magmachamberThermalreactivationoflockedcrystalmushesintheuppercrustisafundamentalsteptowardsvolcanic EarthandPlanetaryScienceLettersxxx2011xxx CorrespondingauthorEmailaddresschristianhubereasg ID: 382753
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Thermo-mechanicalreactivationoflockedcrystalmushes:Melting-inducedinternalfracturingandassimilationprocessesinmagmasChristianHuber,OlivierBachmann,JosefDufekSchoolofEarthandAtmosphericSciences,GeorgiaInstituteofTechnology,Atlanta,UnitedStatesDepartmentofEarthandSpaceSciences,UniversityofWashington,Seattle,UnitedStatesarticleinfoArticlehistory:Received5September2010Receivedinrevisedform11February2011Accepted14February2011AvailableonlinexxxxEditor:R.W.Carlson magmachamberThermalreactivationoflockedcrystalmushesintheuppercrustisafundamentalsteptowardsvolcanic EarthandPlanetaryScienceLettersxxx(2011)xxx Correspondingauthor.E-mailaddress:christian.huber@eas.gatech.edu(C.Huber). EPSL-10805;NoofPages12 seefrontmatter©2011ElsevierB.V.Allrightsreserved. ContentslistsavailableatScienceDirect Pleasecitethisarticleas:Huber,C.,etal.,Thermo-mechanicalreactivationoflockedcrystalmushes:Melting-inducedinternalfracturingandassimilationprocessesinmagmas,EarthPlanet.Sci.Lett.(2011),doi:10.1016/j.epsl.2011.02.022 bealargenumberofmicrofracturesratherthandikes,as(1)thestressstateatthescalesampledbylargedikesisoverallcompressive(duemostlytomelting)and(2)thepresenceofalowviscositycompressiblephase(exsolvedvolatiles)decreasestheefciencyofthestresstransmittedtothefracturetip.Thesefracturingepisodesareexpectedtoloosenupasmallvolumefractionoftheoverlyinglocked-upmushand,consequently,increasethevolumeofmagmaopeneduptowholesaleconvection.Themainadvantagesofthesefracturingepisodesare(1)itincreasestheenergyefciencyrequiredtoreactivatecrystalmushes,asmeltingprovidesmostoftheoverpressure,and(2)itincreasestheaveragecrystallinityofthethesesystemsoncereactivated.Botharerequiredtobettertnaturalobservations(Huberetal.,2010bThismechanicalprocessoffracturingassociatedwithmeltingappliestomushreactivationasaself-assimilationprocess(defrostingtheoverlyinglockedmush,observedbothinvolcanic;e.g.,(Bachmannetal.,2002;Couchetal.,2001;Mahood,1990)andplutonicsequences;e.g.,(PatersonandJanousek,2008;RobinsonandMiller,1999;Wiebeetal.,2007)),butcanalsoplayaroleinassimilatingcountryrocksinthecaseofmagmaevolutionbyAFC(AssimilationFractionalCrystallization;numerouspapers,butseee.g.,(Bowen,1928;Daly,1933;DePaolo,1981;Taylor,1980)).Asblocksofcrystallinewallrocksareincorporatedintohotmagmas,themechanismofmelting-drivenfracturingwillleadtoenhanceddisaggregation,allowingforrapiddisseminationofsmallxenolithsandxenocrystsinthemagma.Inthenextsection,wepresentthephysicalmodelusedinthispaper,describingshortlythethermalmodel(basedon(Huberetal.,2010a))andintroducingthemechanicalmodel(basedandmodiedfrom(HuppertandWoods,2002)).Wealsodiscusstheexpectedfracturingmechanismofthemush(largenumberofmicrocracksratherthanoneorafewlargedikes)onceacriticaloverpressureisreached.Finally,wepresentresultsfromournumericalcalculationsanddiscusstheimplicationsinthescopeofthereactivationoflargecrystal-richmagmabodies.2.PhysicalmodelThissectiondescribesthemodelusedtosolveforthethermalandmechanicalevolutionofasiliciccrystallinemushunderplatedbyanintrusionofmoremacmagma.Westartbydiscussingthemultiphaseheattransferbetweentheintrusionandthemushandproceednexttoasimplemechanicalmodelbasedonmassconservationandlinearelasticitytodescribetheevolutionofthepressureduringthereactivationofthemush.2.1.ThermalmodelThethermalmodelissimilarto(Huberetal.,2010a)(illustratedschematicallyinFig.1).Forsimplicity,theintrusionisemplacedatonceandthevolumeratiobetweenthemushandtheintrusionisafreeparameterinourcalculations.Thecompositionoftheintrusionissettoandesiticandthemushtodacitic.Themushisassumedtobeinitiallysaturatedwithvolatilesandweneglectvolatiledissolutionorexsolutionassociatedwithreheatingandpartialmeltingofthemush.Wealsoassumethat,bythetimetheintrusionreachesitsemplacementdepth(2×10Pa),itsvolatilefractionmostlyconsistsofwaterasalargefractionoftheCOalreadydegassedandescapedtowardsthesurface.Therateofcooling,crystallizationandvolatileexsolutionintheintrusioniscontrolledbytheheattransferinthemush.2.1.1.UnderplatingmagmaWeuseasimpliedrelationshiptodescribetheheatbalancefortheunderplatingintrusion dTdt= |{z}sensibleheat Lici |{z}latentheatwherethesubscriptreferstotheintrusion,andarerespectivelythethickness,thelatentheatofcrystallization,thespeciheat,thedensityandthecrystallinityoftheunderplatingmagmabody.outistheheattransferfromtheintrusiontothemushandthereforecouplesthemagmabodyintermsofheattransfer.Thisheatbalanceequationassumesawell-mixedintrudingmagmawithnegligiblethermalgradientswhichisarelativelygoodapproximationwhenauidbodywithstrongtemperaturedependentviscosityconvects.Weusestagnant-lidconvectionscalingstocalculatetheconvectiveheatoutoftheintrusionusingatemperatureandcrystallinity-dependentviscosity(Huberetal.,2010a).Thecrystallinitytemperaturerelation-shipforanandesiticintrusion(likelycompositionforrechargeincontinentalarcs)iscalculatedwithMELTS(GhiorsoandSack,1995usingthemajorelementcompositionlistedin(Paratetal.,2008)fortheHuertoandesite(SanJuanVolcanicField,Colorado).Weassumeaninitialwatercontentof6wt.O.WealsouseMELTStoparameterizetheexsolutionofvolatiles(wateronlyinthiscase,seesectionbelow)asfunctionoftemperature(see(Huberetal.,2010a)).WeassumethatthetransportofexsolvedvolatilesfromtheintrusiontothemushcanbedescribedbyamultiphaseDarcy arethepermeabilityofthemagmaandtherelativepermeabilityforthevolatilephase,respectively,isthedensitycontrastbetweenthemeltandthevolatilephaseandistheaccelerationduetogravity.ThepermeabilityisrelatedtothecrystallinitybytheCarmanKozenyrelation(Bear,1988 