JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 95, NO. B5, PAGES 6715-6736, MAY 10, 1990

Hotspotsand Mantle Plumes'Some Phenomenology

NORMAN H. SLEEP

Departmentsof Geologyand Geophysics,Stanford University, Stanford, California

The availabledata, mainly topography, geoid, and heat flow, describinghotspots worldwide are examined to constrainthe mechanismsfor swelluplift and to obtainfluxes and excess temperatures of mantleplumes. Swelluplift is causedmainly by excesstemperatures that move with the lithosphereplate and to a lesser extenthot asthenospherenear the hotspot.The volume,heat, and buoyancy fluxes of hotspotsare computed fromthe cross-sectionalareas of swells,the shapes of nosesof swells,and, for on ridgehotspots, the amount of ascendingmaterial needed to supplythe lengthof ridgeaxis whichhas abnormallyhigh elevationand thickcrust. The buoyancy fluxes range over a factorof 20 withHawaii, 8.7 Mg s -1, thelargest. The buoy- ancyflux for Iceland is 1.4Mg s -1 whichis similarto theflux of CapeVerde. The excess temperature of both on-ridgeand off-ridgehotspots is aroundthe 200øCvalue inferred from petrologybut is not tightly constrainedby geophysicalconsiderations. This observation,the similarityof the fluxesof on-ridgeand off- ridgeplumes, and the tendency for hotspotsto crossthe ridge indicate that similar plumes are likely to cause both typesof hotspots.The buoyancyfluxes of 37 hotspotsare estimated;the globalbuoyancy flux is 50 Mgs -1, whichis equivalentto a globallyaveraged surface heat flow of 4 mWm-2 fromcore sources and wouldcool the core at a rateof 50ø C b.y. -1. Basedon a thermalmodel and the assumption that the likeli- hoodof subductionis independentof age,most of the heatfrom hotspotsis implacedin the lower litho- sphereand later subducted.

I.NTRODUCWION ridge plumesusing Iceland as an example. The geometryof flow implied by the assumed existence of a low viscosity Linearseamount chains, such as the Hawaiian Islands, are asthenosphericchannelis illustrated bythis exercise. Then the frequentlyattributed tomantle plumes which ascend from deep methods forobtaining theflux of plumes ona rapidlymoving inthe Earth, perhaps thecore-mantle boundary. Theexcessive plate are discussed withHawaii as an example. These methods volcanismof on-ridge hotspots, such as Iceland, is also often involve determining theflux from the plume from the cross- attributedto plumes. If on-ridgeand midplate hotspots are sectionalareaof the swell and taking advantage ofthe kinemat- reallymanifestations of the same phenomenon, onewould ics of theinteraction of asthenospheric flowaway from the expectthat the temperature andflux of the upwelling material plume and asthenospheric flowinduced by thedrag of the wouldbe similar under both features. In particular, thecore- lithospheric plate. The methods forextending thisapproach to mantleboundary isexpected tobe nearly isothermal sothat the hotspotsonslowly moving plates are then discussed which Cape temperatureofplumes ascending fromthe basal boundary layer Verde as an example. Anestimate ofthe global mass and heat shouldbethe same globally provided that cooling byentrain- transfer byplumes isthen obtained byapplying themethods to mentof nearbymaterial and thermal conduction areminor. 34 additional hotspots. The magnitude ofthis total estimated Finally,theglobal heat loss from plumes should imply areason- flux is compatible withthe heat flux expected fromcooling the ablecooling rate of the core [Davies, 1988a]. corein agreement withDavies [1988a]. Finally, the results are Themost important point of this paper isthat the properties used to obtain general properties ofplumes and inferences on ofmantle plumes areconstrained byobservations, mainlytopog- the underlying mantle dynamics. "• raphy, geoid, and heat flow. I follow Davies [1988a], Richards eta!. [1988],and Sleep [1987a, b] in assumingthat the ICELANDICPLUM•FLUX geometryof plumesconsists of narrowvertical pipes which sup- plieshot mantle to a thinlow-viscosity asthenosphere beneath TheIcelandic hotspot is directlyon theMid-Atlantic Ridge. the movingplate (Figure 1). Suchplumes provide a muchMethods developed for off-ridge hotspots are thus inappropriate. betterexplanation for geoidand topographic anomalies than Theexcess volcanism of theridge near the hotspot is probably doessecondary convection from the cooling of theoceanic plate the best way to constrainthe excess temperature andvolume of Davies[1988a, b]. Thisgeometry allows simplification of the materialsupplied by theplume. discussionand the physicsbecause the model plume is much narrowerthan the hotspot swell and the rapidly flowing layer of ExcessCrustal Thickness andTemperature asthenosphereis thin compared to the thickness of the mantle of Icelandic Plume and the width of the swell. The expenseis somemodel depen- dencyof theresults primarily because the existence of a thin Highertemperatures beneath hotspot ridges lead to morepar- low-viscositychannel has not been established. tial meltingand explain the 20-km-thickcrust beneath Iceland I beginby developingmethods for estimating the flux of on- [McKenzie,1984]. An excesstemperature of the upwelling

materialbetween 200 ø C and250 ø C is neededto generatethe.... excess15 km of crustin the computationsof McKenzie[1984]. This averageexcess temperature is also compatiblewith the Copyfight1990 by the American Geophysical Union. depthand volume of extensivemelting beneath Hawaii [McKen- Papernumber 89IB03587. zie,1984] and with the maximum excess temperature of 300øC 0148-0227/90/89JB-03587505.00 of Wyllie [1988].

6715 6716 SL•,: Ho?s•?s • M•rrL• PLU•_•

Ridge axis

Lithosphere t \ 4 ! \ Lithosphere

Asthenosphere Asthenosphere

Plume material Fig. 2. The geometryof platemotion away from the Icelandhotspot is shownschematically. At large distancesaway from the hotspot,the flux of the plumeis balancedby the flow in the lithosphereat the platevelo- city Vt. and the flow in the entrainedasthenosphere. For convenience, both the lithosphereand the asthenospherethickness are assumedto be 100 km in this paper.

velocity at the top to zero at the bottom. The volume flux is then Qp = Vs(L + A/2) Y (1) where V$ is the full spreadingrate, L and A are the thicknessesof the lithosphereand the asthenosphereaway from the ridge, here takento be 100 km, and Y is the along-strike Fig. 1. Mantleplumes are envisionedto tap a basalchannel near the distancesupplied by the plume. core-mantleboundary and to dischargeinto the low-viscosityastheno- Axial topographyappears to correlateon a globalbasis with sphere. The lithospheremoves over the plumecreating a hotspottrack. The radialflow in the asthenosphereaway from the plumecarries heat to crustal thicknessand magma chemistryvariations attributed to the flanks of the swell. higher temperaturesin the ascendingsource material [Klein and Langmuir, 1987; 1989; cf. Brodholtand Batiza, 1989; Viereck et al., 1989]. The distancesupplied by the plumeY is therefore obtainedfrom topography.An along-axisdistance of 500 km of Furtherquantification of theseestimates would give more Icelandis suppliedmainly by theplume, as it is eithersubaerial informationon the temperatureof the upwellingmaterial. In or shallowshelf. Severalhundred additional kilometers where addition,the geochemical anomaly provides information on the elevationand crustal thickness decrease away from Iceland are motionof theplume material [Schilling, 1986]. Unfommately,parfly suppliedby the plume. The geochemicalanomaly the methodof generationof mid-oceanicridge basalts is not extendsover about 700 km [Schilling,1986]. I obtaina fluxof agreedupon. For example, Stolper [1980] and Elthon et al. 63 m3 s -1 byassuming analong-strike length of 800 km and a [1982]state that mid-ocean ridge basalt (MORB) forms from a full spreadingof 16.5 mm yr -• [Gordonand Jurdy, 1986]. picriticmelt generated around 70 km depth.In contrast,The volume flux of magma Qv is 8 m3s-1. Presnalland Hoover [1984] state that extensive partial melting It is usefulto definea buoyancyflux for latercomparison beginsat 30 km depth. The formerhypothesis implies that withoff-ridge hotspots miningextensiveexcess melttemperatureremains inthefrom manfie crustal andthickness. thus precludesForms ofdeter- the B = p,,,otAT Q/, (2) latter hypothesisare thus used by McKenzie [1984]. For- whereAT is the averageexcess temperature, Pm is the density tunarely,the various melting relationships used by McKenzieof themanfie, about 3300 kg m -3, and 0t is the thermal expan- ß 5o 1 [1984] and a simplifiedrelationship by Sleepand Windley s•oncoefficient, about 3 x 10- C-. Thebuoyancy flux of the [1982]give similar excess temperatures. I thus make no Icelandplume is thusabout 1.4 Mg s -1. Asshown below this attemptto improveestimates of meltingrelationships. An esti- flux is similarto the flux of CapeVerde and much less than the mate of 225øC for the averageexcess temperature of the Ice- flux of Hawaii. landplume is usedbelow. The Jan Mayen hotspotis supposedto exist alongthe ridge north of Iceland [e.g., Vink, 1984]. However, it has litfie topo- Flux of IcelandicPlume graphicexpression along the ridge axis. It is possiblyrelated to southwardpropagation of the Moins ridge axis [Saemundsson, The volume flux of the Icelandic plume may be computed 1986]. The flux of this plume if it exists is includedhere in from the kinematicsof spreading. The plume needs to supply that of the Icelandhotspot. the oceaniclithosphere at least down to the depth of extensive melting, about 80 km, and probably the underlying astheno- HAWAUAN I•UM• FLUX sphereas well. I assumethat the plume flux balancesthe flow at a great distance(Figure 2). The flow is assumedto consistof The Hawaiian hotspotis isolatedfrom other featureson the a lithospheremoving at the platevelocity and and asthenospherePacific plateß Thus much speculationon manfie plumesand channelwhere the velocity decreaseslinearly from the plate hotspotshas used it as the primaryexample. The flux estimates SLEEP:HOTSPOTS AND MANTLE PLUMES 6717 for the Hawaiian plume were obtained by Davies [1988a], shouldbe centeredon the plume. Excesselevation associated Richardset al. [1988], andSleep [1987a]. with excesslithospheric temperature moves at the platevelocity. In thissection, I discussthe originof the topographicswell. Hot asthenosphericmaterial moves at a velocityintermediate Then,estimates of the flux of theplume and the averageexcess between the "fixed" velocityof the plumeand the platevelo- temperatureof the plumematerial are obtainedfrom kinematic city. considerations.Finally, the implicationsof geoid data are dis- The geometry of the Hawaii-Emperor bend is particularly cussed. revealing (Figure 3). As noted by Crough [1978] and Detrick and Crough [1978], the decreasein topographydownstream Geometryand Origin of the Hawaiian Swell (northwestward)along the chain and the subsidenceof Midway The geometry envisioned for plumes in Figure 1 is con- Atoll are compatiblewith coolingof a heatedlithospheric plate. venient for discussionand the origin of the Hawaiian swell. The subsidenceof a seamountin the Emperor chain would fol- Flow in the asthenosphereradiates out from the plume in all low a similar thermal contractioncurve if excesstemperatures moved with the lithosphericplate. The situation is different, directions. Hot, less dense material occurs within the plume, however, if a significant amount of the excess temperature within the asthenosphere,and within material moving with the residesin asthenosphere.Consider, for example, material at a lithospheric plate. Uplift of the seafloor occurs from the middepth in the asthenospherewhere the velocity is half the dynamic pressuregradient needed for material to flow in the plate velocity. Such material is now in an L-shaped region asthenosphereaway from the plume, more or lessisostatic com- defined by the younger half of the Hawaiian chain and a track pensationof the material in the asthenosphere,and isostatic parallel to the Emperor chain half the actual distancefrom the compensationof the material in the lithosphere. The first two hotspot. At this depth, the older part of the Hawaiian chain and effects are forms of dynamic compensation,which are con- the Emperor chain are underlainby normal asthenosphere.In sidered separatelyas the asthenosphericchannel is assumedto general,the hot asthenosphericmaterial shouldhave been swept be thin comparedto the depth from which plumesascend. In the case of Hawaii, these effects can be distinguishedeastward relative to the plate, suchthat the Emperorseamounts phenomenologicallybecause the Pacificplate is moving rapidly and the western part of the Hawaiian chain subsidedmore rapidly after the time of the bend, and the region east of the (Figure 3). The uplift and geoid high from dynamic pressure Emperorchain uplifted as hot materialwas sweptunder it. Data from near the Hawaii-Emperor comer (or similar comers on other Pacific chains) are most useful as hot material had just been implacedinto the asthenosphereat the time of the bend and small eastwarddisplacements of hot material at the top of the asthenosphererelative to the lithospherewould cause the westernside of the swell to subsidemore rapidly. Unfor- tunately, derailed subsidencedata have not been obtained near N the bend. The best approachis probably sedimentologicalstu- dies of atolls and also, when available, turbiditc flow directions on the deep sea. The Emperor chain and those parallel to it would be useful as they have not been underlain by astheno- sphere from the plume since soon after the time of the bend. Currentstudies indicate the expectedsubsidence from coolingof rejuvenated lithospherebut lack resolution [Schlanger et al., 1987]. In particular, the Midway subsidencerecord [Detrick and Crough, 1978] does not show any anomaloussubsidence which could be attributedto normal asthenospherebeing swept underthe swell andreplacing hot asthenospherefrom the plume, but Plioceneand Pleistocenesea level changesmake it difficult to examine the subsidence in detail. E The differencebetween crustal age and volcano age decreases Hotspot northward along the Emperor chain [Clague and Dairytopic, 5 ø 1987] making it difficult to recognize subtle variations in depth-age relationshipsor geoid. No excess elevation in the region east to the Emperor chain is evident on the maps of Dynamic uplift Schroeder[1984] and Renkin and Sclater [1988], and no geoid anomalyis evident on the maps of Sandwelland Renkin [1988]. Fig. 3. The geometryof the Hawaii-Emperorchain permits distinguish- ing variouscauses of uplift and geoidhighs. The volcanicchain after However, the swell associatedwith the Emperorchain itself is Renla'nand Sclater [1988] is shaded. Hot lithosphericmaterial moves not well resolved. with t.heplate and remainsbeneath the volcanoes.Asthenospheric ma- Early heat flow data [Von Herzen et al., 1982] showedthat terial moves slower than the plate velocity. The path of material at a the expected downstream increase as heat in the lower litho- depthwhere the velocityis half the platevelocity is shownas an exam- ple. Hot asthenospheredischarged at the time that the hotspotwas ac- sphereis conductedto the surfaceand subsequentdecrease as tive at pointA hadmoved to pointC whenthe hotspotwas active at the cooling occurs. Unfortunately, more recent data are scattered bendpoint B. This asthenosphericmaterial is now at point D. The hot and do not demonstratethis trend [Von Herzen et al., 1989]. materialimplaced at B at the time of the bendhas now movedto point In summary,Detrick and Crough's[1978] conclusionthat the E. Thus the Emperorchain and the westemHawaii chainare now un- derlainby normal asthenosphererather than asthenospheresupplied by thermal anomaly is basically moving with the lithosphereis the plume. Dynamicuplift from radialflow from the plumeis centered probablyvalid, but the actual distributionof excessheat in the nearthe hotspot(500 km diametercircle). asthenosphereis not yet well constrained. 6718 Stem,:Hoxs•n:•s nm• Mam'•

