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

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 5 cm/yrare presented here. The crustalthickness on 30 kin, as labeled. See text for discussion. Venusis generallyestimated to be lessthan 30 km (Zuberand Parmentier,1990). Resultsare givenfor crustalthicknesses of both20 and30 kin. The bottompanel of Figure4 showsthat Discussion surfaceheat flow variesfrom over 100 mW/m2 within 200 km ofa center of platespreading down to less than 25 mW/m 2. These simplified model calculationsshow that the lower Themost important result of thesecalculations concerns the crustalviscosity must average 1018 Pa s or lessto allow equilibriumtopographic slope as a functionof position(see top decouplingof crustand mantle. In the flattestlowland regions of Figure4). In the areawhere the plateis old the slopesare the viscosityof the lower crust must be at least severaltimes largeand in the areaof mantledivergence the slopesare small. smallerthan this. At temperaturesthat allow the mantleto retain Thisis a resultof the topographicgradient depending on the considerablestrength, flow lawsfor crustalrocks predict higher lowercrustal thickness and viscosity, as givenby Equation6. viscositiesthan assumed here. Partialmelting or the formation Inan area of mantleplate divergence the lower crust is thicker, of shearzones might lead to a local reductionin viscosityat the hotterand weaker than in an area of mantledownwelling. The base of the crust. longwavelength slope of thesurface in thelowlands of Venusis Numericalcalculation of equilibriumtopog?aphic profiles are generallyless than 10 -3 m/m. The valueof/.to in equation4 had beyondthe scopeof this paper. However,it shouldbe clearthat tobe set to 3x1017 Pa s to giveabout this slope. In thecoldest highlandsare predicted to occurover areas where mantle plates areafor a 20 km thickcrust, the lower crustalviscosity is about convergeand downwell. The lowest lowlands occur where 1019Pa s. mantleupwells. Thermalbuoyancy should elevate the mantleat Thenext to thebottom panel shows the calculated values of a siteof platespreading, but the crust should be thinnedthere so tl'•tectonic force G(x) for these calculations. The shear stress is thatthe elevation islower than the average (Figure 1). Themain greaterwhere the heat flow is small,thus most of thetectonic thickeningof thecrust in highlandswould be accomplished by forcebuilds up over the cold part of the mantle plate. A valueof thetransport of lowercrust, in muchthe same way that is (7= 5 x !012N m-1 is aboutthe force required tosupport the discussedby Kieferand Hager (1991b). The spacingof highestelevations onVenus if theaverage crustal thickness is20 lowlandsand highlands ison the order of 1000'sof km which is kin.This is theamount of tectonicforce resulting from an thereason for taking L=5000 km as a representativesizein the averagestress Vc of 1 MPa integratedover a 5000km plate,or 5 exampleshown in Figure4. MPaover the last !000 km of the plate. Decouplingon a globalscale can explain the low rate of TheIbrce that can be transmitted bythe mantle plate without surface deformation inferred for Venus(e.g. Solomon et al., largemagnitude deformation, thelithospheric strength, is the 1991).The strongest crustal deformation should be in thesame integralofthe yield strength over depth. The plots in Figure 4 regionswhere large topographic slopes could be maintained: showthat the mantle lithospheric strength isgreater than the namely,where the plate is cold and so the lower crust isstrong. forcesdue to coupling between crust and mantle. Therefore, the However,simple predictions ofpatterns ofdeformation maybe plateshould not be disrupted. difficultto makesince stress can be transmitted both by the 2114 Buck: GlobalDecoupling of Crustand'Mantle on Venus upper crust and the mantle lithosphere. The tesseraterrain thicknessand thermal gradient, J. Geophys.Res., 93, indicatethat many parts of the uppercrust have failed and 11,911-11,929, 1988. deformed. Hager,B.H., Subductedslabs and the geoid: Constraintson Variabilityin platesize and speed may explain the variability mantlerheology and flow, J. Geophys.Res., 89, 6003- in topographyand deformationpatterns seen in different 6015, 1984. highlands. The crustabove a larger plate wouldbe cooler, Head,J.W.L.S. Crumpier, J. C. Aubele,J.E. Guest and R. S. higher viscosityand so better coupledto the plate. Better Saunders,Venus volcanism: Classificationof volcanic couplingshould lead to strongcompressional deformation as is features and structures,associations, and global seenin plateau-shapedhighlands such as and Thetis distributionfrom data, J. Geophys.Res., Regio. A smallfast-moving plate might not result in significant 97,13,495-13,532, 1992. deformationof the surfaceof the crust. This might produce Kaula,W.M., Venus: A contrastin evolutionto Earth., domalhighlands such as Beta andAria Regiowhich show more Science,247, 1191-1196, 1990. evidenceof extensionthan compression (Bindscharier et al., Kiefer,W.S., andB.H. Hager,A mantleplume model for the 1992). The extensionwould be drivenby thecollapse of the equatorialhighlands of Venus,J. Geophys.Res., 96, hightopography. 