JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 100, NO. E8, PAGES 16,931-16,940, AUGUST 25, 1995

How does lose heat?

Donald L. Turcotte Departmentof GeologicalSciences, Cornell University,Ithaca, New York

Abstract. The tectonicsand volcanismof the terrestrialplanets are controlledby the loss of heat from the planetaryinterior. On the Earth, about 70% of the heat flow throughthe mantle is attributed to the subductionof cold lithosphere.In order to understandthe tectonicand volcanicprocesses on Venus it is necessaryto understandhow heat is transportedthrough its mantle.In this paper, three alternativeend-member hypotheses are considered.The first is the steadystate lossof heat throughthe mantle to the surface in analogyto the Earth. However,without plate tectonicsand subductionon Venus, a steadystate requireseither a very high plume flux or very rapid rates of lithospheric delamination.The requiredplume flux would be equivalentto about 80 plumeswith the strengthof the Hawaiian plume. The required delaminationflux impliesa 50% delaminationof the entire Venus lithosphereevery 10 m.y. Neither appearspossible, so that it is concludedthat Venus cannottransport heat throughits mantle to its surfaceon a steadystate basis.The secondhypothesis is that there has been a strongupward concentrationof the heat-producingelements into the crustof Venus; the heat generated is then lost by conduction.Surface measurements of the concentrationsof the heat- producingelements place constraintson this model. If everythingis favorablethis hypothesismight be marginallyacceptable, but it is consideredto be highlyunlikely. The third hypothesisis that heat is lost by episodicglobal subductionevents followed by long periodsof surfacequiescence. The near-randomdistribution of craterssuggests that the last subductionevent occurredabout 500 Ma. This model impliesa thick thermal lithosphere(•-300 km) at the presenttime, whichis consistentwith a varietyof surface observations.Lava lakes on the Earth are consideredas analogiesto plate tectonics;they also exhibit episodicsubduction events.

Introduction Mountain belts on the Earth are generallyassociated with plate tectonicprocesses. The global mid-oceanridge system Studiesof the surfaceof Venus duringthe Magellanmission stands--•2.5 km above the oceanbasins. This topographyis have provided a wealth of data on its tectonic and volcanic attributedto the thermalcompensation of oceaniclithosphere. processes[Solomon et al., 1992].The radar imagesof the sur- Mountain belts associatedwith subductionzones (e.g., the face are complementedby global topography and gravity Andes) and with continentalcollisions (e.g., the Alps and Hi- anomalydata. It is now clearthat plate tectonics,as it is known malayas)are associatedwith crystalthickening and Airy com- on the Earth, doesnot occuron Venus.At the presenttime, pensation.Volcanism on the Earth is associatedwith zonesof Venus is a one-plateplanet. Nevertheless,there are tectonic plate accretion(mid-ocean ridges), plate destruction(island featureson Venus that certainlyresemble major tectonicfea- arcs), and hot spots(mantle plumes).Magma generationat tures on the Earth. has many of the featuresof a both ocean ridgesand hot spotsis attributed to pressurere- continentalrift on this . It has a domalstructure with a leasemelting; magma generation at island arcsis still poorly diameterof about 2000 km and a swell amplitudeof about 2 understood.Clearly, any comprehensiveunderstanding of tec- km. It hasa well-definedcentral rift valleywith a depth of 1-2 tonismand volcanismon Venus requiresan understandingof km, and there is some evidencefor a three-armedplanform how heat is transportedin the absenceof plate tectonics. (allocogen).Alta, Eistla, and Bell Regioneshave similarrift On the Earth some 70% of the heat transfer through the zone characteristics[Senske et al., 1992; Grimm and Phillips, mantle is attributed to the subduction of the cold oceanic 1992]. , with a length of some 1500 km, is reminiscentof major continentalcollision zones on thisplanet, lithosphereat oceantrenches. The remainderis primarily at- suchas the mountainbelt that extendsfrom the Alps to the tributed to the ascent of hot mantle plumes with a minor Himalayas. is a regionof elevatedtopography with contributionfrom the partial subduction(delamination) of the a horizontalscale of 2000-3000 km. A major featureis Lakshni lower continentallithosphere. Without activeplate tectonics Planum,which is an elevatedplateau similar to Tibet with a the evolutionof Venus is significantlydifferent than the Earth. mean elevationof about4 km. This plateauis surroundedby Three end-membermodels have been proposed, each of which will be discussed in turn. linear mountainbelts, Akna, Danu, Freyja, and Maxwell mon- The first model is the uniformatarian model. In this model tes,reaching elevations of 10 km, similarin scaleand elevation to the Himalayas. the transportof heat throughthe mantle and lithosphereof Venusis in a near steadystate balance with the heat generated Copyright1995 by the AmericanGeophysical Union. by the heat-producingelements and the secularcooling of the Paper number 95JE01621. planet. This requiresa relativelythin, stablelithosphere with 0148-0227/95/95 JE-01621 $05.00 heat transportto its baseby mantleconvection. Heat transport

