A plate model for the simulation of trace element ...

JOURNAL OF GEOPHYSICAL

RESEARCH, VOL. 102, NO. Bll, PAGES 24,771-24,784, NOVEMBER

10, 1997

A plate model for the simulation of trace element fractionation during partial melting and magma transport in the Earth's upper mantle JacquesVerni•res,MargueriteGodard,andJean-LouisBodinier CNRS Unit6 Mixte de Recherche5569 "G6ofluides-Bassins-Eau", ISTEEM, Universit6Montpellier2 Montpellier,France

Abstract. We proposea newplatemodelfor thesimulationof traceelementtransferduring magmaticandmetasomatic processes takingplacein the Earth'suppermantle.As in previouslypublishedplatemodels,porousflow is accountedfor by propagationof fluid batches throughmacrovolumes of mantlerocks.Beingreleasedfrom spatiotemporal constraints, the platemodelallowsmuchmorefreedomthanthe one-dimensional porous-flowmodelsfor the simulationof fluid-rockinteractions. Hencethisapproachmay accountfor a wide rangeof mantleprocesses, includingmeltextractionduringcompaction of moltenperidotites, porous flow associated with chromatographic effects,or fluid-rockreactionsoccurringuponmelt infiltrationat the baseof the conductive mantle.The applications presented in thisstudyshow severalresultsconsistent with publishedtraceelementdatafor mantlerocksandbasalticvolcanism.In particular,the proposedmodelsmay providesimpleexplanations for (1) the ultrarare-earth-element-depleted compositionof peridotitesand interstitialmeltsresidualafter mid-oceanridgebasaltextraction,(2) the negativecorrelationbetweenlightrareearthelement/ heavyrareearthelement(LREE/HREE) ratioandrefractorycharacterof peridotites,as observedin severalsuitesof mantlerocks,and(3) the originof ultra-LREE-enrichedmetasomaticfluidsinfiltratedin the lithosphericmantle. 1. Introduction

From the early works of Gast [1968] and Shaw [1970] on partialmeltingto the mostrecentstudieson porousmelt flow [e.g., Nayon et al., 1996, and referencesherein], lithophile trace elements,such as rare earth elements(REE) have been widely usedto constrainthe processesassociatedwith productionand transportof melt in the Earth'supper mantle. Valuable informationon magmaticand metasomaticmantle processesis provided by trace element studiesof mantle rocks,suchas xenolithsscavengedby basaltsand kimberlites, orogeniclherzolitemassifs,ultramafictectonitesin ophiolites, and abyssalperidotites[e.g., Frey and Green, 1974; Loubet and All•gre, 1982;PrinzhoferandAllbgre, 1985;Frey et al., 1985;Menzieset al., 1987;Bodinieret al., 1990;McDonough and Frey, 1989;dohnsonet al., 1990; Kelemenet al., 1995]. Overall, theserocks are characterizedby large variationsof trace element content. Very often, they are selectively enrichedin the mostincompatibleelements,a featurewhich is classicallyattributedto interactionwith deep-seated fluids. The extentof interactionbetweenuprisingmeltsand shallower mantle has been the subjectof several recent works [e.g., Bodinier et al., 1990; Takazmva et al., 1992; Nielson and Wilshire, 1993; Kelemenet al., 1992, 1995; Van der Wal and Bodinier,1996;Zanettiet al., 1996] andis still a vigorouslydebatedissue[e.g.,Nielsonand Wilshire,1996;Nayon

Copyright1997by theAmericanGeophysical Union. Papernumber97JB01946. 0148-0227/97/97JB-01946509.00

et al., 1996]. Yet, several studiesconvergeon the idea that mantle melts must migrateby intergranularporousflow over significantdistancebefore being eventuallytapped by translithosphericfracturesystems.During this process,the chemical compositionof partial melts is expectedto evolve as a resultof successivereactionswith countryrocks. Melt-rock reactionsassociatedwith extensiveporousflow are thoughtto play a significantrole in the genesisof subduction-related lavas [Kelemen, 1990; Kelemen et al., 1993]. Similarly, interaction between mantle melts and the lower lithosphere has been repeatedly suggestedfor intraplate basalts [Chen and Frey, 1983; Hawkesworth et al., 1987; McKenzie and Bickle, 1988; Arndt and Christensen,1992]. Coupledstructuraland geochemicalstudyof the Rondaperidotite (Spain) has revealedkilometer-scalepercolationin the subcontinentallithosphere,associatedwith melt-rock reactions [Van der I/Val and Bodinier, 1996]. This processis thoughtto occur at the transitionbetweenadiabaticand conductivemantle,duringthermomechanical erosionof the lithosphereabovemantleplumes(seealso Bedini et al., Evolution of LILE-enriched small melt fractions in the lithospheric mantle:A casestudyfrom the East African Rift, submittedto Earth and Planetary ScienceLetters) (hereinafterreferredto as Bedini et al., submittedmanuscript,1997), and may account for the "lithospheric"signaturefrequentlyobservedin continentalflood basalts [e.g., Stewart and Rogers, 1996]. Finally, even the genesisof mid-oceanridge basalt(MORB) involvesinteractionbetweenupwellingmeltsandperidotites, since MORB compositionis thought to integratemultiple melt fractionsproducedat variousdepthsalonga porousflow column [Klein and Langmuir, 1987; Saltersand Hart, 1989; Iwamori, 1993; Kelemenet al., 1995].

24,771

24,772

VERNIERES ET AL.: FLUID-ROCK INTERACTION MODEL IN MANTLE

Thus previouswork tendsto suggestthat basaltgenesisis inadequatelysimulatedby the standardmeltingmodels,which do not consider magma transport (i.e., batch, fractional, continuous, and incremental melting [Gast, 1968; Shiny, 1970; Langmuiret al., 1977;Johnsonet al., 1990]). Likewise, interactionbetweenmantle rocks and melts is only partially accountedfor by modelsof melt-rock reactionwhich do not consider magma circulation (e.g., Kelemen et al. [1992] model based on the Assimilation-FractionalCrystallization (AFC) model of De Paolo [1981]). SinceMcKenzie [1984], one-dimensional(l-D) modeling of trace element fractionation duringporousflow has beenthe subjectof severalstudies, which have pointedout the chromatographic effectsresulting from this process[Nayon and Stolper, 1987]. These studieshave alsotackledsomeaspectsof interactionbetween percolating melt and peridotites,such as diffusional disequilibrium [Bodinieret al., 1990; Vasseuret al., 1991], meltrock reactions [Godard et al., 1995], or melt extraction [I•vamori, 1993]. The chromatographic approachhas proven to be very usefulto understanding traceelementfractionation in peridotitesaffectedby a singlemelt infiltrationevent [e.g., Vander Wal and Bodinier, 1996]. However, none of the publishedporousflow modelscan fully reflectthe complexityof processes involvedin magma genesisand mantlemetasomatism, suchas polybaricmelting of adiabatic mantle or infiltration

of metasomatic small melt

fractionsalong conductivethermalgradients.More complete informationon melting and melt-rock reactionshas become available [Kelemen, 1990; Kostopoulos,1991; Walter and Presnall, 1994; Kelemen et al., 1993, 1995; Walter et al.,

1995], but it is extremelydifficult to insertthesereactionsin the spatiotemporalframeworkof the porousflow models.The more complexthe modelis, the moredifficult it is to solvethe governingequations,which becomenonlinear.Even thougha solution can be found, some of the physical parameters (distance,volume of interaction,fluid velocity,etc.) may be difficult

to constrain.

changebetweenmelt and minerals,as well as dissolutionand precipitationof mineral phases.Since the model is nondimensional,the results are not inscribedin space and time dimensions. The cells are not considered as an actual discreti-

zationof spacebut ratheras chemicalreactorsin which oneof the reactantsis the newly infiltra•tedfluid. The otherreactants are the minerals,with modal proportionsreflectingequilibrium conditionsachieved during the precedingreaction increment.Volumes are measuredagainstan initial cell volume equalto one. Each incrementof the model involvesthe three following stages(Figure 1): (1) the subsystems (cells) are first opened and a new fluid distributionis determined;(2) then the subsystemsare closed and trace elementreequilibrationtakes place, as well as melt-rockreactions;(3) finally, compaction occurswhen the conditionsrequiredfor this processare encountered. 2.1.

