GEOPHYSICALRESEARCHLETTERS, VOL. !9, NO. 21, PAGES2111-2114,NOVEMBER 3, 1992
GLOBAL DECOUPLINGOF CRUST AND MANTLE:
IMPLICA•ONS FOR TOPOGRAPHY,GEOID AND MANTLE VISCOSITY ON VENUS
W. RogerBuck
Lamont
Doherty
Geological
Observatory
andDepartment
ofGeological
Sciences,
Columbia
University
Abstract.
The surfaceof Venusis sohotthatthelowercrust or the BasinandRangeProvinceof the WesternU.S. (e.g.
havenotedthatthehigh
may
beweakenough
toallowdecoupling
ofmantle
andcrust. Burchfielet al., 1989). Manyauthors
of thesurface
of Venusmaycausethecrustto be
Ananalytic
modelof suchdecoupling
assumes
thattheshallow temperature
mande
formsthe top boundarylayers of large scalemantle quiteweakatrelatively
shallow
depth(Weertman,
1979,Grimm
1988)andtheeffectsof localdecoupling
havebeen
convection
cells. Crustalflow is drivenby the motionof the & Solomon,
by severalworkers(e.g.Smrekar& Phillips,1988,
marieandby topographically
inducedpressure
gradients.The modeled
model
predicts
that the lowestlowlandsare sitesof mantle Bindshadier& Parmentier,1990, Kiefer & Hager, 1991b).
mayoccureverywhere
onVenusbecause
itssurface
upwelling
andthinner
thanaverage
crust.Highlands
areplacesDecoup!ing
wheremantledownwells and the crust is thick. Surface heat is 450øConaverage.
flowisinversely
correlatedwith elevation,consistent
with recent
In thispaperI discuss
therequirements
for andconsequences
estimates
of brittle layer thicknessvariationson Venus. If the of globaldecoupling
of crustandmantleonVenus. Thefirst
is toestimate
thevelocityof mantlemotions.
average
crustal
thickness
is about20 km thentheaverage
lower stepin thisprocess
crustal
viscosity
mustbeclose
to 1018Pastoallowdecoupling.
ThermalandRheologicModel
Theobserved
amplitudeof geoidhighsoverhighlands
requires
anEarth-like
increasein manfieviscositywith depth.
By treatingthecoolingof a mantleplatein termsof the
coolingof a halfspace
of constantinitial temperature
we can
estimatethe heat flux out of the plate. Figure 2 showsthe
Oneof the mostsurprisingdifferencesbetweenVenus and boundmy
conditions
assumed
here.Theaverage
heatfluxoutof
Introduction
Earthis thatthelongwavelengthgeoidshowsa strongpositive
correlation
withtopography
onVenus,unlikeonEarth(Sjogren
eta!.,1983). The acceptedinterpretation
of thisobservation
is
thattheconvecting
manfieof Venushasa constant
viscosity
with
depth(Phillipsand Malin, 1984, Kiefer et al, 1986; Kaula;
1990;Kiefer and Hager, 1991a; Bindschadleret al., 1992).
According
to theseworkers,topographyresultsfrom vertical
normalstresses
causedby mantle convection,and highlands
occurwhere mantle upwells and lowlands where mantle
thetopofsuch
a plateoflengthL moving
atvelocity
upis:
Up t/2
qave
=2KAT( rc•:L)
whereK is theconductivity,AT is the temperaturedropacross
the plateand •cis the thermaldiffusivity of the plate (Turcotte
and Schubert,1982).
If theheatbudgetof Venusis similarto thatfor Earththenthe
averagesurfaceheat flux of Venus is about70 mW/m2
(SolomonandHead; 1982). Platerecyclingmightaccountfor
downwells.
Thisviewof Venusis in markedcontrastto theaccepted
view
(1)
about50 mW/m2 of thisflux. Theshallowmantletemperature
of Earth,wheremosttopographyis not a resultof vertical based on parameterized convection models for Venus are
tectonics.Much of geoid variationson Earth are probably somewhathigherthanfor the Earth (e.g. Phillipsand Malin,
related
tomantledynamics,
butviscosity
mustincrease
by about 1984). Herethebaseof themantleplateis setat 1450øC. Crust
twoordersof magnitudethroughthe mantleto explainthese forming rocks can begin to partially melt at relatively low
temperatures,
andmeltingshouldbuffer the temperatureof the
anomalies
(e.g.Hager, 1984).
crust.
The
temperature
of the base of the crust TM is set at
The weaknessof hot Venusiancrust may providean
850øC,
and
this
gives
ziT
=
600øC.TakingK = 4 Wm-2øC'Iand
alternative
explanation
of theobserved
correlation
of geoidand
topography.
