LithospherestructurebeneaththePhanerozoicintracratonicbasinsofNorthAme - PDF document

LithospherestructurebeneaththePhanerozoicintracratonicbasinsofNorthAmericaEdouardKaminski,ClaudeJaupart*InstitutdePhysiqueduGlobedeParis,4PlaceJussieu,75252ParisCedex5,FranceReceived3August1999;receivedinrevisedform4February2000;accepted19February2000FourintracratonicbasinsofNorthAmerica,theHudsonBay,Michigan,IllinoisandWillistonbasins,havesimilaragesandareclosetooneanother.Yet,theyexhibitdifferentsubsidencehistoriescharacterisedbydifferenttime-scalesandsedimentthicknesses.Theycanbeexplainedbylocallithospherethinningandbythecoolingoftheinducedthermalanomaly.Withintheframeworkof1Dthermalmodelsforverticalheattransport,eachbasinrequiresadifferentlithospherethicknessoradifferentboundaryconditionatthebaseofthelithosphere.Heatflowandseismicstudiesshowthat,beneaththeNorthAmericancraton,thelithosphereistoothickfortheassumptionofpurelyverticalheattransfertobevalid.Thermalmodelsaredevelopedtoaccountforfinitethermalanomalywidthandfortwotypesofbasalboundaryconditions,fixedtemperatureorfixedheatflux.Differentsubsidencehistoriesareexplainedbydeeplithosphericanomaliesofdifferentsizes.Thestabilityofthickcontinentalrootsrequiresthemantlepartofthelithospheretobecompositionallybuoyantwithrespectto`normal'convectingmantle.Localisedlithosphericthinning,dueforexampletoplumepenetration,resultsintheemplacementofcompositionallydensermantleintothelithosphere.Thisrepresentsaloadwhichdrivespermanentflexure.Thecoolingtimeandthecharacteristicsofflexureallowconstraintsonthedimensionsofthesedeeplithosphericanomalies.Therearenosolutionsforlithospherethicknesseslessthan170km.TheWillistonandIllinoisbasinsareassociatedwithwide(200km)andthinanomalies(100km),whereastheMichiganandHudsonBayarelocatedontopofnarrow(100km)andtall(200km)anomalies.ß2000ElsevierScienceB.V.Allrightsreserved.Keywords:lithosphere;intracratonicbasins;NorthAmerica;Phanerozoic;thermalanomalies;one-dimensionalmodels1.IntroductionThereisconsiderabledebateaboutthestructureofthecontinentallithosphereandestimatesofitsthicknessvarywithinalargerangeofabout120^400km[1^4].Theseestimateshavebeenobtainedusingdi¡erentgeophysicaltechniquesandcorre-spondtodi¡erentfeaturesoftheboundarylayeratthetopoftheconvectingmantle.Forexample,thedownwardextrapolationofcrustalgeothermsdealwiththeupperpartwhereheattransportoccursbyconduction,whereasseismicmodelsprovideconstraintsonthewholeboundarylayer,which,byde¢nition,isthicker.Analternativemethodistousethetime-dependentbehaviourofcontinentallithospherefollowingathermal0012-821X/00/$^seefrontmatterß2000ElsevierScienceB.V.Allrightsreserved.PII:S0012-821X(00)00067-4 *Correspondingauthor.Tel.:+33-1-4427-6873;Fax:+33-1-4427-2481;E-mail:cj@ccr.jussieu.frEPSL542619-4-00EarthandPlanetaryScienceLetters178(2000)139^149 www.elsevier.com/locate/epsl perturbation,whichissensitivetothickness.Suchtransientshavebeenstudiedusingthesubsidenceofintracratonicbasinslocatedawayfromactiveplateboundaries[4^6].InNorthAmerica,ithasbeenproposedthatthethicknessofthecontinentallithosphereisabout115kmbeneaththeMichiganbasinand270kmbeneaththeWilliston[4,6].Fortwoba-sinsofsimilaragelocatedonthesamePrecam-briancontinent,suchalargedi¡erenceissurpris-ing.ThismotivatedHamdanietal.