wheretheconstantissetto2×10,leadingtoapermeability=10=0.5.Manyempiricalandtheoreticalexpressionshavebeenderivedforthedependenceoftherelativepermeabilityonthevolatilevolumefraction,weusethefollowingexpressionisthevolumefractionofexsolvedvolatiles.Foramoredetaileddescriptionofthevolatiletransportmodel,thereaderisreferredto(Huberetal.,2010a2.1.2.CrystalmushThemushabovetheintrusionhasinitiallyacrystallinityrangingfrom51to67.Wesolveforthemassconservationofvolatiles(initiallyexsolvedfromtheintrusion) g1mushgt= isthecrystallinityofthemush,istheporevolumefractionoccupiedbythevolatilesandistheoftheDarcyvelocityforthevolatilephaseandisparalleltogravity(increasesupwards).Theboundaryconditionattheinterfacebetweenthemushandtheintrusionrequiresmatchingthevolatileux(seeEq.).Weassumeherethatthemeltisvolatile-saturatedandthatnofurtherdegassingordissolutionofvolatilesoccurswithinthemush.TheuxofvolatilesisobtainedfromamultiphaseDarcy kmushkrmushH2O C.Huberetal./EarthandPlanetaryScienceLettersxxx(2011)xxx Pleasecitethisarticleas:Huber,C.,etal.,Thermo-mechanicalreactivationoflockedcrystalmushes:Melting-inducedinternalfracturingandassimilationprocessesinmagmas,EarthPlanet.Sci.Lett.(2011),doi:10.1016/j.epsl.2011.02.022 istheaccelerationduetogravityandiscountedpositivearerespectivelythepermeabilityandrelativepermeabilityofthemushforthevolatilephase.Finally,thedynamicviscosityofthevolatilephasewhich,forsimplicity,wasxedhereto10Pas(Assaeletal.,2000).Formoredetailsonthetreatmentofthemultiphasepermeability,thereaderisreferredtoHuberetal.,2010aWeassumeasimplepower-lawforthecrystallinityrelationshipthatcapturesthemainfeaturesofcalc-alkalinedaciticmagmas(Huberetal.,2010a;Huberetal.,2010b).Thecrystallinityinthemushisgivenby arethesolidusandliquidustemperatures,respectivelysetto700and950°C.Themeltingofthemushisobtainedbysolvingtheenergybalancethatincludesheatdiffusion,absorptionoflatentheatduringthepartialmeltingofthemushandadvectionofheatbythevolatile t= zcgH2Oud;zT zk TzsL InEq.,thespecicheatofthevolatilesisassumedconstant(3880J/kgK)(Lemmonetal.,2003iscalculatedwiththeedRedlichKwongequationofstate(HalbachandChatterjee,1982;Huberetal.,2010a),andistheaveragedensityofthecrystallinephasesubjectedtomelting.Eq.assumesthatthevolatilephaseislocallyinthermalequilibriumwiththemeltandcrystals,whichassumesalowPecletnumber(i.e.Pe=1,Ristheaverageporeradiusandtheaveragethermaldiffusivity)whichisfoundtobeconsistentwithournumericalresults.Thedensity,cheatandthermalconductivityofthesolidmixturearecalculatedwith m1mushSgm+smushcs+H2O1mushgcgm1mushSgsmush+H2O1mushgð10Þk 12 1g2kg+kg+ 1Sgkg+km+ 2kg+ks0@1A12kg8��:ð11Þ+ 1g2ks+kg+ 1Sgks+km+ wherethesubscriptrefertosolid,meltandvolatilesrespectively.ThemixturethermalconductivityisobtainedusingtheWalpolebounds(HashinandShtrikman,1963;Torquato,2001Table1liststhedifferentparametersusedinthephysicalmodel.2.2.MechanicalmodelInthefollowingsectionwederivetheequationsfortheevolutionofpressurefrommassconservation.Weseparatethetreatmentforthepartofthemushopenedtoconvection(wherethecrystallinityislowerthan0.45)fromthepartofthemushstillrheologicallylockedoverlyingit.2.2.1.ReactivatedpartofthemushWeuseananalogoustreatmentasin(HuppertandWoods,2002Frommassconservation,theopenedpartofthemushofvolume Fig.1.Schematicrepresentationofthecoupledmushintrusionsystem.Thetwomagmasexchangeheatandthemushissubjectedtoinjectionsofvolatilesexsolvedfromtheunderlyingintrusion(Huberetal.,2010a,2010bC.Huberetal./EarthandPlanetaryScienceLettersxxx(2011)xxx Pleasecitethisarticleas:Huber,C.,etal.,Thermo-mechanicalreactivationoflockedcrystalmushes:Melting-inducedinternalfracturingandassimilationprocessesinmagmas,EarthPlanet.Sci.Lett.(2011),doi:10.1016/j.epsl.2011.02.022 ,whereisthesurfaceareaandthethicknessofthepartofthemushthatmeltedtoacrystallinitylowerthan0.45,obeys d Vdt= dVdt+V d dt=QJpS :ð13ÞHere isthemultiphasedensityaveragedoverthevolumeofthereactivatedpartofthemush = wherethesubscriptsreferrespectivelytocrystals,silicatemeltandexsolvedvolatiles,isthelocalporosityinthereactivatedvolumeandthelocalvolatileporevolumefraction.InEq.representsthesourceofmassassociatedwiththeinjectionofvolatilesfromtheunderlyingintrusionandrepresentstheuxoutterm k2 beingtheaveragepermeabilityandtwo-phaseviscosity(silicatemeltandvolatiles)attheinterfacebetweenthemushanditsreactivatedpart.Theseparameterswillbedenedinthenextsection.ThevolumechangetermofEq.accountsforthevolumechangeassociatedwithpressurechanges dVdt= Vr istheaveragebulkmodulusoftherockssurroundingthereactivatedpartofthemush(whichtakesintoaccountalsothestiffmushaboveit).Usingthechainruletoexpandthevariationofaveragedensitywithtimeintermsofporosityandpressurechanges d dt= p dpdt d dt= 3 dpdt d isthemultiphaseaveragebulkmodulusobtainedwiththeHashinWalpolebounds(thesuper-scriptreferstothenumberofphasesinvolved,crystals,meltandvolatiles)(HashinandShtrikman,1963;Torquato,2001 12 1 s+ 43Gmin+ Sgg+ 43Gmin+ 1 Sgm+ 43Gmin0B@1CA1 43Gmin+ 1 s+ 43Gmax+ Sgg+ 43Gmax+ 1 Sgm+ 43Gmax0B@1CA1+ isunderstoodasavolumetricaverageofvariabletakenoverthereactivatedpartofthemush(seeEq.respectivelytheminimumandmaximumshearmodulustakenoverthethreephases(respectively0andabout4×10Pa).RearrangingthedifferenttermsofEq.weobtain dpdt= 1r+ 131 Q+ d dtVJpA Oursimplemodeldoesnotaccountforviscoelasticeffectssuchhasviscousrelaxationofthesurroundingcrust.Theseeffectsaretestedbyrunningthecalculationsfortwoend-memberchoicesofhost-rockbulkmodulus.2.2.2.MushThepartofthemushwithacrystallinityabove0.45istreatedseparatelyasthesolidfractionmodiesitsrheologicalbehaviorandthecrystalfractionformsarigidframework.Thelocalmassconservationequationbecomes d = ddtjT+ d dt= uzz+ ddtjp;ð20Þwhere isnowthelocaltwophasevolume-averageddensity(silicatemeltandvolatiles),isthemultiphaseuidmixtureverticalvelocity, ddtjTand