ListofIllustrations
1.1Thegeomagneticfieldelementsconsistofthreeorthogonalcomponents(X, Y, and Z),whichdefinethetotalfield(F),horizontalcomponent(H),andthe anglesofinclination(I)anddeclination(D).
1.2Thepatternofmagneticfieldlinesaroundastraightbarmagnet(theoutlined darkblock)isrevealedbyapowderofironfilingssprinkledonasheetofpaper coveringthemagnet.
1.3ThefieldlinesofamagneticdipoleatthecenteroftheEarth.Theaxisofthe dipoleistiltedatabout10degreestotherotationaxis.Itsmagneticfieldenters theEarthinthenorthernhemisphereandleavesinthesouthernhemisphere.The angle θ isthemagneticco-latitudeofapositiononthesurface.Theangle I isthe inclinationofthefieldatthatplace.Itishorizontalatthemagneticequatorand verticalatthemagneticpoles.
1.4Adipolemagneticfieldisproduced(a)byasphereofmagneticmaterialthatis magnetizeduniformly,aswellas(b)byanelectricalcurrentthatflowsinasmall conductingloop.
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1.5Whenanelectricalcharge q movesatvelocity v throughamagneticfield B,it experiencesaLorentzforce F atrightanglestoboththefieldanditsdirectionof motion,deflectingitcontinuallysothatitspathbecomesacurvedline. 10
1.6IllustrationoftheZeemaneffect.(a)IntheBohrmodelofatomicstructure,the energylevelsofanelectroninasubshellarespecifiedbydifferentvaluesofthe magneticquantumnumber l.(b)Inthepresenceofamagneticfield,thedipole magneticmomentduetotheelectron’sorbitalangularmomentumcausesthe energylevelstosplitbyanamount∆E thatisproportionaltothefield. 13
1.7Anelectromagneticwaveiscomposedofanalternatingmagneticfieldatright anglestoanalternatingelectricalfield,bothofwhichareperpendiculartothe directionofpropagationofthewave. 15
1.8Thespectrumofelectromagneticradiationrangesfromveryhigh-frequency gammaradiationtoultra-low-frequencyradiowavesandveryslowchangesinthe geomagneticfield. 17
2.1Basicdesignoftwotypesoffluxgatemagnetometersensorwith(a)acoreof parallellinearstripsand(b)aring-typecore. 23
2.2Principleofoperationofaproton-precessionmagnetometer.(a)Anelectrical currentinamagnetizingcoilwoundaroundaflaskofproton-richfluidproduces astrongmagneticfieldthatalignsthespinmagneticmomentsoftheprotons. (b)Afterthemagnetizingfieldisswitchedoff,thespinmagneticmomentsprecess aboutthedirectionofthegeomagneticfield.
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2.3Sketchofsomemethodsofmagneticsurveying:(a)airbornesurveywitha fixed-wingaircraftusingmagnetometersinatail“stinger”andtowed“bird,” (b)airbornesurveywithahelicopterandtowedmagneticgradiometer,(c)marine surveywithamagnetometertowedina“fish,”and(d)ground-basedsurveywith ahand-heldgradiometer. 28
2.4(a)Commonpatternofparallelflightlinesandorthogonaltielinesinanairborne magneticsurvey.(b)Flightlinesatconstantaltitudeabovesealevel(top)and constantelevationabovethegroundsurface(bottom). 29
2.5Theglobaldistributionofactivegeomagneticobservatories.(Datasource: InternationalAssociationforGeomagnetismandAeronomy,DivisionV) 32
2.6SomeoftheorbitspresentlyoccupiedbyartificialEarthsatellites.TheHubble telescope,InternationalSpaceStation(ISS),andmostscientificsatellitesoccupy low-EarthorbitsbeneaththeInnerVanAllenradiationbelt(seeSection8.2). Navigationalsatellites(e.g.,GPS)orbitatabout20,000kmaltitudeandcirclethe Earthapproximatelytwicedaily.Geostationarycommunicationsatellitesarein anequatorialorbitatadistanceofabout6.6radiifromthecenteroftheEarth. NavigationalandgeostationaryorbitsliewithintheOuterVanAllenradiationbelt.
2.7GroundtrackoftheØrstedsatelliteonJanuary2,2001.Northwardtracks areshownbysolidlines,southwardtracksbydashedlines.Arrowheadsmark successiveequatorialcrossingsofthesatellite.(Redrawnafter N.Olsen,G.Hulot, andT.J.Sabaka,Sourcesofthegeomagneticfieldandthemoderndatathat enabletheirinvestigation. HandbookofGeomathematics,W.Freedenetal.(eds.), Springer,Berlin,Heidelberg,2015.WithpermissionfromSpringerNature)
2.8GlobalmapoftheinclinationofthegeomagneticfieldattheEarth’ssurface.The heavydashedlineisthemagneticdipequator,wherethefieldishorizontal.The letterSmarksthelocationofthesoutherndippole,wherethefieldisvertically upward;thenortherndippoleislocatedoffthetopofthemap.(Redrawnafter E.Thébault,C.C.Finlay,etal.,InternationalGeomagneticReferenceField:the 12thgeneration. Earth,PlanetsandSpace, 2015.CreativeCommonsLicense)
2.9GlobalmapofgeomagneticfieldintensityattheEarth’ssurface(1 µT = 1000 nT).(Redrawnafter E.Thébault,C.C.Finlay,etal.,InternationalGeomagnetic ReferenceField:the12thgeneration, Earth,PlanetsandSpace, 2015.Creative CommonsLicense)
3.1ThepathsthroughtheEarthofseismicP-andS-waves.DirectP-andS-waves fromanearthquakereturntothesurfacewithinanepicentraldistanceof105◦ , beyondwhichnodirectS-wavesareobserved.TheP-wavethattraversesthe outercore,refractedasitentersandleaves,islabeledPKP;theP-wavethrough theinnercoreislabeledPKIKP;andtheP-wavereflectedatthesurfaceofthe innercoreislabeledPKiKP.
3.2Estimatedradialprofilesof(a)pressureand(b)temperatureandmeltingpointin theEarth.(a)AfterFigs.7.37and9.2inW.LowrieandA.Fichtner, Fundamentals ofGeophysics,3rded.,CambridgeUniversityPress,2020.Reprintedwith permission.
