JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 100, NO. B9, PAGES 17,615-17,636,SEPTEMBER 10, 1995 Dynamicsof differentiation in magma reservoirs ClaudeJaupart and StephenTait Institutde Physiquedu Globe, Paris, France 1919-1994 Abstract. In large magmachambers, gradients of temperatureand compositiondevelop due to coolingand to fractionalcrystallization. Unstable density differences lead to differentialmotions betweenmelt and crystals,and a major goal is to explainhow this might resultin chemical differentiationof magma.Arriving at a full descriptionof thephysics of Crystallizingmagma chambersis a challengebecause of the largenumber of processespotentially involved, the many coupledvariables, and the differentgeometrical shapes. Furthermore, perturbations are causedby the reinjectionof melt from a deepsource, eruption to the Earth's surface,and the assimilationof countryrock. Physicalmodels of increasingcomplexity have been developed with emphasison threefundamental approaches. One is, given that large gradientsin temperatureand composition may occur,to specifyhow to applythermodynamic constraints so that coexistingliquid and solid compositionsmay be calculated.The secondis to leavethe differentiationtrend as the solutionto be found, i.e., to specifyhow coolingoccurs and to predictthe evolutionof the compositionof the residualliquid and of thesolid 'forming. The third is to simplifythe physics so that the effects of coupledheat and mass transfer may be studiedwith a reducedset of variables.The complex shapesof magmachambers imply that boundarylayers develop with densitygradients at various anglesto gravity,leading to variousconvective flows andprofiles of liquid stratification.Early studieswere mainly concerned with describing fluid flow in theliquid interior of largereservoirs, dueto gradients deveioped atthe margins. More recent work has focused onthe internal structure and flow field of boundarylayers and in particularon the gradientsof solidfraction and interstitial melt compositionwhich develop within them.Crystal settling may occurin a surprisinglydiverse rangeof regimesand may lead to intermittentdeposition events even with small crystal concentrations.Incorporating thermodynamic constraints in the studyof the dynamicsof settling hasonly just begun.Many dynamicalphenomena have been found using theoretical arguments, laboratoryexperiments on analogsystems, and numerical calculations on simplifiedchemical systems.However, they have seldombeen applied to naturalsilicate melts whose phase diagrams and importantphysical properties such as thermalconductivity and chemicaldiffusion coefficients remainpoorly known. There is a gapbetween model predictions and observations, as many modelsare designedto explainlarge-scale features and many observationsdeal with the local textureand mineral assemblages of the rocks.This reviewstresses the relevanceto the geological problemof the work carriedout in parallelin otherdisciplines, such as physics, fluid dynamics, and metallurgy. Introduction The geologicalobservations require the physicalprocesses of coolingand of separationof crystalsand residualliquids. The The studyof the physicsof the processesthat may take place tendencyhas been, however,to use the rocksto deducehow a in magma chambershas been a strikingly active researchfield reservoiroperates in a physicalsense. This approachavoids the during the last 20 yearsor so. The main purposeof this review is physicalproblem which hasits own logic. This review concerns to put the contributionof this work into somehistorical context. what causesthe systemto evolvein sucha way as to producethe The issuesof how heat transfer and crystallization take place observed differentiation trend, i.e., how cooling and have been discussedqualitatively, since the early days of crystallization are likely to develop from given starting researchon igneous differentiation [Bowen, 1921, !928; Hess, conditions.We will not attempt an exhaustivesummary of all 1960; Jackson, 1961; Wager, 1963; Wager and Brown, 1968]. recentwork on magma dynamicsbecause it coversa very wide The macroscopicphysical framework necessaryto treat such i'angeof phenomenabut will concentrateon two central difficult physical problemswas not available then. In a sense, questions.First, how do crystallizationand chemical evolution of many of the recentphysical studies have tackled quantitatively magmastake place, and second,what determinesthe rate of problemsthat had been outlined qualitatively many years ago. coolingof a magmabody? These questions are stronglyrelated However, we shall also seethat the focushas shiftedaway from because, on the one hand, chemical evolution of the magma thoseearly questions, as it hasbecome clear that partially dependson wherecrystallisation occurs and how separationof crystallized systems are exceptionally rich in new dynamic crystalsand residualmelt takesplace, while on the other hand, phenomena. the way in which heat loss takes place determines how Copyright1995 by the AmericanGeophysical Union. crystallizationproceeds. This couplingof coolingand chemical evolutionof the liquid, the phasechange, and the macroscopic Papernumber 95JB01239. transportphenomena makes the physicalproblem a difficult one 0148-0227195/95JB-01239505.00 to treat from first principles. 