BuoyancyFlux of Hawaiian Swell

The heatand mass budget of the Hawaiianswell is easily constrainedbecause heat is cardedaway from the hotspot by the rapidlymoving lithosphere at the same rate that it is suppliedby theplume [Richards et al., 1988;Davies, 1988a]. In particular, the cross-sectionalarea several hundredkilometers downstream from the hotspot,where the effectsof lessdense material in the asthenosphereand dynamic pressure are expectedto be minor, hasnot beensignificanfiy reduced by coolingand thermal con- traction.It is convenientto representthe mass anomaly associ- atedwith the swellby the buoyancyflux suppliedto the swell by the plume: ...... •/x/11/!! I. I I IlI///x/• B -- W E (Pro- Pw)VL =Ap•, Qp (3) ...... ///x I//11111111/////x/// whereW is the width of the swell, E is the excesselevation averagedacross the swell, P,n is mantledensity, 0r is water density,VL is platevelocity in thehotspot frame, Ap•, is the averagedensity reduction in the volume flux per time, and Q•, is volumeflux of materialsupplied by th._eplume. For the Hawaiianswell the cross-sectionalarea W E is 1430 km2 and thedensity contrast is about 2300 kgm -3. I usea platevelo- cityof 83mm yr -• computedfrom Gordon and Jurdy [1986, Fig. 4. •ow d•cti•s •r •e me• v•ity • •e asthenosphe•am Table3]. Duncanand Clague [1985] obtain 86+ 2 mmyr -• plottedwi• •e platemov•g to •e leftrelat•e to the ma•e. •e stag- -- nationstreamline (dark line) separates asthenosphere onthe left supplied fromages ofvolcanic rocks inthe chain. The computed buoy- by the plume (star) from normal asthenosphere onthe fight. ancyflux is 8.7Mg s -•. (Anextra decimal place is retained so thatfluxes sum properly and can be compared.)Davies [1988a] givesa crosssection of 900km 2 andassumes a velocity of 96mm yr -•, implyingabuoyancy fluxof 6.3 Mg s -•. materialin the asthenospheredecreases with the inversedistance The buoyancyflux is readilyrelated to heat flux from the from the plume plume. The massreduction in a unit volumeof the mantleis Ap = P,nc•AT (4a) Vplume = (6) where 0t is the thermal expansioncoefficient (about wherethe constant vf rf is definedin termsof thereference 3x 10-5 o C-1) and AT isthe excess temperature. Theexcess velocity is vf at theradial reference distance rf. Theaverage heat in this unit volume is asthenosphericvelocity when unperturbedby the plumeis approximatelyhalf the platevelocity. A stagnationpoint thus AH = P,nC AT (4b) occursrs upstreamfrom the hotspotwhere the radial velocity where C is specific heat per mass (about fromthe plume is equaland opposite to themean unperturbed 1.25x 103Jkg -• øC-•).The total excess heat flux, X, sup-velocity of the asthenosphere pliedby the plume is thusobtained from the ratio of AH/Ap c c (7) X = B - Ap•Q• (5) or solving The excessbuoyancy and the totalexcess heat flux are obtained = (8) directlyfrom the cross-sectionalarea and plate velocity of the vL swell since the density,the heat capacity,and the thermal expansioncoefficient of the manfie are well constrained. Normalasthenosphere exists outside the streamline defined by the stagnationpoint, while asthenosphere inside the stagnation StagnationPoint and Excess Temperature point is suppliedby the plume. Richardset al. [1988] and of Hawaiian Swell Sleep[1987a] have noted that the upstream end Hawarian swell is shapedlike a stagnationstreamline, indicating that swell is Theexcess temperature in(2) of the average material sup- reasonably explained bythe presence ofa plume. The stagna- pliedbythe Hawaiian swellis more difficult todetermine asthe tion distance rs obtained fromtopography ofthe Hawaiian volumeflux Q•, is unknown. Fortunately, thevolume flux may swell isbetween 350and 450 km. beconstrained kinematically fromthe shape ofthe nose ofthe Thetotal flux of material from the plume isthe material swell.awayfrom The the basic plume pointinteracts isthat withthe flowflow inin the asthenosphere flowing outward atthe reference distancerf inducedby thedrag of thelithospheric plate. Quantificationof Q• = 2nrfA vf (9) thisconcept following Richards et al. [1988]and Sleep [1987a] introducessome model dependence into the numericalresults. whereA is thethickness of the asthenospheric channel. Taking Materialflows radially in the asthenosphereaway from the thereference distance to be thestagnation distance rs wherethe plumepermitting the modelkinematics to be determinedby referencevelocity is VL/2, the flux is conservationof mass (Figure 4). Thatis, theradial velocity of Q•, = •r• A vœ (10) SLEEP:HOTSPOTS ANDMnm• PLUMES 6719