Fluid

Distribution

A cell is constituted

in the Column

of a mineral skeleton and an incom-

pressibleand continuousinterstitialfluid. Each incrementis associated with the creationof a new cell at top of the column, until the maximum number of cells allowed in the model

is reached(nstop,the upperlimit of melt infiltration).Further fluid batchesthat reachthe top of the columnare accumulated in an externalreservoir.The accumulated fluid compositionis the sumof all fluid batchesflowing out of the columnduring a given incrementsequence. The redistributionof the fluid alongthe column,following a new increment,is controlledby the void contentof eachcell (porosity).It is assumedthat (1) the amountof melt infiltrated at the baseof the columnis equalto the fluid volume of the bottomcell, (2) the cells form distinctphysicalentitiesof constantvolumeduringfluid redistribution, and(3) the porosity of a new cell createdat the top of the columnis equalto the porosityof the bottomcell at first increment.Assumption 1 implies that the rate of fluid influx is not constantif compactionand/or phasetransitionprocesses occur in the bottom cell. From assumption3, it follows that the size of each new cell is determinedby the volume of fluid infiltrated in the columnat eachnew incrementand by the compactionand/or phasetransition processeswhich have occurredwithin the entirecolumnduringpreviousincrements. Previousplatemodelsassumedfluid transferonly from one cell to the one just above [Heiferrich, 1962; Volliner, 1987]. In contrast,the proposedapproachallowsmorecomplexfluid transferto accountfor variationsof fluid fluxes resultingfrom partialmelting,compaction,and/orfluid-rockreaction(Figure 2). After its creation,a given cell/may be infiltratedby fluid

To overcomethesedifficulties,we proposea new approach basedon the plate model of Heiferrich [1962] and Vol/ruer [1987]. In the plate model, fluid flow is not consideredas a functionof time and distancebut simulatedby propagationof fluid batches through macrovolumes of mantle rocks. Multiple reactionscan then be taken into account,and these reactionsmay be monitoredby the mineralogicalevolutionof mantle rocks and/or the fluid/rock ratio. This approachmay accountfor a wide rangeof magmaticand metasomatic processestaking place in the uppermantle.Simpleprocesses such as batchmelting and the standardchromatographic fractionation can be reproduced.However,the modelis especiallywell adapted to simulate relatively complex mantle processes, batches transferred from one or several cells located at lower involving matrix compaction and/or successivemelt-rock level in the column. When cell./is filled with more than one reactionsduringmagmamigration.

fluid fraction, it is assumedthat these distinct fluid fractions

2. Plate

Model

As in the plate modelsof Heiferrich [1962] and Volliner [1987], the infiltrated medium is consideredas a column formed by a successionof cells. Magma infiltration and/or compactionat the base of the column induce fluid transfer toward the top, which may also resultin the creationof new cells. Betweenfluid pulses,the cells are closedsubsystems in which fluid-rock interactionoccursin thermodynamicequilibrium. The interactionprocessincludestrace elementex-

will mix instantaneously and form a new fluid phase.Mixing of distinct fluid fractionsis typical of cells which are infiltrated by fluid batchessmallerthan their interstitialvolume. This occurswhen porositydecreasesat the baseof the column, becauseof matrix compactionor fluid-rock reactionat decreasingfluid mass.However,mixing may alsooccurwhen fluid batchesare larger than interstitialcell volume, because of partial melting or fluid-rock reactionat increasingfluid mass(Figure 2). Transferof melt batchesfrom cell/to/+ ! as in previousplate models,without mixing, occursonly when porosityis constantthroughoutthe consideredprocess.

VERNIERES ET AL.: FLUID-ROCK INTERACTION MODEL IN MANTLE

• fluid input

incell j=l

,

•,,

24,773

Percolation, fluid-rock interaction trace element

• o• reequilibration • withcompaction

,

Pefcoladen, •

,

Melting

'..........fluid-rockinteract•n • • without compaction and

•

without compact•n •, fluid input melt e•raction

melt distribution inallcells x,

••

.......... •

I

/

] z

mea-rocK reacuon,-

........... • ....... trace element reequilibration

Figure 1. Illustrationof the differentprocesses simulatedby the platemodel.The algorithmaccounts for (1) fluid transportthroughoutthe column,(2) fluid-rockinteraction(regularlydashedline), and possibly(3) matrix compactionand melt extraction(solid line). If no fluid input occursat the baseof the column (irregularlydashedline),meltingandcompaction arethe mainspring of percolation (seetext).

2.2.

Fluid-Rock

Melting is characterized by F, the weightproportionof

Reactions

In a broad sense,fluid-rock reactionsincludepartial melting of the mineral phases,interstitialcrystallizationof the melt fraction, or a combinationof dissolutionand crystallization mechanisms.The combinationof dissolutionand crystallizationis generallyreferredto as "melt-rockreaction"(in a strictsense)when no new mineralphaseis crystallized[e.g., Kelemen, 1990] or "modal (or patent) metasomatism"when the reactionis associatedwith crystallizationof new mineral phasessuch as amphibole,micas, or apatite [e.g., Dm•:son, 1984]. In the proposedmodel, theseprocesses are simulated by local-equilibrium,nonmodal,partial melting and/or crystallization.

dissolvedmaterialrelative to the solid at increment(i-l), and p....the weightproportionof mineralm in melt. Crystallization is characterized by f, the weightproportionof residualfluid relativeto the fluid, and q....the weight proportionof mineral m in the crystallized assemblage.In the parallel reaction scheme,the melting and crystallizationparameters F and f are both considered

in relation

to the state of the cell at

increment(i-1). This is true only for F in the sequentialreaction scheme,where f is consideredin relationto a transitory fluid fractionformedby mixing of the fluid fractionat the end of increment(i-1) with the melt resultingfrom the dissolution stage.A massbalanceis established for eachcell to calculate

composition X -i ßafterreaction, itsnewporosAt theendof the (i-1)thincrement, a givencellj is charac- itsnewmodal

////. terizedby its totalvolume•J_], its porosityqo{_l,andthe ity q•;/,anditstotalvolume ß

weight fraction X)l•,i_ • ofmineral m(m=l.....M).These parametersand the trace elementcompositionof the fluid phase in equilibriumwith the mineral matrix define the initial state of cellj, just beforethe ith increment.At that point, injection of a new fluid fraction

into the cell results in a state of dise-

The densityof the solid matrix p,, and that of the fluid phaseP/ are assumed to be constantthroughout the reaction processes.Hence, becauseof the closed-system assumption,

variationsof fluid/solid ratio resultingfrom mineral dissolution and/orprecipitationimply changesin cell volumesafter eachreactionincrement.Let us pose

quilibrium,which may triggerfluid-rockreaction.In this case, the modal compositionof the reactingrock is simulatedby a "parallel"reactionschemeduringwhich meltingand crystallization occursimultaneously.Another reactionschemecan be envisaged,with dissolutionand crystallizationoccurringsequentially("sequential"reactionscheme).Dissolutionoccurs where 7 is the solid/fluiddensityratioand oe0 and oearethe first, the dissolved fraction is mixed with the interstitial fluid, solid/fluidmassratios at increment(i-1) and i, respectively. then crystallizationtakes place. However, the use of the Porosity rp{ofcellj afterincrement i isthengiven by "sequential"reactionschemeimpliesa goodknowledgeof the actualmechanismsof fluid-rock reaction(e.g., occurrenceof r (2a) r+y-1 transient phases during the reaction). In contrast, the "parallel"reactionschemeis a descriptionof the globalmodal with evolution of the reacting rock at each step of the reaction 1+o•o processandthuscan be usedin mostcases(as in all examples r=• (2b) f +oe0F presentedin this paper).