[7,8]toinvestigatethein£uenceofthermalboundarycon-ditionsatthebaseofthelithosphere.Theyshowedthatsubsidenceisslowerfora¢xed£uxthanfora¢xedtemperatureandhenceattributeddi¡erentsubsidencebehaviourstodi¡erentther-malprocessesatdepth.However,theyprovidednoexplanationforsuchdi¡erences.Allthesestudiesrelyon1Dthermalmodelsforpurelyver-ticalheattransferandhencerequireananomalyofhorizontalextentmuchlargerthanthelitho-spherethickness.TheMichiganandWillistonba-sinshavebeenattributedtoalargeparttoplate£exuredrivenbyadeepload[4^6,9].Thisloadisrelatedtotheinitialthermalanomalyandhasaradiusofabout120kmbeneaththeMichiganbasin[4],whichissmallerthanthethicknessofthelithospherebeneaththeNorthAmericancra-ton[10^12].Undertheseconditions,theassump-tionofpurelyverticalheattransferisnottenableandthethermalmodelsmustbereevaluated.Inthispaper,westudythebehaviourofthelithospherefollowingadeepthermalevent,suchthatpartofthelithosphereisreplacedbymantlematerialfrombelow.Weaccountforthe¢nitelateralextentofthethermalanomaly.Weusethermaland£exuralmodelstodeterminethedi-mensionsanddensityofthenewmaterialincor-poratedintothelithospherebeneathfourintra-continentalbasinsofNorthAmerica,theHudsonBay,Michigan,IllinoisandWillistonba-sins.Thesebasinsareofsimilarageandarelo-catedonlithospheresofsimilarageandcomposi-tion(Fig.1).Subsidencedataareavailableforallofthem(Fig.2andTable1).Theanalysisleadstoconstraintsonlithospherethickness.Theresults Fig.1.FourPhanerozoicintracratonicbasinsofNorthAmerica:HudsonBay,Illinois,MichiganandWilliston.EPSL542619-4-00E.Kaminski,C.Jaupart/EarthandPlanetaryScienceLetters178(2000)139^149 arediscussedintermsofthephysicalmechanismsresponsibleforbasinformation.2.TheintracratonicbasinsofNorthAmerica2.1.SubsidencemechanismsBeneatheachbasin,thepresent-daysedimenta-ryin¢llrequiresapermanentloadtodrivelitho-sphere£exure.Forsucholdbasins,thermalanomalieshavelongdecayedawayandhencetheloadmusthaveacompositionalorigin.Onepossibilityisthattherehasbeenanepisodeofupliftbeforesubsidence,leadingtoerosionandhencetoalocalreductionofcrustalthickness.However,thereisnoevidenceforsigni¢cantcrus-talthinningbeneaththeWillistonandMichiganbasins[17,18].Onealternativeistoinvokecrustalmetamorphism.Severalreactionswithdi¡erentdensitychangeshavebeenused:gabbrotoeclo-gite,greenschisttoamphiboliteandgabbrotogarnet^granulite[4,8,9].However,theextremeheterogeneityofcrustalassemblages[19]impliesthatonlypartofthecrusthastherightstartingcompositionandmayundergothephasechange.Theaveragedensityincreaseissmallerthanpostulatedbyanunknownamount,whichmakesthissubsidencemechanismdi¤culttotest.Directveri¢cationrequiresdetailedknowledgeofcrustalstructurebeneaththebasins,whichisnotavail-able[13].TheMichiganbasinprovidesagoodexampleoftheproblemsencounteredwhensettingupaphysicalmodelforsubsidence.Anearlyshort-livedphaseofsubsidencestartedatabout520Maandlastedforabout20Myronly.Sedimen-tationwasinterruptedforabout60Myrbeforetheonsetofthemajorphasewhichledtotheaccumulationofmorethan3kmofstrata.The¢rstsubsidencephasehasbeenattributedtocrus-talmetamorphismactivatedbyadeepheatingeventandthesecondonetotheensuingthermalrelaxation[20,9].However,thismodelcannotbeappliedtotheneighbouringIllinoisbasin,wheretherehasbeennointerruptionofsubsidence.Infact,thetwosubsidencephasesoftheMichiganbasincorrespondtoseparateeventsbecausetheyarealsorecordedondistantcontinentalmargins[5].Inthisstudy,weproposeasingleframeworktoaccountforbothsubsidenceandemplacementofapermanentload.Togenerateathermalanomalyinthedeeplithosphere,onemustinvokethepen-etrationofamantleplume,adelaminationeventorsomeformofdeepstretching.Inallcases,avolumeoflithosphereisreplacedbymantlema-terialfrombelow.Itisnowestablishedthatthecontinentallithosphereisthickandcolderthanthesurroundingmantle,whichrequiresacompo-sitionalcontrastbetweenthetwo[1,21].Thus,the Fig.2.Evolutionofsedimentationinfourintracratonicba-sinsofNorthAmerica(seeTable1forreferences).IntheWilliston,alatephaseofsedimentationstartingatabout100MaisattributedtowesternCanadianforelandsubsidence. Table1DataforfourintracratonicbasinsofNorthAmericaParameterHudsonBayMichiganWillistonIllinoisTotalsedimentthickness,(km)1.33.43.43.0Flexuralparameter,13090130Timefor90%subsidence,(Myr)100110420240Pointload,N)1.21.53.11.3Subsidencedataareextractedfrom[5,13,14].FlexuralparametersforMichiganandWillistonfrom[6,9].ForIllinoisandHud-son,the£exuralparameterisevaluatedfromtheequivalentradiusinthestructuralmapsgivenin[15,16].EPSL542619-4-00E.Kaminski,C.Jaupart/EarthandPlanetaryScienceLetters178(2000)139^149 newlithosphericmaterialisbothhotterandcom-positionallydenserthanthematerialitreplaces.Withtime,thethermalanomalydisappearsduetodi¡usion,butthecompositionalanomalyremainsandhencethenetresultisapermanentloadre-sponsibleforsubsidence.Thermalandcomposi-tionale¡ectsaredirectlyrelatedandtheobserva-tionscanbeusedtocharacterisethedeeplithosphericanomaliesrequiredbeneaththeba-sins.Inturn,theseresultsmaybeusedtoassessplausiblemechanismsforintracratonicbasinfor-2.2.ParametersextractedfromthesubsidenceTherelaxationofathermalperturbationisarealisticmechanismforsubsidenceoverlargetimes,butadetailed¢ttothepreservedsedimen-taryrecordinvolvesmanyadditionale¡ects,suchasglobalsealevelvariationsandtectonicevents,someofwhichareill-constrained[22].Wetakeasimplerapproachandextracttwoparametersfromthesedimentaryrecord(Table1):thedura-tionofsubsidence,whichcharacterisesthermalrelaxation,andthetotalsedimentthickness,whichisrelatedtoapermanentloadatdepth.Inordertocomparethedi¡erentcoolinghistories,wede-¢nesubsidencedurationbythetimeneededtoachieve90%ofthe¢nalsubsidence,denotedby.Sedimentthicknessesareextractedfrompre-viousstudies(Table1).FortheWillistonbasin,following[6],wedonottakeintoaccountarecentwidespreadepisodeofcarbonatesedimentation.FortheMichiganbasin,wefocusonthemajorsubsidencephasestartingat460Ma,asin[5].2.3.Lithosphere£exureWeconsiderpermanentlithosphere£exureduetoadeepdiskloadofradiusandhencedonotaccountfortransiente¡ectsassociatedwithcreepinthelowerlithosphere[5].Weusetheclassicalthinelasticplatemodel[23,4],whichintroducesthe£exuralparameter, istheelasticthicknessoflithosphere,thebulkmodulus,isPoisson'sratioandistheaccelerationofgravity.Inthisequation,,whereisthemantledensityattheMoho,setto3300kgm,andistheaver-agesedimentdensity.Forauniformload,appliedbetween=0and,theplateverticalde£exionis[23]: ovbsg aQker0 aQ rQ aQkei0 aQ rQ1…2†rsa;w…r ovbsg aQber0 aQ rQ aQbei0 aQ whereker,ber,keiandbeiareKelvin^Thomsonfunctions[24,p.383].Theamplitudeof£exureisproportionaltoScalingthelocalsedimentthickness,),bythemaximumthicknessatthecentreleadstoadi-mensionlessbasinshapewhichdependsonlyonratio.Thebasinshapeisalmostthesameasthatforapoint-loadforvaluessmallerthanabout1.2.Forlargervaluesof,thebasinde-velopsa£at£oorwhichisnotconsistentwiththeobservations,aswillbeshownbelow.Weshallthususetheconstraintthatislessthan1.2.Inthiscase,thebasinwidthisapproximatelyeighttimesthe£exuralparameter[4].WehaveusedthisrelationshipfortheIllinoisandHudsonBaybasins.FortheWillistonandMichiganba-sins,wehavetakenthevaluesofthe£exuralpa-rameterattheendofsubsidencegivenin[6,9].Forgivensedimentdensity,valuesofsedimentthicknessandbasinwidthonlyallowanestimateoftheequivalentpointload,.TheaveragedensityoftheMichiganbasinsedimenta-rystrataiswellconstrained[25]atthevalueof2610kgmandwehaveadopteditforallba-sins.Ourvaluesofareslightlysmallerthanthoseofpreviousauthorswhousedasmallersedimentdensityof2500kgm[4,6].Forade-EPSL542619-4-00E.Kaminski,C.Jaupart/EarthandPlanetaryScienceLetters178(2000)139^149 tailed£exureanalysis,onemustspecifytheanom-alyradius,whichwillbeobtainedfromather-malmodel.3.Thermalmodelforsubsidence3.1.BasicequationsWeconsideralithosphereofthicknesswithacylindricalthermalanomalyofradius(Fig.3).Atthesurface(=0),thetemperatureis¢xedat.Atsteady-state,thebaseofthelithosphereisat.Weas-sumethatthethermallyperturbedregionisatauniformtemperature.Wewritetempera-tureasthesumoftheequilibriumtemperatureandadimensionlessperturbation: istheradialdistance.isasolutionoftheheatdi¡usionequationandwescaletimeusingtheverticaldi¡usiontime-scale: isthermaldi¡usivity(setat10Dimensionlessvariablesareandtheanomalydimensionsde¢netwodi-mensionlessnumbers: bl;hˆ Temperatureis¢xedatthetopofthelitho-sphere.Atthebase,weconsidereithera¢xedtemperatureora¢xedheat£ux.Thermalpertur-bationsarerequiredtovanishatlargeradialdis-tances.3.2.1DsolutionTheinitialconditionissuchthat: For¢xedbasaltemperature,*)=0,theso-lutionis[26,p.94]:†ˆ †…whichshowsthatthetime-scaleforthermaldecay.For¢xedheat£uxatthebase,*)=0,thesolutionis[26,p.113]:†ˆ 2 2n‡12Z sin 2n‡12Zj3…31†n266377sin 2n‡12Zz3 forwhichthepropertime-scaleis.Coolingandsubsidencearemuchslowerthan Fig.3.Schematicrepresentationofthelithosphereandofthedeeptemperatureanomalyatdi¡erentstagesofcooling.EPSL542619-4-00E.Kaminski,C.Jaupart/EarthandPlanetaryScienceLetters178(2000)139^149 inthepreviouscasebecauseheatiscontinuouslybroughtintothelithosphere.Subsidenceisproportionaltotheamountofcontractioninthelithosphere.The¢nal,andto-tal,amountofcontraction,,is: thecoe¤cientofthermalexpansion.Thedimensionlesssubsidence,*)=*)/,is:†ˆ KvTlZ10‰a…z;0†3a…z;t†ŠdzSoˆ13 