Pm The averageexcess temperature from (2) is thus Ea = ctATaA (14b) B Pm -Pw AT = (11) •rs A vt pmCt whereATa is the averageexcess temperature in the asthenos- phericchannel of thicknessA. Thegeoid anomaly is thenthe Substitutingfor B from (3) yields differencebetween the positivegeoid anomalyfor the excess WE (Pro-Pw) topographyand the negativegeoid anomaly from the density AT -- (12) •rs A pact deficiencyat depth.This anomaly is approximatelyindependent of wavelength[Turcotte and Schubert, 1982, p. 223]. whichdoes not involvethe platevelocity. The computedtem- 2•G peraturedepends inversely on thethickness of the asthenos- ANn - ha Ea (Pm- Pw) (15a) phericchannel which is theleast constrained quantity in this go equation.Assuming 100 km for this parameter, the 350-450 km whereG is thegravitational constant, g 0 is theunperturbed sur- rangefor thestagnation distance rs yieldsaverage excess tem- facegravity, and ha is theaverage depth to theas theno spheric peraturesof 300 ø -230øC for theHawaiian swell. The volume density anomaly, and similarly 2•G magmasfluxQt, isimplaced about 300in them 3 scrust-1. Inor comparison, erupted is aboutthe flUX4 mQ •3 '-1of ANt - ht Et (Pm- Pw) (15b) [Wattsand ten Brink, 1989]. The averagefraction of plume go materialwhich melts Qv/Qt, is about1/10 that of Iceland.where the subscriptL indicateslithosphere. For example,1.5 Most of the plumematerial beneath Hawaii remains at lower km of excesselevation compensated at 70 km depthimplies a lithosphericdepths where extensive melting does not occur, geoidanomaly of 10.3m. Neglectinghydrodynamic effects for whileplume material may ascend to shallowdepths along the now, the observedelevation is the sum of elevationcaused by ridgeaxis and melt extensively beneath Iceland. thelithosphere and the asthenosphere The fractionof heat carriedto the surfaceby magmais Eobs= Et + Ea (16) Qvp•CAT• F,, = (133 The geoidheight is similarlythe sum of lithosphericand asthenosphericanomalies wherethe subscript v indicates the magma. Around 10% of the heatbeneath Hawaii is extractedby magmasas the amountof Nobs= Nt + Na (17) coolingAT• of themagma from its source temperature includ- Substituting (15) into (17) wouldallow (16) and (17) to be ingthe effects of latentheat is around1800 øC. Magmapro- solvedfor the two unknownsEL andEA. ductionis thusignored in fluxestimates for off-axishotspots in The elevationanomaly and to a lesserextent the geoidano- this paper. malyare modified by lithosphericflexure and volcanic edifices. Some method is thus needed to estimate an uncontaminated GeoidalMethods and AsthenosphericFlow elevationof the swell. Eyeballextrapolations [McNutt, 1984; I havepresumed that the plume is muchnarrower that the Sleep,1987a] give maximum excess elevations around 1.5 km width the the Hawaiian swell and that downstreamfrom the for the Hawaiian swell. However, an inversion for the compen- hotspotthe excesstemperature is moving basically with the sationdepth, the maximum excess geoid height, and the excess lithosphere.A kinematicimplication of thesepresumptions is elevation gave 70 km, 14 m, and2.5 km, respectively[McNutt that hot materialflows laterallyin the asthenospherechannel and Shure,1986]. An inversionwith an additionalfree parame- awayfrom the plume and transfers its heatto thebasal litho- ter, the excesselevation produced by densityanomalies in the sphereby somesmall-scale convective process. That is, the asthenosphere,is unlikely to provideadditional constraints asthenosphereis abnormally hot for a distancecomparable to without heat flow [seeMcNutt, 1987]. the width of the swell aroundthe plume. Suchhot astheno- However,the magnitudeof the expectedeffect of the swell sphereprovides an explanation forrecent volcanism on the nose beingpartly compensated in the asthenosphere is easily obtained andflanks of the swell [Wallin,1982; Lipman et al., 1989]. from forwardmodels. The main difficultyis that the magnitude The hotmaterial and the flow may be alsodetected by study- and shapeof the publishedmeasured geoid anomaliesare ingtopography and geoid. That is, thelower density of the stronglyaffected by filmtingto removelong wavelength com- asthenosphericmaterial tends to produceisostatic uplift. In ponents(Figure 5). Thecomputed model should be filteredin addition,a pressuregradient is requiredfor materialto flow the sameway as the publisheddata. Fommately,filtered laterallyin thelithospheric channel. These dynamic effects are anomaliesmay be computeddirectly by representingthe excess convenientlytreated separately as the asthenospheric channel is massesof topographyand the two compensating layers as a grid assumedto be thin. Neither effect is well resolved in the of pointmasses at the seafloordepth, the average lithospheric Hawaiian data. compensationdepth, and the averageasthenospheric compensa- Asthenosphericand lithospheric isostasy. The uplift from hot tiondepth. Filtering schemes in commonuse are independent materialin the lithospheremay be estimatedby assumingper- of thelocation of thepole or equivalentlyharmonics of all ord- feet pointwiseisostasy: ers of the samedegree are treatedthe same. A procedureis Pm thusimplemented by sequentiallymaking each mass point the EL = o.ATL L (14a) poleof thecoordinate system. The filtered geoid anomaly then Pm dependsonly on the distancebetween the mass point and the wherethe factor involving densities adjusts for theeffect of the measurementpoint [Morse and Feshbach, 1953, p. 1274] waterlayer on isostasyand AT L is theaverage excess tempera- turein thelithosphere of thicknessL. Similarly,the uplift from AN- GM f nPn (cos 0) n+l (18) hot asthenosphereis go ,•=2 rst 6720 S•se: HoTs•Ts•-n M•m_• Pt.trMSS SLF_•I':.HOTSI•TS • MA.Wrl• PLUM• 6721 where0 is the angulardistance between the measurementand • (1- t2) (26) themass, G is thegravitational constant, g 0 is unperturbedsur- EA= Emax 1-S22 facegravity, M is the pointmass, r 0 is the radiusof the obser- vation(and the Earth),rM is the radiusof the pointmass, fn This is equivalentto a 100-kin thick layer with an excesstem- are filter coefficients(which are all 1 for an unfilteredgeoid), peratureof 170øC in the asthenospherebeneath the hotspot. and n is the degreeof the harmonic. The point massfor excess Downstreamof x = -rs, the asthenosphericcompensating mass topography is assumedto be zero and the topographyand the lithospheric mass are assumedto remain constantin width and to decay Mri = Ei,model•"•irr 2 (Pro -Pw) (19) from cooling whereEi•odel is themodeled elevation at gridpoint i, f•i is Et = E m• (1- t2) exp[-(x + r• )/)4 (27) the angulararea representedby the grid point, and rT is the radius excesstopography. The point mass for lithospheric where t is normalizedto the distanceYs at x =-r s and the reduceddensity is decaydistance )• is 100ø . Thes-dependent parts of thelithos- pheric and asthenosphericcompensating anomalies are defined = 2(p., - (20) to conserveenergy along the axial plane [Sleep, 1987a]. The t wherer L is the averageradius of reducedlithospheric density. dependenceis arbitrary but maintainscontinuity. The model Similarly,the point mass for asthenosphericreduced density is topographyand asthenosphericcompensation are shownin Fig- ure 6. Mai =-Ei•t f•i ra2(P,, -Pw ) (21) The excesstopography, the lithosphericcompensation, and wherer A is the averageradius of reducedasthenospheric den- the asthenosphericcompensation were modeledas layers at 5, sity and 75, and 155 km depth,respectively. The equatorof the coordi- nate systemwas taken to be axis of the swell to maintainsym- El;model= El& + Ei A (22) metry. The masseswere representedon a 1ø grid in latitude for perfectisostasy. The complicationthat reduceddensity in andlongitude in thissystem. The swellwas ramcared 40 o the deeperparts of the asthenospheremay produceless surface downstreamfrom the hotspot,rather than attemptingto model topographythan expectedfrom perfectisostasy [Robinson et al., the Emperorswell. All harmonicsabove 101 were ignored;the 1987; Robinsonand Parsons,1988] is not includedin the model upperlimit in actualdata is unclear. The effect of self-gravity as I am trying to show the difficultyin investigatingeven the in the filteredmodels is only a 2% increaseand is ignored. simplestcase. Permanentgeoid and topographicanomalies The effect of asthenosphericcompensation as illustratedin associatedwith chemical differentiation [Robinson, 1988] are Figure 7 is to increase the anomaly near the hotspot as also ignored. Geoid heightis calculatedat each grid point by expected. The increaseis around2 m and would not be easily summing the geoid contributionsat the relevant harmonic resolvedfrom the observeddata. The effect of filteringis more numbersfor each point mass. The singularityfrom the point complicated. The procedureof McNutt and Shure [1986] of massesbeneath the grid point itself is avoidedby representingretaining only the harmonics11 and aboveresults in side lobes thosethree massesby disks with the samesurface area as the as notedby thoseauthors (Figures 7 and 8). The procedureof grid elements. Sandwelland Renkin[1988] of usingcontinuously varying filter A simple parameterizationis usedfor the swell elevationand coefficientsto degree 25 (fn m 1-exp(-(n-2)2/16))gives the compensatinglayers, as the objectiveis to examinethe only a small reductionof side lobes of the model (Figure 8). effect of compensationin the asthenospherenear the plume on The unfilteredgeoid is muchlarger than the filteredones. geoid anomaliesand the effectsof filtering. The shapeof the The large differencebetween the filmredand unfiltered geoids asthenosphericanomalous mass distribution is obtainedpartly impliesdifficulties in previousapproaches. Filtering cannot be from the kinematics of the assumed flow and conservation of dispensedwith altogetherbecause the low harmonicsin the energy[Sleep, 1987a]. The readeris referredto this paperfor geoid are dominatedby featuresunrelated to the swell. Resi- more detail. dual geoidand topography may be obtainedby removingeffects The edgeof the swell was definedby the stagnationstream- associatedwith plate age and maybe slabs. There is some line of Sleep[1987a] with the stagnationdistance rs takento be dangerof making the samecorrection twice, onceduring filter- 4ø . Upstreamof a distancex > rs, theexcess topography and ing and once in making the residual[McNutt, 1988; Cazenaveet the compensatinglayers are zero. In the distancerange al., 1988]. In addition, the effects of the volcanic edifice and its -r s

i i Topography

- _ Asthenosphere

I I 24 16 8 0 -8

Distance along axis, degrees Fig.6. Theexcess elevation of theparame•rized Hawaiian swell is contouredin units of kilometersasa functionof position onthe swell (above). The maximum excess elevation of 1.43km is indicated bya v. Theuplift owing to asthenospheric com- pensationis contoured below. The maximum of 0.715Ion is atthe hotspo•..

Geoid height

i i i ! I Withasthenospherie compensation _

0

2 4

_ • Onlylithospheric compensation L I I I ] I 8 0 -8

Distance along axis, degrees Fig. 7. The filteredgeoid height in metersis shownfor themodel with asthenosph. ericcompensation near the hotspot (above) andthe model with only lithospheric compensation for the same uplift (below). The maxima are indicated with v's. Both modelsare filtered retaining degrees l 1-101. The'houpotis at theorigin. SLEEP:HOTSPOTS AND MANTLE PLUM• 6723

12

- I I I I I l 8 0 -8

Distance along axis, degrees Fig. 8. The geoidheight along is swell axis is shownfor variousmodels and filters. The hotspotis at the origin. The unfilteredmodel includes asthenosphefic compensation. The modelwith the cutofffilter whichretains degrees 11-101 is the firstmodel in Figure7. The smoothfilter by Sandwelland Renkin[1988] reducesthe sidelobes a litfie. The secondmodel in Figure7 alsouses the cutoff filter but has only lithospheric compensation. The computedgeoid has no closedhigh near the hotspot.

Topographyand geoid anomaliesfrom dynamicpressure. fluxis 10 Mgs-1. The densityreduction in theplume was The pressuregradient needed for asthenosphericmaterial to flow assumedtobe 30 kgm-3. outwardfrom the plume is easily approximatedby flow in a The objectivehere is to obtain the shapeof the geoid ano- conduit between two parallel walls. The total radial volume maly associatedwith dynamicflow in the asthenosphererather flux (that is, the surfaceintegral of horizontalvelocity across an than an estimateof asthenosphericviscosity which from (28) imaginarycylindrical surface a distancer from the axis of the dependson the unknown quantity A-3. Modelswere computed plume)is approximately[Sleep, 1987b, equation (2)] for intep•e•gmanfie viscosities of 1022and 1021 Pa s and asthenospheHcviscosities of 1019-1018 Pas. Upliftand filtered QA- -2•rA3 •PA geoid anomalieswere computed(Figure 9). The computed 12qa •r (28)geoid filtered to retain harmonicsabove degree 10 is mainly whereqA is the effectiveviscosity of the asthenosphericchan- dependenton the flow in the asthenosphereand hence the quan- nel and Pa is the excesspressure in the asthenosphere.An tityqA A-3. Theintervening manfie viscosity affects the dis- uplift of approximatelyPal(pm- p•)g is producedby the tanceover which the radialflow occursand the computedgeqid excess pressure. at lower harmonics. The flux QA in (28) is approximatelythe plume flux Q•, in From Figure 9, it is evident that the computedtopographic (10). However,the flux is not constantwithin a plumeradius andgeoid anomalies are strongestwithin 3 ø of thehotspot and of the plume axis and also not constantat greater•stances thusmay be obscured by theeffects of isostaticcompensation of becausematerial in the asthenospheresupplies a rerumflow to the swell and flexuralcompensation of the volcanicedifice. The the deepmantle. Theseeffects are representedin an analytical geoidanomaly and probably the excesstopography are exces- modelby Sleep[1987b]. The plume is consideredto be fed by sivefor an asthenospheric viscosity of 1019-Pa s. Thatis, there a 100-1cm-thick,low-viscosity channel at the baseof the mantle is no 10-m closurein the observedgeoid. The 3-4 m of geoid and dischargeinto a 100-kin-thick,low-viscosity asthenosphere. height for the models with an asthenosphericviscosity of For convenience,both channels were assumedto have the same 3 x 1018are marginally acceptable. The less than 1-m heights viscosity. The manfie betweenthe two channelshas a constant for an astheno spheric viscosity of 10•8 Pa s areacceptable in higher viscosity. The model plume has constantradius, here that they cannotbe resolvedin the data. 0.5ø , andviscosity which was adjusted so thatthe buoyancy As most of the pressuregradient occurs within a few degrees 6724 SLEEP:HOTSPOTS AND MAm'L• PLUMES

