This page intentionally left blank HEAT GENERATION AND TRANSPORT IN THE EARTH Heat provides the energy that drives almost all geological phenomena and sets thetemperature,andhencetherate,atwhichthesephenomenaoperate.Thisbook provides an up-to-date treatise on heat transport processes. It explains the key physical principles with simple physical arguments and scaling laws that allow quantitativeevaluationofheatfluxandcoolingconditionsinavarietyofgeological settingsandsystems. The thermal structure and evolution of magma reservoirs, the crust, the litho- sphereandthemantleoftheEartharereviewedwithinthecontextofplatetectonics and mantle convection – illustrating how theoretical arguments can be combined with field and laboratory data to arrive at accurate interpretations of geological observations. Recent theoretical advances on free convection in many different configurations and in fluids with complex rheologies are explained, and dem- onstrations of how past climate changes can be reconstructed from temperature data in deep boreholes are presented.Appendices contain up-to-date information on the thermal properties of rocks and melts, as well as measurements of the sur- faceheatfluxandrateofradiogenicheatproductioninalargenumberofrocksand terrains. HeatGenerationandTransportintheEarthcanbeusedforadvancedcoursesin geophysics,geodynamicsandmagmaticprocesses,andisavaluablereferencefor researchers in geoscience, environmental science, physics, engineering and fluid dynamics.Electronicfigurefiles,datasetsandprogramcodesrelatingtotopicsin thebookcanbedownloadedfromwww.cambridge.org/9780521894883. Claude Jaupart graduated from the Ecole des Mines de Paris before obtain- ing a Ph.D. in geophysics from MIT and a doctorat d’Etat at the Universite de Paris7.HehasbeenassociatedwiththeUniversityofParisDiderotandtheInstitut de Physique du Globe since 1982, where he served as director between 1999 and 2004andiscurrentlyProfessorofGeophysics.ProfessorJaupart’sresearchcovers diverse aspects of the physics of energy transport in the Earth including volcanic andmagmaticsystems,continentalheatfluxandmantleconvection.Hisapproach isbasedonacombinationoflaboratoryexperimentsinfluidmechanics,fieldobser- vationsandtheoreticalstudies.Hiscontributionshavebeenacknowledgedbymany distinctions: the Wager prize of the InternationalAssociation of Volcanology and ChemistryoftheEarth’sInterior(1993),thesilvermedaloftheCNRS(1995),the Holweck and the Mergier-Bourdeix prizes of the Academie des Sciences (1995, 1998), the Prestwich medal of the Geological Society of London (1999), and the HolmesmedaloftheEuropeanGeophysicalUnion(2007). Jean-Claude MareschalholdsdegreesintheoreticalphysicsfromtheUni- versitéLibredeBruxelles,appliedgeophysicsfromtheUniversitePierre-et-Marie Curie,ParisandgeophysicsfromTexasA&MUniversity.Followingpositionsat the University of Toronto and Georgia Tech he joined the Université du Québec à Montréal in Canada in 1985, where he is now Professor of Geophysics and teachesgeophysicsandthephysicsoftheEarth.HewasalsoformerlyDirectorof GEOTOP–theQuebecinter-universitynetworkforadvancedstudiesandresearch ingeoscience.ProfessorMareschal’sresearchinterestsincludetheenergybudget andthermalregimeoftheEarth’slithosphere,themechanicalpropertiesofthecon- tinental lithosphere in relation to its formation and evolution, and studies of heat flowatthebaseoficesheetstodetectsignsofclimatechange.Bothauthorshave worked together on the thermal structure and evolution of cratons and have been mappingtheheatflowfieldofCanadaformorethantwentyyears. HEAT GENERATION AND TRANSPORT IN THE EARTH CLAUDE JAUPART InstitutdePhysiqueduGlobedeParis,France UniversitéParis-Diderot JEAN-CLAUDE MARESCHAL GEOTOP-UQAM-McGill, UniversityofQuebec, Montreal,Canada CAMBRIDGEUNIVERSITYPRESS Cambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore, SãoPaulo,Delhi,Dubai,Tokyo,MexicoCity CambridgeUniversityPress TheEdinburghBuilding,CambridgeCB28RU,UK PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork www.cambridge.org Informationonthistitle:www.cambridge.org/9780521894883 ©ClaudeJaupartandJean-ClaudeMareschal2011 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2011 PrintedintheUnitedKingdomattheUniversityPress,Cambridge AcatalogrecordforthispublicationisavailablefromtheBritishLibrary LibraryofCongressCataloginginPublicationdata Jaupart,Claude. HeatgenerationandtransportintheEarth/ClaudeJaupart,Jean-ClaudeMareschal. p. cm. ISBN978-0-521-89488-3 1. Terrestrialheatflow. 