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3.3(a)ToroidalmagneticfieldsformclosedloopswithintheEarth’scoreandcannot bemeasuredoutsideit.(b)Poloidalfields,asinthissketchofaquadrupole,exist withintheEarthandcanbemeasuredatandaboveitssurface. 46
3.4Thefield-linegeometriesof(a)dipole,(b)quadrupole,and(c)octupolefields. Eachfieldisrotationallysymmetricalaboutitsaxis.Shadingmarksalternating zoneswherethemagneticfieldlinesleaveorenterthesurfaceofasphere. 48
3.5Examplesofzonal,sectoral,andtesseraltypesofsphericalharmonicfunctions. Withincreasingdegree n andorder m, thenumberof“patches”increases, enablingthefunctionstorepresenteversmallerdetailsonthesurfaceofasphere. 52
3.6SummarychartshowingthedifferentcomponentsoftheEarth’smagneticfield. Theinternalfieldissubdividedhereintothedipolecomponent,whichhas long-termgeologicalsignificance,andthenondipolecomponentdescribedby higherdegreetermsinthesphericalharmonicanalysis.Someofthehigherdegree termsoriginateinsidethecoreandchangewithtime.Thetermsthatdescribethe lithosphericfieldareduetoinducedandremanentmagnetizationsandarelargely unchanging.
3.7Historicalsecularvariationsofthedipolefieldduringthe20thcentury,computed fromthefirst-degreecoefficientsoftheIGRF-12referencefield.(a)Thedipole magneticmoment,expressedintermsofthestrengthoftheequatorialmagnetic field;(b)thetiltofthedipoleaxistotherotationaxis,and(c)thelongitudeofthe geomagneticpole.
3.8Comparisonoftheverticalcomponentofthenondipolefieldin1780and 1980;thecontour-lineintervalis2µT.(AfterFig.11.12inW.Lowrieand A.Fichtner, FundamentalsofGeophysics,3rded.,CambridgeUniversityPress, 2020.Reprintedwithpermission)
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3.9Thespatialpowerspectrumofthegeomagneticfielddeterminedbythe MAGSATsatelliteatanaltitudeof450km.Thepartofthespectrumassociated withdegree n ≤ 13isusedtomodeltheInternationalGeomagnetic(Reference Field. Datasource:Cain,J.C.,Z.Wang,D.R.Schmitz,andJ.Meyer,1989.The geomagneticspectrumfor1980andcore-crustalseparation. GeophysicalJournal, 97,443–447) 58
3.10TheWorldDigitalMagneticAnomalyMap,version2,2015.(J.Dyment,V. Lesur,M.Hamoudi,Y.Choi,E.Thébault,M.Catalan,theWDMAMTask Force,theWDMAMEvaluators,andtheWDMAMDataProviders. World DigitalMagneticAnomalyMapversion2.0—availableat http://www.wdmam.org) 61
4.1ThepathofahorizontallymovingobjectattheEarth’ssurfaceisdeflectedbythe CoriolisaccelerationduetotheEarth’srotation.Thedeflectionistotherightin thenorthernhemisphereandtotheleftinthesouthernhemisphere. 67
4.2(a)Thetangentcylinderisanimaginarycylinderthattouchestheinnercoreat theequatorandisparalleltotherotationaxis.Itdividesthepatternsofflowin theoutercoreintotworegimes.(b)OutsidethetangentcylindertheCoriolis accelerationdominatestheflow,forcingittoformcylindricalcolumnsinwhich theflowhasahelicalconfiguration. 70
4.3Magneticfieldlinesofathree-dimensionalsimulationofthegeomagnetic dynamo(G.A.GlatzmaierandT.Clune,Computationalaspectsofgeodynamo simulations, ComputinginScience&Engineering,2,61–67,2000).Reprintedwith permissionfromtheInstituteofElectricalandElectronicsEngineers(IEEE). 72
4.4Theverticalcomponentofthegeomagneticfieldatthesurfaceofthecorein 1990.Bluecolorindicatesdownwarddirectionofthefield(i.e.,fieldlinesentering thecore),andorangecolorindicatesupwarddirection(i.e.,fieldlinesleavingthe core).Theintensityscaleisinunitsof105 nT.(After Fig.31inA.Jacksonand C.Finlay,GeomagneticSecularVariationandItsApplicationstotheCore. TreatiseonGeophysics,2ndedition,chiefeditorG.Schubert,Elsevier,Amsterdam, 2015.Vol.5, Geomagnetism,editorM.Kono,pp.137–184.Withpermissionfrom Elsevier) 74
4.5 Upper:Variationofthemagneticmomentofthegeomagneticdipoleduring thelast7,000years,basedonselecteddatafromtheArcheoIntpaleointensity database. Lower:Theagedistributionofthedata,groupedin250-yearbins.(Data sources:M.KorteandC.G.Constable,Centennialtomillennialgeomagnetic secularvariation. GeophysicalJournalInternational,167,43–52,2006; A.Genevey,Y.Gallet,C.G.Constable,M.Korte,andG.Hulot,ArcheoInt:An upgradedcompilationofgeomagneticfieldintensitydataforthepasttenmillenia anditsapplicationtotherecoveryofthepastdipolemoment. Geochemistry, Geophysics,Geosystems,9,43–52,2008) 76
5.1(a)Theparallelalignmentofmagneticspinsinaferromagneticmetalproducesa strongintrinsicmagnetization.(b)Theantiparallelalignmentsofalternating equal spinsinanantiferromagneticcrystalresultinzeronetintrinsicmagnetization. (c)Theantiparallelalignmentsofalternating unequal magneticspinsina ferrimagneticcrustalproduceanetmagnetizationandmagneticpropertieslike thoseofaferromagneticmetal.