,

24,774

VERNIERES ET AL.' FLUID-ROCK INTERACTION MODEL IN MANTLE

eachzone. Fluid-rock reactionis stoppedwhen the peridotite matrix is consideredto have attained mineralogicalequilib-

new cell • no mix .''

rium with infiltrated

fluid. The number of reaction increments

necessaryto meet this condition (ilim) determinesthe total number of cells in a reactiondomain. In the case of partial melting, ilim is determinedby the maximum melting degree

mix

allowed in the model. Once the increment ilim is reached,the

reaction(or melting) zonesmove upward,leavinga domainof nonreactivecellsat baseof the column(Figure3).

mix

2.3.

Redistribution

of Trace

Element

Between

Fluid

and Solid Phases

At increment i, c/,0/ is thefluidcomposition afterfluid

mix

redistribution alongthe column.This composition may record

.....''" • mix

knumberi

fluidinputin cellj=l Column at

theendof increment i-1

percolatlon front .... ½i;iiiiiiiiiiiiiiiiiiiiii%

Melt

redistribution at increment i

::::::::::::::::::::::::: .............

Figure 2. Schematicrepresentationof fluid redistributionat incrementi. The compositionof the fluid fraction filling a given cellj of the columndependson the size and porosityof the underlyingcells. The different fluid fractionsare representedby various shadedpatterns,and the limits of cells are markedby bold solidlines.

(R3,R2)R1

(R2)

R1 __

_(R_2• R_I)_ _ (R1)

for the parallelapproachand

=

ilim

l+rx0

)

a

(3)

The residualmassfractionof a reactedmineral(dissolvedor crystallized)is givenby

I

Xm/,i = X,•,i_ • - p,,F+q,,•

½/ V,./I r,./ I(l_f)l aa0qo/_i

ao

(4)

for the parallelapproachand

(l-f a0 •//-IV//--I x"l•'i [ / P,nF. q-l+aøF a0 a ½/ r/i = '¾m,i-I --

qm

numberi

c)

forthesequential.approach. Fromporosityrp/ is deduced thetotalvolumeof cellj ß

½/

• increment

(5)

for the sequentialapproach. Different fluid-rock reactionsmay occur in the different cells alongthe column,becauseof the existenceof a significantpressure/temperature gradientand/oras a resultof a chemicalevolutionof the percolatingfluid. As illustratedin Figure3, the verticalvariationof the reactionis simulatedby consideringseveralsuperposedreactionzones.The reaction parameters(F, p.... f, andq,,) are fixed at boundariesbetween

fluid-rock

reaction path

b

Figure 3. (a) Arrangementof the fluid-rockreactionzonesin the cell column.Reactionsbeginin new cellsassoonasthey are created,that is, for the conditioni =j which definesthe "percolation front" of the plate system(heavyline). The developmentof the fluid-rockreactiondomaincomprises two main stages.(1) Until the maximum numberof reactionincrements(ilim) is reached,the newly createdcellsareaffected by reactionswhich are constantfor a given cell but variable from one cell to another.At this stage,the boundaries of the reactionzonesare parallelto the i axis(e.g., R1, R2, andR3).

(2) For i> ilim, the reactionzoneboundaries moveupward, andare parallelto the "percolationfront",and leavea domain of "nonreactive" cellsat baseof the column.(b) Composition of the columnat incrementi (> ilim). In bracketsareindicated the reactionzonesin whichthe cellshaveundergone former stagesof fluid-rock reaction.For instance,the cells involved in the reaction zone R2 at increment i have followed a reac-

tion path involving former fluid-rock reactionsin the R3 zone. Similarly, the cells involved in the reactionzone R1 have previouslyreactedin the R2 zone, as well as in the R3

zonefor mostof them.Even the cellswhichbelongto the nonreactivedomain(at baseof the column)haveundergone variable reactionpaths, involving either only the reaction zone R1 or both R1 and R2. As a result of these variable

reactionpaths,the columnis characterized by an heterogeneousmodalcomposition.

VERNIERES ET AL.' FLUID-ROCK INTERACTION MODEL IN MANTLE

the mixing of batchesof fluid of differentorigins(Figure2), whereasthe matrix still has the compositionresultingfrom

24,'/75

the consideredelementin cell j, and km is the partition coefficient of this element between the fluid and mineral m.

previous pulsecx,i-I 'i ß Atthatpoint, fluidandmatrix canbein

When no fluid-rock reaction occurs, the bulk partition stays constant, A isequal to a0, andM[ isgiven disequilibrium.To obtain the trace elementcontentin the coefficient fluid and in the matrix, we useda two-stepapproach.The first by stepconsistsin calculatingthe total mass.of the considered ß

traceelements in thecell.Themassm•- of a giventrace

(8a)

If a reactionoccurs,the final trace element concentrations

elementin cellj is written ß

.

M/= p#p•L,•L•

.

.

cI mJ.=p/½{_l(C{o+O•o ,,,,_1) V/_i (6)

The secondstep consistsin redistributingthe elementsbe-

in the fluid and in the peridotitetake into accountthe modal and/or porositychanges.The bulk partitioncoefficientat incrementi is then calculatedby usingthe modalcomposition

on the chosen tweenfluid andsolid.phases. The final traceelementconcen- of the matrixgiven by (4) or (5), depending ß

trationinthefluid(c/) andintheperidotite ( c:•) isgivenby

reaction scheme. A isequalto a, and M/ iswritten

M/= p/c/F,/

M/•+D/A)

(7a)

2.4. Melt Extraction and Compaction

with M

D/ =Z k,,,X •ß

(7b)

111,1

(8b)

m=l

and

Whena significantamountof melt is producedby partial meltingor fluid/rockreactionsat increasing fluid mass,compactionmay occur.In the model,a cell is instantaneously compacted when its porosityincreases in excessof a fixed

po.rosity limit (•nin)' After compaction, the cell volume

(7c) V/I ,fhl is givenby

c/'= o'd ß

whereM[ is themassof interstitial fluidin cellj, A is the rock/fluid massratio,DJ is thebulkpartition coefficient of

a

fluidinexcess

b

at thetopof thecolumn

rn

•

mix

P-

nomix

•

•/,fin 1-½/ =1_-'• 7•n fluid volume extracted percell

mix

}m,x nomix

nomixingbetween thedifferent fluid batches

Figure4. Schematic representation of thetwo end-rnember processes proposed for theextraction of melt fromcompacted cells.(a) Interstitial meltformsa column of fluid,whichis assumed to be incompressible. Compaction of thesolidmatrixresults in upwardmigration of interstitial meltrelativeto thematrix.Fluidin excess at thetopof thecolumncaneitherforma newcell(whenthecellnumberis lowerthannstop)or be extracted. (b) Distinctfluidfractions areextracted fromeachcompacted cellandaccumulated intoexternal reservoirs.