1200I 12 ••.x•/./O Geoidheight,m

800 -- Topography, m 8

400 4

• A18'M21-2-----A• • A18,M21 •

4 2 0 2 4

Distance from hotspot, degrees Fig. 9. The computedtopography and geoidheight for dynamiccompensation near the swell are plottedas functionsof radial distancefrom the axis of the plume. The modelnumbers indicate the logarithmof the asthenospheric(A) and the intervening manfie(M) viscositiesin Pa s. The geoidanomalies are filteredretaining degrees 11-101. The modelswith high asthenospher- ic viscosityare unacceptable.The geoidheight of modelA18.M22 is too smallto plot.

of the plume, the derived asthenosphericviscosity relates to mate of the averageexcess temperature of the Icelandicplume. asthenospherepartly chargedwith hot materialfrom the plme. This temperatureneeds to be comparedwith the maximin The distributionof viscosity around the plume should be excesstemperature at the centerof the plume which provides laterallyheterogeneous, but thereis little pointof moresophisti- evidenceon the temperaturecontrast across the basalboundary catedmodels until a dynamicpressure effect is recognized.The layer. Fortunately,the volumeflux and the temperatureflux are upperlimit of asthenosphericviscosity of about3 x 1018Pa s easilycomputed in a tubularconduit [Sleep, 1987b]. For sim- near the hotspot is compatible with the upper limits of plicity, it is assumedthat viscosityvaries as asthenosphericviscosity near fracture zones of 1019Pa s [Craig andMcKenzie, 1986] and 102o Pa s [Robinsonetal., 1988]. 11= fluexp(-AT/Tn) (29) However,the "normal"viscosity of Pacificasthenosphere is where11M is theviscosity outside the plume is thenormal man- toopoorly constrained to search for localvariation near the fieand T n is a scalingparameter. The temperature difference at hotspot. a point relativeto the surroundingmantle is for convenience It wouldbe nice to concludethat dynamicpressure is also assumedto be the conductionsolution [Carslaw and Jaeger, unimportantfor all otherhotspots, which, as shown below, have 1959,p. 258] volume fluxes much less than Hawaii. The thickness and viscosityof the asthenospheric channel,however, maybe AT= ATm,xexp(-r2/r/) (30) differentfor each hotspot. Although I have found no example of whereATma x is thetemperature contrast of thecenter of the significantdynamic pressure around a hotspot inthe course of plumewhich its surrounding andrt, isa measureofthe radius this work,examples of significantdynamic pressure around of theplume. The flux of materialthrough the plume is plumes may still be found. The reader is further cautionedthat dynamic pressure and asthenosphehccompensation can be separatedonly if a thin well-definedasthenospheric channel QP= 12zcrvdr (31) o exists. wherer! is theupper limit of integration(here 2r•, ) andv is AverageExcess Temperature of Hawaiian Plume the vertical velocity within the plume assumingthat flow is drivenby the densitycontrast within the plume. That is, v (r) Crudeestimates of the temperatureof materialin the astheno- is obtainedby integrationof the shear stressequation inward spherebeneath the Hawaiian hotspot and hence the average from rI. Themean excess temperature ofupwelling is excesstemperature of the Hawaiian swell were obtainedabove from the geometryof the stagnationpoint and from analyzing rt topographyandgeoid. The preferred estimate isaround 200øC • = Q•71121rr ATvdr (32) with considerableuncertainty, similar to the petrologicalesti- 0 SLEEP:.HOTSPOTS AND MAma_• Pt,tJM• 6725

The ratioT/ATma x dependsof the totalviscosity contrast across the plume. Although Courthey and White [1986] and McNutt theplume or on ATmax/T•l.This ratio is 0.64for 2 ordersof [1987, 1988] give detailedanalyses, the essenceof their reason- magnitudeviscosity contrast across the plume and 0.77 for 3 ing is simply explained. Heating has been going on long ordersof magnitude.A 200ø C averagetemperature contrast enough that the geothermfrom passiveheating in the litho- thusimplies a maximumtemperature contrast of 310ø -260 ø C. spherewithout an underlyinghot source(as would occur if the lower lithospheredelaminated and sank to great depth) should CAPE VERDE PLUME FLUX resemble the geotherm in younger oceanic crust. Thus the square-root-of-agelaw representsheat flow The Cape Verde hotspot(Figure 10) is selectedas an exam- ple of a plume on a slowly movingplate. Althoughuncertain- q = q0/•a (33) ties in the relativevelocity of the hotspotto the underlyingman- and topography fie createdifficulties in the kinematicanalysis of the swell, the slow velocity simplifies the analysisof heat flow and geoid $ = Sr - Sox•a (34) anomalies. where ta is the apparemthermal age of the crust,the constant q0implies 500 mW m -2 on1-m.y.-old crest, the constant Er is Heat Flow and AsthenosphericTemperatures ridge elevation,and the constantE 0 impliessubsidence of 350 Over 10 m.y. are required for heating of the lower litho- m in the first million years. The heat flow anomalyrelative to a sphereto producea heat flow anomalyat the surfaceif only half-spacemodel is 20 mWm -2 [Courtneyand White, 1986] conductionis important. The heat flow anomalyfor Hawaii is and the topographicanomaly is 1900 m [Courtneyand White, thusexpected to be far downstreamof the hotspot[Von Herzen 1986] to 2400 m [McNutt, 1988]. Taking the seafloorage as et al., 1982] and provideslittle evidenceof the detailsof ther- 125Ma, theunperturbed heat flow is 45 mWm -2. Heatflow mal structureat the hotspot. However, the Cape Verde hotspot 20 mWm -2 higheris equivalentto59 Ma crust.An elevation has moved slowly relative to the lithosphereand a pronounced changeof 1220 m is expectedbetween normal crustsof these heat flow anomalyhas had time to reach the surface[Courtney ages. Thus somewherebetween 700 and 1200 m of the uplift and White, 1986]. Volcanismand uplift beganat least 20 m.y. may be attributedto sublithosphericeffects. This is similar to ago in this area, long enoughfor heatingin the deeplithosphere the amountof thermaluplift in the astheno sphere obtained from to producethe heat flow anomalies[McNutt, 1988; Courtney the kinematicanalysis of the Hawaiian swell. and White, 1986]. These authorsconclude that at leastpart of The geoid anomaly is somewherebetween 8 rn [Courthey the uplift and geoid anomaliesare related to sublithosphericand White, 1986] and 12 rn [McNun, 1988]. These authorsnote mass deficiencyor dynamic uplift from fluid flow away from that this anomalyis compatiblewith asthenosphericcompensa-