arerespectivelytheporevolumechangesassociatedwithpressure(xedtemperature)andwithmelting(xedpressure). Table1Listofparametersandsymbols.SymbolDescriptionValueUnitscheatforphaseAccelerationduetogravityMushthickness2000mThermalconductivityatintrusionmushinterface2W/m/KThermalconductivityofvolatile,crystalsandmelt0.31,1.4,and2W/m/KPermeabilityandrelativepermeability(mushorintrusion)Latentheatofcrystallization(intrusion/mush)270kJ/kgSurfaceareaofcontactbetweenintrusionandmush2×10porevolumefractionoccupiedbyvolatilesInitialtemperatureofintrusion850°CVerticalcomponentofDarcyvelocityforvolatilephase(mush)Volumeofratiointrusiontomush0.1,0.25,0.33,0.5and1Expansioncoefcient(thermalandcrystallinity)3×10BulkmodulusofphaseCrystallinityofintrusion/mushCriticalcrystallinity0.45Thermaldiffusivity10DensityofagivenphaseDynamicviscosityofagivenphasePasC.Huberetal./EarthandPlanetaryScienceLettersxxx(2011)xxx Pleasecitethisarticleas:Huber,C.,etal.,Thermo-mechanicalreactivationoflockedcrystalmushes:Melting-inducedinternalfracturingandassimilationprocessesinmagmas,EarthPlanet.Sci.Lett.(2011),doi:10.1016/j.epsl.2011.02.022 Recastingdensityvariationsintermsofpressurevariations(recognizingherethatthemeltingtermisalreadyaccountedforin ),weget dT= matrix wherematrixisthebulkmodulusofthesolidmatrix.UsingDarcy'sequationfor,weobtain dp matrix 21 1 z k2 pz o Thelocalaveragesarecalculatedwith Sgg+ 1Sgm0@1A1;ð23Þand2= 12f Sgg+ 2g+ 1Sgm+ 23g0B@1CA1 23g+ Sgg+ 23m+ 1Sgm+ 23m0B@1CA1 arerespectivelythedynamicviscositiesofthevolatileandsilicatemeltphases.Wenotethatthesepropertiesdependontwophases(meltandgas)insteadofthreeasinthereactivatedpartofthemush,becausecrystalsherearenolongerassumedtobepartofthesuspension,butformarigidframework.Theeffectofthesolidfractiononthepressureeld(compactionforexample)isincorporatedintothetermofEq..Similarlytheresistancetotheowofmeltandgasisnotaccountedforinthemultiphaseviscosityasforthereactivatedpart,butisintroducedbythepermeabilityinEq..Themechanicalandthermalmodelsarecoupledbytheequationofstateforthevolatilephase(hereusingaedRedlichKwongrelationship,(Huberetal.,2010a))thatrelatesthepressureandtemperatureinthevolatilephasetoitsdensitywhichinturnsaffectthevolatilesaturation.Themechanical,thermalandtransportpropertiesinthemusharestronglycontrolledbythevolatilephasesaturation.2.3.FracturingversusdikingThepressureinthemushincreasesduringthereactivationbecauseoftwoeffects(thersttwotermsoftheright-handsideof).First,theinjectionofvolatilesfromtheintrusionincreasestheoverallmasscontainedinthemushsystem.Duetothedifferenceofdensitybetweenthevolatilephaseandtheotherconstituentsofthemagmaanditsgreatercompressibility,thiseffectremainsrelativelyweakaslongastheinjectionrateisnottooelevated.Second,thedensitydifferencebetweenthemeltandcrystals(about10)andthelowcompressibilityofthesetwophasesleadtoanincreaseofpressureresultingfrommelting(averagedensityofthemagmadecreases).Theoverpressurethereforebuildsupwherethemeltingisthemostintense,nearthemushopeningfront.Theoverpressureisassumedtobemostlyhomogeneousinthereactivatedpartofthemush,however,inthelocked-uppart,theporepressurediffusesupwardfromthereactivatedpartalongthehydraulicgradient.Themultiphasehydraulicdiffusivityofthemush(whichdependsonthepermeabilityofthemush,theviscosityofthemagmamixtureandtheeffectivecompressibilityofthemushhostrocksystem)isexpectedtoreducethebuild-upofoverpressureinthereactivatedpartofthemushaswellasthepressuregradientbetweenthetwopartsoftheWeassumethatthelocked-upmushbehavesasabrittlesolid,which,aswewillseebelow,isconsistentwithournumericalresults,theperiodbetweenfracturingepisodesbeingusuallymuchshorterthantheviscousrelaxationtimescaleforthemush(Karlstrometal.,2010)).Wethereforeexpectthatiftheoverpressurereachesacriticalvalue,crackswillstarttopropagate.(Rubin,1998showedthattheexpectedoverpressuretopropagatedikesinpartiallymoltenrocksisabout10to10Pa.Foramushataconningpressureofabout2kb,thefracturethresholdisonlyabout5oftheeffectivepressureinthemushandisthereforenottoodifculttoreachforadynamicalsystemwithphasechangesandinjectedwithvolatilesfromadifferentmagmaticsource.Weassumethatonceacriticaloverpressureisreached,afracturingeventistriggered,reducingthepressureinthemush.Avalidquestionsubsists:onceafractureisinitiated,doesitgrowtoformadike?Weusetwoqualitativeargumentsthatargueforanotherpossibleprocessthandiking.Mid-sizetolargesilicicmushhavealargeaspectratio(greaterwidththanthickness),consequentlymostoftheoverpressurizedmushisnotexpectedtobesubstantiallyinuencedbytheedgesofthemagmabody.Fracturesareexpectedtoinitiateattheweakestpointsboundingthereactivatedmush.Weassumethatthepartofthemushjustabovethereactivationfrontistheweakestasitscrystallinitybarelyexceedsthelockingpointthreshold.Bydenition,themushatthecontactwiththereactivationfrontisattherheologicaltransitionbetweenauidandbrittlesolid.Theinitiationofcracksisexpectedtoloosenuptheweakestpartofthemushbeforethefracturesgrowtoformdikes.Thestrengthofthelowermostpartofthelockedmushisexpectedtoincreasebecauseofthesharpcrystallinitygradientsabovethemeltingfront,whichwouldtendtodeectpropagatingcrackshorizontallyastheypenetratehighercrystallinityenvironments.Apossiblescenarioisthedevelopmentandopeningofmicrofracturesatthecontactbetweencrystalsorientedsub-paralleltothenormalofthemushfront(seeFig.2foranillustration).Theincreasedpore-pressureisalsoexpectedtoreducethestrengthofthemushatthemeltingfront.Asthelargestgradientsofpressureareexpectedtobelocatedatthefrontbetweenthereactivatedandlocked-upmush,wherevolatilesareexpectedtobepresent,initiatedcracksopenandareexpectedtollupmoreefcientlywithvolatilesowingtotheslowresponseoftheveryviscousmelt.Thecracksshouldthereforecontainalargefractionofvolatileswhichismuchmorecompressiblethanmeltorcrystals.Inourmodel,unlike(MenandandTait,2001),theopeningofcracksispressure-driven.Thepropagationoftheoverpres-sureatthecracktipisthereforeexpectedtobelessefcientthanforacracklledwithanincompressibleuid.Insummary,wehypothesizethatoncetheoverpressureinthemushreachesacriticalvalue,amicrofracturingeventistriggered,wherealargenumberofcloselyspacedcracksareinitiated.Thesecracksdonotpenetrateasdeepinthemushaswewouldexpectforatypicaldike.Theoverpressureisrelievedbecauseofthehighdensityofcracksthatleadstothelossofstrengthofthelowermostpartofthelocked-upmush(seeFig.2).Apartofthemushisthereforeassimilatedmechanicallyintothereactivatedpart,thevolumeofwhichdependsontheabilityofthisprocesstorelieveoverpressure.AnotherwaytounderstandthisprocessistoviewthemicrofracturingeventasasinkofoverpressureinEq.associatedwiththesuddenchangeoftheaveragedensityofthemagmainthereactivatedpartofthemush.Theassimilationresultsinanincreaseofaveragecrystallinityinthereactivatedpartandconsequentlyanincreaseindensity.Thedropinpressureassociatedwiththemicrofracturingeventisgivenby