17,615 17,616 JAUPART AND TAIT: MAGMA CHAMBER DYNAMICS The difficulty involved may be illustratedby the following time, in equilibrium with a precise mineral assemblage.The example.One early model for igneouslayering was double- main physical idea invoked to explain magmaticdifferentiation diffusiveconvective phenomena [McBirney and Noyes, 1979; was the gq'avitationalsettling of crystalsfrom lessdense liquid. Turner, 1980]. In fluids in which two or more components The qualitative physical picture of a magma chamber was contributeto the densityand diffuse at differentrates, a kind of foundedon two principlepieces of evidence:that of the overall "staircase"stratification can develop,in whichlayers convect on stratigraphicrelations of mineralogicaland chemicalvariations vertical scales that are much less than the overall thickness of the and that of the cmnulate textures of the rocks. The textures were liquid body and are separatedby thin diffusive interfaces. interpreted as indicating that the crystals were depositedas a Various suggestionshave been madefor how suchlayering in sediment.The physical history of the formationof a rock was the liquid statemight be translatedin the final rock [e.g., Kerr subdividedinto a phaseof deposition,one of enlargementof the and Turner, 1982; Irvine, 1980]. This idea has not proved as depositedcrystals when closeto or at the top of the cumuluspile fruitful as might originally have been thought.The physical (so-calledadcumulus growth) and one of crystallizationof the reason,first pointedout by McBirney [1985] andMorse [ 1986], interstitialtrapped liquid [Wageret al., 1960].The mainphysical is that in a crystallizingsystem temperature and composition agentof masstransport during adcumulus growth was thought to cannotbe variedindependently because one is constrainedby the be chemical diffusion. The fact that the cumulate rocks became liquidusrelationship. In all the experiments,the liquids were progressivelymore evolved as a functionof stratigraphicheight superheated,and layering occurs because a significantamount of was taken to show that the whole volume of liquid in the thermal buoyancyis available [e.g., Chen and Turner, 1981]. chamber was evolving chemically because of crystallization This is unlikely in a system constrainedto lie close to its [Morse, 1979a,b]. It was thus supposedthat crystalsettling was liquidus. efficient in the sense that it occurred at a much faster rate than Research on the dynamics of crystallizationhas been very crystallizationof the body of liquid. active because it has applications in many different fields One additionalconsequence of theseideas is the requirement including metallurgy and the crystal growth industry. Thus thatthe partially crystallizedlayer at the floor of a reservoirnmst severalcollective booksand reviews have been publishedin the be thin, because the diffusive chemical flux is not large and recentpast [Loper, 1987;Huppert, 1990; Davis et al., 1992]. To cannot supply high temperature chemical components for set the stagefor the presentdiscussion, we first summarizethe adcumulusgrowth over large volumes[Wager, 1963]. This led basic framework adopted by petrological studies. This to important conclusions regarding the heat budget of frameworkhas been gradually adapted to accomodatenew facts, crystallizationat the floor. Taking into accountthe t•ct that the but its basictenets have beenkept. We alsoinclude a discussion bottom contact is initally cold, as shown by the common of the respectiveroles of physical,geochemical and petrological occurrenceof basalchill zones,the temperaturegradient through models.This is importantbecause the three approachesdo not a thick layer of adcumulate rocks nmst be directed downwm'd deal with the same pieces of evidence and differ in their and small. Thus, if heat is removed by conductionthrough the predictiveabilities. For example,there are few physicalmodels bottomcontact, the melt region whosetemperature is closeto the of igneous textures, and yet these constituteone of the key liquidus. where adcumulus growth occurs, is thick. This is observationsused by petrologists.Physical models are only able inconsistentwith the chemical budget considerationsoutlined to addressgross features of igneous