16,931 16,932 TURCOTrE: HEAT LOSS ON VENUS through the lithospheremust be conductionor another un- with plumeshave been carriedout by Davies[1988] and Sleep specifiedmechanism. [1990].These studies relate the rate of creationof plumeswells The secondmodel is the catastrophicmodel. In this model to the mantleheat flux.Davies [1988] estimates that the mantle the present loss of heat to the surfaceof Venus is not in fluxdue to plumesisQp = 2.5 x l0 •2 W, andSleep [1990] balancewith its internal heat generation.The global lithos- estimatesthe value to beQp = 2.3 x l0 •2 W. Sleep[1990] phere stabilizedabout 500 Ma, and the interior of the planet considered37 plumesfrom both the oceansand the continents. has been heating up since then. Heat is lost in episodesof The heatflux associated with the Hawaiianplume is QpH = global subductionof the thickenedlithosphere. 0.36 x 10•2 W, 15%of thetotal plume flux and twice as large The third model is the differentiatedplanet. In this model as any other plume. the heat-producingelements have been almost entirely frac- Taking the mean of the two estimatesgiven above, the tionated into the crust,and the heat generatedis lost by con- plumeflux is Qp = 2.4 x 10•2 W. However,this is only 26% duction to the surface. of the mantleheat flux of Qm -- 0.92 x l0 •3 W that is attributedto processesother than subduction.An important questionis the processor processesthat contributethe other Uniformatarian Model 74%.Of course,the original estimate of Qm = 9.2 x 10•2 W Before consideringa uniformatarianmodel for Venus, a couldbe in error. However,it is difficultto acceptthat it is a brief discussionof how heat is transportedthrough the mantle factor of 4 too large. There are three possiblesources for the of the Earth will be given.A comprehensivereview has been discrepancy: givenby Turcotteand Schubert[1982]. The total heatloss at the The first possiblesource is plumes that do not generate surfaceof theEarth is closeto Q•r = 3.55 x 10•3 W withan well-definedvolcanic hot spotsand swells.The smallesthot estimated error of less than 5%. With a total surface area of spotsconsidered by Sleep [1990] have a heatflux of aboutQp = •1œ= 5.1 X 10s km2 the meansurface heat flow is q•r = 10• oW sothat we would require some 700 of theseto makeup 70 mW m-2. The originof thisheat is the decayof theradio- themissing flux of Q? = 6.8 x l0 •2 W. It shouldbe noted, active isotypesof uranium, thorium, and potassiumand the however, that the lack of subsidence in continental cratons secularcooling of the planet. The Urey number Ur is defined indicatesheating from beloweven without surfaceevidence for to be the ratio of radioactiveheat generationto the total heat plumes.McKenzie [1984] hasproposed that epeirogenicuplift loss; 1 - Ur is the fraction attributed to secular cooling. is due to intrusive volcanism near the base of the continental Estimatesfor the Urey numberfor the Earth fall in the range crust without surfacevolcanics. Thus the studiesby Davies 0.6 < Ur < 0.8. [1988] and Sleep[1990] may representonly a fractionof the Heat transport in the ocean basinsis dominatedby plate actualmantle plume flux. tectonics,whereas heat is lost conductivelythrough the stable The secondpossible source is delaminationof the continen- continentallithosphere. The oceansand marginalbasins have tal lithosphere.The continentallithosphere is gravitationally an areaA o = 3.1 x l0 s km2 (60%) anda heatloss Qo = stable, and there is no evidence that it can be subducted as a 2.42 x 10•3 W (68%). Of thistotal, $clater et al. [1980] whole.However, the mantleportion is gravitationallyunstable, attribute 90% to the subductionof the conductivelycooled and there is considerableevidence that the mantle lithosphere lithosphere(Qos = 2.18 x 10• 3 W) and10% to basalheating andlower crust separate from the uppercrust and descend into (Qorn= 0.24 x 10•3 W). The coolingof theoceanic litho- the mantle [Bird, 1979].This is delamination,and it will con- spheregenerally follows a half-spacecooling model to agesof tributeto the mantleheat flux in the sameway that subduction about 100 Ma; the subsequentflattening of topographyis at- of the oceaniclithosphere does. There is observationalevi- tributed to basalheating of the lithosphereby secondarycon- dence for lithosphericand lower-crustaldelamination in the vectiveprocesses such as the impingementof mantle plumes. Himalayas,Alps, and Colorado Plateau. However, the rates The continentsand continentalmargins have an areaA c = are so small that the associatedmantle heat flux is generally 2 x 108km 2 (40%) anda heatloss Qc = 1.13 x 1013W assumedto be negligiblysmall. (32%). Of this total, Turcotteand Schubert[1982] attribute The third possiblesource is other secondaryconvective pro- 40% to radioactiveisotopes in the continentalcrust (Qcc = cessesin the mantle. In order for secondaryconvection to 0.45 x 10•3 W) and60% to eitherbasal heating or delami- convectsignificant heat it must contain either ascendinghot nationof the continentallithosphere (Qcm = 0.68 x 10•3 rock or descendingcold rock. But ascendinghot rock is gen- W). Inherent in this balanceis the assumptionthat the conti- erally associatedwith mantle "plumes" and descendingcold nental lithospherehas, on average,a steadystate balancebe- rock with descendingsubducted or delaminatedlithosphere. tween basal input, internal heat generation,and surfaceheat Thus it is not clear that it is appropriateto discussheat trans- loss.The continentallithosphere is not a thickeningthermal port associatedwith secondaryconvection except in the con- boundarylayer. Observationalevidence for this steadystate textof eitherplumes or delamination(subduction). The lossof balanceis the lack of thickeningsediment piles associated with heat to the surfaceof the Earth is illustratedin Figure l a and continentalcooling and subsidence. tabulatedin Table 1. The valuesgiven are preferredvalues but From the above values the total heat flux from the mantle is are subjectto the errors discussedabove. estimatedto be Qm = 3.10 x 10•3 W. Of thistotal, 70% is The first hypothesisfor Venus is that it is in a near steady attributedto the subductionof coldlithosphere (Qs = 2.18 x statebalance between radioactive heat productionand secular 10•3 W) and30% to othertransport processes in the mantle coolingand the surfaceheat loss.Many of the argumentsfor (Qm = 0.92 x 10•3 W). Twoprimary candidates have been such a hypothesishave recentlybeen given by Phillipsand put forward as other mantle transport processes,mantle Hansen [1994]. For a near steady state heat loss model, a plumesand lithosphericdelamination. Other mechanismsof logicalestimate for the presenttotal requiredsurface heat flow secondaryconvection have alsobeen proposed. on Venus is obtainedby scalingthe Earth's heat loss(Q•r = Quantitativestudies of the mantle heat transportassociated 3.55 x 10•3 W) to Venususing the masses of thetwo TURCOTTE: HEAT LOSS ON VENUS 16,933