(9)

24,776

VERNIERES ET AL ßFLUID-ROCK INTERACTION MODEL IN MANTLE

The mass fraction of melt extracted from the cell is

Z•_,.j --(p/ --(Pmin p!•.j 1--(Pmi n

Note that this processis associatedwith melt transferalong the columnonly when a fluid is infiltratedat its base.

(10)

Two end-memberprocesseshave been envisagedfor the extractionof melt from compacteddomains(Figure 4). The first one simulatesmelt extractionby pervasiveporousflow (seemodels1 and 2 of the applicationsdescribedbelow). The column of interstitial

fluid remains immobile

while the solid

matrix is compacted.This producesan upward fluid flow relativeto the matrix. The top of the fluid columncan either form new percolationcells or be extractedfrom the column (Figure 4a). At that point, within eachcell, the trace element contentof the fluid phaseis homogenizedthentraceelements are redistributed betweenfluid andsolidphases(equations(6) to (8b)). This approachsimulatesthe evolutionof a columnin which percolationis triggeredby partial melting and compaction without melt infiltration at its base.In this situation, melt migrationoccursin all the cells situatedabovethe lowest cell from which melt is extracted.

The second mechanism

aims to simulate melt extraction

focusedinto dykes or narrow porous flow channels(see models2 and 3 of the applications).Insteadof beingtransferred to the cells above, the melt fractions extractedfrom a

compactedcell are segregatedinto an external reservoir (Figure4b). The compositionof the segregated melt is given for each compactedcell and corresponds to the sum of all melt fractionsextractedfrom the cell duringcompaction.The compositionsof the fluid and solid phasesare not modified.

3. Comparison With Previous Models 3.1. Melting and Fluid-Rock Reactions Without Fluid Transport

When only the lower cell is considered(} = 1), the proposed approachcan reproducemost of the modelsused in previousstudiesfor the simulationof partialmelting.In particular, when no fluid is infiltrated at base of the column, batchmelting [Gast, 1968; Shaw, 1970] is reproducedin the lower cell for i = 1 and (Pmin= 0. When i > 1, incremental

melting[dohnson et al., 1990] is reproduced for rPlni n = 0, andcontinuous melting[Langmuiret aL, 1977] is reproduced for (Pmin> 0. For very smallmeltingincrements (F-> 0), fractionalmelting[Shaw,1970]is simulated when (Pinin = 0, andthe criticalmeltingmodel[Sobolevand Shimizu,1992] is simulatedwhen (Pinin> 0. When a fluid is infiltratedin the column, melting in the lower cell reproducesthe model of melting in open system proposedby Ozawa and Shimizu [1995]. The AFC approachusedby Kelemenet al. [1992] to simulate fluid-rock reactionscan be approximatelyreproduced with the plate modelby consideringonly the new cellscreated at the top of the column(i.e., cell j = i at the ith increment). These cells must be affectedby a reactioninvolving mineral dissolutionand precipitation,inducedby infiltratedfluid. As in the AFC model, this allows us to monitor the evolution of a

singlebatchof fluid as a resultof successive reactionincrementswith a peridotiteof fixed composition.However, significant differences with the AFC model may arise when importantporosityvariationsoccur in the lower part of the column. As discussedabove, this may result in mixing the considered

batches of fluid with

other fractions

from lower

partsofthe column(Figure2). o.1-

-

3.2. Chromatographic Effects AssociatedWith Fluid Transport: Plate Versus 1-D Modeling

_

In 1-D porous-flowmodels,the percolationsystemis describedby settingup equationsat the scaleof representative elementaryvolumes((REV) [de Marsily, 1986; Vasseuret al., 0.01 -1991]). The REV are large enoughto averagethe physical and chemicalpropertiesof the mediumbut small enoughfor La Ce Nd Sm Eu Ho Yb Lu thesepropertiesto be continuousfrom one REV to the other. The equationsare establishedas a functionof time and space, Figure 5. Simulationof the standardone-dimensional porous flow model with the plate model, reproducingthe chroma- and fluid transportis consideredon the basis of physical tographicfractionationof rare earth elements(REE) during assumptions(e.g., the fluid velocity). In contrast,the plate infiltrationof a LREE-enrichedfluid ill LREE-depletedperi- model is basedon a step-by-stepapproachinvolvingdiscondotites [Navon and Stolper, 1987]. For the calculation,we tinuousmacrovolumes(the cells). This approachallows spaused a column of 20 cells, without fluid-rock reaction nor tiotemporalparametersand physical constraintsto be elimipartialmeltingof the peridotitematrix.The REE composition nated.Porousflow is simulatedby fluid transferfrom one cell _

of the peridotite,that of the infiltratedmelt, the solid/liquid to the other. Since diffusion in solids is not taken into acpartitioncoefficients,and the porositywere fixed after Nayon count,eachincrement j of the plate approachshouldrepresent and Stolper [1987]. The resultsare illustratedby the REE only processessignificantlylonger than the critical time of compositionof the peridotitein the uppercell for different mineralreequilibrationby diffusion.In fact, shorterdurations increment numbers i between 20 and 80. In terms of fluid/rockratio, thesevaluesare equivalentto the time range may be envisagedwhen mineral-melt equilibration is enand/or extensiverecrystc to 4 tc used by Navon and Stolper [1987, Figure 4]. For hancedby dissolution-precipitation

theseauthors,tc is the critical time of percolation,that is, the time it takes for the infiltratedfluid to reachthe top of the column. REE abundances are normalized to chondrite values

afterSunandMcDonough[1989].

tallization [Van der Wal and Bodinier, 1996]. The validity of the plateapproachmay be demonstrated by its ability to reproducethe chemicaleffectstypical of porous flow, suchas the chromatographic fractionationof REE dur-

VERNIERES ET AL.: FLUID-ROCK INTERACTION

ing infiltrationof a LREE-enrichedfluid in LREE-depleted peridotites[Navonand Stolper, 1987]. To simulatethe standard 1-D porous-flowmodel, we used a column of 20 cells continuouslyinfiltrated by melt but without fluid-rock reaction or partial melting of the peridotitematrix. Hence the modal compositionand the porosity are constant,and no compactionoccurs.In Figure 5 are shownthe chondrite-normalized REE compositionof the peridotitein the upper cell (cell 20) for incrementnumbersfrom 20 to 80. The REE patternsobtainedwith the plate model are very similar to thosereportedby Navon and Stolperfor the top of their 1-D column(seetheir Figure 4). In both cases,the patternsshow strong interelementfractionationtypical of the transient chromatographic effectsassociatedwith porousflow. Here the platemodelcanbe comparedeasilywith the 1-D modelin terms of fluid/rock ratio, which is the ratio of the volume of fluid infiltrated

in the column to the volume of the infiltrated

matrix. This ratio varies from 1% to 4% in this example.

MODEL IN MANTLE

24,777

melting after 100 increments,leaving a harzburgiticresidual mineralogy (5% clinopyroxene).Once initiated in a given cell, melting was stoppedafter 100 increments.The whole column reachedthe harzburgiticmineralogyafter 200 increments. No melt segregationoccurs along the column. The melt producedin the columnis transferredupward(seeFigure 4a), and melt fractionsthat reach the top of the column are accumulatedin a singlereservoir. At the end of the melting and percolationprocess,it is assumedthat residualmelt fractionsstill presentin the column are either trapped in peridotitesor entirely drainedfrom the column. Both situationsare illustratedfor peridotitecompositionsin Figure 6, showingthat the differenceis significant only for light REE (LREE). Lanthanum,for instance,is enriched by a factor of 3 to 10 in peridotiteswith trappedmelt, comparedwith melt-free peridotites.However, the chondritenormalized REE patterns are qualitatively similar in both situations.