C.Huberetal./EarthandPlanetaryScienceLettersxxx(2011)xxx Pleasecitethisarticleas:Huber,C.,etal.,Thermo-mechanicalreactivationoflockedcrystalmushes:Melting-inducedinternalfracturingandassimilationprocessesinmagmas,EarthPlanet.Sci.Lett.(2011),doi:10.1016/j.epsl.2011.02.022 istheeffectivebulkmodulus 1r+ Thedifferenceinaveragemagmadensitybeforeandafterthecrackis = after before= mushVfrac+ openVopenVopen+Vfrac open;ð27Þwhere istheaveragecrystallinityofthemushjustabovethereactivationfront, istheaveragedensityinthereactivatedpartofthemush,isthevolumeofmushreactivatedbeforethefracturingepisodeandisthevolumeoflocked-upmushassimilatedbecauseofthefracturingevent.UsingEq.togetherwithEq.,wecanwrite peff mush open Assumingforsimplicitythattheaveragecrystallinityandvolatilesaturationinthereactivatedpartofthemusharerespectively0.3and0.2,andusinganaveragecrystallinityof0.5forthemushjustabovethereactivatedfront(usingthesamevolatilesaturation),then mush= 4,andEq.canbereducedapproximatelyto InEq.isassumedtobeabout10Pa(overpressureisfullyrelievedbyfracturing).Thismicrofracturingprocessactslikeaself-assimilationmecha-nismdrivenbythemechanicalenergy(overpressure)associatedwiththephasechangeduringthereactivationofthemush.Oncethefragmentsofthelocked-upmushareassimilatedintheconvectingpartofthemush,theenergyefcientreactiveassimilationprocessesdescribedby(Beardetal.,2005)canreducethesizeofthefragmentsfromasizeequivalenttothepenetrationdepthofcracks(cmscale,seeresults)tothescaleofcrystals.Astheassimilatemixesinamagmawiththesamecomposition,thisprocessispetrologicallytransparent.3.NumericalmodelThethermalmodelingissimilarto(Huberetal.,2010a).The1Denergyandmassconservationequations,togetherwiththeconstitu-tiveequationsforthecrystallinitytemperaturerelationships,thepermeabilityporosityrelationshipandthemultiphasepermeabilityaresolvediterativelyateachtimestep.Eqs.(19)and(22)introducedintheiterativeschemeforthemushevolutiontocalculatetheoverpressureevolutioninthereactivatedandlocked-uppartofthemushrespectively.Asaresultoftheinjectionofvolatilesfromtheintrusionandmelting,thepressureinthemushincreases(seeEq.).Weuseathresholdvaluefortheoverpressureof=100Pabeyondwhichafractionofthelocked-upmushisexpectedtoexperiencebrittlefailure(fracturing).Eachfracturingepisodeisexpectedtoefrelievetheoverpressureofthesystem(resetto0).Ournumericalmodeldoesnotdirectlysolvefortheeffectoffracturingontheevolutionofthemush,butallowsustocalculatethefrequencyof ppt timeppt timeppt pppReactivated mushLocked up mush Overpressure Overpressure ab Fig.2.Ourconceptualmushfracturingmodel.Theupperrowillustratesthetermporalevolutionofthemushandthebuild-upofoverpressureassociatedwithmelting.Oncetheoverpressurereachesacriticalvalue,theweakestpartofthemushbreaksandisassimilatedbythereactivatedpart.Thelowestrowdepictsschematicallythefracturingprocessatthecrystal-scale.C.Huberetal./EarthandPlanetaryScienceLettersxxx(2011)xxx Pleasecitethisarticleas:Huber,C.,etal.,Thermo-mechanicalreactivationoflockedcrystalmushes:Melting-inducedinternalfracturingandassimilationprocessesinmagmas,EarthPlanet.Sci.Lett.(2011),doi:10.1016/j.epsl.2011.02.022 fracturingepisodesandestimatethevolumeofmushaffectedbythemicrocracks.4.ResultsWecalculatedthethermalandmechanicalevolutionofthemushfortherst1000yearsaftertheemplacementofanandesiticintrusion.Weassumeapowerlawrelationshipforthecrystallini-temperaturerelationshipofthemush(power-lawexponentof0.5inEq.)andamagmavolumeratio(intrusion/mush)of1/10,1/4,1/3,1/2and1.Theinitialcrystallinityofthemushwasassumedtobe0.505,0.55,0.6,0.65and0.67.Theresultsshowingthetemperature,pressureandvolatilesaturation(porevolumefraction)prolesobtainedafterathousandyearsforanintrusiontomushvolumeratioof1/3,aninitialmushcrystallinityof0.55andassumingthebulkmodulusofthehost-rockstobe10PaarepresentedinFig.3Fig.3ashowsthattheheattransferredbytheintrusionreachedabout1/5ofthethicknessofthemush,whichisconsistentwiththeporosityprole(melting)showninFig.3b.Thethirdpanel,Fig.3c,showsthevolatilecontentwhichpenetrateddeeperintothemushthantheheatassociatedwiththeintrusion.AsdiscussedbyHuberetal.,2010a),themaximumvolatilesaturationobservedis0.2,consistentwiththechoiceofcriticalsaturationthresholdwherevolatilesbecomemuchmoremobile.Thelastpanel(d)showstheoverpressureinthemush.Inthereactivatedpartofthemush,theoverpressureishomogenousat7×10Pa.Thepenetrationdistanceinthelocked-upmushiscontrolledbythehydraulicdiffusivityofthemagmamixtureinthelocked-upmush.Theoverpressuredoesnotpenetratedeepintothelocked-upmushbecauseofthelargeviscosityofthemagmaandthemoderatepermeabilityofthemush(setupheretoatacrystallinityof0.5).Thefrequencyoffracturingepisodescanbededuceddirectlyfromthecalculations.Eachtimetheoverpressurereachesthecriticalthresholdcorrespondstoafracturingevent,afterwhichtheoverpressureisresettozero,beforebuildingupforthenextevent.Fig.4ashowstheperiodoffracturingeventsversustimeforamushwithinitialcrystallinityof0.55,withanintrusiontomushvolumeratioof1/3andassumingahost-rockbulkmodulusof10Pa.TheperiodincreaseswithtimeaccordingtopowerFig.4bshowsthepositionofthemeltingfrontcoincidingwiththetransitionfromarheologicallylockedmushtoitsreactivatedpart.Thelawweobserveisconsistentwiththesimplicationmadeinthethermalmodel,whereweassumedtheheattransferinthemushtobeconductiveexceptfortheadvectivetransferassociatedwiththeriseofbuoyantvolatiles.Thesteppednatureoftheresultshereisduetothespatialresolutionlimitationofthenumericalmodel,reasonablytsarehowevereasytoobtaintogetanaveragemeltingtrend.Fig.5showsthattherelationshipbetweenthefracturingperiodandtimedependsstronglyonthevolumeratioofthetwomagmasThefracturingfrequencyissignicantlyhigherforlargerintrusions.Theeffectoftheinitialmushcrystallinity(notshownhere)ishowevermuchmoretenuous.UsingthepowerlawsobtainedbyttingtheprogressofthemeltingfrontandtheevolutionofthefracturingperiodwithtimetogetherwithEq.,wecancalculatetheeffectoffracturingeventsonthereactivationofcrystalmushes.Theevolutionofthepositionofthemeltingfront(Fig.4b)allowsustoestimatethegrowthofthereactivatedfractionbetweenfracturingepisodes.Thegrowthofthe 750 760 770 780 790 800 810 820 830 840 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 T [C] 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Porosity 0 0.05 0.1 0.15 0.2 0.25 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sg (volatile pore fraction)distance from intrusion 0 10 20 30 40 50 60 70 80 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 5 Pa] Fig.3.lesoftemperature(a),meltfraction(b),volatilesaturation(c)andoverpressure(d)withverticaldistancefromthemushintrusionboundary.Theseprolesshowthestateofamushwithaninitialcrystallinityof0.55,underplatedbyanintrusionwithavolumethreetimessmallerthanthemushafter1000years.Thehostrocksbulkmodulusissethereto10C.Huberetal./EarthandPlanetaryScienceLettersxxx(2011)xxx Pleasecitethisarticleas:Huber,C.,etal.,Thermo-mechanicalreactivationoflockedcrystalmushes:Melting-inducedinternalfracturingandassimilationprocessesinmagmas,EarthPlanet.Sci.Lett.(2011),doi:10.1016/j.epsl.2011.02.022 reactivatedportionofthemushcanbeobtainedwiththefollowingiterativeprocedure|{z}|{z}priortofracturingn )isthevolumeofreactivatedmushafterthefracturingattimeistheperiodbetweenfracturingepisodearethetwottingconstantsobtainedfromthemeltingfrontpropagation.Thesetofperiods)arealsoobtainedbyattingprocedure(seeFig.4a).Fig.4showstheeffectofthefracturingprocessonthereactivationofamushforachoiceof=1/2,amushinitialcrystallinityof0.67andassumingthatthebulkmodulusofthehostrocksis10Pa.Wequantifytheefciencyoftheself-assimilationprocess(fracturing)bycomputingtheratioofvolumereactivatedwithandwithoutfracturingepisodes(seeFig.6 meltingWeobserveingeneralthattheefciencyincreasesstronglyatearlytimes(values1)anddecreasessteadilyafterwardsalthoughremainingsubstantiallygreaterthan1.ThelastpanelofFig.6showsthedepthoverwhicheachfracturingepisodepenetratesinthelockedpartofthemush.Weseethatthecracklengthsaretypicallyunderthemeterscale.Althoughthevolumeassimilatedduringeachcrackingepisodeisrelativelysmall,thenumberoffracturingeventsislargeowingtothelowcriticalthresholdforfracturing(10especiallyshortlyaftertheemplacementoftheintrusion.Thesegeneralfeaturesarecommontoallthecalculationsweconducted,Fig.7showssomeofourcalculationsfor(1)aconstantmagmavolumeratio=1/3inthersttworowsand(2)aconstantcrystallinity(=0.6)forthelasttwo.Thedependenceofthevolumeofmushreactivatedontheinitialcrystallinityofthemushiscomplexbecauseofthecompetitionbetweentwoeffects.Thevolumeofmushreactivatedbymeltingalonetendstobesmallerforhighinitialcrystallinity,asthepropagationofthemeltingfrontisslower.Thegreateramountofmeltingrequiredinducesahigherfrequencyoffracturationepisodes,however,eachofthesefracturationeventleadstoasmalleramountofassimilatedmushfromEq.Wecalculatedthefracturingef=1000years)forarangeofinitialmushcrystallinity(0.51,0.55,0.6,0.65and0.67)andarangeofintrusiontomushvolumeratio=1/10,1/5,1/3,1/2and1.Fig.8showstheeffortwodifferenthost-rockbulkmodulusvalues,therstone(a)representsthecasewherehostrocksremainedrigidandthesecond(b)representstheotherend-memberwhenheattransferanddeformationduringtheemplacementoftheintrusionmadethehostrocksmuchweaker.Wearbitrarilychoseaneffectivebulkmodulusconsistentwiththechoiceofhost-rockandmultiphasemagmabulkmoduliforthesetwoend-membercases.Weobservethatthemajorcontrolontheefciencyisthevolumeofintrusionemplacedratherthanthecrystallinityofthemushpriortomelting.Theefciency,althoughtimedependentandmonotonicallydecreasingafterashortamountoftime(lessthanayearfromourcalculations),remainssubstantiallygreaterthan1formostcases.5.Discussion5.1.Mechanicalself-assimilationThenon-linearinteractionbetween(1)melting,whichaffectstheproportionsofthethreephasesaswellasthemobilityofthephases,(2)themasstransferofvolatilesand(3)thepressureevolutionofthesystem,whichaffectsthedensityandsaturationofthevolatilephase(hencetheirmobility),makesanintuitivepredictionoftheevolutionofamushduringitsrejuvenationparticularlychallenging.Inthissection,weattempttoextractabetterunderstandingoftheresultsweobtainedfromthenumericalexperiments.AsobservedfromEq.,theabilityofthereactivatedfractionofthemushtobuildupsomeoverpressuredependsonmanyfactors.Thetworstfactorsarethesourcetermsforthepressureincrease,the 10 20 30 40 50 60 70 80 0 100 200 300 400 500 600 700 800 900 1000 Fracturation event period [yrs]time [yrs]calculations 0.036 t1.12 0 20 40 60 80 100 120 140 160 180 0 100 200 300 400 500 600 700 800 900 1000 Distance from intrusion [m]time [yrs]calculations 4.3 t0.5 b Fig.4.(a)Periodbetweenfracturingepisodesversustime(shownwithapowerlawand(b)thepropagationofthemeltingfrontwithtime(alsowitht).Theinitialcrystallinityofthemushis0.55,theintrusionmushvolumeratiois1/3andthehost-rockbulkmodulusis10Pa.Thesteppednatureofthemeltingfrontpropagationresultsfromtherelativelylowspatialresolutioninthemush(seethetextformoredetails). 