogeneou saccretion scenario, theaccretedmaterialswereallofthesame com-

p osition.The primordial Earthwas therefore a large sphere ofuniform composition which

then di¡erentiated through a large melting phenomena to make the core, the mantle, and

the atmosphere and perhaps even an embryonic crust as on the Moon.The energy of this

general melting episode came from accretion (tran sformation of potential energy into heat

above all through impacts at the end of accretion), extinct radioactivity and above all

235

and

K radioactivity, whichweremore‘‘active’’atthetime (see Chapter1).

Theotherscenariois thatof heterogeneousaccretion, whichas sumesthatthe Earth¢rst

accretedits iron core,then subsequently the silicate mantle, and ¢nallythe atmosphere and

o cean.This raises many questions.What was the relative timing of these processes? What

are the mutual relations between them? In an extreme scenario, condensation, accretion,

and di¡erentiation occurred in succession. In more complexscenarios all three operations

are considered as more orless simultaneousorcombined.

We have already answered three essential questions using radiogenic isotopes with long

half-lives.Firstofall,thedi¡erenti ationofthe continentalcrusto ccurredthroughoutgeolo-

gical time but was more active in the past and has an average age of 2^2.3 Ga (this was

derived from Sr^Nd isotope pairs).The core di¡erentiated very early on, with a mean age

of 4.4 Ga (this information was obtained from lead isotopes). The atmosphere outgassed

Core differentiation and

final bombardment

HOMOGENEOUS ACCRETION

HETEROGENEOUS ACCRETION

4.55 4.50 4.454.60

Final

bombardment

Mantle

accretion

Core

accretion

Age (Ga)

Figure 6.74 The two types of accretion.

342 Radiogenic isotope geochemistry

relativelyearlyonwithanaverageageof3.3 Ga(thiswasobtainedfrom

Ar).Wearegoingto

testor re¢ne these assertionsusingextinctradioactivities.

6.7.1 The age of the atmosphere and the way it formed

From the

Ar balance, it has been established that 50% of the

Ar was in the atmosphere

and 50% in the mantle. Fromthis,and from th e

Ar/

Ar isotope compositions measured

in the atmosphere and mantle, we have calculated a ‘‘model age’’ for the atmosphere of

3.3 Ga. Isthis mo delage reliable?

Letuslook¢rstatthebalanceof

Ar, the non-radiogenicisotope.Weknowthatthe man-

tle is made up of two layers convecting separately: the upper one is largely degassed, the

lowerone little d egassed.The

Ar/

Ar ratios ofthese two reservoirs havebeen measured.

In the upper mantle,

Ar/

Ar ¼40 000 while the ratio in the lower mantle is 4000. The

ratiointheatmosphereis

Ar/

Ar ¼296.8.

Exercise

What is the extent of degassing of

Ar?

Answer

From the quantities of

Ar in the atmosphere and mantle, it can be estimated that the

quantity of

Ar in the atmosphere is 2.3  10

g and the quantity of

Ar in the lower mantle

is 1.7  10

g (the quantity of

Ar in the upper mantle 5  10

g is negligible). Therefore, in

total

Ar ¼2.3  10

þ1.7  10

¼2.47  10

g. Therefore the extent of degassing is 93%.

How can we explain the enormous di¡erence highlighted in the pre ceding exercise

between the extent of degassing of

Ar (50%) and of

Ar (93%)? It is b e cause

Ar is

purely radiogenic.Therewas no

Ar atthebeginningofth e Earth, only

Arand

Ar. The

extentofdegassing of

Ar m easures ab ove al l outgas sing throughout geological historyby

volcanism and particularly along ocean ridges.The extent of degassi ng of

Ar measures

boththatrelated totheprimordial historyandthat relatedtosubsequentgeological history.