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5.2Therangesofmagneticsusceptibilityincommonsedimentaryandigneousrocks, representedbytheverticallimitsofeachbox.Thehorizontalbarineachbox isthemedianvalue.(Redrawnafter Fig.11.19ainW.LowrieandA.Fichtner, FundamentalsofGeophysics,3rded.,CambridgeUniversityPress,2020.Reprinted withpermission) 85
5.3Therelationshipbetweentheremanent(Mr),induced(Mi),andresultingtotal (Mt)magnetizationsinarock.(a)Whenneithercomponentofmagnetization dominates,thedirectionofthenetmagnetization Mt liesbetween Mi and Mr; (b)if Mi » Mr,theresultantmagnetization Mt iscloseto Mi;(c)conversely,when Mr » Mi,theresultantmagnetization Mt iscloseto Mr.
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5.4(a)Contourlinesofmagneticintensity(innT)overananomalouslymagnetized structure;(b)interpretationprofilealongthelinefromNtoSacrossdistinctive featuresoftheanomaly. 89
5.5(a)Sketchoftheanomalousmagneticfieldlinesofaverticallymagnetizedbody; (b)variationoftheamplitudeoftheanomalyalongahorizontalprofileoverthe body. 90
5.6Modelofhowoceanicmagneticanomaliesareformed.(1)Risingmagmaerupts constantlyatanoceanicridge,spreadslaterally,andbecomesmagnetizedwhile
ListofIllustrations
coolingintheambientfield.(2)Irregularreversalsofmagneticfieldpolarity duringsea-floorspreadingattheridgearerecordedasalternatelymagnetized blocksofoceaniccrustonbothsidesoftheridge.(3)Amagneticsurveyacross theridgemeasurespositiveandnegativeanomaliesover(4)alternatingblocksof normallyandreverselymagnetizedcrust. 93
5.7Thesequencesofmagneticpolaritychronsrecordedinthemagnetizationofthe oceaniccrust.Subsequentreviseddatingassociatesslightlydifferentageswith thereversalsthanthoseindicated.(Redrawnafter:Fig.1inW.LowrieandD.V. Kent,GeomagneticPolarityTimescalesandReversalFrequencyRegimes.In TimescalesofthePaleomagneticField,GeophysicalMonographSeries145,editors: J.E.T.Channell,D.V.Kent,W.Lowrie,andJ.G.Meert.AmericanGeophysical Union,2004) 95
6.1(a)Acquisitionofthermalremanentmagnetization(TRM)whenanigneous rockcoolsthroughtheNéeltemperatureofitsferrimagneticminerals.(b)The directionsofthemagneticmomentsofferrimagneticgrainsarerandomabovethe Néeltemperature(right)andpartiallyalignedaftercooling(left).(c)Acquisition ofpost-depositionalremanentmagnetization(pDRM)insediments.(Redrawn after Figs.12.07aand12.09ainW.LowrieandA.Fichtner, Fundamentals ofGeophysics,3rded.,CambridgeUniversityPress,2020.Reprintedwith permission) 98
6.2ThelocationsofNorthAmericanpaleomagneticpolesofPleistoceneand Plioceneage(<2Ma)areclusteredaroundtherotationaxis,whileolderpoles ofPermianage(>230Ma)areclusteredovernortheastChina.(Redrawnafter Fig.12.20inW.LowrieandA.Fichtner, FundamentalsofGeophysics,3rded., CambridgeUniversityPress,2020.Reprintedwithpermission)
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6.3Theformationofanapparentpolarwanderpath(APW)foramovingtectonic plate.(a)Astheplatemovessouthward,rocksbecomemagnetizedatdifferent times,withinclinationscorrespondingtothedistance p fromthepole(rotation axis)anddeclinations D determinedbythedegreeofrotationateachposition. (b)Atalatertime,theapparentpolepositioniscalculatedforeachstageofthe motionanddefinestheapparentpolarwanderpathrelativetotheplate. 104
6.4(a)ComparisonofapparentpolarwanderpathsforEuropeandNorthAmerica withthecontinentsintheirpresentpositionsrelativetoeachother.(b)A clockwiserotationoftheEuropeanplateby38◦ closestheAtlanticOceanand causesthetwoAPWpathstooverlap.(Datasource:R.VanderVoo,Phanerozoic paleomagneticpolesfromEuropeandNorthAmericaandcomparisonswith continentalreconstructions, ReviewsofGeophysics. 28,167–206,1990.With permissionfromJohnWiley) 105
6.5ThePermo-TriassicconfigurationofPangeaat260MaintheLatePermian. (After Fig.23inM.Domeier,R.VanderVoo,andT.H.Torsvik,2012. PaleomagnetismandPangea:Theroadtoreconciliation. Tectonophysics,514–517, 14–43.WithpermissionfromElsevier) 106
6.6Evolutionofthemagneticpolaritytimescaleforthepast5Myr.Thepolarity chronsestablishedincontinentallavasweredatedradiometrically.Thepolarity historywasconfirmedandextendedbycorrelationwiththereversalsequence foundindeep-seasediments.(Datasources:Cox,Doell,andDalrymple,1963,
1964,1968;DoellandDalrymple,1966;McDougallandChamalaun,1966; Opdyke,1972)
6.7Correlationof(a)thelateCretaceousmagneticstratigraphyintheBottaccione sectionatGubbio,Italy,with(b)thepolaritysequencesinterpretedfrommarine magneticprofilesindifferentoceanicbasins.(Redrawnafter:W.Lowrieand W.Alvarez,LateCretaceousgeomagneticpolaritysequence:detailedrockand paleomagneticstudiesoftheScagliaRossalimestoneatGubbio,Italy. Geophys. J.R.astr.Soc., 51,561–581,1977)
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6.8ReconstructionofthepositionsofEuropeandAfricarelativetoNorthAmerica duringtheopeningoftheCentralandNorthAtlanticOceans.Numberson theEuropeanandAfricanplatesaretheirestimatedagesattheindicated positions.(After:W.C.PitmanIIIandM.Talwani,Seafloorspreadinginthe NorthAtlantic. GeologicalSocietyofAmericaBulletin, 83,619–646,1972.With permission) 112
6.9ThemagneticpolaritytimescalefortheLateTriassicderivedfromoverlapping drill-coresintheNewarkbasin,datedbycyclostratigraphy.(Datasource:P.E. OlsenandD.V.Kent,Long-periodMilankovitchcyclesfromtheLateTriassic andEarlyJurassicofeasternNorthAmericaandtheirimplicationsforthe calibrationoftheEarlyMesozoictime-scaleandthelong-termbehaviourofthe planets. Phil.Trans.R.Soc.Lond.A, 357,1761–1786,1999)
6.10PaleointensityresultsforthePrecambrianandthePhanerozoiceons.Thedataare selectedfromthePINTpaleointensitydatabase(v.8.0.0,2022)andpassatleast threeofthetencriteriaforreliability.Additionally,theymusthaveawell-dated age,lacksignsofalteration,andhavemagnetizationsthatarenotcarriedby multidomain-sizedmagnetite.