Thesolutiondependsweaklyontheanomaly.Fig.4showstheratiobetweenvaluesofsubsidencetimeforanomaliesatthebaseofthelithosphere(=1)andextendingtodepth.For¢xedtemperatureboundaryconditions,thethermalanomalygetsdissipatedatsimilarratesthroughthetopandbottom.Theclosertheanomalyistooneoftheboundaries,thelargeristheheatlossandhencethefasteristhermalrelaxation.For¢xedbasalheat£ux,theanomalydecaysonlythroughheatlossatthetop.Forin-,theanomalyisincreasinglyfartherfromthetopandhencethecoolingtimeincreases.Observedvariationsofsubsidencetimeamongstthefourbasinsstudiedhere,whichamounttomorethanafactoroftwo,cannotbeaccountedforbydi¡erencesofanomalydepth.Wedonotfavourtheexplanationsputforwardbypreviousauthors,whicharetoinvokedi¡erentbasalboundaryconditionsorlargevariationsoflithospherethickness[4,6,8].Asimplerhypothesisistoinvokedeeplithosphericanomaliesa¡ectingthesamelithospherebutwithdi¡erentwidths.3.3.HorizontalheattransportFortheboundaryconditionsofthisproblem,onemaywritethetemperatureperturbationasfollows[26,pp.33^35]:†ˆ†…Theverticalcomponent,,isthesameasbeforeandtheradialcomponent,,satis¢es:†!Thecorrespondingsolutionis[26,p.260]:†ˆ exp…3r2=4th2†2th2Z10exp3 r24th2o theBesselfunctionofthe¢rstkindandorder0.Forthissolution,thesizeoftheheatedregionnexttotheanomalyissmallandtemper-aturesthereremainsmallatalltimes.Atthe†ˆ whichprovidesasimplemeasureoftheaccelera-tionofcoolingduetohorizontalheatloss.Forthermalanomalieswithellipticalorrectangularplanforms,lateralheattransferisdominatedbythesmallesthorizontaldimension. Fig.4.Subsidenceduration,(seetextforde¢nition),asafunctionofanomalyheightfor1Dthermalmodel.Thesub-sidencetimeisscaledtothevaluefor=1,correspondingtoananomalyatthebaseofthelithosphere.EPSL542619-4-00E.Kaminski,C.Jaupart/EarthandPlanetaryScienceLetters178(2000)139^149 Wedenotebythe1Dand2Dvaluesofthesubsidencetimerespectively.Fig.5showstheratiobetweenthesetwotimesasafunc-tionofdimensionlessanomalyradius.Inthe¢xed£uxcase,horizontalheatlossesremainimportantupto=3.Forthesakeofexample,Fig.6comparestheMichiganbasinsubsidencerecordtothepredictedthermalcontractionwithonepar-ticular2Dthermalmodelintheisostaticapprox-4.Deeplithosphericanomaliesbeneathintracratonicbasins4.1.LithospherethicknessandanomalywidthForeachbasin,we¢rst¢x=0.5andcalculatetheradiusofthethermalanomalywhichaccountsfortheobservedsubsidencetimeasafunctionoflithospherethickness(Figs.7and8).Forverythicklithosphere,thesubsidencetimeismuchsmallerthantheverticaldi¡usiontime-scaleInthiscase,coolingisachievedpredominantlybyhorizontalheatlossandhenceismostlysensi-tivetotheanomalyradius.Forgivensubsidencetime,theanomalyradiusincreasesasthelitho-spherethicknessisdecreased.Withdecreasinglithospherethickness,theanomalywidthtendstowardsin¢nityasthe1Dcoolingtimetendsto-wardstheobservedsubsidencetime.Thisde¢nesthethinnestlithospherewhichcanaccountfortheobservations.Thislowerboundisafunctionofthebasalboundarycondition.TheWillistonbasinhasthelongestsubsidencehistoryandhenceprovidesthemoststringentconstraintonlithospherethickness.For¢xedtem-peratureatthebase(Fig.7),thereisnosolutionforthisbasinifthelithospherethicknessissmall-erthan200km.For¢xedheat£ux(Fig.8),litho-spheresthinnerthan125kmareruledout.Ifwe