10 20 30 40 50 60 70 80 0 100 200 300 400 500 600 700 800 900 1000 fracturation period [yrs]time [yrs]Vr r r r r Fig.5.Illustrationofthedependenceoftheperiodbetweenfracturingepisodesonthemushvolumeratio.Thesecalculationsaredoneforamushwithaninitialcrystallintiyof0.6andahost-rockbulkmodulusof10C.Huberetal./EarthandPlanetaryScienceLettersxxx(2011)xxx Pleasecitethisarticleas:Huber,C.,etal.,Thermo-mechanicalreactivationoflockedcrystalmushes:Melting-inducedinternalfracturingandassimilationprocessesinmagmas,EarthPlanet.Sci.Lett.(2011),doi:10.1016/j.epsl.2011.02.022 liquidphasechangeassociatedwithmeltingandtheinjectionofvolatilesfromtheintrusion.Theresultsofournumericalcalculationspointstronglytomeltingasthemainsourceforthepressureincrease(testedbyremovingsequentiallyeachtermoftherighthandsideof).Themoresubtleeffectoftheinjectionofvolatilescanbeexplainedwiththefollowingargument.Asthevolatilecontent(and 10001500 40 60 80 100 120 140 160 0 2 4 6 8 12 14 16 18 20 1000 1500 0.2 0.3 0.4 0.5 0.6 10-4104time [yrs]time [yrs]time [yrs]Mush openingReactivation efficiency vs timeFracturation distance Fig.6.Resultsobtainedforamushinitiallywith67%crystals,anintrusionmushvolumeratioof1/2andahost-rockbulkmodulusof10Pa.(a)showsacomparisonbetweenthetemporalevolutionofthepositionofthemeltingfrontwithandwithoutfracturing.(b)showstheevolutionof(t),seeEq..(c)showsthepenetrationdistanceofeachfracturingepisodecalculatedwithEq. Htot (m)Htot (m)Htot (m)time (years)time (years)time (years) Vr=1/3effeff eff 100 150 200 100 150 200 2 4 6 8 100 150 200 0.5 0200400600800100002004006008001000 =0.65 =0.60 =0.67 =0.55 eff eff eff eff eff eff eff eff eff eff 2 3 4 5 eff eff eff =0.65=0.60=0.67=0.55=0.505 =0.65=0.60=0.67=0.505 Fig.7.Examplesofresultsobtainedforthetemporalreactivationofcrystalmushes.Thersttworowsshowcalculationsconductedforaxedintrusionmushvolumeratioof1/3andthelasttworowsforaxedinitialmushcrystallinityof0.6.C.Huberetal./EarthandPlanetaryScienceLettersxxx(2011)xxx Pleasecitethisarticleas:Huber,C.,etal.,Thermo-mechanicalreactivationoflockedcrystalmushes:Melting-inducedinternalfracturingandassimilationprocessesinmagmas,EarthPlanet.Sci.Lett.(2011),doi:10.1016/j.epsl.2011.02.022 thereforethetotalmass)inthemushincreases,theeffectivebulkmodulus,morespecicallytheHashinWalpolebounds)forthebulkmodulusofthemixture,decreases.Inotherwords,theinjectedvolatilephaseincreasethecompressibilityofthemagmamixtureandthepressurebuild-upbecomeslessefAnotherimportantfactortestedduringournumericalcalculationsisthehost-rockbulkmodulus.Onecanimaginetwoendmembercases,(1)wherethehost-rockarestrongandnotaffectedbythemagmaticsystem(wechose=10Pa),and,(2)acasewherethehost-rocksaresignicantlyweakerbecauseoftheheatofthemushsystemaswellaspossiblysomemechanicalweak-eningassociatedwiththeemplacementofmagma(=10Thelastvariablewetestedthatcanhaveasignicantimpactonthemushbehavioristhevolumeoftheinjection(againassumedtobeemplacedatonceforsimplicity),orsimilarlythevolumeratiobetweentheintrusionandthemush.Ourresultssuggestthatthevolumeratioofintrusiontomushexertsthemaincontrolontheefciencyoffracturingepisodestoassistthereactivationofthemush.Theimportanceofthevolumeofintrusionliesinthefactthatamorevoluminousandesiticintrusion(givenacertainemplacementtemperature)providesmoreenthalpytothemush.Italsoallowstheintrusiontoremainatagreatertemperature(closertotheemplacementtemperature)foralongertime.Theheatuxfromtheintrusiontothemushremainsimportantforalongerdurationthanforsmallerintrusions.Asecondarypositiveeffectisthatagreaterintrusionwiththesameinitialweightfractionofdissolvedvolatilesisexpectedtobeabletoexsolve(bysecondaryboiling)andtransfermorevolatilestothemushoverthecourseofitscooling.However,thecoolingratebeingsmallerforlargerintrusions,thetransferofvolatilesfromtheintrusiontothemushisexpectedtotakemoretime.Thecrystallinityofthemushpriortothereactivationplaysamorecomplicatedroleinthereactivationofthemush.Afterareactivationeventofaboutathousandyears,itappearsthattheinitialcrystallinityisnotanimportantfactorintermsofthefracturingciency.Onehastoremember,however,thatthedenitionofpointstotherelativeeffectoffracturingepisodesonthereactivation.Inabsolutevalue,amushwithagreaterinitialcrystallinityrequiresagreaterinputofenthalpytoberejuvenated.Theabsolutevolumeofmushreactivatedisthereforestronglycontrolledby.Theeffectoftheself-assimilationthenappearstobesimilarforvarioushoweverthelikelihoodofthemushbeingreactivatedismuchgreaterforvaluesofclosertotherheologicaltransition.Varioustestsillustratethatthevalueofthebulkmodulusofthehostrocksandofthemultiphasemagmaticmixtureinthereactivatedpartofthemush,ortogetherashasasigniuenceonboththefrequencyoffracturingepisodesandonthevolumeofmushassimilatedduringeachoftheseepisodes.FocusingonthedominanttermofEq.forthebuild-upofoverpressure,wecanuseasimpleargumenttoshowthatthefracturingperiod dpdt eff d Theperiodcanbeobtainedbyrearrangingthepreviousequation eff d isagaintheoverpressurerequiredforfracturing(herePa).Assumingforsimplicitythat remainsroughlyconstantduringthereactivation(thedifferenceindensityandbulkmodulusbetweenthemeltandsolidphaseisnottoolarge),theonlytime-dependenttermis =dt d dt= 1 )isthethicknessofmushremobilized.Duetosmallweneglectheattransferduetotheexpectedsluggishconvection whereisthemultiphaseaveragethermaldiffusivityofthemagma.Thecoef(St)dependsontheStefannumberSt=intrwhereisthemultiphaseaveragespecicheatofthemagma,the 0.2 0.4 0.6 0.8 1 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Opening efficiency 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 00.20.40.60.81 crystallinity=0.55crystallinity=0.65crystallinity=0.67 crystallinity=0.67 =1e-11, b=0.5, effeff VrVr Fig.8.Openingefciencies()asfunctionofintrusionmushvolumeratioandinitialmushcrystallinityfortwodifferentend-membersforthehost-rockbulkmodulusandalawexponentinEq.setto0.5.