The Earth’s history fallsi ntotwo episodes:

Geological historyPrimordial history

IfwecalltheextentofprimordialdegassingP andthe extent ofsubsequent degassing G,the

Ar content of the mantle is equal to (1 P) (1 G). We can estimate 1 G ¼0.5 and

1 P ¼0.07 , hence P ¼86%.The extent of primordial degassing of the Earth is enormous

and dominant. Most of the atmosphere formed therefore at the begin ning of the Earth’s his-

tory (Figure 6. 7 5).This is not the impression we gained from the

Ar balance! Remember,

though, that

Ar was not present initially. It has built up progressively over time. It is

notagoodrecordingsystemforearlytime,butitisagoodrecordingsystemforgeologicaltime.

We are going to re-examine the p roblem addressed with the argon isotopes but this time

using extinct radioactive

129

I, which, as we know, decays to give

129

Xe. Xenon-130 is the

343 The early history of the Earth

stablereferenceisotope. To dothis, wetake abalanceofradiogenic

129

Xe. Supposethe Earth

is degassed to x%.The quantity of

130

Xe in the atmosphere is

130

total

 x.The quantityof

129

Xe* (

129

Xe* is the excess of

129

Xe relativeto theusualabundance in meteoritesrelativeto

other isotopes) of the atmosphere is estimate d at 3.63 10

g. If x% degassing is high, the

quantity of

129

Xe* in the atmosphere is equal to that of

129

I at the time the Earth began to

retain its atmosphere quantitatively, thatis, thetimethe Earthwasbigenough for xenon not

to escape.

For primordial gas, we take a rate analogous to that of

Ar of 9 0%. If

130

atmosphere

¼8 10

g and the extent of degassing is 90%, we therefore have a balance:

130

total

¼8.8 10

Therefore

129

Xe/

130

Xe ¼(

129

130

Xe)

accretion

¼0.4125.

But

129

Xe/

130

Xe ¼(

129

127

I) (

127

130

Xe) .

This expression is intended to bri ng out the isotope ratio of iodin e which does not frac-

tionate atthe time of accretion but varies with the radioactive decayof

129

I. Iodine-127 may

be estimated at 25 ppb of iodine in 4 10

g, which is the mass of the mantle, making

1 10

g in all.Wethereforeobtain

127

130

Xe ¼1.13 10

,hence

129

127

I ¼ 0:36  10

6

We canthen calculatea modelagerelativetoameteoritewhose initialiodineisotoperatio

has been determined. The carbonaceous meteorite taken as the reference has a

(

129

127

initial

ratio ¼1.1 10

4

4321 0

Ar flux (10

g yr

–1

)

10 20

4 3 2 10

Ar flux (g yr

–1

)

g a

10 20

3 2 1

129

Xe* flux (10

g yr

–1

)

Age (Ga)

20 40

Radiogenic gas

Figure 6.75 Scenario of primordial degassing of the Earth’s atmosphere. After Sarda

.(1985).

344 Radiogenic isotope geochemistry

DT ¼

129

127



initial

129

127



Earth

;

therefore T=148 Ma.Th e Earththe refore retained itsatmosphere150 Maafter theform a-

tionofthe carbonaceous chondrites, or as an absolutevalue,

acc

¼ T

 0:148 ¼ 4:565  0:148 ¼ 4:41 Ga;

an average age, which, it should be noted, corresponds almost to the mean age of the core

determinedusing lead isotopes.

Wehavejustseenthenthat mostoftheatmospherewasdegassedveryearlyon, but10%or

so comes from subsequent degassing, probably from the upper mantle and in conjunction

with the plate tectonics cycle.We accordingly have a picture of the primordial Earth with a

veryhigh extentofdegassing, intensebombardmentbylarge objects, volcanism, and di ¡er-

entiation ofthe core.

6.7.2 The age of the Earth’s core and the mode of terrestrial

accretion

Wehave alreadydetermined an age for the Earth’s corewith lead isotopes using thefactthat

lead has a great a⁄nity for lead sul¢de (PbS). We can test this result using extinct

182

Hf^

182

Wradioactivity, for wh ichT

1/2

¼9 Ma.This isotope pair has a peculiar chemical

prope rty which is that tungsten is a si derophile element: it enters metallic iron when ever it

can, whereas hafnium is l ithophile.The i ron^silicate division therefore corresponds to a

very imp ortant W^Hf chemical fractionation. This is how it has been possible to date

meteoritesand studythe evolutionofthis form ofradioactivity in thesolar nebula.