2. Earth–Internalstructure. I. Mareschal,Jean-Claude,1945– II. Title. QE509.J38 2010 551.1–dc22 2010033853 ISBN978-0-521-89488-3Hardback Additionalresourcesforthispublicationatwww.cambridge.org/9780521894883 CambridgeUniversityPresshasnoresponsibilityforthepersistenceor accuracyofURLsforexternalorthird-partyinternetwebsitesreferredto inthispublication,anddoesnotguaranteethatanycontentonsuch websitesis,orwillremain,accurateorappropriate. Contents Introduction page ix Credits xii 1 Historicalnotes 1 1.1 Introduction 1 1.2 KelvinandtheageoftheEarth 1 1.3 Thediscoveryofradioactivity 3 1.4 ThedebateonthecoolingmechanismoftheEarth 4 1.5 Heatfluxmeasurements 5 1.6 EnergybudgetoftheEarth 5 1.7 Platetectonics 6 2 InternalstructureoftheEarth 8 2.1 Introduction 8 2.2 Gravityandgeodesy 10 2.3 Seismology 15 2.4 Petrology,mineralphysicsandseismology:Composition andstateoftheEarth’sinterior 17 2.5 Lateralvariationsofseismicstructure 23 2.6 Coreandmagneticfield 28 2.7 TheshallowEarth 28 Exercises 34 3 Basicequations 35 3.1 Heattransportmechanisms 35 3.2 Definitions.Thermodynamicrelationships 37 3.3 Conservationofmass 40 3.4 Conservationofmomentum 41 3.5 Energyequation 42 3.6 RadialvariationsofdensityintheEarth 46 3.7 Equationsforfluidflow 47 v vi Contents 4 Heatconduction 51 4.1 Heatconduction:Generalities 51 4.2 Steady-stateheatequation 53 4.3 Diffusiveheattransport:Basicprinciples 60 4.4 Generalsolutionstothesteady-stateheatequation 72 4.5 Transientproblems 81 4.6 Thermalstresses 95 Exercises 96 5 Heattransportbyconvection 99 5.1 Isolatedheatsources:Plumesandthermals 99 5.2 Rayleigh–Benardconvection 111 5.3 ScalinglawsforheatfluxandvelocityinRayleigh–Benard convection:Generaltheory 123 5.4 Convectioninporousmedia 136 Exercises 145 6 Thermalstructureoftheoceaniclithosphere 146 6.1 Continentalandoceanicheatflow 146 6.2 Coolingmodelsforoceanicheatfluxandbathymetry 149 6.3 Hotspotsandthermalrejuvenationoftheoceanicplates 165 6.4 Othereffectsofoceanicplatecooling 170 Exercises 175 7 Thermalstructureofthecontinentallithosphere 176 7.1 Continentalheatflux 176 7.2 Continentallithosphereinsteadystate 178 7.3 Long-termtransients:Stabilizationandsecularcooling ofthecontinentallithosphere 194 7.4 Thermalperturbationsincompressionalorogens 201 7.5 Thermalregimeinregionsofextension 208 7.6 Passivecontinentalmargins.Sedimentarybasins 218 7.7 Geophysicalconstraintsonthermalstructure 224 Exercises 230 8 Globalenergybudget.Crust,mantleandcore 232 8.1 ThermodynamicsofthewholeEarth 232 8.2 Heatlossthroughtheoceanfloor 239 8.3 Heatlossthroughcontinents 244 8.4 HeatlossoftheEarth 252 8.5 Radiogenicheatsourcesinthemantle 253 8.6 Heatfluxfromthecore 257 Contents vii 8.7 Mantleenergybudget 259 Exercises 260 9 Mantleconvection 261 9.1 Introduction 261 9.2 Elongatedconvectioncells 262 9.3 Theimpactofcontinentsonconvection 266 9.4 Convectionwithinternalheatsources 271 9.5 Temperature-dependentviscosity 278 9.6 Non-Newtonianrheology 284 9.7 Mantleplumesaspartofalargeconvectivesystem 291 9.8 Twoscalesofconvection 296 9.9 Conclusion 299 10 ThermalevolutionoftheEarth 300 10.1 Initialconditions 300 10.2 Thermalevolutionmodels 307 10.3 Fluctuationsofthemantleheatloss 310 10.4 ContinentalgrowthandcoolingoftheEarth 315 10.5 Conclusion 316 11 Magmaticandvolcanicsystems 317 11.1 Afewfeaturesofcrustalmagmareservoirs 317 11.2 Initialconditions:Super-heatedmagma? 323 11.3 Coolingandcrystallizationofmagmasheets: Conduction 326 11.4 Coolingbyconvection 342 11.5 Kineticcontrolsoncrystallization 353 11.6 Conclusion 356 12 Environmentalproblems 357 12.1 Therecordofpastclimateintemperatureprofiles 357 12.2 Icesheetsandglaciers 375 Exercises 379 13 Newandoldchallenges 380 AppendixA AprimeronFourierandLaplacetransforms 382 A.1 ImpulseresponseandGreen’sfunctions 382 A.2 Fourierseriesandtransforms 392 A.3 Cylindricalsymmetry.Hankeltransform 401 AppendixB Green’sfunctions 404 B.1 Steady-stateheatequation 404 B.2 Transientheatequation 406 viii Contents AppendixC Aboutmeasurements 408 C.1 Landheatflowmeasurements 408 C.2 Oceanicheatfluxmeasurements 413 AppendixD Physicalproperties 415 D.1 Thermalconductivity 415 AppendixE Heatproduction 425 E.1 Heatproductionrateduetouranium,thoriumandpotassium 425 Listofsymbols 435 References 437 Index 462 Thecolorplateswillbefoundbetweenpages84and85.