After 100 increments,the mineralogyis variable alongthe column from fertile lherzolitewith only incipient melting at 4. Applications top (15% cpx in cell 100) to harzburgitewith 20% melting at The plate model was appliedto three geochemicalmantle bottom(5% cpx in cell 1). Heavy REE (HREE) steadilydeprocesseswith an increasing degree of complexity, from creaseas a functionof melting degree,with the exceptionof melting in a two-phasesporous-flowcolumn to superposed the lower part of the column (i.e., for the highestmelting degrees)where the concentrationis constant.This occurs melt-rock reaction zones at the transition between adiabatic from cell 20 downward,where melting degreeis in the range and conductive mantle. The FORTRAN code used for these simulationsas well as input and result files of model 3 are 16-20%. LREE strongly decreasefor moderatedegree of availableupon requestfrom the authors.Calculationswere melting,in the upperpart of the column(< 6% in cells 70 to performedfor REE becausetheir peridotite/meltpartition 100) but remain remarkablyconstantin the two lower thirds coefficientsare reasonablywell known [e.g., Hart and Dunn, of the column in spite of the wide range of melting degrees 1993; Kelemenet al., 1993]. In addition,theseelementshave and modal variations(5 to 12% cpx). This resultis worthy of been widely used to monitor magmatic and metasomatic mention since constant LREE concentrationin peridotites with variable mineralogy (lherzolites to harzburgites) and processes in the uppermantle[e.g.,LoubetandAllbgre,1982; HREE content has been observed in several suites of mantle Prinzhoferand Allbgre, 1985; Frey et al., 1985; Navon and rocksor in cpx separatedfrom them [Prinzhoferand Allbgre, Stolper, 1987; Song and Frey, 1989; Johnsonet al., 1990; 1985; Songand Frey, 1989; Bodinier et al., 1991; Downeset Bodinier et al., 1990; Godard et al., 1995]. al., 1991; Frey et al., 1991]. In particular,the REE patterns obtainedwith the plate model are stronglyreminiscentof the 4.1. Model 1: Partial Melting in a Two-Phase REE variation observedin Lanzo, where all the peridotitesare Porous-Flow Column LREE-depleted but the LREE/HREE ratio increaseswith The simplestmodel envisagedfor this study involvesa increasingresidual character[Bodinier et al., 1991]. This columnaffectedby partial melting,with no deep-seated melt variationwas shownto be inconsistentwith simplemodelsof infiltrated at base. Thus melt migration from lower to upper partial melting and has been ascribedto the effect of melt cells is driven only by compaction.Melting occursin the transportduring partial melting. This effect was shown by lowest cell until the melt fraction(porosity)reachesthe limit Ozmvaand Shimizu[ 1995] for a singlecell affectedby partial fixed for compaction.The melt fractionbeinggenerallycon- melting coupled with melt infiltration. The increase of sideredto be of the order of a few percentduringmeltingof LREE/HREE ratio is attestedto by the plate model for meltadiabaticallyrising mantle [e.g., McKenzie, 1984; Nicolas, ing degreeshigherthan 6%, corresponding to cpx proportions 1986; Sobolevand Shimizu, 1993], the limit was fixed at 3% in the range 12-5% (Figure 6). Furtherresults,not shownin for this study.Then, the excessmelt volume is transferredto this paper, indicatethat LREE/HREE ratio increaseseven at the cell(s) above(Figure4a). As melt transportis drivenby lowermeltingdegreewhencompactionoccursat lessthan 3% compaction,no percolationoccurs in the cells that have porosity. After 200 increments,all the cells have reachedthe maxireachedthe maximummeltingdegreeallowedin the model. The resultsshownin Figure 6 were calculatedwith a col- mum meltingdegreeallowedin the model(20%). Hencethe umn of 100 cells. The modal compositionof the initial peri- columnhas homogeneous refractorycompositioncharacterdotite and its REE contentwere establishedfrom published ized by 3% cpx. At the bottom(cell 1), the peridotiteshave data on fertile spinel lherzolitesin orogeniclherzolitesand retained their REE compositionachieved after 100 incremantle xenoliths [Jagoutz et al., 1980; Frey et al., 1985; ments.However,the peridotiteslocatedat higherlevelsin the Bodinier, 1988; Jochum et al., 1989]. REE abundancesare column are more depleted,especiallyin LREE, in spite of similar to those generally inferred for the depletedMORB their similar melting degree and modal composition.The mantle (DMM) [e.g., Jochum et al., 1989], with YbN enhancedLREE depletionof the uppercellsresultsfrom their (chondritenormalized)=2.4, (La/Yb)N- 0.2, and(Sm/Nd)N= interaction with LREE-depleted melts extracted from the 1.42. The melting reaction was adjustedto achieve 20% lowerpart of the column.In otherwords,meltingin the lower

24,778

VERNIERES ET AL.' FLUID-ROCK INTERACTION MODEL IN MANTLE

1 oo

1

o.1

LU

O.Ol

rr Z

o.ool

¸ 0

o.oool

0

o.oooo1

•oo Z

La Ce Pr Nd lOO

PERIDOTITES

PERIDOTITES + TRAPPED MELT Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

La

Ce

Pr

Nd

I

I

I

I

=

Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

lOO

Z 105

200

: _

0

O.Ol

o.ool

ACCUMULATED

MELTS

•oo

INTERSTITIAL

MELTS

-

o.oool

La Ce Pr Nd

$m Eu Gd

b Dy Ho Er Tm

b Lu

La Ce Pr Nd

$m Eu Gd

b Dy Ho Er Tm Yb Lu

Figure 6. Resultsof model 1, simulationof REE evolutionduringpartialmelting in a two-phaseporous-flow column. The resultsare shown for residualperidotiteswith trapped interstitialmelt, melt-free peridotites, interstitialmelt, and melt accumulatedat top of the column.Calculationswere performedwith a column of 100 cells and up to 200 increments.Peridotiteand interstitialmelt compositionsare shownafter 100 (thin solid lines) and 200 increments(bold solid lines). Resultsare given for the bottomcell (number1), then for every 10 cells up to the upperone (number100). The heavydashedline represents the initial REE contentof the peridotite column. Its initial modal compositionis as follows: cpx - 0.15, opx - 0.255, and olivine = 0.595. Accumulatedmelts are shownfor the first incrementat which a melt fractionreachesthe top of the column (increment 105) and then for every 10 incrementsup to increment200. REE abundancesare normalized to chondritevalues after Sun and McDonough [1989]. The model assumesequilibrationin the spinel stabilityfield, but spinelwas neglectedbecauseof the very low partitioningof REE in this mineral [Stosch, 1982]. Melting proportionswere adjustedto matchthe modalcompositionof residualperidotitesproposedby Kostopoulos[1991, Table 3] after 20% melt ext.raction(cpx - 0.05, opx - 0.26, and olivine: 0.69). Cpx/melt partition coefficientwere taken from Hart and Dzmn [1993] for La, Ce, Nd, Sin, Eu, Gd, Dy, and Yb and interpolatedfor other REE. Opx/melt and olivine/meltpartitioncoefficientswere establishedfrom opx/cpx and olivine/cpx valuestaken from Gatfido [1995], for most REE. Exceptionsare opx/cpx valuesfor La and Ce and olivine/cpx values for La, Ce, and Nd, which were taken from Ke/emenet aL [1993]. In addition, opx/cpxand olivine/cpxvaluesfor Pr were interpolated.Otherparametersare given in text.