(ME = 5.97 x 1024 kg, My- = 4.87 x 1024 kg). The result Table 1. Preferred Values of Heat Loss for the Earth and isthat the present heat loss from Venus is Qv = 2.91 x 10•3 for the Three HypothesizedModels for Venus W andthe meansurface heat flow is q•, - 63 mW m-2. It Venus shouldbe emphasizedthat this calculationimplicitly assumes that Venus and the Earth have similar concentrations of the Q, 10•3 W Earth ss e c heat-producingelements. This is certainlyreasonable in terms Total heat loss 3.55 2.91 2.91 2.00 of presentmodels of planetaryaccretion, and we will returnto Subduction 2.18 ... 2.62 ... thispoint when we discussthe measurementsof the surface Plumes 0.90 0.88 0.29 .-- concentrationsof the heat-producingelements on Venus.With Delamination 0.02 2.03 ...... the steadystate hypothesis and a thermalconductivity k = 3.3 Conduction 0.45 ...... 2.00 W m-• øK-• the mean surfacethermal gradient on Venusis Here, ssdenotes steady state; e, episodicsubduction; and c, crustal dT/dy = 19øKkm -•. Assuminga linear conduction gradient conduction. throughthe lithosphereand a AT = 850øK,the meanlitho- spherethickness is YL = 45 km. The mechanicalarguments againstsuch a thin lithosphereon Venushave been given by be viable.Without the participationof cold subductedlithos- Turcotte[1993]; here we are concernedwith the thermalim- pherethe temperaturedifferences associated with ascending plications.It shouldbe notedthat the lithosphere can be thick- hot materialand descendingcold material through the mantle ened if a significantfraction of the planet'sheat-producing of Venuswill be considerablyless than on the Earth. In order elementsare concentratedin it; this model will be discussedin to transportthe sameamount of heatwe requirelarger mate- a later section. rial fluxesthrough the mantle. The implicationis that the If Venus behaveslike the Earth, the relative contributionsof Rayleighnumber will be higheron Venus;since the Rayleigh radioactiveheat generation and secular cooling are likelyto be numberis principallysensitive to the viscosity,the conclusion nearlyequal on the two planets.The expectedsecular cooling is that the mean viscosityin the mantle of Venus must be of Venusfor the last500 m.y.is givenin Figure2 for Ur = 0.8, considerablyless than on the Earth in order to providethe 0.6. A typicalrate of coolingis 70øKb.y. -1. necessarysteady state heat transport. Based on the abovedis- Since plate tectonicsis not availableto transportheat cussionof the Earth we considertwo mechanisms,plumes and throughthe mantleof Venus,alternative mechanisms for heat lithosphericdelamination. The formercould be attributedto transportmust be foundif a nearsteady state hypothesis is to instabilitiesin a hot basal boundary layer, and the latter to partialinstabilities in the coldsurficial boundary layer, i.e., the lithosphere. Conduction ~ 13% The topographyand associatedgravity anomalies of the equatorialhighlands on Venushave been attributedto the dynamicprocesses associated with mantleplumes by several authors[Phillips et al., 1991;Kiefer and Hager, 1991, 1992]. The extensivedistributions of coronasthat cover the planet have Plumes also been attributed to mantle plumes [Stofanet al., 1991, - 25% Delamination 1992].It is certainlyreasonable to acceptthat thereis obser- -1% vationalevidence for the impingementof mantle plumeson

I the baseof the Venusianlithosphere [Koch, 1994]. The ques- Subduction tion is whetherthe plumesare sufficientlylarge and numerous -61% ! enoughto transportthe requiredheat. To carrya substantial ! ; fractionof thetotal heat (Q •, = 2.9 x 10• 3 W) wouldrequire about 80 plumeswith the strengthof the Hawaiianplume (QpH= 3.6 x 10• • W).With a thin,hot lithosphere, such a large numberof strongplumes would be expectedto have surfacesignatures including extensive volcanism; these signa- tures are not seen. Quantitative studies of the strength of activeplumes on Venusindicate that the present plume flux is lessthan on the Earth [Smrekarand Phillips,1991]. Also,plumes are associatedwith the instabilityof hot basal

