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Global Decoupling of Crust and Mantle: Implica•Ons for Topography,Geoid and Mantle Viscosity on Venus

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Global Decoupling of Crust and Mantle: Implica•Ons for Topography,Geoid and Mantle Viscosity on Venus GEOPHYSICALRESEARCH LETTERS, VOL. !9, NO. 21, PAGES2111-2114, NOVEMBER 3, 1992 GLOBAL DECOUPLING OF CRUST AND MANTLE: IMPLICA•ONS FOR TOPOGRAPHY,GEOID AND MANTLE VISCOSITY ON VENUS W. RogerBuck LamontDoherty Geological Observatory andDepartment ofGeological Sciences, Columbia University Abstract.The surfaceof Venusis so hot thatthe lowercrust or the Basinand Range Province of the WesternU.S. (e.g. maybe weak enough to allowdecoupling of mantle and crust. Burchfielet al., 1989). Manyauthors have noted that the high Ananalytic model of suchdecoupling assumes that the shallow temperatureof the surface of Venusmay cause the crust to be mandeforms the top boundarylayers of large scalemantle quiteweak at relatively shallow depth (Weertman, 1979, Grimm convectioncells. Crustalflow is drivenby the motionof the & Solomon,1988) and the effects of localdecoupling have been marieand by topographicallyinduced pressure gradients. The modeledby severalworkers (e.g. Smrekar & Phillips,1988, modelpredicts that the lowestlowlands are sitesof mantle Bindshadier& Parmentier,1990, Kiefer & Hager, 1991b). upwellingand thinner than average crust. Highlands are places Decoup!ingmay occur everywhere on Venus because its surface wheremantle downwells and the crust is thick. Surface heat is 450øCon average. flowis inverselycorrelated with elevation,consistent with recent In thispaper I discussthe requirements for andconsequences estimatesof brittle layer thicknessvariations on Venus. If the of globaldecoupling of crustand mantle on Venus. Thefirst averagecrustal thickness is about20 km thenthe average lower stepin thisprocess is to estimatethe velocity of mantlemotions. crustalviscosity must be close to 1018Pa s toallow decoupling. Theobserved amplitude of geoidhighs over highlands requires Thermaland Rheologic Model anEarth-like increase in manfieviscosity with depth. By treatingthe coolingof a mantleplate in termsof the Introduction coolingof a halfspaceof constantinitial temperaturewe can estimatethe heat flux out of the plate. Figure 2 showsthe Oneof the most surprisingdifferences between Venus and boundmyconditions assumed here. The average heat flux out of Earthis thatthe long wavelength geoid shows a strongpositive thetop of such a plateof length L movingat velocity up is: correlationwith topography on Venus, unlike on Earth(Sjogren Up t/2 eta!.,1983). The acceptedinterpretation of this observationis qave= 2 K AT ( rc•: L ) (1) thatthe convecting manfie of Venushas a constantviscosity with depth(Phillips and Malin, 1984, Kiefer et al, 1986; Kaula; whereK is the conductivity,AT is the temperaturedrop across 1990;Kiefer and Hager, 1991a; Bindschadleret al., 1992). the plate and •cis the thermaldiffusivity of the plate (Turcotte Accordingto theseworkers, topography results from vertical and Schubert,1982). normalstresses caused by mantle convection,and highlands If theheat budget of Venusis similar to thatfor Earththen the occurwhere mantle upwells and lowlands where mantle averagesurface heat flux of Venus is about70 mW/m2 downwells. (Solomonand Head; 1982). Plate recyclingmight accountfor Thisview of Venusis in markedcontrast to the acceptedview about50 mW/m2 of thisflux. The shallowmantle temperature of Earth,where most topography is not a resultof vertical based on parameterized convection models for Venus are tectonics.Much of geoid variationson Earth are probably somewhathigher than for the Earth (e.g. Phillipsand Malin, relatedto mantle dynamics, but viscosity must increase by about 1984). Herethe base of the mantleplate is setat 1450øC. Crust twoorders of magnitudethrough the mantleto explainthese forming rocks can begin to partially melt at relatively low anomalies(e.g. Hager, 1984). temperatures,and melting should buffer the temperatureof the The weaknessof hot Venusiancrust may providean crust. The temperatureof the base of the crust TM is set at alternativeexplanation of theobserved correlation of geoidand 850øC,and this gives ziT = 600øC.Taking K = 4 Wm-2 øC'I and topography.If crustis very weak thentopography can result •c= 10'6 m2 s'l, theplate velocity would have to bejust over 5 fromhorizontal manfie motions. For this 'to occur, topographic crrdyr to givean average heat flux of 50 mW/m2 forL = 5000 gradientsmust drive crustalflow as fast as flow causedby km. mantleshearing. This situation is termed decoupling. Neglecting heat producing elements in the crust, and Decouplingrequires that crust is thickenedwhere mantle assumingthe crustis in thermalequilibrium with the heatflux downwe!Isandthinned where mantle upwells (Figure !). To comingout of the plate,the temperatureat depthz in the crust