Fig.7.Anomalyradiusasafunctionoflithospherethicknessfor¢xedbasaltemperatureandfor=0.5.Foreachbasin,thesubsidencedurationmustbeequaltotheobservedone.Forlargelithospherethickness,lateralheattransportdominatesandtheanomalyradiusisalmostconstant.Forthinlithosphere,theanomalyradiusincreasesasthetime-scalefor1Dthermalrelaxationtendstowardstheobservedsubsidencetime. Fig.6.ThermalmodelforsubsidenceintheMichiganbasinfor¢xedbasalheat£ux.Thelithospherethicknessissetat300kmandtheanomalyradiusis30km.Thecurvepre-dictedbya1Dmodelisgivenforcomparison. Fig.5.Theaccelerationofsubsidenceasafunctionofanom-alywidthforthetwobasalboundaryconditions.Thedi-mensionlessanomalydepth,,issetat0.5.Accelerationisgivenastheratiobetweenthetimesneededtoachieved90%ofthetotalsubsidencein2Dand1Dmodels.EPSL542619-4-00E.Kaminski,C.Jaupart/EarthandPlanetaryScienceLetters178(2000)139^149 addtheconstraintthatislessthan1.2,whichwasdiscussedabove,valuesofthe£exuralparam-eterinTable1implythatissmallerthanabout160km.Thisimpliesinturnthatthelithospherethicknessislargerthan300and170kmfor¢xedtemperatureand¢xedheat£ux,respectively(Figs.7and8).For¢xedlithospherethickness,subsidencedu-rationleadstoanestimateofloadradiushence,forgiven,toapredictedbasinshape.Allelsebeingequal,thewidthoftheanomalyismuchsmallerforthe¢xedheat£uxmodelthanforthe¢xedtemperatureone.Thisisbecausethe1Dcoolingtimeismuchlargerintheformermodel,whichrequiresanenhancementofhori-zontalheatlosstoachievethesamesubsidenceduration.Fig.9showsacross-sectionthroughthepresent-dayWillistonbasin,from[6],aswellasthe£exurepro¢lepredictedfromthetwother-malmodelsfor250km-thicklithosphere.The¢xedtemperaturecaserequirestoowideananom-alyandimpliesabasin£oorwhichismuch£atterthanobserved.The¢xedheat£uxcase,however,providesasolutionwhichisconsistentwiththeobservations.Furthermore,thiscaseisthemostrealisticfromaphysicalpointofviewbecauseitaccountsforthelimitedthermale¤ciencyofman-tleconvection.Modelsforlithospherestabilisa-tionrelyonsmall-scaleconvectiontoprovidethedeepheat£uxrequiredforthermalsteady-state[27,3].Inthe¢xedtemperaturesolution,themantlebelowthelithosphereisrequiredtosustainaspeci¢cheat£uxvariationasafunctionoftime.4.2.AnomalydepthandcompositionaldensityInthefollowing,we¢xthelithospherethick-nessat250km,following[3].Theanomalyradiuscanbedeterminedfromthethermalmodelandhencetheknownvalueofpointload1)leadstoanestimateoftheloadperunitarea,.Forananomalyofheight,whereistheden-sityofthecontinentallithosphere.Forgiventhethermalmodelisrunforthecorrespondingvalueoftoproduceanestimateoftheanomalyradius.Thisleadstovaluesfor.TherelationshipbetweenisillustratedinFig.10fortheMichiganbasin. Fig.9.DimensionlesssurfacedisplacementduetoadeeplithosphericanomalybeneaththeWillistonbasin.Theplainanddashedcurvescorrespondtothe¢xed£uxand¢xedtemperaturesolutionsfor=250km.Thecrossescorrespondtostackedsedimentarypro¢lesfromdeepboreholes,from Fig.8.SameasFig.7fora¢xedheat£uxbasalboundary Fig.10.Compositionaldensitycontrastinthedeeplitho-sphericanomalyasafunctionofanomalyheight.ParametersarethoseoftheMichiganbasinandthelithospherethicknessissetat250km.EPSL542619-4-00E.Kaminski,C.Jaupart/EarthandPlanetaryScienceLetters178(2000)139^149 