Plumes boundarylayers. For a fluid heatedfrom within, heat is trans- - 30% portedprimarily by instabilitiesin near-surfacecold boundary layers[Parmentier et al., 1994].For Venusthis means, for the steadystate model, that heat would be transportedprimarily by Delamination delaminationof the cold lithosphere.A mechanismfor litho- - 70% sphericdelamination on Venushas been proposed by Buck [1992].He decouplesthe uppercrust from the uppermantle with a low-viscositylower crust, a lowercrustal asthenosphere. The uppermantle participates in a plate tectonicsubduction Figure 1. (a) Illustrationof howheat is transportedto the surfaceof the Earth by subduction,plumes, delamination, and cycle,but the uppercrust behaves as a scumthat floatsand lithosphericconduction. Estimates for the relativecontribu- doesnot participatein the subduction.A similarmodel has tionsare given.(b) Illustrationof howsteady state heat trans- beenproposed by Arkani-Hamed [1993]. port on Venus might be accommodated. The equivalentsurface heat flux due to the subductionor 16,9.34 TURCOTI'E: HEAT LOSS ON VENUS

lOO

- Transientheating

5O 0.6 ß

•T oT

0

-5O Figure2. Thechange in temperatureAT ofthe interior of Venus is given as a functionof time t. Thesteady statecooling results are applicable for a uniformitarianmodel, and the rate of coolingis givenby the Urey numberUr. Thetransient heating would be applicable to theepisodic subduction hypothesis during periods of lithosphericstability and conductive thickening; no heatloss to the surfaceis assumed.

delaminationof cold li•thosphereis easilyestimated. The en- The equivalentmean surface heat lossesQ2> for 02>= 0.4, ergy associatedwith a globalsubduction event is givenby 0.6., 0.8 are givenin Figure3 as a functionof the delamina- [Turcotteand Schubert,1982, p. 281] tion interval t. If the entire mantle heat flux is attributedto delamination,then it mustoccur sufficiently often to transmit Es-- 8•'r•,pc(rm-Ts) (1) Q2>= 2.91 x 10]3 W. WithT2> = 1470øK(02> = 0.8) the entirelithosphere would have to delaminate,on average,at whererv is the radiusof Venus,Ts the surfacetemperature, intervalsof t2>= 1.2 m.y.,with T2> = 1290øK(02> = 0.6) we T,• the mantletemperature, and •( the thermaldiffusivity. This requiret2> = 6 m.y.,and with T2>= 1110ø K (02>= 0.4) we relation assumesthat the lithospherehas thickenedconduc- requiret2> = 19 m.y. It seemsinconceivable that globaldel- tiv½lyfrom zero thicknessfor a periodt. This is clearlya aminationevents could take placeat suchshort intervals. Also, limitingcase in that anybasal heating of the lithospherehas globaldelamination events would be expectedto disruptthe beenneglected. The equivalentmean surface heat lossQ s is upper crust,resulting in intensivevolcanism, volcanism that is obtainedby dividing(1) by t with the result not observed.This is not to say,however, that delaminationis not occurring.Delamination may play an importantrole in creatingthe high plateautopography of IshtarTerra. Never- Qs= 8,rr•pc(Tm-Ts) • (2) theless,it seemsinconceivable that delaminationcould make a significantcontribution to the globalheat flow.This is consis- Takingrv = 6050 km, Tm - Ts = 880øK, and •( = 1 mm2 tent with our understandingof the role of delaminationon the s-•, theheat loss is given as a functionof t in Figure3. If the Earth. totalrequired heat loss from the interior of Venus(2.91 x 1013 A schematicsteady state model for Venus is illustratedin W) were associatedwith subduction,then the lithosphere Figurelb andis tabulatedin Table 1. However,since a large wouldhave to subduct,on average,at an ageof t = 85 Ma. plumeflux and/or extensive lithospheric delamination is a pre- The aboveresult can also be used to determinethe efficiency requisitefor any steadystate hypothesis, it is necessaryto of delaminationin transportingheat through the lithosphere of concludethat uniformatarianmodels are not applicable.We Venus.If thetemperature separating delaminating lithosphere next turn to an alternativecatastrophic model. from stablelithosphere is Tt), then we define = rs)/(rm- rs) Catastrophic Model andthe mean surface heat loss due to delaminatinglithosphere On the Earth, platetectonics continuously creates new oce- is given by anic crust.Thus the age of the surfacerocks has considerable variability.There is conclusiveobservational evidence that this Qo= 8,rr•pc(Tm-Ts)(1 - Oo) • (3) is not the case for Venus. Based on the near-random distribu- TURCOTTE: HEAT LOSS ON VENUS 16,935

Qs,D 1013 w

0.6

0.8

100 200 300 400 500 t, Myrs Figure3. Themean surface heat flux Qs,o is givenfor lithosphericsubduction (S) anddelamination (D) at intervalst. The curveS is for total subductionof the lithosphere.The parameterO is a measureof the fractionof the lithospherethat participatesin delamination;O - 0 is equivalentto subduction.The heat loss denoted by V is the required steadystate value obtainedby scalingfrom the Earth.