will be: explainthe correlation of geoid and topography, the viscosity of q(x) themantle must increase with depth. T(z)=Ts + • z (2) Localrecoupling of crustand mantle is inferredto occuron Earthinareas of anomalously thick and hot crust such as Tibet where Ts is the temperatureof the surface,Kc is the crustal conductivityassumed to be half that of the mantle. A linear temperaturegradient is assumedbetween the depth where Copyright1992by the American Geophysical Union. T= 750øC and the baseof the crust,as shownin Figure3. The Papernumber 92GL02462 baseof the crustmay be coolerthan 850øC if the heat flux from 0094-8534/92/92GL-02462503.00 the mantleplate is low enough.The temperaturesin themantle 2!11 2112 Buck:Global Decoupling of Crustand Mantle on Venus Fig.1. Cross-sectionillustrating the model of decouplingof relatively static upper crustal lithospherefrom moving mantle lithosphere. T s = 450 øC TM = 850øC Temperature Viscosity Yield Strength 450 850 1250 18 22 26 30 5 6 7 8910, 0.0•• f" 3o.o-1 \\ 10 60.0q 90 F -I Fig. 2. Boundaryconditions for subcrustalmantle plate 70.0{••80.01 • thermal model. The shaded area is the weak lower crustal 450 850 1250 22 26 30 5 678910 channel. (øC) Log (Pa s) Log (Pa) platewhere the crustis coolerare then given by thesolution for Fig. 3. Profilesof temperature,effective viscosity and yield half-spacecooling with a lower topboundary temperature. The strengthfor thecrust and mantle for threeplate cooling ag• small error due to this approximationshould not significantly givenin unitsof millionsof yearson the plots. The viscosity affect the results. is calcualted for a deviatoric stress of 1 MPa the yield When minerals are hot enoughfor ductile flow to occur, strengthfor deformation ata strainrate of 10-14 s -1. resultsof laboratorydeformation experiments can be expressed in termsof thestrain rated as a functionof the applieddeviatoric is adjustedin thesecalculations tomatch observations. Fig...ure 3 stresscr and temperatureT as: showsyield strength and effective viscosity profiles used in the presentcalculations. 6= A o n exp (•TT) (3) Crustal Flow wheren is the powerlaw exponent,E is the activationenergy andR is the universalgas constant. In the modelcalculations Crustalflow can be drivenin two ways:by the relative the valuesof A, E and n for the crustand mantleare givenby motionbetween mantle and crust, and by pressuregradleto parametersdetermined for anorthisite(Koch, 1983) and olivine relatedto topography.Consider the lower crust to consistofa (Kirby and Kronenberg;1987), respectively.The strengthof a channelof viscosity,u and thicknessH. The flux Fs of • materialis thedeviatoric stress that can be maintainedfor a given movedlaterally due to mantleshear is UsH/2, whereus is strmnrate and temperature. relativevelocity between crust and mantle. The flux Fp of cn• The effective Newtonian viscosity of the crust can be drivenby pressuregradients is (H$/J2l.t) 3P/3x,where expressedas: pressure(see Turcotte and Schubert, 1982). The press'•'ue gradient o•P/o•xis related to isostatic topographyas o•P/o•x=gpc&,V/O•x,whereg is theacceleration of gravity, w g= go ex•R•+-•J-•}] (4) topography,h is crustal thickness, and Pc is thedensity where/.tois theviscosity of thecrust at T= TM. Thevalue of/2o crust. Foraconstant shear velocity usequal to the plate velocity, 0. Surface Slope topographycanbe maintained insteady state aslong as Fp -- Fs •'. / ..........'' ' • ...........' • asnoted byKiefer andHager (1991b). Forthis case the • equilibriumtopographic gradient is: • •w • -- •x =6up•gpcH 2 . (5) -4. Calculationsshow that most of theflow driven by pressure 13. Mantle LithosphericStrength gradientsina layer with a depthdependent viscosity occurs in • theregion where the viscosity iswithin ten times the layer • minimum(Buck, 1991). Thus, the lower crustal channel is • takento be the region with a temperaturewithin 50øC of TM. • Theaverage viscosity of thechannel is takento bethe viscosity 10. o.f•e baseof the crust. Tectonic Force, G In this model the highlandsare supportedby stress 23. ' I i I .... i - -- transmittedlaterally bythe crust and mantle. The magnitude of • thisstress can be estimated byintegrating theshear stress atthe • baseof the crust with horizontaldistance. For a mantle '• lithosphericplatemoving ata velocity Uprelative tocrust which --• hasa lowviscosity layer of thicknessH andviscosity )t, the 10. shearstress •c is Hug//-/.The maximum tectonic force G per Heat Flow unitlength maintained by a mantleplate and the upper crust due 100. to the shearbetween them is just the integral of Vc over •' horizontaldistance from where the plate originates (i.e.at an • upwelling).Thisinteraction willcause the crust tobe in •: compressionandthe mantle in extension. • - 50O0 Results Distance (kin) Resultsfrom two model calculationsfor a 5000 km plate Fig. 4. Calculationresults for two crustal thickness,20 and movingat
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