Weshallexaminethis aspect¢rstbefore concerningourselveswiththe ageofthe Earth.It

is possible, as we saw when studying chronological methods, to make precise datings of

eventswhichtook placewhen

182

Hfradioactivity wasnotyet‘‘dead.’’

To study these events, we have isochron diagrams of anc ient objects (

182

Hf/

184

182

184

W) (see Chapter 4). The slope of the isochron gives the

182

Hf/

184

W ratio. This

182

Hf/

180

Hf isotope ratio does notfractionate during the chemical fractionation processes.

It deca ys by the law

182

Hf=

180

Hf ¼ð

182

Hf=

180

HfÞ

l

;

which allows us to determine a relative age as soon as a reference has been ¢xed for the

(

182

Hf/

180

Hf)

initial

ratio. In thisway time canbe measured in absoluteterms.

We also have the (

182

184

initial

) ratios of isochrons constru cted for meteorites

(Figure6.76).Thisratioincreasesasageincreases(thereforeas

182

Hfdecreases).

If it is supposed that meteorites derive from the condensation of the primordial solar

nebula and supp osing thatthis nebulaevolves in a closed system, the (

182

184

initial

ratio

varieswiththe equation:

345 The early history of the Earth

182

184



initial

tðÞ ¼

182

184



present



180

184





182

180



If we draw a g raph, positing Y ¼

182

184



and x ¼ e

lt

182

Hf=

180

Hf,theevolu-

tion of the primordial nebula is therefore a straight line whose (negative) slope

is ^(

180

Hf/

184

W), and therefore proportional to the Hf/Wchemical ratio.When we plot on

the graph the values extracted from the chondrite isochrons and the current

182

184

ratio of carbonaceous chondrites C

, we do indeed de¢ne a straight line whose slope corre-

sponds to the chemical Hf/W ratio of C

180

Hf/

184

W ¼1.55, which value corresponds to

Hf/W ¼1.31.

This graph is the equivalent of the (

Sr/

Sr, t) isotope evolution diagram, except that

timeisgraduated exponentiallyby the

182

Hf/

180

Hfratio.

It is interesting to situate two types of di¡erentiated meteorite on this diagram: iron

meteorites and basaltic achondrites. For iron meteorites, the straight line of evolution in

the isotope evolution diagram is horizontal since Hf ¼0. Now , the

182

184

W ratios are

very low, among the lowest measured for meteorites. These ratios correspond to very

an cient, primordial ratios.This shows that iron di¡erentiated veryearlyon inthe small par-

ent bodies known as plan ete si mal s. Basaltic achondrites have very high

182

184

W ratios

and their initial ratios lie far above the straight line of evolution of the nebula. The H f/W

ratio of silicates of the parent body, which c an be estimated, set the di¡erentiation at 3 to

8 Ma after that of the iron meteorites, but at the same time as di¡erentiation of meteorites

compos edofthe iron^metal mixture.

Andthe Earth? TheEarth hasa

182

184

W valuethatstandsapartfromthatofthe carbo-

naceous chondrites. This shows that Hf/W di¡erentiation, that is, segregation of the core

from the mantle, occurre d when

182

Hf was not yet extinct (Figure 6. 77). But what, then, is

the model age ofthis di¡erentiation?

Exercise

We are given

182

184



Earth

present

¼ 0:8650. The

182

184



carbonaceous

chondrites

present

ratio is equal to that of

the nebula, 0.864 83. The Hf/W ratio of the nebula is 1.31 and the Hf/W ratio of the Earth’s

mantle is 20. We suppose that:

182

Hf/

184

182

Hf/

180

=(1.0

0.5)

–4

(σ)

NM-3

NM-2

Forest Vale

NM-1

4 6

-2

NM-3

St.Marguérite

NM-1

182

Hf/

180

(0.85

0.05)

–4

(2σ)

2 6 10 14

NM-2

Figure 6.76 Graphs of

186

Hf–

186

W isochrons of two chondrites. After Kleine

. (2004).