tion of cratersin its surface,Schaber et al. [1992]postulated sphereand duringthe periodof volcanicactivity and tectonism that a global resurfacingevent occurredon Venus about 500 that would follow. An alternativeexplanation is that mantle Ma. Further statisticaltests have confirmedthis hypothesis convectionis episodicdue to chemicaldifferentiation [Parmen- [Bullocket al., 1993; Strom et al., 1994]. Although there has tier and Hess,1992; Herrick and Parmentier,1994]. certainlybeen somesurface volcanism since that time, it is The limitingbehavior of the lithosphereduring surface qui- clearthat a large fraction(-80-90%) of the surfacewas cov- escencewould be that the lithospherehas been thickening ered by volcanismduring a relativelyshort period of time conductivelysince that time with no significantconvective heat [Namiki and Solomon,1994]. This observationis direct evi- flux to its base.In this limit the thicknessof the lithosphereis dence that the geologicevolution of Venus is far more cata- now near 300 km. Sucha thick lithosphereis consistentwith a strophicthan the Earth [Herrick, 1994]. An essentialquestion number of observations:(1) it providessupport for the high is whetherthe thermalevolution of Venusis alsostrongly time topography,up to 10 km; (2) it is consistentwith the high dependent. observedgeoid-topography ratios, up to 33 m/km [Smrekarand If it is hypothesizedthat the present heat loss from the interior of Venus is not in balance with the internal heat Phillips,1991]; (3) it is consistentwith the observedunrelaxed craters[Grimm and Solomon,1988]; and (4) it is consistent generation,several alternativemodels can be postulated.In onemodel, plate tectonicssimply ceased some 500 Ma [Arkani- with the thick,elastic lithospheres inferred from flexuralstud- Hamed and Toksoz, 1984; Arkani-Hamed et al., 1993; Arkani- ies [Sandwelland Schubert,1992a]. Hamed, 1994].According to this hypothesisthe globallithos- There is also direct observationalevidence that episodic phere stabilized at that time and will remain stable. The subductionis an applicablemechanism for heat transferin a principalproblem with thishypothesis is that the interior tem- convectingsystem with a very viscous(rigid) upper thermal perature will increasewithout plate tectonicsor alternative boundarylayer. A natural analogfor mantle convectionis the heat transportmechanisms. The rate of temperatureincrease thermalconvection in a lavalake. Atmospheric cooling creates is givenin Figure 3 for two valuesof the Urey number,Ur = a "solid"crust which is gravitationallyunstable with respectto 0.6 and 0.8. Over 500 m.y. the mantle temperaturehas in- the moltenmagma beneath. Episodic subduction has been creasedabout 100øK; the correspondingdecrease in viscosityis observedin lava lakes.Wright et al. [1968]describe the behav- aboutan order of magnitude. ior of the Makaopuhi lava lake during the eruption of the An alternativemodel is that this temperatureincrease will Kilauea volcanoin March 1965. They describea particularly eventuallytrigger another episode of global volcanismand graphicepisode of episodicsubduction of the stabilizedupper tectonics.Without sufficient surface heat loss the lithosphere thbrmal boundary layer (p. 3191):"During the nightof March onVenus will thicken during the period of surfacequiescence. 5 theentire, apparently stable crust of thelava lake foundered One suggestionis that the thickeninglithosphere eventually in a spectacularoverturn" and "Crustal founderingwas ob- becomessufficiently unstable that a globalsubsidence event is servedrepeatedly during the eruption."These authors (pp. triggered[Turcotte, 1993]. Heat storedin the interior during 3191-3193)also describe in somedetail the subduction(foun- the period of surfacequiescence is lost to the subductedlitho- dering) mechanism: 16,936 TURCOTTE: HEAT LOSS ON VENUS