N

Cape Verde

Geoid height 500 km Fig. 10. The geoidheight in meters[after Courtney and White,1986] is contourednear the CapeVerde hotspot. The stagna- tion curveis fit by eye and is definedby the breakin slopeto the northeastand the 13-m contourto the southwest.The as- sumedposition of the hotspotis indicatedby a dot. 6726 SLEEP:HOTSPOTS AND MAm'LE PLUM• tion. As with Hawaii, the difficulties in filtering preclude asthenosphericcompensation is needed on the slowly moving obtainingmore detailfrom the geoidanomaly. African plate [McNutt, 1988] may be an effect of sampling. For Hawaii, only a small fraction of the swell near the hotspotis Total EnergyFlux and VolumeFlux underlainby abnormallyhot asthenosphere,while the rest of the swell is compensatedmainly in the lithosphere.Inversion for a The kinematic assumptionthat the plate is rapidly moving single compensationdepth will thus pick a lithosphericone over a hotspot, which simplified analysisfor Hawaii, is not appropriatefor most of the swell. Conversely,hot astheno- appropriatefor Cape Verde. An estimateof plume flux may be sphereunderlies much of the Cape Verde swell and is more obtainedfrom the shapeof the swell. The global model used easily detected. Volcanic magrnas also have more time to here [Gordon and Jurdy, 1986] predictsnortheast to southwest penetratethe lithospherenear Cape Verde and thus erupt away movement of the hotspot relative to the lithosphere at from the axis of the swell. In contrast, the flanks of the Hawaii 18 mmyr -1. UnlikeHawaii, the absolute plate velocity is the swell are also underplatedby hot material but volcanicactivity, sourceof considerableuncertainty for Cape Verde. For exam- thoughpresent [Wallin, 1982; Lipman et al., 1989], is lessobvi- ple,Courtney andWhite [1986] •:ive 12 mm yr -1 and Duncan's ous. [1984] tablesimply 13 mm yrTM. The tabulateddirection and rate of the model hotspotare largely controlledby the Walvis GLOBAL PLUME FLUX Ridge to the south. Unfortunately,the swell directionand the track directionare The plume fluxesdetermined above vary by a factorof 6. A not clearly evident on either a geoid (Figure 10) or topographic uniformaverage excess temperature of around200øC is compa- map. If southwestpropagation is assumedthe geoid anomalyto tible with both geophysicaland petrologicaldata. I next apply the west northwest must be attributed to an unrelated feature, the methodsdiscussed above to 34 more plumes. Averageplate but the Cape Verde Plateauto the northeastis explainedas the velocities for the last 10 m.y. [Gordon and Jurdy, 1986] are track. The swell front to the southwestmay be fit to a stagna- usedbecause material takes aboutthat long to flow away from tion curve (Figure 10). The stagnationdistance of 390 km the plume to produce a swell. Consistentmethods are used impliesa volumeflux of 70 m3 s -1 for a platevelocity of throughoutso that the relative fluxes of plumes may be com- 18mm yr -1 (equation(10)). Thisis aboutabout 1/4 of the pared. Eyeball estimatesfor the cross-sectionalarea of swells Hawaiian flux. and stagnationstreamlines are used. The reader may easily The cross-sectionalarea of the swell after removing the 700 adjustthem if desired. The weakesthotspots have no obvious m of uplift for asthenosphericcompensation obtained above by swells or geoid anomalies. The relative errors in their small consideringthegeoid and heat flow is about1200 km 2, whichfluxes are greater,and for the most part, upperlimits are used impliesa buoyancyflux of 1.6Mgs -1 about1/5 of the as estimates. Hawaiian flux. Within the accuracyof the data, the average For hotspotswith swells, the method is similar to that of excesstemperature, which is obtainedfrom the ratio of buoy- Davies [1988a]. The main differencesare that Davies assumed ancy flux to volume flux, is the same for Hawaii and Cape that the cross-sectional areas of swells were all 750 km times Verde. the swell heightand used plate velocities from Minsterand Jor- The hotspothas beenstationary long enoughthat a minimum dan [1978] andPollack et al. [1981] whichimply thatthe Afri- estimateof the total energyflux might be obtainedfrom the sur- can plate is nearly fixed. Davies [1988a] used swell height, face heat flow. This requiresextrapolating the data of Courthey which is parfly associatedwith thicker crust,to obtainan esti- and White [1986] over the areaof the swell. From Figure9 of mate for Iceland. He also made no correction for asthenos- Courtneyand White [1986] the half width of the swell is 600 pheric compensation.Although I obtain a similar global flux, km andthe average heat flow anomaly is about10 mWm -2. more accurateestimates for individual plumes strengthenhis The length of the swell is 1500 km. This implies an excess conclusionand permit additionalphenomenology. heatflow of 1.Sx101øW. Multiplyingby {x/C givesthe equivalentbuoyancy flux of 0.4Mgs -1 whichis muchless Which Hotspots Are AssociatedWith Plumes? than the direct estimate. The assumptionthat heat flow has comeinto steadystate with heat supplyis probablynot justified. Not all off-ridge volcanism is necessarilyassociated with As discussedlater, this is a general feature of hotspots,and plumes. Some criteria to selecthotspots are obtainedfrom the much excessheat suppliedto the lower lithosphereis ultimately phenomenologicalpredictions of the plume theory. Mantle subducted. plumes,as envisionedhere, supplyhot material to the astheno- spherebeneath hotspots. The hot material spreadslaterally in the asthenosphericchannel. Heat and material are exchanged Cape Verde Results betweenthe lower lithosphereand the asthenosphereby convec- In summary,the buoyancyand volume fluxescan be obtained tion. Even if plumes exist, some off-axis volcanismmay be for hotspotson slowly moving platessuch as Cape Verde. One associatedwith cracks(see reviews by Sleep[1984] and Clague sourceof error is that the computedfluxes scaleto the velocity and Dalrymple [1987] for references). of the plate which has a large relative uncertainty.Another is The existenceof well-definedhotspot tracks is evidencefor that material downstream from the hotspot has cooled plumes. In particular, Morgan [1981], Crough [1983], and significantlyso that the cross-sectionalarea of the swell is deter- Duncan [1984] have noted that several hotspot tracks have mined right at the hotspot. A correctionfor uplift associatedcrossed a ridge axis either in the Ariantic Ocean or the Indian with hot material in the asthenosphereis thus needed. For- Ocean. If true, this is supportfor plumesoriginating at great tunately,the correctionis constrainedby geoid and heat flow depth. Cracks would be expectedto stop when they reach a data. free edge. The evidencefor anomalouslyhot asthenosphereand The difficulty that lithospheric compensationalone can ascendingmaterial beneath Iceland, Hawaii, and Cape Verde is explain swells on the fast moving Pacific plate but that furtherstrong support for plumesand againstpassive delamina- SLEEP: HOTSPOTS AND MANT• PLUM• 6727 tion along a crack. At present,the geophysicalarguments that the active East Pacific Rise is consideredto be stressrelated. suchhot material actualoccurs are somewhatmodel dependent Fortunately, as noted by Davies [1988a], these uncertain or even for thesehotspots. The other lessstudied and lessisolated omittedhotspots have small buoyancyfluxes. hotspotsare ill suitedfor applicationof thesemethods. In prin- cipal,improved estimates ofthe mount of hot plume material Atlantic Hotspots in the sourceregions of on-axishotspots could be obtainedfrom petrologicalconsiderations following Klein and Langmuir [1987, In additionto Cape Verde, Duncan [ 1984] lists the following 1989]. I do not attemptthis here anduse only topography. hotspotsin the Atlanticocean south of 40øN: Azores,Madeira, Hotspots in regions of active rifting or recent continental Canary, Bermuda, Great Meteor, Fernando, Helena, Martin, breakup constitutea difficulty. Morgan [1981] shows that Tristan, Discovery,Meteor, and Bouvet. The Bermudahotspot hotspot tracks weaken continentallithosphere so that breakup is the most investigatedgeophysically. Hoggar is includedin can occur. However, off-ridge volcanismis expectedalong the this section even though it is on the African continent. The entire Atlantic margin before spreadingbecomes established. Azores, Tristan, and Bouvet hotspotsare modeledhere as on- Postorogenicalkalic centersin Aftfica,Eurasia, and North Amer- ridge featuressimilar to Iceland. ica occur along preexistingweakness and thus are often attri- Bermuda. Bermudais similar to Cape Verde in that it is on buted to intraplatestress [Sykes, 1978; Black eta/., 1985; Giret a slowly moving plate and that heat flow data are available. and Laineyre, 1985; Bbdard, 1985; McHone et al., 1987; Still- The hotspotis moving to the east. It also appearsthat activity man, 1987]. For example, the Monteregian-Hillsand White has waned over the last 20-30 m.y. [Detrick et al., 1986]. The Mountain magma series in easternNorth America, which is presentheight of the swell is about 1000 m [Crough, 1983] and clearly associatedwith a seamount chain on the adjacent the wavelengthis about 2000 km [Detrick et al., 1986]. The seafloor, is attributed by Bbdard [1985] and McHone et al. heat flow is 57 mWm -2 near the crestof the swell on 116 [1987] to variationsin intraplatestress. In addition, evidence m.y. crust [Detrick et al., 1986]. The expectedhalf-space heat on land from absoluteages of a well-definedtrack is equivocal flowis 46 mWm-2, andthe apparent thermal age from the [McHone and Butler, 1984]. Excessive volcanism along observedheat flow is 77 Ma. The expectedelevation is thus breakupmargins is evidencefor plumes [White and McKenzie, 700 m. Thus about 300 m of uplift are associatedwith 1989]. However, Mutter et al. [1988] have proposeda delami- asthenosphericprocesses in general agreementwith Detrick et nation mechanism involving convectiondriven by the lateral al. [1986]. It is not unexpectedthat this is lower than the temperaturegradient along the breakupmargin. amountfor Cape Verde becausethe Bermudaplume appearsto A furtherfeature is that the hot materialfrom plumesshould have wanedso that the hot asthenospheresupplied 40 m.y. ago spreadlaterally in the asthenosphereand be transportedfor large has had time to cool. The computedflux is a measureof the distances. Following Schilling [1973, 1986] and Morgan averageflux over that time and probablyan overestimateof the [1978], severalareas of volcanismcan be explainedif plumes current flux. are considered sources of hot material that flows out rather than The cross-sectionalarea of the swell is about 1300 km2. as separatepoint sourcesof heat. Some of the areasare easily Making a correctionfor asthenosphericcompensation yields a explainedin this way onceone acceptsthe existenceof plumes. swellarea of 1000km 2. Theplate velocity of 15mm yr -• The Reykjanesridge is the result of hot material flowing away impliesa buoyancyflux of 1.1Mgs -•. Assumingan excess from the Iceland plume [Schilling, 1973, 1986] and Darwin temperatureof 225øC gives a volumeflux of 48 m3 s -• anda Islandis the resultof materialfrom the Galapagosplume reach- stagnationdistance of 320 km. The upstreampart of the swell ing the spreadingaxis [Morgan, 1978]. Material entrainedwith may be fit by a stagnationcurve (Figure 11). the lithosphereis evidentlythe causeof CocosIsland northeast Other Atlantic off-ridgehotspots. Courthey, McNutt, Detrick, of the Galapagoshotspot [Castillo et al., 1988]. Slowlymoving and their coworkersappear to have selectedthe hotspotswith plates loiter for a long time in the area of hot asthenosphere.the strongestgeoid anomaliesfor their studies. Bermuda and For example,a singleisland in the Canarychain has a recordof Cape Verde are both obviousin the filteredgeoid maps of Vogt volcanismfrom 65 Ma to present[Stillman, 1987]. et al. [1984], Bowin et al. [1984], Jung and Rabinowitz[1986], This late or prolonged volcanism also requires intraplate and Cazenaveet al. [1988]. No resolvedanomaly is associated stressesfavorable to the ascentof magma. Thus evidenceof with Great Meteor, Fernando,Martin, Discovery,Meteor, and stressand structurecontrol of volcanismdoes not preclude a Helena. Crough [1983] gives swell heightsof 1200, 500, 500, plume source for the hot asthenosphere.In the compilation 600, 600, and 500 m, respectively.Obvious broad topographic below, hotspotswhich have tracks in the general direction swells are not associatedwith the latter four hotspots[Hayes, expectedfrom plate motions are attributedto plumes. Some 1988, Figure 7]. traditionalhotspots are excluded: JanMayen is consideredpart A geoid anomalyis associatedwith the Canaryhotspot, but it of the Iceland hotspotas noted above. Madeira is includedwith is somewhatobscured by the nearnessto the Afi'ican margin. Canary. The Comores Islands are considered to be a This anomaly is most evident on the map of Jung and Rabi- combination of a stress-related feature, near a continuation of nowitz [1986] and may be 2/3 of the Cape Verde anomaly. the East African rift [Grimison and Chen, 1988], and hot Madeira doesnot have a geoid anomalyindependent of Canmy material from older packs. ,a•msterdamand Roch'iguezare con- a_n•here is includedin the Canary.flux. sidered to be associated with hot material entrained into the The fluxes from theseplumes are thus not well constrained ridge axis [Morgan, 1978]. Eifel is relatedto the Rheingraben.but cannot be large. I usea buoyancyflux of 1 Mgs -1 forthe No attempt is made to separate stress- and plume-related Canary (includingMadeira) hotspotand a upper limit flux of featuresin Africa, exceptHoggar, or to obtain fluxesfor Mount 0.5 Mgs -1 forthe other six hotspots. This history of theGreat Erebusand Raton. Only a preliminaryestimate is obtainedfor Meteor track will be discussedin detail in a futurepaper. The Yellowstone. Revillagigedonear the intersectionof the extinct buoyancy flux when it crossed the ridge was less than Mathematiciansspreading center [Mammerickx et al., 1988] and 0.5 Mgs-1; previously, it had been much stronger. 6728 Snv_•v: HOTSPOTS AND M•q'I•

Bermuda Tristan. The flux of the Tristan hotspot appearsto have waned with time. In the Cretaceous Period, the Rio Grande Rise on the west and the Walvis ridge on the eastwere highly elevated platformssimilar to Iceland at present. There were N severalridge jumps before 71 Ma ago [Barker, 1983]. The flux at the time the Rio Granderidge was activemay be estimated by usingthe spreading rate of 52.6mm yT -1 [Lawveret al., 1985, Table 1] from 84 to 64 Ma and an effectiveridge length of 800km. Thisimplies a volumeflux of 200 m• s-1 anda buoyancyflux of 4.5 Mgs -a. The hotspotis now on the African plate and associatedwith a 500km more subtle trace. The affected ridge length betweenTristan Hotspot and Gough is 800 km. The spreadingrate from Gordon and Jurdy[1986] is 40.9mm yr -1. Assumingthat the plume sup- plies half of the material over that length, the volume flux is 78 m3 s -a, and the buoyancy flux is 1.7Mg s -1. Hoggat. The Hoggar hotspot has been studiedby Crough [1981]. The excess elevation is about 1 km. A track is not obvious from available data, but the edifice is aligned in the generaldirection of plate motion. Gordon and Jurdy's [1986] platevelocity is20 mmyr -1, andthe cross-sectional areameas- 0 ! 1 uredacross the expected strike is about400 km 2. Thisimplies 500 km a buoyancyflux of 0.9 Mg s -1. (Notethat a densitycontrast of Geoid height 3300kg m -• isused for tracks on land.)