cells is responsiblefor a "sink" effect which is transferredto the upper cells by melt transport[Godard et al., 1995]. This effect is superimposed on the effect of in situ partialmelting. This resultmight providea simpleexplanationfor the observation that most abyssaland ophioliticrefractoryperidotites are too depleted in LREE to be in equilibrium with MORB [Johnsonet al., 1990; Kelemenet al., 1995]. Interstitial melt shows REE variationswhich are qualitatively comparableto those observedin peridotites(Figure 6). A striking feature of these residualmelt fractionsis that only few of them are similarto MORB with regardto REE

melt found by Sobolev and Shimizzt[1993] as inclusion in olivine. Our results are consistentwith the interpretation proposedby these authorsfor the ultradepletedinclusions. These inclusionsare consideredto representsmall melt fractions produced by the high degree of critical melting (i.e., near-fractionalmelting, with melt fractionstrappedin residual peridotites).Melt accumulatedat the top of the columnis less variable and showsREE contentroughly consistentwith NMORB composition.A more realistic model of MORB extractionshouldprobably involve focusedmechanismsof melt segregation,suchas hydrofracturing[Nicolas, 1986] or chanabundance and distribution. Most interstitial melts are more neled porousflow [Kelemenet aL, 1995], ratherthan diffuse LREE-depletedthan MORB and resemblethe ultradepleted percolationtoward the top of the column. Focusedmelt ex-

VERNIERES ET AL.' FLUID-ROCK INTERACTION MODEL IN MANTLE

Two end-memberprocessesare envisagedfor the extractionof melt from compactedcells.The first one assumes that melt extraction is driven by pervasive porous flow [McKenzie,1984;Ribe, 1985].Melt fractionsin excessof the limit fixed for compaction(3%) are transferredto the cells above,togetherwith percolatingmelt, and accumulated in a singlereservoirat the top of the column.The secondmechanism is more akin to magmatransportfocusedinto fracture conduits[Nicolas, 1986; Sleep, 1988] or saturatedporousflow channels[Kelemenet al., 1995]. Melt fractionsextracted by compaction arenottransferred to othercellsbutsegregated alongthe columnandaccumulated intoasmanyreservoirs as thereare compactedcellsin the model. Peridotite compositionsobtained after 100 increments show strong dependenceupon melt extraction processes (Figure7). Melt extractionby pervasiveporousflow yields peridotiteswith homogeneousHREE and middle REE (MREE) abundances, in spiteof their wide rangeof minera-

tractionmay be simulatedby the plate[nodel,as exemplified in [nodel 2 below.

4.2. Model 2' Partial Melting in a Two-Phase Porous-Flow Column, With Deep-Seated Melt Infiltrated

at Base of the Column

This [nodel is similar to the previous one, except that LREE-enriched melt with ocean island basalt (OIB) com-

positionis continuouslyinfiltrated at base of the column. Suchmeltingprocesscoupledwith infiltrationof deep-seated melt is roughlyequivalentto melt-rockreactionat increasing melt mass[Kelemen,1990]. Comparedwith previousmodeling of melt-rockreactiontakinginto accountmagmatransport [Godard et al., 1995], the plate model is different in consideringthe effect of matrix compaction.For the results illustratedin Figure 7, the fluid/rock volume ratio is 2.05% after 100 increments and is 4.09% I

I

I

I

I

I

after 200 increments. I

I

I

I

I

I

I

I

I

1 )o

1

•

__• I'LI•I I I I\I I I I I I I I __ •1102 •__

o.1

0.01

1

•

200 I

I

I

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I

La Ce Pr Nd

0.001

I

I

I

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I

I

I

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I

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Sm Eu Gd Tb Dy Ho Er Tm Yb Lu _

o.oool

PERIDOTITES (A) [

•

0

: •..-

]

24,779

[

[

La Ce Pr Nd

[

[

[

[

]

[

[

[

[

100 102• • • • .-.. ---• ••

SmEu GdTb Dy Ho Er Tm Yb Lu

-

10

200

:1

1•1

-10, -

0.1-•

I

I

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La Ce Pr Nd

-E--

I

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ACCUMULATED MELTS (B) I

I

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Sm Eu Gd Tb Dy Ho Er Tm Yb Lu I

I

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I

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-

--

0.01

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1

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-_ _

60'

1

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96 .....

•---__

---

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=•=,

'

_

_

_

5( I PERIDOTITES (B) --_-

0.0001 -•_ lOO _

I

I

La Ce

I

I

Pr

Nd

: SEGREGATED MELTS (B) -

I

Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

La Ce Pr Nd

Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

Figure 7. Resultsof model2, simulationof REE evolutionduringpartialmeltingin a two-phase porous-flow column,with deep-seated melt infiltratedat baseof the column.Model A involvesmelt extractionby pervasiveporousflow. ModelB involvesmeltsegregation alongthe column(seetext).The resultsareshownfor peridotiteandmelt accumulated at the top of the columnandfor segregated melt (only for modelB). The calculated peridotitecompositions areshownfor every10 cellsasin Figure6, after100 increments (cells1 to 50, thin solid line; cells 60 to 100, thin dashedline) and 200 increments(bold solid lines). The bold dashed line represents the initial REE contentof the peridotitecolumn.Segregatedmelts(model B) are shownfor cell 1 and then for every 10 cells from cell 10 to the uppermostcell affectedby compaction,that is, cell 96 after 100 increments(from cell 1 to 50, thin solid lines, from cell 60 to 96, thin dashedlines) and cell 100 after 200 increments(bold solid lines).Accumulatedmeltsare shownfor the first incrementat which a melt fractionreachesthe top of the column(increment102) andthenfor every 10 increments up to increment200.

On meltdiagrams,the bolddashedline represents the initialREE contentof melt infiltratedat the baseof the column(OIB [afterSunandMcDono•tgh,1989]).Otherparameters andchondrite-normalizing valuesarethe sameas for model 1 (Figure 6).

24,780

VERNIERES ET AL.' FLUID-ROCK INTERACTION MODEL IN MANTLE

logical compositions(5-15% cpx). The only marked differ- melt extractionby pervasiveporousflow, meltsaccumulated ence between fertile lherzolite froin the top of the column at top of the columnhaveconvexupwardREE patterns with (e.g., cell 100) and harzburgitefroin the base(e.g., cell 1) is very low HREE content(3.2 to 5 timesthe chondritic value). more pronouncedLREE depletionin the former.REE patterns Onlythevery firstmeltfractionextracted fromthe column,at are convexupward,as a resultof significantdepletionof both increment102, is more enrichedin REE. To our knowledge, such REE compositionis very uncommonamong mantle LREE and HREE relative to MREE. The overall convexity of volcanics. REE patternsand the distinct evolutionsof LREE and HREE The convexREE patternswith low HREE contentare not within the column result from the superimposedeffects of observedin any of the magmasobtainedwith the modelaspartial melting and reequilibrationwith infiltrated melt. Becausethey are moderatelyincompatible,the I-IREE are not strongly affected by partial melting. Hence they tend to be melt fraction controlled by the OIB compositionthroughoutthe column. per½olationfront o .02 .03 This feature is responsible for their depletion relative to 300 • MREE. Being more incompatible,the LREE are more affectedby partial melting. As a result,they are controlledby infiltrated melt only in the lower part of the column. The uppercellsshowthe effectof partialmelting,markedby a depletion of LREE relativeto MREE. 250 With the model assuming focused melt extraction, the peridotitesshow more complex REE variation, as well as more contrastedREE patternsbetween lherzolite and harzburgite. The fertile lherzolitesfrom the upper part of the column (down to cell 60, with cpx fraction in the range 1015%) are LREE-depletedand show steadilydecreasingabun200 dances of both LREE and HREE downward, that is, with

increasingrefractory character.In contrast,the harzburgites from the lower part of the column (from cell 20 downward, with cpx in the range 3-5%) are LREE-enrichedand show increasingREE abundancesdownward. Between these extremes (cells 20 to 60, with cpx in the range 5-10%), the peridotiteshave intermediateREE patternsand shownegative correlation

between LREE

150

and HREE.