20,947-20,966, 199 la. Predictingthe regionalstyles of volcanismassociated with Kiefer, W.S., and B.H. Hager,Mantle Downwellingand thismodel requires assumptions regarding the composition of CrustalConvergence: A Model for Istar Terra,Venus, J. themantle and crust. Without making those assumptions I can Geophys.Res., 96, 20,967-20,980,199 lb. saythat melting of theupwelling mantle should be greatest in the Kiefer, W.S., M.A. Richards,B.H. Hager, and B.G. Bills,A regionsof mantleplate divergencein the lowlands. Many dynamicmodel of Venus'sgravity field, Geophys.Res. topographicallylow regions are coveredwith relatively Lett., 13, 14-17, 1986. undeformedvolcanics, though the mostobvious sources are at Kirby, S.H. and A.K. Kronenberg, Rheology of the higherelevations (Head et al., 1992). Crustalmelting might lithosphere: Selected topics,Rev. Geophys.,25, 1219- occurin the highlandswhere thick crust could be veryhot. 1244, 1987. The highestheat flow is predictedto occurin the lowest Koch,P.S., Rheology and microstructures of experimentally lowlands of Venus and the lowest heat flow should occur in deformedquartz aggregates, Ph.D. thesis,Univ. Calif. Los topographicallyelevated areas. This is qualitativelyconsistent Angeles,464pp., 1983. with a recent estimate of the variation of heat flow based on Phillips,R.J., andM.C. Malin, Tectonicsof Venus,Ann. Rev. tectonicfeatures. Suppeand Conngrs(1992) showthat the Earth . Sci.. 12.411-44q l o•zt amplitudeof the topographicstep acrosscompressional Sjogren, W.L., B.G. Bills, P.W. Birkeland,P.B. Esposito, mountain belts scaleswith the elevation of the lower side of the A.R. Konopliv, N.A. Motfinger, S.J. Ritke, and R.J. belt. Theyargue that the topographic step is roughlyequivalent Phillips, Venus gravity anomaliesand their correlations to the thicknessof the brittle layer of upper crust. The data with topography,J. Geophys.Res., 88, 1119-1128,1983. cannotbe explainedsolely by thelapse rate in theatmosphere, Smrekar, S.E., andR.I. Phillips,Gravity-driven deformation butrequires that heat flow be inverselycorrelated with elevation of the cruston Venus, Geophys.Res. Lett., 15, 693-696, (Suppeand Connors, 1992). Whetherthe presentmodel can 1988. quantitativelymatch these observations can only be addressedSolomon, S.C., J.W. Head, W.M. Kaula, D.P. McKenzie,B. with numericalmodels of decoupling. Parsons,R.J. Phillips, G.Schubert,and M.Talwani, Venus tectonics: Initial analysisfrom Magellan, Science,252, Acknowledgments.Thanks to JohnSuppe and Maria Zuber 297-312, 1991. for helpfuldiscussions and to WalterKiefer, John Hopper and Solomon,S.C. andJ.W. Head,Mechanisms for Lithospheric two anonymousreviewers for commentson the manuscript. HeatTransport on Venus: Implicationsfor TectonicStyle Supportcame from NSF grant OCE-91-04076. Lamont- and Volcanism,J. of Geophys.Res., Vol. 87, No. B1 I, DohertyGeological Observatory contribution 4999. 9236-9246, November 10, 1982. Suppe,J. andC. Connors,Critical Taper Wedge Mechanics References of Fold-and-Thrust Belts on Venus: Initial Results from Magellan, J. of Geophys.Res., Vol. 97, 13,545-13,562, Bindschad!er,D.L., G. Schubert,and W.M. Kau!a,Coldspots 1992 and hotspots:Global tectonicsand mantledynamics of Turcotte,D.L., andG. Schubert,Geodynamics, 450 pp.,John Venus,J. Geoœhys.Res., 97,13,495-13,532, 1992. Wiley, New York, 1982. Bindschadler, D.L., and E.M. Parmentier, Mantle flow Weertman,J., Height of mountainson Venusand the creep tectonics: The influence of a ductile lower crust and propertiesof rock,Phys. Earth Planet.Inter., ] 9, 197-207, implicationfor the formationof topographicuplands on 1979. Venus,J. Geophys.Res., 95, 21,329-21,344,1990. Zuber, M. T. and E. M. Parmentier, On the relationship Buck,W. R., Modesof continentallithospheric extension, J. betweenisostatic elevation and the wavelengths of tectonic Geophys.Res., 96, 20,161-20,178, 199!. surfacefeatures on Venus,Icarus, 85, 290-308, 1990. Burchfiel, B.C., D. Quidong,P. Molnar, L. Royden,W. Yipeng, Z. Peizhen, A. Weiqi, Intracrustaldetachment W. R. Buck, Lamont-DohertyGeological Observatory, within zonesof continentaldeformation, Geology, 17, 448- Palisades,NY 10964. 452, 1989. (Received:June 9, 1992; Grimm, R.E., and S.C. Solomon, Viscous relaxation of revised:August 24, 1992; impactcrater relief on Venus: Constraintson crustal accepted:September 9, 1992)