Fig. 11. The geoid height in meter• near Bermudais ½ontoun•din me- Tasman Seamount Chains ters [Detrick et al., 1986]. A 500-km stagnationcurve is fit by eye to the anomaly. The model hotspotis at the dot. The singlevolcanic McDougall and Duncan [1988] define three hotspottracks: edificeis representedby the 6-m contour. one on the east coast of Australia, one in the center of the Tas- man basin, and one on the east of the Tasmanbasin. Propaga- tion to the south is demonstratedby absoluteages of volcanic Other on-ridge Atlantic hotspots. The remainingon-ridge rocks from the first two seamountchains. The expectedpropa- hotspots,Azores and Bouvet, have not producedlarge islands gationrate from Gordon and Jurdy [1986], 63 mmyr -1, agrees like Iceland. The temperatureor the flux for thesefeatures is with this progression.Two of the chainsoccur along conjugate thus likely to be less than that of Iceland. In particular,the rift margins, and the third occurs along the extinct spreading fluxesare likely to be too low to fully supplya lengthof ridge center of the Tasman basin. Without the excellent evidence for so that both plume material and normal mantle are entrained tracks,this volcanismwould probablybe attributedto intraplate into the ridge axis. stress. The Bouvet hotspotis near a triple junction of ridges. The The widths of the swells associated with the two marine elevated crust associated with Bouvet Island extends about 100 tracks are not evident. The seamountshave subsidedsimilarly km alongthe strikeof the India-Antarcticridge. Speissridge, to the rate expectedif they rest on normal oceaniccrust. For which is on the next segmentto the northwestextends over a example, Recorderseamount which rests on 55 Ma crust has similar distance[Sclater et al., 1976, Plate 1]. The spreading rateon this segment is 16.6 mm yr -a [Sclateretal., 1976, Fig- subsided500 m since 25 Ma [McDougall and Duncan, 1988]. The expectedsubsidence is 680 m. Even allowing time for the ure 6]. The buoyancyflux is thus about 1/4 of Iceland or 0.4 Mgs -a. seamountto erode and for reduced apparentsubsidence from sealevel decrease,only a few hundred meters of extra sub- Enhanced volcanism on the North American, Africa, and sidenceare permittedby the data. For example,subsidence of European plates is associated with the Azores hotspot. 900 m over the last 25 m.y. would imply resettingof the Subaerial volcanism occurs from Flores on the North American apparentage to 23.5 Ma from 30 Ma and an uplift of 200 m. plate to Sao Miguel 500 km to the East on the Africa-Europe The width of uplift of the track along the coastof Australia spreadingcenter [Saemundsson,1986]. However, a track is not may be determinedfrom topographyand the scatterof volcanic obviousfrom the topography.The flux from this plume appears centersfrom the track. Uplift is harderto determineas the track to be intermediate between Iceland and Bouvet. A large follows a youngAtlantic type margin. If 700 m of uplift and subaerialplateau has not formed but a 500-km-longregion 300 km cross section are assumed,then the cross-sectionalarea along the strike of the Mid-Atlantic Ridge is elevatedand lacks is 140km 2. The buoyancyflux is 0.9Mgs -1. The two a centralrift. An elevatedregions is also producedalong the marine tracks appearto have waned and have sparsevolcanism third slowly spreadingridge. The spreadingrate of the Mid- at present. The flux of the land hotspotis an upperlimit for the AtlanticRidge here is somewhat more rapid (22 mm yr -a tothe other two tracks. The current flux could be much smaller. southand 26 mmyr -1 to thenorth) than at Iceland,implying that more materialis neededto suppliedthe oceaniclithosphere Pacific Hotspots at the ridge. Assumingthat 450 km of lithosphereand astheno- spherecome from the plume at a rateof 24 mmyr -1, equation Numerousactive hotspotsin additionto Hawaii occurin the (1) givesa volumeflux of 51 m3 s -a anda buoyancyflux of Pacificbasin. Unfortunately,it is more difficult to estimatethe 1.1Mg s -1 forthis hotspot. fluxes of these hotspotsthan it is for Hawaii. The southern S•P: HoTseoTs• M•'x• I•trM• 6729

Pacifichotspots are closelyspaced and sometimes considered a 200mm yr -1. Thevolume flux is thus 140 m 3 s -1. Assuming hot line [Bonattiet al., 1977]. The near-ridgehotspots, Cobb an averagetemperature of 225øC the buoyancyflux is on the Juande Fucaridge, Easter on the EastPacific Rise, and 3.3 Mgs-1, equivalentto the averagefor the superswell the Galapagoshotspot have not createdlarge areas of subaerialhotspots. ridge like Iceland. The Galapagoshotspot is strongenough to produceseamount Superswellhotspots. McNutt and Fischer [1987] have called chainson eachside of the spreadingcenter and also to be asso- the topographicfeature associated with the Easter,Pitcam, ciatedwith variousridge reorganizations [Hey, 1977;Hey et al., Marqueses,Macdonald, and Tahiti hotspots the PacificSupers- 1977]. The stronglyaffected region is againabout 300 km well. This feature is not simply overlappingswells. Hot long,but the full spreading rateis only 60 mm yr -•. Thusthe materialis entrainedat the ridgeand the depth-agerelationships volume flux is 43 m3 s -1, andthe buoyancy flux is 1.0Mg s -1. are different from normal crust. It is hard to determine the flux NortheastPacific hotspots. The Juande Fuca and Bowie of individualplumes because hot materialvented into alreadyhotspots are associatedwith ill definedchains. Neither feature hot asthenosphereproduces no additionalanomaly. The total showsany anomalous Sr isotoperatios [Eaby et al., 1984;Allan buoyancyflux of 13.3Mg s -1 canbe estimated from the cross et al., 1988]. It is possiblethat bothchains are not associated sectionalarea of 2200km 2 in Figure3 of McNuttand Fischer with plumesbut are stress-relatedeffects of reorganizationof [1987]and the plate velocity of 83 mmyr -•. Davies[1988a] the ridge axis andnearby plate boundaries. Flow of material givesa totalbuoyancy flux of 15.9Mgs -1. Attributingthis from the Yellowstoneplume or the plumehead associated with flux to the four off-ridgehotspots gives a buoyancyflux of the Columbiabasalts is anotherpossibility. The approachof the 3.3 Mgs -1 to each,about 3/8 of Hawaii.The stagnation dis- Juande Fucahotspot toward the ridgeas expectedfrom abso- tancefor this flux is lessthan 200 km precludingswells which lutevelocities is the strongestevidence for consideringit to be a can be easilydistinguished from the effectsof flexureand the plume[Karsten and Delaney,1989]. Thesehotspots are dis- volcanic edifice. Heating of the lithosphereis recognizedcussed to showthat the fluxesof theirplumes, if they exist, are mainlythrough the subsequent subsidence of atolls [e.g., Detrick small. andCrough, 1978]. The situationis thusanalogous to theolder The Juande Fuca hotspotis clearlymuch weakerthan the Marshall island track where multiple heatingevents and even- Galapagosone. No islandsare produced and the hotspot does real coolingare indicatedby studiesof sediments[Schlanger et not producelarge seamounts on bothsides of the axis. The al., 1987]. regionwith excesselevation is only 100 km long. Assuming The Caroline,Samoa, Juan Fernandez, and San Felix hotspots thatthe plume supplies half the material over that length gives a are probablyweaker than the other SouthPacific hotspots. volume flux estimateof 17 m3s-1 and a buoyancyflux of Crough [1983] gives no swell heightsfor the former two 0.3 Mgs -1. hotspotsand heights of 500 and700 m for thelatter. Noneof This estimate is also used for the nearby Bowie seamount them have obvious swells. The Caroline hotspot appears to chainfor whichCrough [1983] gives a swellheight of 300 m. have weakened as the volcanic edifices decrease to the east A well-defined track is not associatedwith Bowie [Dalrymple et [Keatinget al., 1984]. Samoais near the Tongaarc. Some al., 1987]. It is unclearwhether this hotspot is on-ridgeat Dell- morerecent volcanism may be associatedwith flexure[Wright woodKnolls or off-ridgenear Bowie. FollowingDuncan and and White, 1987]. Juan Fernandezand San Felix have been Clague[1985], I considerBowie hotspotto be on the ridge. attributedto intraplatestress similar to that whichbroke the The same flux estimateis also assignedto the Baja hotspot plate along the Galapagosspreading center [Marnmeric•, which is associated with a similar ill-defined chain. 1981]. There is some possibilitythat San Felix taps hot Yellowstone.The SnakeRiver plain definesthe track of the materialentrained by theplate at the Easterhotspot. Half of the Yellowstonehotspot. The propagation rate, 35 mmyr-• is flux of the othersuperswell hotspots is assignedto thesefour definedby a varietyof studies[Anders et al., 1989]. The ther- hotspots. mal uplift is about1 km from the subsequentsubsidence and Louisville. The Louisville hotspot has waned drastically from heat flow data [Brott et al., 1981]. The cross-sectional [Wattset al., 1988;Lonsdale, 1988]. It is markednow onlyby area for the swell and the distanceto the stagnationpoint are a small volcano at 138.1øW. The seafloor is at most 300 rn muchmore difficult to determineas uplift needsto be separated shallowerthan the expected4800 rn depth of 43 Ma crest. fromprevious elevation differences. More field work is needed Bathymetryand and geoiddata are insufficientto definethe to relate seismicityand field geologyto uplift aheadof and active end of the swell. The flux of this hotspotis clearly less lateralto thehotspot track (M. Anders,personal communication, thanthe smallersuperswell hotspots. I assignas an upperlimit December1988). It is importantto determineif thiscontinental theflux of 0.9 Mgs-1 as thehotspot and plate velocity are feature is similar to oceanic hotspots. For now, the cross- similar to the Tasman Sea chains. As will be discussed in a sectionalarea of theswell is assumedto be 400 km2, givinga futurepaper, it was previouslymuch stronger. buoyancyflux of 1.5Mg s -1. Pacificnear-ridge hotspots. The flux of the Easterhotspot may alsobe estimatedfrom the along-strikearea where the Indian Ocean Hotspots ridgecrest is elevated.Unlike Iceland and to someextent the Azores,a largearea of subaerialexposure is not'-•,-'• ... • The The Crozet,R6upJon, and Ker•m,o.len hotqpo_[shave produced main effectsof thishotspot extend about 300 km alongstrike. tracksin the Indian Ocean[Morgan, 1981]. The Afar hotspot Partof theflux of theplme is returnedto theEast Pacific Rise, hasproduced a subaerialplateau near a triplejunction. partremains on theNazca plate, and a little crossesthe ridge Crozet. Crozet is similar to Cape Verde in that the excess andends up beneatheither the Eastermicroplate or thePacific heatflow, the excesstopography, and the geoidanomaly imply plate. I assumethat half thelithosphere and the asthenospheresome compensation in the astheno sphere [Courtney and Recq, of the spreadingridge along an equivalentlength of 300 km is 1986]. The hotspotis placedby Morgan [1981] beneaththe related to the plume and that the full spreadingrate is Del Canoplateau near 45 ø S, 45øE. However,the Del Cano 6730 SL•: HOTSPOTS AND Ma_m'I• PLUMm feature appearsto be much more shallowly compensatedthan 53 m3 S -1. Thebuoyancy flux (assuming it takes an average the Crozet Bank to the east [Gos!in and Diament, 1987; excessof 225øCto make subaerial plateaus) is 1.2 Mg s -1. Sandwell and MacKenzie, 1989]. I place the hotspotnear the CrozetIslands around 46 ø$, 50ø E (Figure12). A stagnationGrand Total Global Flux curvewith rs = 140 km may be fit to the west-northwestend The buoyancyfluxes estimatedfor the 37 hotspotsdiscussed of the swell. The expectedplate motion, however, is N96øW. above along with a reliability are given in Table 1 along with A volumeflux of 22 m3 s q is obtainedfrom the stagnation dis- the flux estimatesof Davies [1988a]. The Hawaiian hotspotis ranceof 140km anda platevelocity of 16 mmyr q. Againclearly the largest. The fluxes determinedfor hotspotsvary by assumingan averageexcess temperature of 225ø C, the buoy- a factor of 20 even consideringonly plumes with good tracks. ancyflux is 0.5Mg s -1, similarto whatI haveassigned to Thus one shouldnot extrapolatethe Hawaiian flux by multiply- other weak hotspots. ing by the global numberof hotspots. The total buoyancyflux Kerguelen. The Kerguelentrack has crossedthe ridge axis. is 54.9Mg s -•. Somehotspots, particularly continental ones, The current elevation anomaly is difficult to separatefrom the are omitted,and the flux of someof the weakerhotspots overes- plateauformed while the hotspotwas closerto the ridge [Storey timate& Although the estimatesfor individual hotspotsdiffer, et al., 1989]. The historyof this track is thustoo complicated the total is in excellentagreement with Davies' [1988a] estimate to resolvehere and the Crozet flux assignedto Kerguelen. of 41.3Mgs -1, whichomits on-ridge hotspots but includes R•union. The ba•ymetry and geoidof the R•unionhotspot more continental hotspots within Africa. The difference havebeen studied by Bonnevilleet al. [1988]. The swellis evi- betweenthe two estimatesindicates the true uncertainty. Multi- dent from both data sets. The stagnationdistance is about300 plying by C/{z gives an equivalentsurface heat flow of lcm (Figure 13). The swell height is 1100 m [Crough, 1983]. 4.48mW m -2 averagedover the planet. The crosssection is about900 km 2. Thespreading rate is 28.5mm yr -1. Thebuoyancy flux is thus1.9 Mgs -1. The DISCUSSION AND PI•IENO•NOL•Y voltuneflux from (10) is 85 m3-s-1. Thetemperature implied As noted by Davies [1988a], the total heat flux from plumes by these numbersis 225øC in agreementwith the other is compatiblewith the heat comingfrom coolingthe core. The hotspots. globalheat flow coming from the mantle is about74 mWm -2 Afar. The Afar hotspot is similar to Iceland in that a [Sleep and Langan, 1981]. About half this heat comes from subaerialplateau exists but complicatedby the narrow width of internal radioactivity and half from cooling [e.g., Christensen, the ocean and the spreadingon the East African Rift. The 1985]. About 4/5 of the heat capacityof Earth is in the mantle stronglyaffected length of the Red Sea and Gulf of Aden rifts is and 1/5 in the core if latent heat is ignored [Stacey, 1980]. about 600 km and the averagespreading rate over this interval Thus, if the core and manfie cool at the same rate, cooling of is about17.mm yr -1 [Joffeand Gaffunkel, 1987]. About 400 the core supplies 10% of the heat in comparisonto the km of the •East African Rift' with a spreadingrate of estimated6%. Moreprecisely, a heat loss of 4 mWm -2 would 2.5mm yr -1 iss•ongly affected. Assuming thatthe flow sup- cool the core at 50ø C in 1 b.y. if notbalanced by heatsources. plies lithosphereand asthenospherethicknesses of 100 km, as Crhe specificheat for the core given by Stacey [1980] implies was done for Icelan• equation (1) yields a volume flux of that1 W m-2 coolsthe core 12.84øC in 1 m.y.)