3 X 10-5 øK-l, Tm- Ts = 1300øK,/• = 1021 Pa s, •c= 10-6 m2s-•,andRac = 1700, we findfrom (4) thatyz.= 110 km. For a conductivelythickening thermal boundary layer the thicknessis related to its age by (a) YL= 2-32(Ktt)'/2 (5) With Yz. - 110 km we obtain tL = 100 Ma. These estimates for the typicalthickness and age of subductinglithosphere on the Earth are quite good.Turcotte and Schubert[1982, p. 166] estimate tz. = 121 Ma. As an approximatemodel for episodicsubduction on Venus we assumethat the globallithosphere thickens conductively for (b) 500 m.y.; basal heating of the lithosphereis neglected.The correspondingthickness of the subductedlithosphere from (5) is Yz. = 290 km. The mean heat loss due to the global sub- ductionof thislithosphere is, from (3), Qs = 1.23 x 10•3 W. Thisrepresents 42% of thetotal required flux (2.91 x 10•3 W) duringthe interval.The 58% deficit mustbe made up duringa period of active volcanismand tectonics.While the global lithosphereis stable,the only coolingto the interior is due to the heatingof the previouslysubducted lithosphere. This heat- ing is likely to be spread over severalhundred million years. From the resultsgiven in Figure 2 the net increasein temper- ature of the mantle during the 500 m.y. of stablelithosphere is estimated to be about 60øK; the correspondingdecrease in mantleviscosity is about a factor of 5. We utilize (4) to esti- Figure 4. Schematic illustration of an episodic subduction mate the mantle viscosityat the time of the global subduction event. The processdescribed for a Hawaiian lava lake is the event.With Yz. = 290 km,we findthat/x = 1022 Pa s. model, but the processmay also be applicableto Venus. We assumethat the period of rapid plate tectonicslasts for 50 m.y. In order to make up the deficit in heat lossduring the period of lithosphericstability, the mean lossof heat is Q = Most major founderingbegan at a point or line near the margin 20 x 1013W. From(3) thiscorresponds to an ageof subduc- of the lake. The founderingpropagated along a seriesof arcsof tion t• = 1.9 Ma. From (5) the correspondingthickness of the increasingcircumference away from the point of origin. The be- ginningof founderingwas marked by the appearanceof a crackin subductedlithosphere is Y•s = 18 km. And from (4) the the lake surface,which exposedfresh magma. Either from loading mantle viscositycorresponding to this lithospherethickness is behind or from upward pressurein front of the crack a second /x = 3 x 10TM Pa s.Thus the mantleviscosity must be a factor fracture opened ahead of the first, and the crustbounded by the of 3500 larger duringthe time of globalsubduction than during two crackstilted upward along the edge boundedby the second crack and then slid backwardbeneath lava welling out of the first the time of rapid plate tectonics.This must be the caseeven crack. Formation of a third crack ahead of the second was fol- though the mean mantle temperature varies by less than lowedby tilting of the crustbetween the secondand third cracks; 100øK. the crust then slid beneath the new lava behind the second crack; The strongvariation in mantleviscosity is easilyattributed to and so forth. the variation of viscositywith depth. At the time of global subductionthe relevantviscosity is at a depth of 290 km; at the A schematicillustration of this processis given in Figure 4. time of rapid plate tectonicsthe relevantviscosity is at a depth Although there is no direct evidencefor a global subduction of 18 km. Sincethe mantle solidushas a much steepergradient event on Venus, there is evidencethat the presentlithosphere than the mantle adiabat, the mantle at a depth of 300 km is is on the vergeof subduction.Sandwell and Schubert[1992a, b] well below the solidus.This is the explanationfor-pressure proposeda model in which the large coronason Venus are releasevolcanism. The episodicmodel is illustratedschemati- incipient circular subductionzones. The foundering lithos- callyin Figure 5. Sleep[1994] hassuggested that a hemispheric phere is replacedby ascendinghot mantle in a mannersimilar subductionevent on Mars resulted in the hemisphericdi- to back arc spreadingon the Earth. chodomyon that planet. The initiation of subductionis a long-standingproblem in plate tectonics.The problem has been reviewed,and a new model has been proposedby Fowler [1993]. The simplestap- Conduction Model proach to the instabilityof a thermal boundarywas given by Howard [1966]. Instead of applyingthe Rayleigh stabilitycri- As discussedpreviously, 13% of the Earth's heat loss is terion to a convectinglayer, he appliedit to the boundarylayer. attributedto thermalconduction through the continentalcrust. Thus the boundarylayer becomesunstable when Differentiationof the incompatibleelements into the continen- tal crust has led to a substantial enrichment of the heat- Rac= pogc•(Tm-Ts)y3•/IX•C (4) producingelements. Within the continentalcrust there is an While it is certainly not clear that this result shouldbe appli- upward enrichment so that most of the heat-producingele- cable to a mechanicallyrigid lithosphere,it is of interestto test ments are concentratedin the upper 10 km. Prior to the gen- it on theEarth. Taking Po = 3300 kg m-3, g = 10 m S-2, O•= eral acceptanceof plate tectonicsand mantle convection,it was TURCOTTE: HEAT LOSS ON VENUS 16,937

Stable lithosphere widely believedthat virtually all the heat-producingelements in the Earth were concentrated in the continental crust. This

Active volcanism and tectonics upward concentrationwas required becauseconductive pro- cessescould not get the heat out of the mantlewithout melting • 100Myr • it. The third hypothesiswe considerfor Venus is a similar upwardconcentration of its heat-producingelements into the crustof that planet. 1600 In order to do this we must consider the constraints on the Tm oK concentrationsof the heat-producingelements both in the mantle of Venus and in its crust. Overall concentrations of 1500 uranium,thorium, and potassiumin Venus are estimatedfrom terrestrial values. Values for the crust of Venus are obtained directlyfrom data collectedby the Vega and landers. 2O Before doing this, however,the concentrationsof the heat- Qs producingelements in the silicatemantle of the Earth will be discussed.As upper and lower limits to the Urey numberwe lO take Ur = 0.8 and 0.6. Publishedestimates of the correspond- 1013W ing concentrationsof the heat-producingelements and the rates of heat generationare given in Table 2. The valuesof mean heat generationfor the bulk silicateEarth range from H = 7 x 10- •2 to 5.2 x 10-•2Wkg-•. Mean valuesfor chrodriticmeteorites are alsogiven in Table 2. It is seenthat the Earth is enriched in the refractory elements U and Th relative to the volatile element K. In the absence of other constraintswe assumethat the range of concentrationsasso- ciatedwith the Earth are also applicableto Venus. Mid-oceanridge basalts(MORB) are taken as direct melt productsof the Earth's mantle. However, the upper mantle is 1018• certainlydepleted in incompatibleelements relative to the bulk Figure 5. Schematicrepresentation of a cycle of episodic silicate earth due to the concentration of these elements in the subductionon Venus. The upper mantle temperature Tm, continentalcrust. Sun and McDonough[1989] arguethat nor- total surfaceheat lossQm, andviscosities of the asthenosphere mal (N type) MORB representsthe meltingof this depleted /J•aand upper mantle/xm are shown. sourceregion; as evidencethey givethe consistentdepletion of