Xenolithstudiesindicatethatthemagnitudeofchemicallyinduceddensityvariationsintheman-tlepartofthelithospheremaybeaslargeas110kgm[1].Withinthisrange,thevalueof100kgallowsasolutionforallbasinsandisconsistentwiththemagnitudeofgravityanoma-lies(seebelow).Weadoptthisvalueandlistre-sultsforthe¢xedheat£uxthermalmodelonly.FortheMichiganbasin,theanomalyheightis220kmandtheassociatedradiusis50km(Fig.10).FortheWillistonbasin,thelongersubsidencehistoryimpliesawideranomaly,with110kmradiusand105kmheight.Wealsousegravityanomaliestoobtainanin-dependentrelationshipbetween.Pre-viousauthorsusedthinandshallowdiskloads[4,5],interpretedasdensecrustalmaterialduetophasechanges,andadjustedtheloadradiusinorderto¢ttheobservedgravitysignal.Here,theloadradiusisconstrainedbythethermalmodel,andthesamegravitysignalcanbegener-atedbyanarrowanomalyoveralargeheight.In[5],arough¢lteringprocedureallowsanestimateofabout+5mgalforthegravityanomalyabovetheMichiganbasin.Agloballookatthefourbasinsindicatesthattheirnetgravityanomaliesaresmall,iftheyexistatall.Toallowforerrorsingravityanalysis,welookforsolutionssuchthatthenetanomalyis0þ10mgal.Wecalculatethesolutionforaburiedcylinderandkeepthesamedensitycontrastof100kgm.FortheMichiganbasin,we¢ndthatmustbelargerthan210km,whichisconsistentwiththepreviousresults.Thehalf-widthofthegravityanomalyisabout90km,whichisinagreementwithobservation[4,5].5.Discussion5.1.LithosphericanomaliesbeneaththeNorthAmericancratonResultsforthefourNorthAmericanbasinsareillustratedinFig.11,foralithospherethicknessof250km,¢xedbasalheat£uxand=100kg.Wefoundtwotypesofanomalies:wideandthinfortheWillistonandIllinoisbasins,narrowandtallfortheMichiganandHudsonBaybasins.Interestingly,thisgroupingalsocorrespondstotheonsetofsubsidence(Fig.2),whichoccurredatthesameageofabout520MaintheWillistonandIllinoisbasins,incontrasttotheyoungerageofabout460MafortheMichiganandHudsonBay.Thetallandnarrowintrusionshapefoundhereisverysimilartoacylindricalanomalyde-tectedbeneaththeTrans-HudsonOrogen,whichhasaradiusandheightofabout60and160km,respectively[28].Errorsontheseresultsarisefromseveralsour-ces.Weequatetheuncertaintyonsubsidencedu-rationtothelongestdiscontinuityinthesedimen-tationrecord,whichamountstoaboutþ10%.Forthethermalmodel,thisimpliesanerrorofþ5%ontheanomalywidth.Theerroronintru-sionheightisduetouncertaintiesonboththesedimentaryloadandintrusionwidthandthecu-mulativee¡ectisaboutþ20%.Thesameerrora¡ectsthecompositionaldensitycontrastesti-5.2.Plumepenetrationintothelithosphere?Thesimplestexplanationforintracratonicba-sinsisthepenetrationofmantleplumesintothecontinentallithosphere.Currentmodelshavebeendevelopedforthinoceaniclithosphere,andthickcontinentallithosphereintroducesimportantef-fects.Withinthelowerlithosphere,stressesatthetopoftheplumemaydrivesigni¢cantlocalreturn£ow,whichreducestheamountofdynamicuplift.Akeyfeatureisthatthedensitycontrast Fig.11.PredictedshapesofdeeplithosphericanomaliesforfourintracratonicbasinsofNorthAmericain250kmthickEPSL542619-4-00E.Kaminski,C.Jaupart/EarthandPlanetaryScienceLetters178(2000)139^149 