Crozet

N Geoid height

1Iotspot

%- 4

200km / Fig. 12. The geoid height in metersnear Crozet is contouredin meters [Courtneyand Recq, 1986]. A 140-km stagnation curveis fit by eye to the anomaly. The modelhotspot is at the dot. SLEEP:HOTSPOTS AND MANTLE PLUMES 6731

N

I 5.0 200 km

Fig.13. The ocean depth inmeters near R6union iscontoured inkilometers [Bonneville etal., 1988]. The 5-, 4.5-, 4-, and 0- kmcontours are plotted. The 4.75-km contour isplotted in thebasin between Madagascar andR6union. The interval between 4- and0-kin depth is shaded. A 285-kmstagnation curve is fit by eye to the 5-kin contour. The model hotspot isindicated by the dot.

SpatialDistribution of Plumesand their Fluxes total. This impliesthat captureof the ridge by hotspotsis inefficientor that largehotspots do not frequentlyencounter the It is well establishedthat hotspotsare nonrandomlydistri- ridge axis. buted on a global basis [Vogt, 1981; Pollack et al., 1981; The most activehotspots occur only on the rapidlymoving Stefanickand Jurdy, 1984; Richards et al., 1988;Weinstein and Olson, !989]. There are enoughplumes and enoughvariation plates,while weak hotspots occur on bothfast and slow plates. in plumefluxes to makeadditional inferences from the distribu- This distributionis partlythe resukof the effectof plumeson tion. These fluxes provide an instantaneouspicture, which plateboundaries. A stronghotspot on a slowlymoving plate couldbe improvedby flux historiesfor hotspottracks. Several weakensthe plate and may cause breakup of theplate [Morgan, 1981]. Thus the plate velocitymay increase.For example, hotspots,including Bermuda, Louisville, Tristan, Great Meteor, R6unionis associatedwith the breakupof India. andCaroline, appear to havewaned recently. (The older strong trackpermits location of thesehotspots which might otherwise Onceeffect of plmes on ridgelocation is considered,it can be missed.) Others, including Crozet, may have become be seenthat hotspottracks are often obliviousto the surface stronger. plategeometry. I haveakeady made the argumentthat ridge Hotspotsare preferentially located near ridge axes [Weinstein crossing is strongevidence that plumesfrom greatdepth pro- and Olson,1989]. This is partlythe result of a capturemechan- ducehotspots. An argumentagainst stress and for plumescan ism. If the ridge axis is not fixed in the hotspotframe, it may be madefor otherhotspots near plate boundaries. The Samoan collidewith a hotspot.Once the ridge axis is on the hotspot, hotspothas followedthe generalPacific track directioneven continualridge jumps are requiredto keep there. When the throughit has approachedthe northernend of the Tongaarc hotspotvolume flux is comparableto thematerial normally sup- where intraplatestresses should be complicated.A similar plied to a significantlength of ridge,axis jumps occur, as in argumentmight be madefor the Carolinehotspot, although it Iceland [Vink, 1984]. It helps also if the velocityof hotspot has waned to some extent. perpendicularto the ridgeis smallas with Juande Fucaand Plumefamilies. Somehotspots can be groupedinto closely Galapagos.Conversely, the weakerAtlantic hotspots appear to spacedfamilies. Bouvet, Meteor, Discovery, and Tristanare have crossedthe ridge withoutcapturing it. Tristanwas an on- one group that might includeMartin and Fernando.Cape ridgehotspot umil it waned. The currenttotal buoyancyflux Verde, Canary,and Madeira(if it is consideredseparate) are for the on-ridgeor near ridge hotspots,Easter, Iceland, Afar, another. The East Australia and two Tasman sea chains are a Azores, Galapagos,Tristan, Juan de Fuca, and Bowie is thirdgroup. Juan de Fucaand Bowie are another if theyare in 9.3Mg s -1 similarto Hawaiiand less than 1/5 of theglobal fact associatedwith plumes. As noted alreadythe Pacific 6732 SLEEP:HOTSPOTS AND Mnm'I• P•m

TABLE 1. HotspotBuoyancy Flux between this mantle cooling rate and core cooling rate of 50ø C b.y. -1 inferredfrom the global heat flux from hotspots Flux,* Flux,•' impliesthat the temperaturecontrast just abovethe core-mantle Hotspot Mgs -1 Reliability Mg s-1 Afar 1.2 good boundary has increasedwith time. The viscosity contrast Australia, East 0.9 fair between the upwelling material and the surroundingmantle Azores 1.1 fair whichpermits the rapid ascentof plumesthus has alsoincreased Baja 0.3 poor with time. Sleepet al. [1988] usedthis reasoning to showthat Bermuda 1.1 good 1.5 Bouvet 0.4 fair plumesmay be a geologicallyrecent occurrence on Earth. They Bowie 0.3 poor 0.8 notedthat plumes might first originatein familiesat the expense Canary 1.0 fair of two-dimensionaltabular upwellings. They used the CapeVerde 1.6 good 0.5 occurrenceof plume families as supportof this hypothesis. Caroline 1.6 poor Recognitionof the 1267 Ma MacKenzieigneous events as the Crozet 0.5 good Discovery 0.5 poor 0.4 effects of a plume head [LeCheminantand Hearnan, 1989] Easter 3.3 fair pushesthe initiationof vigorousplumes back to that time. Femando 0.5 poor 0.9 New hotspots. Plumes penetratingpristine mantle are Galapagos 1.0 fair mushroom-shapedwith a large head and a thin stem [Whitehead GreatMeteor 0.5 poor 0.4 and Luther, 1975; Olson and Singer, 1985]. Isolatedplumes Hawaii 8.7 good 6.2 Hoggar 0.9 fair 0.4 whichpenetrate pristine manfie might be expectedto havelarger Iceland 1.4 good headsthan family plumeswhich grow at the expenseof an Juan de Fuca 0.3 fair alreadyhot upwelling. There is someinformation to support JuanFemandez 1.6 poor 1.7 thisinference. The Deccantraps and the R6unionhotspot track, Kerguelen 0.5 poor 0.2 Louisville 0.9 poor 3.0 the most obviousexample of a new hotspot[Courtillot et al., Macdonald 3.3 fair 3.9 1986; Richards et al.; 1989], is more or less isolated. Other Marqueses 3.3 fair 4.6 examplesof isolatedfeatures, include the Ontong-Javaplateau Martin 0.5 poor 0.8 and the Louisville track. The Crozet, here associatedwith the Meteor 0.5 poor 0.4 Karroo basalts[Richards et al., 1989], is also isolated. Parana Pitcam 3.3 fair 1.7 R6union 1.9 good 0.9 basaltsare, however, associatedwith the Tristan track, which is St. Helena 0.5 poor 0.3 the dominantmember of the family of SouthAtlantic hotspots. Samoa 1.6 poor The Columbiabasalts and Yellowstone track are isolated only if SanFelix 1.6 poor 2.3 Juan de Fuca, Bowie, and Raton are not associatedwith their Tahiti 3.3 fair 5.8 own plumes. Tasman,Central 0.9 Ix)or Tasman,East 0.9 poor The area stronglyaffected by modemplume heads is typi- Tristan 1.7 fair 0.5 cally 1000 km in radius (data from White and McKenzie Yellowstone 1.5 hir [1989]). Such regions are observedfrom Greenland(Iceland Sum 54.9 plume),Parana (Tristan plume), Deccan (R6union plume), Afar, and Karroo (Crozet plume). In contrast,much more modest *This paper. areasof excessvolcanism are associatedwith familiesof pla- tDavies [1988a]. team on the coasts of western Australia and the eastern United States(data from White and McKenzie[1989]). No attemptis madehere to estimatethe volumeof plumeheads. This taskis Superswellhas been considereda hot line [Bonattiet al., 1977], somewhatdifficult becausethe ratio of plume materialto melt extendingfrom Caroline to San Felix and/or JuanFernandez. varies by a factor of 10 between Hawaii and Iceland. The In contrast,some hotspotsare isolated. In particular,the extentof flood basaltsis partly controlledby dikeswhich radi- strongesthotspot, Hawaii, is isolated with the nearest active ate from the hotspot,rather than underlying melting. For exam- hotspotsover 2000 km away. Iceland and maybe R6union ple, suchdikes radiate 2400 km from the centerof the 1267 Ma belong to this class. These plumesmay be at the centersof MacKenzie swarm [LeCheminantand Hearnan, 1989]. columar upwellings. Other hotspots,such as Azores,Bermuda, Only a smallfraction of the hotspotsare associatedwith pos- Crozet,Kerguelen, and St. Helenaare neitherwidely separated tulatedheads. Either a significantfraction of plumesformed fi'om otherhotspots nor obviousmembers of families. withoutlarge heads, or plumeslast longenough that older heads The close spacingof many hotspotshas been used as an cannotbe found and matchedwith plumes. The presenceof argumentagainst mantle plumes [e.g., McHone et al., 1987] long-livedtracks, such as Great Meteor-MonteregianHills, is becauselong closelyspaced conduits from the core seemunrea- supportfor the latter. So doesthe recognitionof the 1267 Ma sonable. Alternatively,some plumesmay arise fi'om tabular MacKenzieigneous event as a plume head [LeCheminantand upwellingsof the basal thermalboundary layer in the mantle Heatnan,1989]. I do notethat the new plumesdiscussed above [Sleepet al., 1988]. The temperaturedependence of viscosity all (exceptCrozet where the early flux is unknown)had buoy- shouldcause the slowly movingparts of the upwellingto cool ancyfluxes over 1.4 Mg s -• soonafter they became active. andbecome more viscous while therapidly moving parts remain Fate of Heat Suppliedby Plumes hot andtake up the bulk of the flow. If plumefamilies are real, material may ascendfrom the basal mantle boundarylayer Plumematerial is suppliedinitially to the asthenosphereand partly as two-dimensionaltabular upwellings which break-up thenthe heat is transferredto the lowerlithosphere. Some of into plumesat shallowerdepths. this heat eventually reachesthe surface as excessheat flow, The Earth's mantle is believed to have cooled 200øC to while the rest of the heat is subductedwith the lithosphere 300øC overthe last 3 b.y. [Christensen,1985]. The difference[Davies, 1988a]. An estimate of this division is needed if one SLEEP:HOTSPOTS AND MAm'• Pt,UM• 6733 wishesto includeplumes in a parameterizedconvection model. Statisticalestimates are obtainedby consideringplumes a ran- m-- ts -1 I exp[--2t;12/ts 112]exp [-tv/t •] dt v dom phenomenon.Direct estimatesare obtainedusing currently o subductingswells or extrapolatingcrest near active hotspotsto = 1 - e •1/2effc (1) = 0.24 (39) trenches. Statistical estimate. Hotspotsmay be treated as a statistical wheretio is thedummy variable for plate age and ts is thesub- feature on the oceaniccrest. The approachis practicalbecause duction time constantfor both normal lithosphereand hotspot hotspotsseem independent of the detailsof plate geometryand lithosphere. This result is independentof the average life of oceanic crest. the probability that ocean crust gets subductedis relatively independentof its age [Sclater et al., 1980]. First, hotspot Somedirect inferences. As noted earlier, plumesare not ran- swells are generally wider than the depth at which heat is domly distributedon Earth. If plumes in fact originate at the implaced. Horizontal conductionis thus ignored,and the heat base of the manfie, they shouldavoid cool regionswhere many sourceis consideredan infinite horizontalplane within a half- slabs have penetrated[Chase and Sprowl, 1983]. There thus space. The excess temperature from a heat source which shouldbe some tendencyfor hotspotswells to form away from liberatesQ pc heat per area at depth z0 is [Carslawand subductionzones and to get subductedlater than typical crest. To some extent this is true. The swells of the Ariantic and Jaeger, 1959, p. 259] Indian hotspotsare mostly betweenpassive margins and ridges and cannot be subductedwithout a major plate reorganization. AT=-• (mct)-•/2 The Emperorswell is being subductedat the farthestpossible point away from Hawaii. Only Samoa,San Felix, JumaFernan- dez, Bowie, and Juan de Fuca are near active subduction zones. 4•[ - exp '4'•t' (35) The swells thus are subductedless frequently than ordinary oceaniccrest. I model this effect by assumingthat swells take proportionallylonger to subducton the averagethan ordinary wherez is depth,lc is thermaldiffusivity, and t is timesince oceanic crest. Then equation (38)becomes the heat sourceappeared. The excessheat flow is I qexp (-t/t•)dt = (Q pc)exp [-2zo/(4•Cts•) m] (40) q= k 3Tz=0 =4z0kQ •-x/2(4•ct)-3/2 exp4}ct (36)where tsw is the subductiontime constantfor swells. Tlfis sub- ductiontime and the time constantts which governsthe distri- These equationsare intendedto be valid after the lithosphere has moved away from the hotspot and convection has butionof the plate age of the lithospherereactivated by hotspots need to be distinguishedin (39) transferredthe excessheat to the lower lithosphere. They do not representthe actualheating in detail. If no subduction occurred, the total heat flux would eventu- F = C• I exp[-2tvm/t• 2]exp [-tv/t •] dtv ally be that suppliedby the heat source o