Such negative correlationand the coexistenceof LREEenrichedharzburgites(or dunites)with LREE-depletedfertile lherzolites

are classical features in various

suites of mantle

rocks from ophiolites [Prinzhofer and Allbgre, 1985], orogenic peridotites[Bodinier et al., 1991; Dowrieset al., 1991; Takazawaet al., 1992; Van der Wal and Bodinier, 1996], and xenoliths [McDonough and œrey, 1989, and references herein]. With the plate model, we confirm that this feature may be explainedby a single-stageprocessinvolvingmelting (or melt-rock reactionat increasingmelt mass)coupledwith infiltration of enricheddeep-seatedmelts, as previouslysuggestedby Godard et al. [1995]. After 200 increments,differences between the two models of melt extractionare less marked (Figure 7). In both cases, the peridotitesshowa wide rangeof REE contents,in contrast with their h9mogeneousharzburgiticmodalcomposition(5% cpx). Most of them are eithersteadilyenrichedfrom HREE to LREE, or at least selectivelyenrichedin LREE relative to MREE, with "spoon-"or U-shapedREE patterns.It is, nevertheless,worth noting that the model assumingfocusedmelt extractionyields more pronouncedinterelementfractionation, with REE patternsvery similarto thoseobtainedwith the 1-D chromatographic models [Navon and Stolper, 1987; Bodinier et al., 1990; Vasseur et al., 1991]. Such fractionated REE patternsare frequentin refractorymantle rocks. Our results indicatethat they may develop during the late stagesof the percolation-reaction processes responsiblefor the individualization of the refractoryfacies. Finally, thesetwo different modesof melt extractionyield very differentmagma compositions(Figure 7). In the caseof

lOO

•melt .

.

.

. .

5o

.. . .

. . . . . . .

. .,

.

., _

.e'.-> olivine fraction Figure 8. Illustrationof model 3, superposed melt-rockreaction

zones at transition

between

adiabatic

and conductive

mantle,showing(left) the final positionof reactionszonesin the column and (right) the correspondingcalculatedolivine and melt fractions along the column. The initial peridotite mode is 0.1 cpx, 0.25 opx, and 0.65 olivine. The reaction schemeis as follows: (1) at baseof reactionzone R1, melting reactionsimilar to the one used in models 1 and 2; (2) at R1R2 boundary,melt-rockreactionmarkedby dissolutionof cpx and opx and precipitationof olivine at increasingmelt mass; (3) at R2-R3 boundary,melt-rock reactionmarkedby dissolution of opx and precipitationof olivine at constantmelt mass; and (4) at top of R3, melt-rock reactionmarked by dissolutionof opx and precipitationof cpx at decreasing melt IllaSS.

VERNIERES ET AL.' FLUID-ROCK INTERACTION MODEL IN MANTLE

sumingfocusedmelt extraction.Melts accumulatedat top of the column have relatively flat REE pattern,with moderate LREE enrichment.Those segregatedalong the column have variable compositionsdependingon the level of melt segregation(i.e., cell number).In the upperpart of the column,the REE patternsvary from flat, with relatively elevated REE abundances(e.g., cell 96 after 100 increments),to LREEdepleted(e.g., cell 100 after 200 increments).In the lower part, the segregatedmagmas have REE patterns variably enrichedin LREE. Compositionsnearly identicalto infiltrated OIB are typical of the lower cells at any incrementnumber (e.g., cell 1 in Figure 7). Note that the REE variationrangein segregatedmelts obtainedafter 200 incrementsis very similar to the one observedin oceanicbasalts,from E type to N type MORB [e.g., Woodet al., 1979].

24,781

R3). Between these extremes, the melt-rock reaction is domi-

natedby olivine precipitationat increasing(R1-R2 boundary) or constant(R2-R3 boundary)melt mass.Up to increment50, the only existingreactionzone is RI at the baseof the column. Then R2 and R3 are successively developedupward,up to increments100 and 200, respectively.From this stage,the entire reaction domain migrates upward with the aim of simulatingerosionof the lithosphericmantle. For the results illustratedin Figures 8 and 9, the processwas stoppedafter 300 increments.

To accountfor the lithosphericcharacterof the initial peridotite, we used a more refractorycoinpositionthan in the

previousmodels(cpx = 10%, insteadof 15%,andYbN= 1.2, insteadof 2.4). However, this differencehas actually little effect on the results.Other parametersare the sameas before (e.g., infiltratedmelt equalsOIB), and the fluid/rockvolume

4.3. Model 3: SuperposedMelt-Rock Reaction Zones at

ratio is 2.04%

after 300 increments. The results are illustrated

for porosityand olivine modal proportionin Figure 8. The Transition Between Adiabatic and Conductive Mantle This model was inspired by studies of mantle metaso- lower part of the column (from cell 100 downward) shows matism and particularlyby recentworks suggestingthat the refractorymodal compositionand constantporosityvalue at metasomaticagentsare formeduponreactionbetweenplume- 3%, which is the limit fixed for compaction.In fact, the most derivedmelts and lithosphericperidotires(Bedini et al., sub- refractoryrocks are not observedat the very baseof the column but rather between cells 20 and 50. This is because the initted manuscript,1997). The suggestedprocessis basedon lowest cells have mainly undergonemelting, whereas the coupledtextural and geochemicalstudy of mantle xenoliths others have suffered olivine-forming reaction. The latter is froin the East African Rift, constrainedby the kilometer-scale more efficient than the former in producingrefractorymodal variationreportedfor the Rondaorogenicperidotire[Van der Wal and Bodinier, 1996]. During thermomechanicalerosion compositions[Kelernen, 1990]. Above a relatively sharp of the mantle lithosphereby a plume, basalticmelts would porosityfront betweencells 100 and 150,the upperpart of the infiltrate into its base and react with peridotires.As inferred columnis characterizedby very small porosityvalues(< 1% for Ronda, partial dissolutionof peridotitesmay generatea down to 0.001% at top of the column) and modal composihigh-porositydomain of regional extent at the boundarybe- tions which tend to be more fertile than the initial peridotite tween adiabatic and conductive mantle. However, becauseof

(cpx= 10-12%).

the conductivethermal gradient,the reactionmusteventually occurat decreasingmelt massand producesmall fractionsof volatile-richresidualmelt. Becauseof their low viscosityand solidificationtemperature,thesemeltswould migrateupward and infiltrate large volumes of lithospheric peridotires [Watsonet al., 1990]. This reactionprocessat decreasingmelt massis thoughtto accountfor the pervasiveforms of mantle metasomatism,includingthosewhich have been ascribedto carbonatiticmelts [Yaxley et al., 1991; Dautria et al., 1992; Rudnicket al., 1993; Ionov et al., 1993]. Thesereactionprocesseswere simulatedby a plate model assuming the existence of three melt-rock reaction zones (Figure 8). Since the reaction parameters (melting/crystallizationdegrees and proportions of dissolved/precipitated minerals)are fixed at zoneboundaries, the reaction schemeis characterizedby steadyvariationsrather than marked discontinuities.It is a simplifiedversionof the one proposedby Bedini et al. (submittedmanuscript,1997), which involves microphasessuch as apatite and Ti-oxides. These minerals were neglectedin the present study. The model is constrainedby the observationof melt-rockreactions in the Ronda massif [RemMdi, 1993; Van der Wal and Bodinier, 1996] and mantlexenoliths[e.g., Berger and Vannier, 1984], as well as by the theoreticalconsiderations developed by Kelemenand coworkersconcerningmelt-rockreactionsin adiabaticand conductivemantle [e.g., Kelemen,1990; Ke/emen et al., 1995]. Schematically,the reaction varies from dissolutionof all mineralphasesat baseof the reactiondomain (lower boundaryof R1 in Figure 8) up to cpx-forming reactionat decreasingmelt massat top (upper boundaryof