7.1ImageofasunspotandsurroundinggranulationontheSun’sphotosphere, observedwiththeSwedish1-mSolarTelescopeonLaPalma,CanaryIslands. Thesolarmagneticfieldisverticalatthedarkcenter,orumbra,andmore horizontalintheadjacentarea.ThesuperposedimageoftheEarth(diameter 12,800km)givesanimpressionofthecolossalsizeoffeaturesontheSun. (Imagecredit:TheRoyalSwedishAcademyofSciences,V.M.J.Henriques, D.Kiselman,andNASA(EarthImage).
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7.2SketchofthelayeredinternalstructureoftheSun.Thephotosphere, chromosphere,andcoronaformtheSun’satmosphere.Thecoronaismuch greaterthandepictedandextendsformillionsofkilometersintospace. 122
7.3Theannualnumberofsunspotssince1700illustratesthe11-yearcyclicityof solaractivity.Thedataareannualmeansbefore1749,andsmoothedmonthly meansafter1749.(Datasource:SunspotIndexandLong-termSolarObservations (SILSO),RoyalObservatoryofBelgium,Brussels) 125
7.4VariationofsolarrotationwithlatitudeandwithdepthintheSun’sinterior, measuredbytheMichelsonDopplerImager(MDI)instrumentaboardtheSolar andHeliosphericObservatory(SOHO)spacecraft.Thenumberoneachcurve isthelatitudeatwhichtherotationwasmeasured.(Datasource:Fig.13inA.G. Kosovichev,J.Schou,etal ,1997.Structureandrotationofthesolarinterior: initialresultsfromtheMDIMedium-Lprogram. SolarPhysics,170,43–61) 126
7.5ModeloftheSun’smagneticfieldatatimeoflowsolaractivity.Thegreenfield lines(outwarddirected)andvioletfieldlines(inwarddirected)are“open”:they connectwithdistantmagneticfieldsinthesolarsystem.Thewhitemagneticfield linesare“closed.”Thatis,theyleaveandthenreturntothesolarsurface.(Image credit:ScientificVisualizationStudio,NASA’sGoddardSpaceFlightCenter, https://svs.gsfc.nasa.gov/4124)
7.6Thespeedofthesolarwindat1AU,thedistanceofEarth’sorbitfromthe Sun.(Redrawnafter:Fig.4ainJ.T.Gosling,R.M.Skoug,andD.J.McComas, Low-energysolarelectronburstsandsolarwindstreamstructureat1AU, JournalofGeophysicalResearch,109,A04104,2004. https://doi.org/10.1029/ 2003JA010309)
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7.7Sketchillustratingtheformationofspiral-shapedflowlinesofthesolarwindand interplanetarymagneticfieldasaresultoftherotationoftheSunduringthe emissionofplasma. 130
7.8Wave-likeappearanceoftheheliosphericcurrentsheet.Itsmassivesizeis emphasizedbyitsrelationshiptotheorbitsoftheplanetsMercury,Venus,Earth, Mars(visibleassmalldots),andJupiter.(Imagecredit:NASA/GoddardSpace FlightCenter. https://www.nasa.gov/content/goddard/heliospheric-current-sheet)
7.9EruptionofafilamentofplasmafromtheSun’scoronaonAugust31,2012. TheimageoftheEarthprovidesascaleforthesizeofthecoronalmassejection. (Imagecredit:NASA/GoddardSpaceFlightCenter/SolarDynamicsObservatory. https://svs.gsfc.nasa.gov/11095)
8.1Schematicdiagram(nottoscale)toillustratetheeffectofthesolarwind inshapingtheEarth’smagnetosphere.Majorfeaturesarethebowshock, magnetosheath,magnetopauseandmagnetotail.PointsmarkedR1 andR2 are locationsofpossiblemagneticreconnectionduringcoronalmassejectionevents. ReconnectioncanoccuratR1 whentheinterplanetarymagneticfield(IMF)is directedsouthwardasinthediagram.
8.2Sketchofthehelicalmotionofanelectricallychargedparticletrappedbya geomagneticfieldline.Astheparticlemovesdownafieldline,thepitchofthe spiralbecomessmaller;theparticle’sdirectionreversesatthemirrorpoints.
8.3Schematicdiagram(nottoscale)showingthelocationsoftheinnerandouter VanAllenradiationbeltsinrelationtotheEarth.Theboundariesofthebeltsare notasdistinctasinthesketch.
8.4DiagramshowingthealtitudesabovetheEarth’ssurfaceoftheupperatmosphere, thelayeredionosphere,andtheVanAllenbelts.Thepositionsofsatelliteorbits, theozonelayer,andthealtitudesfavoredbylong-distancecommercialaircraftare indicatedforcomparison.
8.5Thelayeredstructureoftheionosphere.ThelayersDandE,whichareprominent onthedaysideoftheEarth,areveryweakonthenightsideandmayeven disappear.