346 Radiogenic isotope geochemistry

180

184



chemical

 0:845:

Calculate the model age of core–mantle differentiation estimated by

182

Hf–

182

W chronology.

Answer

We wish to calculate the initial (

182

Hf/

180

Hf)

initial

ratio of the Earth’s mantle. The time at

which it acquired its current chemical ratio is written

diff

. The equation for evolution of the

solar nebula is:

182

184



present

182

184



diff



180

184



nebula

182

180



initial

Likewise:

182

184



Earth

182

184



diff



180

184



mantle

182

180



The solution to this system of two equations with one unknown gives:

182

Hf=

180

HfÞ

initial

¼ 1:1  10

5

0.8650

0.8649

0.8648

0.8647

0.8646

10 20 30

182

Hf/

180

Hf×10

182

184

Bulk Earth

TLA

Iron

meteorites

Basaltic

achondrites

Ordinary

chondrites

Solar

nebula

Figure 6.77 Isotope evolution diagram for W–Hf. M, St. Marguerite; CC, carbonaceous chondrites; TLA,

Tlacotepec (an iron meteorite); FV, Forest Vale; carbonaceous chondrites.

347 The early history of the Earth

If we consider the initial reference ratio for the Solar System is

182

Hf/

180

Hf ¼2.4  10

4

, then:

DT ¼

2:4  10

4

1:1  10

5



and 1/

¼13 Ma. Hence 

¼40 Ma after the formation of the chondrites.

The Hf^W age of 40 Ma calculated in the previous exercise is very di¡erent from the

150 Ma estimated from Pb isotopes. How can we overcome this contradiction? By coming

backto meteorites and remembering that in their small parent bodies, iron became di¡er-

entiated very early on.The bodies that accreted to form the Earth were the refore probably

already di ¡erentiated bodies where the iron was already separated from the silicates. The

age of 40 Ma is a mixed age between these primordial ‘‘meteorite’’ ages and the average

age of di¡erentiation of the core indicated by lead isotopes. It is therefore an indication

that accretion of th e Earth involved solid bodies that were already di¡erentiated. This is

an i nter me diate sc enar io between homogeneous and heterogeneous accretion.Itis

homogeneous accretion of a heterogeneous p roduct! The core di¡erentiated 150 Ma

after primitive condensation but its di¡erentiation occurred on solid bodies in which sili-

cate^iron had already di¡erentiated.The Hf^W 40 Ma age is a mixture between the two

events.

Exercise

The isotope ratios of the Earth and carbonaceous chondrites are known with a precision of 15

ppm. The initial ratio is known with precision of 20%. Uncertainties on Hf/W ratios are

assumed negligible. What are the uncertainties on the estimation of 

of Earth–core

differentiation calculated by Hf–W?

Answer

¼ 40

þ44

35

Ma, or 10 Ma, which does not alter the reasoning.

6.7.3 The primitive crust and

146

Sm–

142

Samar ium-14 6 de cays to

142

Nd by  decay w ith a decay constant l ¼6.849 10

9

(nearly a

thousandtimeslessthan

147

Sm!).Itisanexti nctradioactivity.Wehaveseenthatthecontinen-

tal cru st has a lower Sm/Nd ratio than the mantle. Accordingly

143

Nd/

144

Nd ratios of

MORB are positive when expressed in "

, whereas values for the c ontinental cru st are

n egative.The i death en was to try to determine whether a pr imitive crust had separated out

during the early di¡erentiation of the Earth and if such segregation had left traces in the

142

Nd/

144

Nd ratiosuchas arefoundfor the

129

Xe/

130

Xe ratio .

This ideawas put forward by Stein Jacobsen of Harvard University. He and his student

Chris Harper (Harperand Jacobsen,1992)claimedtohavefoundapositive

142

Ndanomaly

inveryancient rocksofGreenland.Thiswasnot 

measured in10

butdi¡erences inppm

6

(100 ")

1

.They reported enrichm ents of 30 pp m of

142

Nd comparedwithun iform and

identical valu es of MORB, OIB, and recent and ancient rocks. The measurements were

348 Radiogenic isotope geochemistry