Peridotitesand interstitialmelts show a wide diversityof REE patterns(Figure 9). Broadly,the refractoryperidotites froin the lower part of the column(from cell 80 downward) are depleted in REE, with LREE/HREE ratio close to one. They have convex-upwardREE patternstypical of mantle rocksequilibratedwith alkalinebasalts[e.g., Irving, 1980; Bodinieret al., 1987, 1988].In the centralpartof the column, froincell 80 to cell 22, theperidotites areselectively depleted in LREE, mostof them beingevenmoreimpoverished than the initial peridotite.This resultis worth mentioningsince infiltrationof deep-seated meltsinto lithospheric peridotitesis generallythoughtto be associatedwith LREE enrichment. However, LREE-depletedperidotitesfrom the Ronda massif and mantlexenolithshave beenrecentlyascribedto extensive reactionwith percolatingmelt [Van der Wal and Bodinier, 1996; Bedini et al., 1997]. In contrast,the top of the columnis stronglyenrichedin LREE, with lanthanumin the interstitial melt in excess of 1000 times chondrites.

This value is much

higherthan the concentration of the infiltratedmelt (LaN = 156.1 [Sun and McDonough, 1989]). Such strong LREE enrichmentwas predictedby the percolation-reaction model of Godardet al. [ 1995], as a resultof sourceeffectsproduced by melt-rockreactionat decreasingmelt mass,coupledwith chromatographiceffects resulting from porous flow. For Bedini et al. (submittedmanuscript,1997), this processwould accountfor the evolution of large ion lithophile elementenriched small melt fractions such as those responsiblefor carbonate-melt

metasomatism.

Finally, it is worth notingthatthe melt fractionssegregated froIn the compactiondomaindisplay a restrictedrange of

24,782

1000

VERNIERES ET AL.: FLUID-ROCK INTERACTION MODEL IN MANTLE

SEGREGATED

--

MELTS

_

_

_

variationof REE, comparedto the percolatingmelts.They are moderatelyenrichedin LREE, with REE patternsreminiscent of those observed in many intraplate basalts, such as continental

_

flood basalts.

_

5. Conclusion

1

100

N _

_

_

_

_

_

10--

tl.I I

I

z

0

I

La Ce

n-

I

I

I

Pr

Nd

I

I

300

Sm Eu Gd

b Dy Ho Er Tm Yb Lu INTERSTITIAL

MELTS

1000

o

x \\•

o z IO0

z

lO

La Ce lO

allows much more freedom for the simulation

_

I

I

Pr

Nd

I

I

300!•

Sm Eu Gd Tb Dy Ho Er Tm Yb Lu PERIDOTITES

of fluid-rock

interactionsthan the 1-D porous-flowmodels [e.g., Nayon and Stolper, 1987;Bodinieret al., 1990; Vasseuret al., 1991; I•vamori, 1993; Godardet al., 1995]. Simple processessuch as batch, incremental,and continuousmelting can be reproduced[Gast, 1968; Shaw, 1970; Langmuir et al., 1977; Johnsonet al., 1990], as well as the chromatographiceffects associatedwith porous fluid flow [Navon and Stolper, 1987]. However, this approachis especially well adaptedto simulatemore complex mantle processes,such as melt extractionassociatedwith compactionof molten peridotites, or fluid-rock reactions occurring upon melt

o o

The plate modelproposedin this studyis a new approach for the simulationof trace elementtransferduringmagmatic and metasomaticprocesses taking place in the Earth'supper mantle.As in the platemodelpublishedby Heiferrich[1962] and Follmer [1987], porousflow is not consideredas a function of time and distancebut simulatedby the propagationof fluid batchesthroughmacrovolumesof mantlerocks.Being releasedfrom spatiotemporal constraints,the plate approach

infiltration

at the base of the conductive

mantle.

For

relatively simple situationssuch as percolationwithout mineralogicalreaction[Navon and Stolper, 1987], or with a single reaction occurring along the column [Godard et aL, 1995], the plate model may be comparedwith 1-D modelsin terms of fluid-rock

ratio.

The applicationspresentedin this study show severalresults consistentwith publishedtrace elementdata for mantle rocks and basalticvolcanism.The strongLREE depletionof peridotitesresidualafter MORB extractionis reproducedby the melting model. It is shownthat an extremedepletionof LREE in peridotitesand interstitialmelt (as observedin melt inclusionstrappedin minerals[Sobolevand Shimizu, 1993]) 0.1 is especiallyexpectedin the upper part of the moltenregion. When partial melting, or melt-rock reaction,is triggeredby infiltration of LREE-enriched deep-seatedmelt, the plate approach accounts for the paradoxical increase of La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu LREE/HREE ratio with increasing refractory characterof peridotites,as frequently noted in various suitesof mantle Figure 9. Results of model 3, simulation of REE evolution rocks [Prinzhoferand All•gre, 1985; McDonoughand Frey, within superposedmelt-rock reactionzonesat transitionbe- 1989; Bodinier et al., 1991; Takazm•,aet al., 1992]. These tween adiabatic and conductive mantle. Calculations were results also lend supportto the models assumingthat melt performedwith a 300-cell columnand300 increments (Figure extraction is driven by focusedmechanisms[Nicolas, 1986; 8). The resultsare illustratedfor peridotite,interstitialmelt, Ke/emen et al., 1995], rather than by diffuse porousflow. and melt segregatedfrom compactedcells. Peridotite and Finally, the proposedapproachprovidesnew insightsinto the interstitialmelt compositionsare shownfor cell I andthen for origin of ultra-LREE-enrichedmetasomaticfluids infiltrated every 10 cellsup to cell 300. The bold solid linescorrespond to cells 1 to 100, the thin solid linescorrespond to cells 110 to in the lower lithosphere,as a result of melt-rock reactions 200, the thin dashedlinescorrespond to cells210 to 300, and occurring at transition between adiabatic and conductive the bold dashedline (on the bottomdiagram)corresponds to mantle(Bedini et al., submittedmanuscript,1997). the initial peridotitecomposition.The segregatedmelt comAcknowledgments. This researchwas supportedby PICS 275 positionsare shownfor cell 1 and then shownfor every 10 Montpellier-Grenade "Percolation en milieu mantellique cells from cell 10 to the uppermostcell affectedby compac- mecanismeset transfertschimiquesassoci6s"(Centre National de la tion (cell 49). The bold dashedline corresponds to the com- RechercheScientifique- Minist6redesAllhires Etrang6res,France). positionof infiltratedmelt (OIB [afterSunand McDonough, The manuscriptwas greatly enhancedby the helpful reviews and 1989]). Other parametersand chondrite-normalizing values commentsof Kazuhito Ozawa and Timothy Lutz. Finally, we thank arethe sameas for model 1 (Figure6). ElianeNadal for her help in preparingthe manuscript. I

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Montpellier2, case courrier57, Place E. Bataillon, 34095 Montpellier cedex5, France.(e-mail:bodin•dstu.univ-montp2.fr; margot•dstu.uni-montp2.fr; vemier•dstu.univ-montp2.fr)

(Received November 8, 1996;revised April30, 1997; accepted July3, 1997.)