(37) = 1 - (t•/t•)•/2 exp(t•/t•)rcmerfc(t••/2 /t•) •/2 (41) Qpc=Iq dt [Gradshteynand Ryzhik,1965, integral3.462,5]. If swellstake Assumingthat the probabilityof subductionis independentof twiceas longto subductas normal crest, tsw = 2ts, the fraction bothplate age and hotspotage requiresweighting the heatflow of heat which escapesis 34%. by the probability(an exponentialof time) that the crest still Some correction is also needed for plumes on continents exists (has not been subducted) at time t after the hotspot where all the heat can eventually escape. However, larger occurred.The heat which actuallyreaches the surfaceis then plumes break continentalplates and thus erupt on continents only briefly. The presentcontinental plumes are likely to have fluxes between that of Yelowstone and those of the weaker I qexp (-t/t•)dt = (Qpc ) exp[-2z 0/(4•cts (38) 0 Atlantic hotspots. Thus about 10% of the heat and buoyancy flux of global hotspotsmay be associatedwith continentalones. where ts is the time constantfor subduction.The fractionof That is, between 1/4 and 1/3 of the 90% of the heat associated heatthat escapes,rather than being subducted, is the exponential with oceanichotspots and all of the 10% of the heat on con- tinentsescape. This implies that globally33-40% of the heat The depthof implacementof the heat sourcez0 is relatedto suppliedby plumes escapesbefore it is subducted. In their the plate thicknessand hence the plate age at the time of the parameterizedconvection calculations,Sleep et al. [1988] hotspot. That is, excessheat is suppliedto near the baseof the assumedthat all the heat lost by the core becamemixed into the previous thermal lithosphere[e.g., Cazenave et al., 1988]. mantle rather than escapingat the surface. From the above Here, this depth is crudely es'•matedas the scale •clmess of analysis this assumption should not lead to gross errors, thelithosphere x/4rt v , wherett, isplate age. At thatdepth, the althoughimproved calculations could be made takingthis effect lithospherehas cooledto 84% of its originaltemperature. into account. The global fraction of heat which escapesis obtainedby assumingthat heat introducedby plumes on the average is CONCLUSIONS independentof plate age. The escapingfraction then needsto be weightedby the amountof plate of each age at the time of The hypothesisthat mantle plumes ascendfrom the base of the hotspot the mantle was originally proposedto explain the track direc- 6734 SL•m,: HOTSlOTS AI• M•er• PLUM•

tions of hotspots. This hypothesisprovides an explanationof latestQuartemary faulting: Migratory pattem and associationwith several additionalfeatures. In particular,plumes supply Yellowstonehotspot, J. Geophys. Res., 94, 1589-1621, 1989. materialwhich spreads out horizontally beneath the lithosphere. Barker, P. F.,Tectonic evolution andsubsidence history ofthe Rio GrandeRise, Initial Rep. Deep Sea Drill. Proj., 72, 953-976, 1983. Heatis then transferred from the abnormally hotasthenospheric Btdard, J.H., The opening ofthe Ariantic, theMesozoic New England materialto the lithosphereby convectionand conduction. The igneousprovince, and mechanisms of continental break-up, Tectono- excessheat and buoyancyof swellsdownstream from hotspots physics,113, 209-232, 1985. movewith the lithospheric plate. The shape of thesnout of Black,R., L. Lameyre,and B. Bonin, The structural setting ofalkaline complexes,J. Aft. Earth Sci., 3, 5-16, 1985. swellsis attributedto stagnation streamlines which separate Bonatti, E.,C. G. A. Harrison, D.E. Fisher, J.Honnorez, J.G. Schil- materialsupplied by theplmnes from ambient asthenosphere. ling,J. J. Stipp,and M. Zentelli,Easter volcanic chain (southeast Hot asthenospherenear the plume may be detectedby geoid Pacific):A manfiehot line, J. Geophys.Res., 82, 2457-2478,1977. andelevation anomalies. The geometryfor doingthis is beston Bonneville,A., J.P. Bardot,and R. Bayer,Evidence from geoid data of

slowlymoving plates. Unforttmately, the effects of long- Islandsa hotspot(Indian origin Ocean),for the J. southemGeophys. MascareneRes., 93, 4199-4212,Plateau and 1988. Mascarene wavelengthgeoid anomalies, volcanic edifices, and flexure need Bowin, C., G. Thompson, andJ. G. Schilling, Residual geoid anomalies to be filteredfrom the model and the data in a consistent in theAriantic Ocean basin: Relationship to manfie plumes, J. Geo- manner. Observationsare consistentwith an averageexcess phys.Res., 89, 9905-9918,1984. temperaturearound 200øC in theasthenosphere. Although the Brodholt,J.P., and R. Batiza,Global systematics of unveraged mid- errorbounds on thistemperature aregreat, an excessof oceanridge basalt compositions:chemistry with Comment axial depthon and "Global crust correlationsthickness" byof 1000øCis not compatible with the observations. Thisposes a E.M.Klein and C. H. Langrnuir, J. Geophys. Res.,94, 4231-4239, difficulty in having the core much hotter than the overlying 1989. manfiebecause the temperaturecontrast in vigorousplmnes is Brott,C. A., D. D. Blackwell,and J.P. Ziagos,Thermal and tectonic expectedtoscale to the temperature contrast in across the basal implicationsofheat flow in the eastem Snake River Plain, Idaho, J. Geophys.Res., 86, 11,709-11,734, 1981. boundarylayer [Davies, 1988a]. Carslaw,H.S., and J. C. Jaeger, Conduction ofHeat in Solids, 510pp., The flux of on-ridgehotspots such as Iceland,Azores, and Clarendon,Oxford, 1959. Afar is similar to that of off-ridge hotspots. The excesstem- Castillo,P., R. Bativ_a,D. Vanko,E. Malavassi,J. Barquero,and E. Fer- perarete obtained from petrologicalstudies of Icelandic and nandez,Anomalously young volcanoes on old hot-spottraces, I, Geol- ogy and petrologyof CocosIsland, Geol. Soc.Am. Bull., 100, 1400- Hawaiianlavas are similar, around200 ø C. Again the error 1414, 1988. bounds on the temperatureare large, particularly becausethe Cazenave,A., K. Dominh, M. Rabinowicz, and G. Ceuleneer,Geoid and origin of mid-oceanicridge basaltsis not well understood.Thus depth anomaliesover ocean swells and troughs: Evidenceof an on-ridge and off-ridge hotspotsmay be the effect of similar increasingtrend of the geoidto depthratio with age of plate,J. Geo- plumes. This inferenceis further supportedas hotspotsappear phys.Res., 93, 8064-8077, 1988. Chase,C. G., and D. R. Sprowl, The modem geoid and ancientplate to have crossedridge axes or in the case of Tristan recently boundaries,Earth Planet. Sci. Lett., 62, 314-320, 1983. evolvedto being off-axis. Christensen,U., Thermal models for the Earth, J. Geophys.Res., 90, Theglobal excess heat flux at hotspotsis 4 mWm-2 in 2995-3008, 1985. agreementwith the compilation of Davies[1988a]. As notedby Clague,D. A., andG. B. 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