8.6Streamlinesoflarge-scaleelectricalcurrentcirculationintheionosphereatnoon (universaltime)onaquasi-equinoctialsolarquiet-day(March16,2011).Solid contoursindicateclockwisecurrentflow;dashedcontoursindicateanticlockwise currentflow.Theequatorialelectrojetflowsintheshadedbandoflatitudes
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within±3◦ oftheequator.(Redrawnafter:M.Guzavina,A.Grayver,andA. Kuvshinov,2018.Dooceantidalsignalsinfluencerecoveryofsolarquiet variations? Earth,PlanetsandSpace, 70:5. https://doi.org/10.1186/s40623017-0769-1.CreativeCommonsAttribution4.0InternationalLicense, http:// creativecommons.org/licenses/by/4.0)
8.7Averagequiet-daydiurnalvariationsofgeomagneticfieldcomponentsatdifferent latitudesineasternAsiaduringMay–Augustof1996–2007.Theobservatories areidentifiedbythree-lettercodenamesfromtheInternationalAssociation ofGeomagnetismandAeronomy(IAGA).(Datasource:Y.YamazakiandA. Maute,2017.SqandEEJ—AReviewontheDailyVariationoftheGeomagnetic FieldCausedbyIonosphericDynamoCurrents. SpaceScienceReviews,206, 299–405.CreativeCommonsAttribution4.0InternationalLicense, http:// creativecommons.org/licenses/by/4.0)
8.8Verticalprofileofelectricalconductivityinthelithosphereanddeepermantle, inferredfromtheanalysisoftime-varyingsignalsduetomagnetosphericand tidalelectriccurrents.(Redrawnafter Fig.7inA.Kuvshinov,A.Grayver,L. Tøffner-Clausen,andN.Olsen,2021.Probing3-Delectricalconductivityof themantleusing6yearsofSwarm,CryoSat-2,andobservatorymagneticdata andexploitingmatrixQ-responsesapproach. Earth,PlanetsandSpace,73:67. https://doi.org/10.1186/s40623-020-01341-9.CreativeCommonsAttribution4.0 InternationalLicence, http://creativecommons.org/licenses/by/4.0)
8.9VariationofthehorizontalcomponentofthegeomagneticfieldattheHermanus observatory,SouthAfrica,inNovember2001showingtwomagneticstorms.A diurnalvariationwithamplitudeof~50nTissuperposedonthemainfieldof ~10,700nT,whichisdepressedonNovember6–8andNovember24–26by magneticstormswithamplitudesof~200nT.(Redrawnafter:Y.YamazakiandA. Maute,2017.SqandEEJ—AReviewontheDailyVariationoftheGeomagnetic FieldCausedbyIonosphericDynamoCurrents. SpaceScienceReviews,206, 299–405. http://creativecommons.org/licenses/by/4.0)
8.10Continuoustonerepresentationofgeomagneticfieldintensityat450kmaltitude, accordingtotheCHAOS-7fieldmodel.Theblueandgreencontoursmarkthe SouthAtlanticAnomaly.BlackdotsshowthelocationsoftheSwarmsatellites whentheywereaffectedbysingle-eventupsetsduetoradiationimpacts.(C.C. Finlay,C.Kloss,N.Olsen,M.D.Hammer,L.Tøffner-Clausen,A.Grayver, andA.Kuvshinov,2020.TheCHAOS-7geomagneticfieldmodelandobserved changesintheSouthAtlanticAnomaly, Earth,PlanetsandSpace,72:156. https:// doi.org/10.1186/s40623-020-01252-9.CreativeCommonsAttribution4.0 InternationalLicence, http://creativecommons.org/licenses/by/4.0)
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TheEarthasaMagnet
Severalearlypioneeringstudiescontributedtounderstandingthemagneticfieldand theideathatitisapropertyoftheEarth.In1269,amedievalFrenchscholar,known asPetrusPeregrinusdeMaricourt,wrotealetter(calledinshortform EpistoladeMagnete)toafriendinwhichhedescribedexperimentshehadcarriedoutonthemagnetic propertiesofironneedlesandlodestones.Heobservedthatthemagnetismofasphere oflodestone,whichhecalleda terrella (orlittleEarth),variedoveritssurfacebutwas concentratedatdiametricallyoppositepoints.Heusedtheterm pole (fromtheLatin word polus,meaningtheendofanaxis)torefertothesecentersofmagneticforce, andhenotedthatthereweredifferenttypesofpolesattheopposingendsofthemagneticaxis.Heestablishedthatmagneticpolesofthesametyperepeleachother,whereas unlikepolesattracteachother.However,insteadofrecognizingtheabilitytoaligninthe north–southdirectionasanintrinsicpropertyofthemagnet,heattributedittoacelestial cause,suchastheinfluenceofPolaris,thepolestar.Thisnotionwastopersistforalmost threecenturies.Therewaslittlefurtheradvanceintheunderstandingofmagnetismor themagneticfieldduringtheMiddleAgesthatfollowed.
Thenorthdirectionindicatedbyamagneticcompassandthetruegeographicalnorth directionarenotquiteidentical.Thediscrepancyiscalledthe declination ofthefield (Fig. 1.1).Theearliestrecord,in1088,oftheangleofdeclinationisattributedtoShen Kuo,aChineseintellectualwhowasknowledgeableinmanysubjects.Thedeclination arisesbecausethemagneticpolesdonotexactlycoincidewiththegeographicpoles. Theverticalplanethatpassesthroughthehorizontalcomponentofthefieldintersects thesurfaceoftheEarthonagreatcirclecalledthe magneticmeridian.In1576,Robert Norman,anEnglishcompass-maker,showedthatamagnetizedneedlethatisfreeto swinginthemeridianplanealignsatanangletothehorizontal.Thisobservationappears tohavealreadybeenmadein1544byGeorgHartmann,aGermaninstrumentmaker, buthisresultdidnotbecomepublicknowledgeuntilitwasdiscoveredcenturieslater. Theanglebetweenthefieldandthehorizontaliscalledthe inclination (or dip)ofthefield (Fig. 1.1).Itisdefinedbyconventiontobepositivewhenthefieldpointsdownward,as itdoesinmostofthenorthernhemisphere.
In1600,WilliamGilbert,anaturalscientistwhobecamethephysiciantoEngland’s firstQueenElizabeth,publishedahistoricallyimportantscientificworkonmagnetism, titledinshortform DeMagnete.Inthisworkhesummarizedallthatwasknownatthat timeabouttheEarth’smagneticfield,withduerecognitionoftheearlierworkofPetrus Peregrinusonthemagnetismofasphereoflodestone.Healsoaddedhisownobservationsbasedoncarefulscientificexperiments.Forexample,heshowedthatwhena magnetisdividedintotwoparts,eachpartisalsoamagnet,withapoleofattraction atoneendandapoleofrepulsionattheotherend.MostimportantlyforunderstandingthemagnetismoftheEarth,heshowedthatsmallmagnetizedneedlesadheredto thesurfaceofalodestonesphereatanglesthatresembledtheknownvariationofthe inclinationoftheEarth’smagneticfieldalongacircleoflongitude.Thedirectionofthe fieldisparalleltothesurfaceoftheEarth(i.e.,horizontal)atthemagneticequatorand
1.3 TheOriginofMagneticFields 5 perpendiculartoit(i.e.,vertical)atthepoles.Gilbertinferredfromhisobservationsthat theEarthitselfisagiantmagnet.Thisfindingwasanimportantstepphilosophically because—incontrasttoPeregrinus—herecognizedthatthemagneticfieldisaproperty oftheEarthandnottheexpressionofacelestialforce.