(a)showsacasewherethehost-rocksbehaverigidlyand(b)acasewherethermalormechanicaleffectsassociatedwiththeemplacementofthemagmamadethehost-rocksmuchweaker.TheeffectofisassociatedwithadecreaseoftheslopeoftheefVrrelationshipbyhalffromlefttoright.C.Huberetal./EarthandPlanetaryScienceLettersxxx(2011)xxx Pleasecitethisarticleas:Huber,C.,etal.,Thermo-mechanicalreactivationoflockedcrystalmushes:Melting-inducedinternalfracturingandassimilationprocessesinmagmas,EarthPlanet.Sci.Lett.(2011),doi:10.1016/j.epsl.2011.02.022 latentheatassociatedwithmeltingandisthetemperatureatthemushreactivationfront.Assumingthatthebulkofthemeltingoccursoveranarrowregionofroughlyconstantthicknessattheinterfacebetweenthereactivatedandlockedpartsofthemush, Thethicknessofreactivatedmush,withoursimplifyingassump-tionthattheheattransferismostlydiffusivealsodependsontime Accordingtothissimplescalingargument,theperiodbetweenfracturingeventsbecomes Theprefactorforthetime-dependenceoftheperiodbetweenconsecutivefracturationepisodes 01,whichisingoodagreementwiththeslopeof0.036foundinFig.4a.Wenotethatassumingthattheheattransferismostlyadvectiveleadsalsotoalinearrelationshipbetweentheperiodoffracturingandtime.Indeed,assumingthattheadvectiveheatuxisroughlyconstantovertime,constantand.Thisscalingargumentpredictsalinearrelationshipbetweentheperiodbetweenconsecutivefractur-ingepisodesandtime,however,itbasicallyassumedthatthetemperatureattheinterfacebetweenthemushandtheintrusionremainsconstantovertime.Foracoolingintrusion,oneshouldexpecttheefciencyofmeltingtodecreasewithtimeandthereforethatthepowerlawexponentismorerealistically1.Wefoundpowerexponentsrangingbetween1.1and1.25withournumericalcalculations.Weshowedthatthesolidliquidphasetransitiondominatesthepressureevolutioninthemushduringitsreactivation,providedthereisasufcientdifferenceindensitybetweenthetwophases.Similarly,whiletheintrusioncoolsandcrystallizes,oneshouldexpectthepressureintheintrusiontodecrease.Apressuredecreaseintheunderlyingintrusioncouldpartiallyabsorbtheoverpressureinthemushanddecreasethefracturingefciency.Thecrystallizationoftheintrusioninduceshowevertwoopposingeffects.First,itisresponsiblefortheexsolutionofvolatiles,whichbufferthepressureevolutionintheintrusion(HuppertandWoods,2002).Second,amushyboundarylayerbetweentheintrusionandthemushwillgrowatthecontactwiththecoolermush,and,asobservedfromthepressurediffusionproleabovethemeltingfrontinourcalculationsFig.3d),thediffusionoftheoverpressureinthemushisfairlyTable2summarizestheeffectofthesedifferentvariablesinthescopeoftheefciencyofthemechanicalself-assimilationmechanismforthereactivationofcrystalmushes.5.2.MechanicalbulkassimilationInavastnumberofmagmaticprovincesaroundtheworld,fractionalcrystallizationcoupledwithsomecountryrockassimilation(AFC)isreferredtoasthedominantprocessbywhichmagmasdiversify(laidoutinthescienticliteratureatleastsince(1928;Daly,1914)).Althoughthisprocessiswellcharacterizedchemically(obviouscorrelationsbetweendifferentisotopicsystems;e.g.,(Taylor,1980),presenceofxenocrysts,particularlyobviouswhentheycanbedated;e.g.,amongmany(Bindemanetal.,2008;LanphereandBaadsgaard,2001;Schmittetal.,2003;VazquezandReid,2002orisolatedchemically;(Charlieretal.,2007)),thephysicalprocessesattheoriginofthisassimilationremaincontroversial(Beardetal.,2004;Beardetal.,2005;ClarkeandErdmann,2008;GlaznerandBartley,2006;GlaznerandBartley,2008;Patersonetal.,2008;SperaandBohrson,2004;YoshinobuandBarnes,2008;Yoshinobuetal.,Therearetwoendmemberprocessesbywhichassimilationcanoccurinmagmas:(1)assimilationbypartiallymeltingthewall-rocksandincorporationofthepartialmeltinthedifferentiatingmagmaSperaandBohrson,2004),and(2)bulkassimilation(wholeblocksofcrustbeingincorporatedintothemagma,generally,butnotnecessarily,byamechanismrefertoasstopingafterthepracticeofworkingtheroofsofundergroundmines).AlthoughmeltassimilationisstillconsideredasapotentiallyimportantprocessinthecrustandusedinAFCmodels(BohrsonandSpera,2007;GlaznerandBartley,),multiplelinesofevidencesuggestthatbulkassimilationisgeologically,mechanicallyandenergeticallymorelikely(Beardetal.,2005;YoshinobuandBarnes,2008),atleastintheuppercrust.Asshowninthispaper,themeltingprocessthatnecessarilyoccurswhenfusibleblocksofsolidiedcrustenterincontactwithhottermagmaswillaidthedisaggregationofwallrockpiecesintosmallxenolithsorxenocrysts.Thisreductioningrainsizewillallowefcientperitecticreactionstotakeplace,leadingtothetexturallycrypticassimilationpresentedby(Beardetal.,2005).Thisbulkassimilationprocessdiffersfromself-assimilationastheassimilatedmassisrelatedtopre-existingwallrocksthatwereoncefullycrystallized(andnotearlierco-geneticmagmaintrusionsthatmayhavenevergonebelowtheirsolidii).However,mechanically,thosetwoprocessesareequivalent(inbothprocesses,meltingandfracturationleadtobreakinganddispersionofassimilatedmaterial).6.ConclusionsThemechanicalweakeningofthelocked-upmushinresponsetomeltingandgasaddition(lossofstrengthandbuildupofoverpressure)offersaplausiblehypothesistoexplaintheobservationoflargereactivatedcrystalmushesthateruptwithaveragecrystal-linitieshigherthan40vol.Asshownby(Huberetal.,2010bmeltingmodelsaloneprovetobe(1)unabletoexplainthehighaveragecrystallinityofforexampleMonotonousIntermediatesandalso(2)requireunrealisticvolumesofintrusionforthereactivationoflargecrystal-richmagmabodies.Themechanicalself-assimilationmechanismproposedherepotentiallyalleviatesthesetwoproblems.Eachfracturingeventallowsforamixingbetweenthemagmainthealreadyreactivatedpartofthemushwiththeassimilate(crystallinitysimilartothemush).Theserepeatedepisodesleadtoagreatercrystallinitythanexpectedfrommeltingaloneintherejuvenatedmush.Moreover,theself-assimilationmechanismistriggeredbytheoverpressurebuild-upbymeltingandthereforedoesnotrequiremoreenergythanwhatisalreadyaccountedforinthecaseofathermalreactivationbymelting.Ourcalculationsrevealthat,insomecases,thevolumeofmushreactivatedforagiventhermalenergyinputcanbeincreasedsubstantially(about1000%atearlytimesandabout60%after1000years).Althoughnotdiscussedhere,theeffectofsmallerbutrepeatedintrusionsisexpectedtoincreasetheef Table2SummaryofthecouplingbetweenthedifferentprocessesandtheireffectonthereactivationefFactorEffectCorrelationwithEnthalpyinjected,heatversustimeRigidityofthecontainer+foruxfromIncreasemass,decrease0butMeltingIncrease,phasechange+C.Huberetal./EarthandPlanetaryScienceLettersxxx(2011)xxx Pleasecitethisarticleas:Huber,C.,etal.,Thermo-mechanicalreactivationoflockedcrystalmushes:Melting-inducedinternalfracturingandassimilationprocessesinmagmas,EarthPlanet.Sci.Lett.