betweenplumematerialandsurroundingconti-nentalmantleisthesumofcompositionalandthermalcomponents,suchthatitsnetbuoyancyissmallinitially,implyingasmallamountofsur-faceupliftafteremplacement.Further,thewidthandascentrateofthe£owarelikelytodependonthermalstructureandhencethicknessofthelitho-sphere,withimportantimplicationsfortheevolu-tionofplumetemperatureanddecompressionmelting.Laboratoryexperimentsandsimplethe-oreticalargumentsonplumeinteractionwiththicklithospherehavebeendevelopedtoaddresstheseissues(KaminskiandJaupart,2000,inprep-aration).Acompletetestoftheplumehypothesisisoutsidethescopeofthispaperandweonlydiscusstwoissues:thebuoyancyrequiredtodriveplumepenetrationandtheanomalyshape.Thecompositionalandthermalcomponentsofplumedensity,,aresuchthattheformerispositiveandthelatternegative.Thepresent-dayHawaiianplumeisabout300Khot-terthan`normal'convectingoceanicmantle[29].Suchaplumewouldneedtorise¢rstthroughtheconvectiveboundarylayeratthebaseofthelitho-sphere,acrosswhichthereisatemperaturedi¡er-enceofabout200K[3].Thus,itwouldreachthebaseofthelithospherewithatemperaturecon-trastofabout500K.Forathermalexpansioncoe¤cientof4andanaveragemantledensityof3.5kgmat250kmdepth,70kgm.Fortheplumetorisethroughthecontinentallithosphericmantle,itmustbebuoyantwithrespecttoit,i.e.suchthat0.Inthesolutionsabove,100þ20kgm,whichisclosetothisre-quirement.The`cratonic'plumesbeneathNorthAmericacouldhavebeenhotterthantheHawai-ianplume.Theremayalsobeanadditionalloadbeneaththebasinsduetoasmallamountofphasechangeoroferosion.Forexample,alocalcrustalthinningof4km,whichmayexistundertheWillistonbasin[17],wouldlowerthedeeplithosphericcompositionaldensitycontrasttoabout85þ20kgmThetwotypesofdeeplithosphericanomalies(Fig.11)maybeexplainedintwodi¡erentways.Onemayenvisionplumeswithdi¡erentbuoyancy£uxes,withtheweakeronesbeingun-abletopenetratedeepintothelithosphereandpoolingatitsbase.Alternatively,onemayinvokeplumeswithdi¡erentlifespans,withonlythelong-livedonesbeingabletoa¡ectthelithosphereoverlargethicknesses.5.3.SubsidenceanalysisInsubsidenceanalysis,onemustdistinguishbe-tweenthermal,tectonic,metamorphicandeu-staticcontrolsusingthespeci¢cfeaturesofeachone.Forexample,BondandKominz[30]relyontheassumptionthatthecontinentallithospherehasacharacteristiccoolingtimeofabout60Myr,followingthein£uentialpaperbySleep[31].Therefore,theyattributesubsidencephaseswhichlastsigni¢cantlylongerthanthistoothere¡ects,suchasrenewedtectonicactivityforexam-ple.Suchexplanationsarenotwarrantedforthickcontinentallithospherewithlargethermalre-sponsetime,asillustratedinthepresentstudy.6.ConclusionThermalmodelsillustratehowthewidthofadeeplithosphericanomalycontrolsthetime-scaleofsubsidenceinthicklithosphere.Itisnotpossi-bletoaccountforsubsidencedatainthefourintracratonicbasinsofNorthAmericaifthelitho-sphereisthinnerthan170km.Ifthecratoniclithosphereisthick,theinevitableconsequenceisthatthemantlepartofthelithospheremustbecompositionallybuoyantwithrespecttothecon-vectivemantlebelow.Inturn,thisimpliesthattheemplacementofdeepmantlematerialintothelithosphereleads:(1)toathermalanomalyinduc-ingcontractionandsubsidenceand(2)aperma-nentpositivedensitycontrastdrivingsteady-state£exure.Thedimensionsofthedeeplithosphericanomalieswhichunderliethesebasinsshouldproveusefulforinvestigatingthephysicalmecha-nismofbasinformation.AcknowledgementsWethankNormanSleepandtwoanonymousEPSL542619-4-00E.Kaminski,C.Jaupart/EarthandPlanetaryScienceLetters178(2000)139^149 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