Itsometimeshappensthatdifferentscientistsmaybestudyingthesamephenomenon atthesametimeandinasimilarway.IndependentlyofGilbert,aFrenchnobleman, GuillaumeleNautonier(WilliamtheNavigator),wasalsointerestedinthemagnetic behaviorofthelodestone.In1603,hepublishedanaccountinwhichheconcluded thattheforcethatproducedthealignmentofacompassneedleoriginatedwithinthe Earthitself.BothGilbertandleNautoniertooktheboldstepofattributingtheEarth’s magneticfieldtoaninternalpropertyoftheplanetinsteadoftoacelestialcause.This pointofviewwasnotsharedbythecontemporaryChristianchurch,whichregarded manytheoriesthatdifferedfromitsteachingsasheretical.However,thesepioneering investigations,basedonexperimentationratherthanspeculation,formthebeginnings ofgeomagnetismasascience.
GilbertimaginedthemagneticfieldatanypointonEarthtobeconstantandinvariablewithtime.Thisconceptwasdisprovedin1635byHenryGellibrand,anEnglish mathematician,whonoticedthattheangleofdeclinationinLondonhadchangedby 7degreesin54years.Thisslowchangeofthefieldwithtimeiscalledits secularvariation.Itisalsoobservedinothercomponentsofthefieldandisatopicofgreatinterest tomodernexpertsingeomagnetismasitsanalysisrevealsimportantinformationabout howthefieldisgenerated.
Gradually,systematicmeasurementsofthegeomagneticfieldweremadeovermuch oftheEarth’ssurface,sothatitsspatialvariationwithpositionbecameincreasinglywell known.Forexample,in1701EdmondHalley—anEnglishastronomer,afterwhomthe cometisnamed—producedachartofdeclinationthroughouttheAtlanticOcean.To doso,heintroducedthetechniqueofinterpolatingcontourlinesbetweentheactual measurementpositions.Theuseofcontourlinesbecameanindispensabletechniquein map-makingandotherscientificanalyses.However,itwouldtakemorethananother 200yearsbeforetheoriginofmagnetismanditsrelationshiptomacroscopicand atomicelectricalcurrentswereestablished.Thisfundamentalknowledgederivedfrom laboratoryinvestigationsearlyinthe19thcentury.
1.3 TheOriginofMagneticFields
Beforeproceedinganyfurther,wemustdefinewhatismeantbytheterm magneticfield. Theexpressioncanbeunderstoodintwoways.Inphysicsitmayrefertothe strength ofaforce,inwhichcaseitisexpressedastheforceperunitofthequantitythatproducestheforce.Forexample,thegravitationalfieldofanobjectistheforceofattraction itexertsonaunitofmass(e.g.,kilogram).Similarly,thestrengthofanelectricfield istheforceitexertsonaunitofelectricalcharge.Electricalchargescanbenegative orpositive,andtheforcebetweentwochargesisattractivewhenthechargesareof
oppositekindsandrepulsivewhentheyareofthesamekind.Thestrengthofamagneticfieldrepresentsa“forceperunitofmagnetism,”butthisnotionisbothvagueand inexactbecausemagnetismoriginatesfromelectricalcurrents,thatis,movingelectrical charges.
Theotherusageoftheterm magneticfield istodescribethe geometry oftheregion inwhichtheforceacts.MichaelFaraday,apioneeringEnglishscientist,introducedthe termin1845todescribetheeffectofamagnetbyimaginingthelinesofforcesurroundingit.Theconceptcanbeappliedtodescribeanyforcefield.Forexample,thedirection ofanelectricalfieldisdefinedbyitsforceofrepulsiononapositivecharge.Thus,electricalfieldlinesactradiallyinward(attraction)aroundanegativechargeandradially outward(repulsion)aroundapositivecharge.Thestrengthofthefielddecreasesalong afieldlinewithincreasingdistancefromthecharge,followinganinverse-squarelaw, butitsdirectionremainsradial.
Themagneticfieldofasimplemagnethastwocentersofforce.Whenafinepowder ofironfilingsissprinkledonasheetofpaperthatliesontopofastraightbarmagnet, themagnet’slinesofforcebecomevisible(Fig. 1.2).Eachgrainofthepowderediron behaveslikeatinymagnetandalignswiththeforcefieldofthemagnet.Thetinyparticles tendtoclumptogether,formingraggedbutdistinctlinesthatconvergeontwocenters offorce,oneateachendofthemagnet.Thelinesofforceenterthemagnetatoneend andleaveattheother.Theyspreadoutinthespacebetweenthem,outliningclearlythe geometryoftheforcefieldofthebarmagnet.
Fig.1.2 Thepatternofmagneticfieldlinesaroundastraightbarmagnet(the outlineddarkblock)isrevealedbyapowderofironfilingssprinkledonasheetof papercoveringthemagnet.
Thecentersofforcearecalledthe poles ofthemagnet,asfirstnamedbyPeregrinus. Theyareofequalstrengthbutoppositesign.Eachpoleexertsaforceofrepulsionona similarpole,whiletheotherpoleisattractedtoit.IthasbeenknownsincetheobservationsofPeregrinusinthe13thcentury,reinforcedbyGilbertinthe17thcentury,that whenamagnetisdividedintosmallerparts,eachpartisobservedalsotohavetwopoles ofoppositesign;thatis,magneticpolesalwaysoccurinpairs.Theabilityofafreely suspendedmagnettorotateintoalignmentwithanexternalmagneticfielddependson thestrengthandseparationofthemagnet’spolesandiscalledits magneticmoment.The conceptisusedtodescribethestrengthoftheEarth’sfieldaswellasmagneticbehavior atanatomiclevel.