Table 2. Concentrationsof Heat-ProducingElements and Rate of Heat GenerationH for a Variety of PlanetaryBasalts and Source Rocks Uranium(U), Thorium(Th), Potassium(K), HeatProduction •(H), ppm ppm ppm Th/U K/U 10-12 W kg- Reference

Chrondrite 0.008 0.029 545 3.6 68,000 3.5 SM89 Bulk silicateearth (Ur = 0.8) 0.029 0.116 290 4.0 10,000 7 TS82 Bulk silicateearth (Ur = O.6) 0.021 0.085 250 4.0 11,900 5.2 SM89 Earth Basalts N type MORB 0.047 0.12 600 2.6 12,800 10 SM89 E type MORB 0.18 0.60 2,100 3.3 11,700 41 SM89 OIB 1.02 4.20 12,000 4.1 11,800 255 SM89 Moon Basalts Low-Ti olivine(sample 12002) 0.22 0.75 415 3.4 1,900 43 H91 Low-Ti olivine(sample 15545) 0.13 0.43 330 3.3 2,500 25 H91 Low-Ti pigeonite(sample 12064) 0.22 0.84 580 3.8 2,600 46 H91 Low-Ti pigeonite(sample 15597) 0.14 0.53 500 3.8 3,600 30 H91 High-Ti, low K (sample70215) 0.13 0.34 415 2.6 3,200 23 H91 High-Ti, highK (sample10049) 0.81 4.03 3,000 5.0 3,700 197 H91 Low-Ti aluminous(sample 14053) 0.59 2.1 830 3.6 1,400 117 H91 Venus Basalts 0.64 1.5 4,500 2.3 7,000 118 S87 0.68 2.0 4,000 2.9 5,900 134 S87 2.2 6.5 40,000 3.0 18,000 531 S87 0.60 3.65 4,700 6.1 7,800 172 S87 Venera 10 0.46 0.70 3,000 1.5 6,500 74 S87 ...... 33,000 ...... S84 ...... 1,700 ...... S84

Referencesare asfollows: SM89, Sunand McDonough[1989]; TS82, Turcotteand Schubert[1982]; H91, Heikenet al. [1991,pp. 261-263]' S87, Surkovet al. [1987]; and S84, Surkovet al. [1984]. 16,938 _TURCOTTE: HEAT LOSS ON VENUS

T• øK MORB but lower than typical OIB. Two landersgive values 700 900 11 O0 1300 1500 1700 moretypical of silicicrocks on the Earth. In termsof modeling, an essentialquestion is whether the surfacevalues are typical of crustalvalues at depth. Certainly,fractionation and crystal- 0•• I I I I I I lization are likely to lead to an upward concentrationof the incompatibleheat-producing elements. In the continentsof the Earth the concentrationsof the heat-producingelements decay exponentiallywith depth on a scaleof 10 km. But it is impos- sible to estimate such variations in the crust of Venus. As a limiting casewe assumethat all the heat-producing 5O elementsin Venus are concentrateduniformly in a crust of thicknessY c. Secularcooling is alsoneglected, so that the heat flow to the base of the crust is taken to be zero. In this limit the temperaturedistribution in the crustis [Turcotteand Schubert, 1982,p. 145]

(6)

IO0 where Ts is the surfacetemperature and T m the uniformtem- Figure 6. Temperatureprofiles through a thick crustwith a peratureof the mantle. In addition,we require uniform concentrationof heat-producingelements and zero mantle heat flow. qs = pcHcYc (7)