(2011),doi:10.1016/j.epsl.2011.02.022 oftheself-assimilationprocessbysustainingtheheatuxfromtheintrusiontothemushtogreatervaluesforlongerdurations.Similarprocessesofoverpressurebuild-upduringthepartialmeltingofcountryrocksarealsoexpectedtoplayanimportantroleinfacilitatingbulkassimilationprocesses.Inthisparticularcase,meltingbothweakensthecountryrockincontactwithamagmaticintrusionandalsoprovidessomemechanicalworktodisaggregateblocks(approximatelytothecmscale)whichcanbefurtherdownsizedbybulkassimilationprocesses.AcknowledgementTheauthorswouldliketothanktheeditorR.Carlson,ananonymousreviewerandJ.Beardfortheirusefulcommentsandsuggestions.C.H.wasfundedbyaSwisspostdoctoralfellowship,O.B.acknowledgesfundingfromNSF-EAR0809828andJ.D.fromNSF-EARReferencesAssael,M.J.,Bekou,E.,Giakoumakis,D.,Friend,D.G.,Killeen,M.A.,Millat,J.,2000.Experimentaldatafortheviscosityandthermalconductivityofwaterandsteam.J.Phys.Chem.141,1.556056Ref.Data.Bachmann,O.,Dungan,M.A.,Lipman,P.W.,2002.TheFishCanyonmagmabody,SanJuanvolcaniceld,Colorado:rejuvenationanderuptionofanuppercrustalbatholith.J.Petrol.43,1469Bachmann,O.,Charlier,B.L.A.,Lowenstern,J.B.,G.W.,2007.ZirconcrystallizationandrecyclinginthemagmachamberoftherhyoliticKosPlateauTuff(Aegeanarc),35,pp.73Bear,J.,1988.DynamicsofFluidsinPorousMedia.Dover,p.784.Beard,J.S.,Ragland,P.C.,Crawford,M.L.,2005.Reactivebulkassimilation:amodelformantlemixinginsilicicmagmas.Geology33(8),681Beard,J.S.,Ragland,P.C.,Rushmer,T.,2004.Hydrationcrystallizationreactionsbetweenanhydrousmineralsandhydrousmelttoyieldamphiboleandbiotiteinigneousrocks:descriptionandimplications.J.Geol.112,617Bindeman,I.N.,Fu,B.,Kita,N.T.,Valley,J.W.,2008.OriginandevolutionofsilicicmagmatismatYellowstonebasedonionmicroprobeanalysisofisotopicallyzonedzircons.J.Petrol.49(1),163Bohrson,W.A.,Spera,F.J.,2007.Energy-constrainedrecharge,assimilation,andfractionalcrystallization(EC-RAFC):avisualbasiccomputercodeforcalculatingtraceelementandisotopevariationsofopen-systemmagmaticsystems.Geochem.Geophys.Geosyst.8.Bowen,N.L.,1928.TheEvolutionofIgneousRocks.Doverpublications,NewYork,p.332.Charlier,B.L.A.,Bachmann,O.,Davidson,J.P.,Dungan,M.A.,Morgan,D.,2007.Theuppercrustalevolutionofalargesilicicmagmabody:evidencefromcrystal-scaleRb/SrisotopicheterogeneitiesintheFishCanyonmagmaticsystem,Colorado.JournalofPetrology48(10),18751894(verylargevolumeignimbrites:Geol.Mag.,v.6,p.669-681.).Clarke,D.B.,Erdmann,S.,2008.Isstopingavolumetricallysignicantplutonemplacementprocess?:Comment.Geol.Soc.Am.Bull.120(78),1072Couch,S.,Sparks,R.S.J.,Carroll,M.R.,2001.Mineraldisequilibriuminlavasexplainedbyconvectiveself-mixinginopenmagmachambers.Nature411,1037Daly,R.A.,1914.IgneousRocksandTheirOrigin.McGraw-Hill,London,p.563.vol.Daly,R.A.,1933.IgneousRocksandtheDepthsoftheEarth.McGrawHill,NewYork.vol.DePaolo,D.J.,1981.Traceelementandisotopiceffectsofcombinedwallrockassimilationandfractionalcrystallization.EarthPlanet.Sci.Lett.53,189Dufek,J.,Bergantz,G.W.,2005.Lowercrustalmagmagenesisandpreservation:astochasticframeworkfortheevaluationofbasaltcrustinteraction.J.Petrol.46,21672195.Glazner,A.F.,Bartley,J.M.,2006.Isstopingavolumetricallysignicantplutonemplacementprocess?Geol.Soc.Am.Bull.118(910),1185Glazner,A.F.,Bartley,J.M.,2008.ReplytocommentsonâIsstopingavolumetricallysignicantplutonemplacementprocess?Geol.Soc.Am.Bull.120(78),Ghiorso,M.S.,Sack,R.O.,1995.ChemicalmasstransferinmagmaticprocessesIV:arevisedandinternallyconsistentthermodynamicmodelfortheinterpolationandextrapolationofliquidsolidequilibriainmagmaticsystemsatelevatedtemperaturesandpressures.Contrib.Mineralog.Petrol.119,197212.Halbach,H.,Chatterjee,N.D.,1982.AnempiricalRedlichKwongequationofstateforwaterto1000°Cand200kbar.Contrib.Mineralog.Petrol.79,337Hashin,Z.,Shtrikman,S.,1963.Avariationalapproachtothetheoryofelasticbehaviorofmultiphasematerials.J.Mech.Phys.Solids11,127Hildreth,W.,1981.Gradientsinsilicicmagmachambers:implicationsforlithosphericmagmatism.J.Geophys.Res.86,10153Huber,C.,Bachmann,O.,Manga,M.,2010a.Twocompetingeffectsofvolatilesonheattransferincrystal-richmagmas:thermalinsulationvsdefrosting.J.Petrol.51,Huber,C.,Bachmann,O.,Dufek,J.,2010b.Thelimitationsofmeltingintherejuvenationofsiliciccrystalmushes.J.Volcanol.Geoth.Res.195,97Huppert,H.E.,Woods,A.W.,2002.Theroleofvolatilesinmagmachamberdynamics.Nature420,493Karlstrom,L.,Dufek,J.,Manga,M.,2010.Magmachamberstabilityinarcandcontinentalcrust.J.Volcanol.Geoth.Res.190,249Koyaguchi,T.,Kaneko,K.,2001.Thermalevolutionofsilicicmagmachambersafterbasaltreplenishment.Trans.R.Soc.Edimburgh91,47Lanphere,M.A.,Baadsgaard,H.,2001.PreciseKAr,40Ar/39Ar,RbSr,U/Pbmineralagesfromthe27.5MaFishCanyonTuffreferencestandard.Chem.Geol.175,Lemmon,E.W.,McLinden,M.O.,Friend,D.G.,2003.Thermophysicalpropertiesofsystems.NISTChemistryWebBook,NISTStandardReferenceDatabase,69.Mahood,G.A.,1990.AsecondreplytoCommentbyR.S.J.Sparks,H.E.Huppert,andC.J.N.WilsononEvidenceforlongresidencetimesofrhyoliticmagmaintheLongValleymagmaticsystem:theisotopicrecordintheprecalderalavasofGlass.EarthPlanet.Sci.Lett.99,395Menand,T.,Tait,S.R.,2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Pleasecitethisarticleas:Huber,C.,etal.,Thermo-mechanicalreactivationoflockedcrystalmushes:Melting-inducedinternalfracturingandassimilationprocessesinmagmas,EarthPlanet.Sci.Lett.(2011),doi:10.1016/j.epsl.2011.02.022