TheattractionoftheEarth’smagneticfieldononeendofacompassneedleand therepulsionoftheotherendcausethecompassneedletoaligninthenorth–south magneticmeridian.Byconvention,thenorth-seekingmagneticpoleofthecompasswas associatedwiththenorth geographic pole,andtheplacetowhichitpointedwascalled the northmagneticpole.Thelocationsareinfactquitefarapart:thenorthmagnetic poleiscurrentlylocatedinthenorthofCanada,severalhundredkilometersfromthe geographicpole.Thehistoriclabelingofthemagneticpolesisunfortunate.Inphysics, magneticfieldlinesaredefinedsothattheyleavemagneticnorthpolesandreturnto magneticsouthpoles.Moreover,theEarth’smagneticfieldisdefinedtoactnorthward anddownwardinthenorthernhemisphere(Fig. 1.1).Paradoxically,thismeansthatthe northpoleoftheEarth’smagneticfieldmust physically beamagneticsouthpole.The contradictionarisesfromassociatingthemagneticfieldlineswithfictitiousmagnetic poles.
Theclassicalphysicsofmagnetismisbasedontheassumptionthatindividualmagneticpoles(referredtoasmonopoles)donotexist;thisassumptionisborneoutby experience.Modernphysicshasneverestablishedtheexistenceofmagneticmonopoles, althoughexperimentaleffortshavebeenmadetofindthem.Althoughtheyareafictitious concept,magneticpolescanbeusefulingeophysics.Theyare,forexample,ausefulaid tounderstandingthemagneticsignaturesofgeologicalstructuresandorebodiesinthe shallowsubsurface.
Along,thin,magnetizedneedle—whosepolesarefarapartandcannotinfluenceeach other—canbeusedtounderstandthepropertiesofmagneticforces.Eachendoftheneedleapproximatesasinglepole,andthelinesofmagneticforceactradiallytoit.Themagneticforcedecreaseswithdistancefromasinglepoleasthe inversesquare ofthedistance. However,thisisanartificialsituation.Inpractice,amagnetisusuallyshortenoughfor bothpolestoaffecttheshapeofitsmagneticfield,whichisdescribedbycurvedlinesthat leadfromonepoletotheother.Thedecreaseoffieldstrengthwithdistanceisthenmore complicatedandfasterthandescribedbyaninverse-squarelaw.Thefieldlinesmarkthe magnet’sdirectionofforce;atanypoint,itactsparalleltothedirectionofthefieldline atthatpoint.Thegeometryofthefieldlinesthereforedescribestheshapeofthemagneticfield.Theterm magneticflux describestheamountofmagneticfieldthat“flows” throughaunitofareainadirectionnormaltoitssurface.Wherethefieldlinesareclose together(e.g.,nearthemagneticpoles),themagneticfluxishigh;wherethefieldlinesare farapart,itislow.
8 WhatisMagnetism?
A dipole fieldariseswhenthepolesaresoclosetogetherthattheirseparationisnegligiblecomparedtothedistanceoftheobserverfromthem(Fig. 1.3).Atanypoint inthefieldofadipole,theeffectsofbothpolesarefelt.Asaresultofthissuperposition,thestrengthofthemagneticfielddecreasesastheinverse cube ofthedistance fromthemidpointofthedipole.Ataconstantdistancefromthedipole(i.e.,ona sphericalsurfacearoundthedipole),thedirectionofthefieldvarieswiththeangular distancefromthedipoleaxis.Itpointsverticallyinwardoroutwardoverthepolesof themagnet,and—byanalogytotheEarth’sfield—itis“horizontal”overthe“magnetic equator.”
Fig.1.3 ThefieldlinesofamagneticdipoleatthecenteroftheEarth.The axisofthedipoleistiltedatabout10degreestotherotationaxis.Itsmagnetic fieldenterstheEarthinthenorthernhemisphereandleavesinthesouthern hemisphere.Theangle θ isthemagneticcolatitudeofapositiononthesurface. TheangleIistheinclinationofthefieldatthatplace.Itishorizontalatthe magneticequatorandverticalatthemagneticpoles.
Thedipolefieldisthemostimportantandfundamentaltypeofmagneticfield.Itis, forexample,thetypeofmagneticfieldaroundauniformlymagnetizedsphereofmagneticmaterial(Fig. 1.4a),suchaslodestone,whichiswhyGilbert’sexperimentswere successfulindescribingsomepropertiesofthegeomagneticfield.Itisalsotheshapeof themagneticfieldproducedbyanelectricalcurrentinasmallloopofconductingwire (Fig. 1.4b).Atamoreelementallevel,itisthetypeofmagneticfieldproducedbyan electronorbitingthenucleusofanatom.
1.4 ElectricalCurrentsandMagneticFields
Anelectricalcurrentisaflowofelectricallychargedparticles.Inaconductor,itconsists ofnegativelychargedelectrons;inaliquid,itconsistsofpositivelyornegativelycharged atoms(calledions).AstreamofchargedparticlesfromtheSunismadeupofboth electronsandions.Themeasureofhoweasilyamaterialallowsanelectricalcurrentto passthroughitiscalledits conductivity;itisexpressedinunitsofSiemens/meter(S/m). Theinverse,thatis,howstronglythematerialopposesacurrent,iscalleditsresistivity andismeasuredinohmmeters.Thegeomagneticfieldisproducedbyvariouselectrical currents,flowingprimarilyintheliquidcore,butalsoinspacearoundtheEarth,inthe atmosphere,intheoceans,andinthesolidinterioroftheplanet.
Thephysicalrelationshipbetweenelectricityandmagnetismwasdiscoveredas aresultofexperimentscarriedoutintheearly19thcentury.In1820aDanish scientist,HansChristianØrsted,showedexperimentallythatamagnetizedironneedlewasdeflectedinthevicinityofanelectricalcurrent.Inexperimentsthataugmented thisobservation,theFrenchscientistAndré-MarieAmpèredemonstratedthataforce ofrepulsionorattractionexistedbetweentwoparallelcurrent-carryingconductors, dependingonwhetherthecurrentswereinthesameoroppositedirections.Thelaw governingthedirectionandstrengthofthemagneticfieldaroundeachconductorwas developedbytwoFrenchphysicists,Jean-BaptisteBiotandFélixSavart.