1 Tm-- Ts= •qsyc/kc (8)

whereHc is the rate of heat productionin the crustand qs is the light rare earth elementsin theserocks relative to chron- the surface heat flow. drites.On the other hand,they point out that enriched(E type) For a steadystate heat balance and Ur - 0.8 we require MORB havegenerally chrondritic rare earth distributionsand q• = 50 mW m-2;with Ur = 0.6, q• = 38 mW m-2. We also shouldrepresent the partialmelting of a sourceregion that has near-bulk earth concentrations. The concentrations of the takeT• - 750øK,k - 2 W m-• øK-i, andPc = 2900 kgm-3. If the crust is thick, the temperaturewithin it will exceedits heat-producingelements in E type MORB as givenin Table 2 liquidus(assumed to be undesirable).If the crustis thin, the are •7 times the estimatedbulk earth values, leading to a heat productionH will be large (exceedingthe observedval- reasonable12% basalticcomponent in the undepletedmantle ues). Solutionsfor the two casesin which the basaltempera- with completetransfer of incompatibleelements to the liquid ture approachesthe liquidus (Tm • 1700øK) are given in fraction. Also given in Table 2 are typical concentrationsof Figure6. ForUr = 0.8we haveyc - 75km and Hc - 230x 10-12 heat-producingelements in ocean island basalts (OIB). W kg-•, andfor Ur - 0.6 we haveYc = 100 km andHc - Clearly, thesebasalts have enrichedconcentrations of the in- 130 x l0 -•2 W kg-•. Comparingthe rates of heatgeneration compatibleelements. with the Venusian values given in Table 2, we see that the Before consideringresults for Venus, we turn to the Moon. valuesfor Ur - 0.6 are generallyconsistent. Concentrationsand heat productionare givenfor sevenmare Thus it is possibleto constructa model for the upward basaltsin Table 2. Certainly, lunar basaltsare very complex, concentrationof the heat-producingelements that has a man- and there are significantdifferences between the interior of the tle temperaturebelow the solidusand ratesof heat generation Earth and the Moon. However, the more "primitive" lunar compatiblewith the surfaceobservations. However, this does basalts(i.e., olivineand pidgeonite)have concentrationsof U require extremeassumptions: (1) almostcomplete transfer of and Th rather similar to E type MORB. The depletionin K is the heat-producingelements to the crust,(2) negligiblesecular consistentwith the depletion of all volatile elementsin the coolingof Venus,and (3) uniformconcentrations of the heat- Moon, presumablyassociated with the giant impact (or other producingelements through the crust. processes)responsible for its formation. Presumably,if this model is to be valid, the crustof Venus The concentrationsof heat-producingelements and heat would havethickened with time with little crustalrecycling. An productionfor five landing sites on Venus (Vega 1, 2 and expectedconsequence of this processwould be the systematic Venera 8, 9, 10) are given in Table 2 [Surkovet al., 1987]. depletion of the mantle heat-producingelements with time; Potassiumvalues are givenfor two additionalsites. Venera 8 this should lead to a reduction in the content of the heat- and 13 sampledupland plains with weeklydifferentiated mela- producingelements in the mostrecent volcanics and a gradual nocraticalkaline gabbroidswith high potassiumcontent. Ven- decay of volcanismwith time. A valid questionwould be era 14 sampleda lowlandarea coveredwith tholeiiticbasaltic whether this type of decaycould be consistentwith the crater tuff with a low potassiumcontent. Young shield structures counts. were sampledby Venera 9 and 10 with lavasclose in compo- sition to tholeiitic basalts but with a calc-alkaline trend. The Venus data are certainlyless reliable than the labora- Conclusions tory studiesof terrestrialand lunar rocks.However, the results are generallyconsistent with values expectedfor basic rocks. The loss of heat from the interior of a terrestrialplanet Five landersgive values that canbe associatedwith moderately drivesthe surfacetectonics and volcanismof the planet.On the radiogenicbasaltic rocks, 2-3 times higher than the E type Earth the platesof plate tectonicsare thermalboundary layers TURCOTTE: HEAT LOSS ON VENUS 16,939 of mantle convectioncells. The subductionof thesecold plates paperis that the bulk of the presentlyavailable evidence favors is responsiblefor 70% of the heat transferthrough the Earth's the episodicsubduction hypothesis. mantle. There is no evidence for active subduction on Venus, An important questionto answeris, Why does the Earth soan alternativemechanism for mantleheat transportmust be have plate tectonicsand Venus does not? One suggestionis provided.Three limiting caseshave been consideredin this that while subductioncan occuron Venus,seafloor spreading paper. cannot. It is recognizedthat the temporal evolution of plate The Earth is in a near steady state balance between the tectonicsrequires intraplate deformation. On the Earth, al- sourcesof heat, radioactivedecay of U, Th, and K and secular most all this deformationtakes place in the continentalpor- cooling,and the surfaceheat loss.A uniformitarianhypothesis tions of the surfaceplates. The westernUnited Statesis an is that Venus alsohas a steadystate balance. However, without example.The rheologyof continentallithosphere is soft rela- active subductionthe vertical transport of heat through the tive to oceaniclithosphere due to the siliciccomposition of the Venusian mantle must be accomplishedeither by ascending continentalcrust. Without continents,it is suggestedthat this hot plumesor descendingcold delaminated lithosphere. If the intraplatedeformation cannot occur on Venus, and thus Ve- heat was transported by plumes, about 80 Hawaiian size nus cannothave a globalsystem of seafloorspreading centers plumeswould be required. If the heat was transportedby which are necessarycomplements to subductionin plate tec- lithosphericdelamination, a 60% delaminationof the entire tonics.Without seafloorspreading, episodic global subduction Venusianlithosphere would be requiredevery 20 m.y.There is eventsrecycle the cold, unstablelithosphere. no evidencefrom Magellandata for either the requiredplume An obviousquestion is, What happenedon Venus prior to the last resurfacing?It is the basictheme of this paper that flux or the requireddelamination flux. Heat transferconsider- episodesof globalsubduction have occurred throughout much ations argue strongly against a uniformatarian model for Venus. of the evolutionof Venus.But are there anyrelict fragmentsof thisearly history? It is difficultto explainthe highmountains of Mechanical considerationsprovide independentevidence IshtarTerra unlessthey are of siliciccomposition. They maybe against the uniformatarianhypothesis. This hypothesisre- continentlikerelicts of the past on Venus which were com- quiresa meanlithospheric thickness for the planetof about50 pletelyreworked during the resurfacingevent but did not par- km. With the highsurface temperature, such a thin lithosphere ticipatein the last globalsubduction because of their gravita- is inconsistentwith the high topography,large gravityanoma- tional stability. lies, lack of crater relaxation, and large observedflexural rigidities. Crater statisticssuggest that a global volcanicresurfacing Acknowledgments.This researchhas been supported by the NASA event occurredon Venus about 500 Ma. This suggeststhat a Venus Data AnalysisProgram under grant NAGW-3597 and by the NASA PlanetaryGeophysics Program under grant NAGW-1420. De- rigid globallithosphere then stabilizedand hasthickened con- partmentof GeologicalSciences, Cornell University,contribution 880. ductivelysince. 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