Anelectricalcurrentproducesamagneticfieldinaplaneperpendiculartothecurrent. Forexample,asteadycurrentthroughastraightwirecreatesamagneticfieldaroundthe wirethathastheshapeofclosedcirclesinaplaneperpendiculartothewire.Conversely, acurrentthroughasmallloopofwirecreatesadipolefieldaroundit(Fig. 1.4b).The directionofthemagneticfieldalongtheaxisoftheloopisdefinedbyaright-handrule: withthefingersoftherighthandpointingalongthedirectionofthecurrent,thethumb indicatesthedirectionofthemagneticfielditproduces.
(a)(b)
Fig.1.4 Adipolemagneticfieldisproduced(a)bya sphereofmagneticmaterialthatismagnetizeduniformly,aswellas(b)byanelectricalcurrentthat flowsinasmallconductingloop.
WhatisMagnetism?
Animportantcorollaryoftheseobservationsisthatastationaryelectricalchargedoes notproduceamagneticfield,whichonlyresultswhenelectricalchargesareinmotion.In acomplementaryway,asteadymagneticfielddoesnotproduceanelectricalcurrent,but a changing magneticfielddoes.ThiswasshownbytheEnglishscientistMichaelFaraday, who—althoughhehadlittleformaleducationormathematicaltraining—wasagifted experimenter.In1831,bymovingamagnetintoandoutofacoilofwire,hedemonstratedthatacurrentwasinducedinthewireonlywhenthemagnetwasinmotion.The processiscalledelectromagneticinduction(orsimplymagneticinduction).In1834, aRussianscientist,EmilLenz,establishedthatthedirectionoftheinducedcurrentis suchthatitsownmagneticfieldopposestheinitialchangeinthemagneticfield.The fundamentalexperimentalresultsobtainedbyFaradayandLenzestablishedthefact thatelectricalcurrentsandmagneticfieldsarenotindependent.
Anelectricallychargedparticlethatmovesthroughamagneticfieldexperiencesa forcethatactsperpendiculartoboththefieldandthedirectionofmotion.Thisrelationshipwasestablishedin1895byaDutchphysicist,HendrikLorentz,afterwhomthe forceisnamed.Ifthevelocity v oftheelectricalcharge q makesanangle θ withthemagneticfield B (Fig. 1.5),thechargeexperiencesadeflectingforce F givenbytheLorentz equation
IntheLorentzequation,theelectriccharge q isascalarquantity;ithasamagnitude butnodirection.Incontrast,eachofthequantities F, v, and B isavectorwithbotha magnitudeandadirection.Therulesbywhichvectorsarecombinedinmathematical equationsneedtoaccommodatetheirdirectionalpropertiesaswellastheirnondirectionalvalues.TheLorentzequationisastraightforwardexample.Themultiplication
Fig.1.5 Whenanelectricalcharge q movesat velocity v throughamagneticfield B,itexperiencesaLorentzforce F atrightanglestoboth thefieldanditsdirectionofmotion,deflecting itcontinuallysothatitspathbecomesacurved line.
1.5 MagnetismattheAtomicLevel:TheBohrModeloftheAtom 11
symbolinEq.(1.1)standsforthevector-product(alsocalledthecross-product)ofthe twovectors v and B.Itdefinesthedirectionofthedeflectingforce F tobeperpendicular toboththevelocityandmagneticfieldateachpointofthepathofthemovingcharge. Thiscausesthepathtobecurved(Fig. 1.5).
Themagnitudeoftheforce F isascalarproduct:
where θ istheanglebetweenthevectors v and B andsinisthetrigonometricsinefunction oftheangle.Theforceonaunitofelectricalchargeistheelectricfieldandisdenoted E.DividingbothsidesoftheLorentzequationbythecharge q leadstothefollowing alternativeformoftheequation,
TheLorentzforcehasimportantconsequencesfortheinteractionofelectricalcurrents andmagneticfieldsandplaysanimportantroleinthedefinitionofthefundamentalunits ofelectricityandmagnetism.Itisabasicprincipleinthedesignofstrong-fieldphysics equipmentsuchascyclotronsandotherparticleaccelerators.Itisalsoanimportant factoringeneratingthegeomagneticfieldintheEarth’sfluidcore.
TheLorentzforcealsohelpsustounderstandhowthegeomagneticfieldprotectsthe Earth.WhenanelectricallychargedparticlefromtheSun,ordistantregionsofspace, impactsontheEarth,itencountersthesurroundingmagneticfield.TheLorentzforce actsonchargedparticlesanddeflectstheirpathssothatmostpassaroundtheplanet.
1.5 MagnetismattheAtomicLevel:TheBohr ModeloftheAtom
Inordertomeasurethemagneticfieldsofdistantstarsortostudythemagneticfieldat thesurfaceoftheSun,astrophysicistsuseamethodbasedonthequantummechanical propertiesofatoms.Themethodmakesuseofthefactthatthefrequencyoftheenergy radiatedbyanatomisalteredinthepresenceofamagneticfield.Apracticalstarting pointforexplaininghowthischangehappensistheBohrmodeloftheatom,whichuses theconceptsofclassicalphysics.Themodelisunabletoexplainallaspectsofatomic behaviorandbecomesinadequate,forexample,whentheangularmomentumofthe electronspinmustbetakenintoaccount.Aprofoundanalysisrequiresknowledgeof quantummechanics,whichisbeyondthescopeofthisbook.Nevertheless,itispossibletoappreciatesomeaspectsofmagnetismattheatomiclevelwithoutgettingdeeply involvedinthisadvancedtopic.
Allmagneticfieldsarisefromelectricalcurrents;eveninapermanentlymagnetized solid,suchasaneedleoranironbar,themagnetismresultsfrommovingelectrical charges.In1913aDanishphysicist,NielsBohr,presentedasimplemodelofthestructureoftheatom.Itresemblesthestructureofthesolarsystemandsupplementssimilar