If crustis very weakthentopography
canresult •c= 10'6 m2 s'l, theplatevelocitywouldhaveto bejustover5
crrdyrto giveanaverage
heatflux of 50 mW/m2 forL = 5000
from
horizontal
manfie
motions.
Forthis'tooccur,
topographickm.
gradients
mustdrive crustalflow as fast as flow causedby
mantleshearing. This situation is termed decoupling.
Neglecting heat producingelements in the crust, and
Decoupling
requiresthatcrustis thickened
wheremantle assumingthe crustis in thermalequilibriumwith the heatflux
comingoutof the plate,the temperatureat depthz in thecrust
downwe!Is
andthinned
wheremantle
upwells
(Figure
!). To will
be:
explain
thecorrelation
ofgeoidandtopography,
theviscosity
of
q(x)
themantle
must
increase
withdepth.
T(z)
=Ts+• z
(2)
Localrecoupling
of crustandmantleis inferred
to occuron
Earth
inareas
ofanomalously
thickandhotcrust
such
asTibet
Copyright
1992
bytheAmerican
Geophysical
Union.
Paper
number
92GL02462
0094-8534/92/92
GL-024
62503.00
2!11
where Ts is the temperatureof the surface,Kc is the crustal
conductivityassumedto be half that of the mantle. A linear
temperaturegradient is assumedbetween the depth where
T= 750øCandthe baseof thecrust,as shownin Figure3. The
baseof the crustmay be coolerthan 850øC if the heatflux from
the mantleplateis low enough.The temperatures
in themantle
Buck:GlobalDecoupling
of CrustandMantleonVenus
2112
Fig.1. Cross-section
illustrating
themodel
of decoupling
of relatively
staticupper
crustal
lithosphere
frommovingmantlelithosphere.
T s = 450 øC
450
850
1250
18
0.0••
3o.o-1
60.0
q
F
Fig. 2.
-I
Boundaryconditions
for subcrustal
mantleplate
22
26
30
5
6
7
8910,
f"
\\
10
90
70.0{••
•
80.01
450
thermal model. The shaded area is the weak lower crustal
850
1250
(øC)
channel.
platewherethecrustis coolerarethengivenby thesolutionfor
half-spacecoolingwith a lower topboundarytemperature.
The
small error due to this approximationshouldnot significantly
YieldStrength
Viscosity
Temperature
TM = 850øC
22
26
Log (Pa s)
30
5
678910
Log (Pa)
Fig. 3. Profilesof temperature,
effectiveviscosityandyield
strengthfor thecrustandmantlefor threeplatecoolingag•
givenin unitsof millionsof yearsontheplots.Theviscosity
is calcualted for a deviatoric stress of 1 MPa the yield
When minerals are hot enoughfor ductile flow to occur, strength
fordeformation
ata strainrateof 10-14s-1.
resultsof laboratorydeformationexperiments
canbe expressed
in termsof thestrainrated asa functionof theapplieddeviatoric isadjusted
inthese
calculations
tomatchobservations.
Fig...ure
3
stresscrand temperatureT as:
shows
yieldstrength
andeffective
viscosity
profiles
used
inthe
affect the results.
6=Aonexp
(•TT)
(3)
presentcalculations.
Crustal Flow
wheren is the powerlaw exponent,E is theactivationenergy
andR is the universalgasconstant.In the modelcalculations
the valuesof A, E andn for the crustand mantleare givenby
parameters
determined
for anorthisite
(Koch,1983)andolivine
(Kirby andKronenberg;1987),respectively.The strengthof a
materialis thedeviatoric
stressthatcanbemaintained
for a given
Crustalflow can be drivenin two ways:by therelative
motionbetweenmantleandcrust,andby pressure
gradleto
relatedto topography.
Consider
thelowercrusttoconsist
ofa
channelof viscosity,u and thicknessH. The flux Fs of •
movedlaterallydueto mantleshearis UsH/2, whereusis
strmnrate and temperature.
relativevelocitybetweencrustandmantle.The flux Fp of cn•
The effective Newtonian viscosity of the crust can be
expressedas:
pressure(see Turcotte and Schubert, 1982). The press'•'ue
g=go
ex•R•+-•J-•}] (4)
where/.tois theviscosityof thecrustat T= TM. Thevalueof/2o
drivenby pressure
gradients
is (H$/J2l.
t) 3P/3x,where
gradient o•P/o•xis related to isostatictopography
as
o•P/o•x=gpc&,V/O•x,
whereg is theacceleration
of gravity,
w
topography,
h iscrustal
thickness,
andPcis thedensity
crust.
For
aconstant
shear
velocity
usequal
totheplate
velocity, 0. Surface Slope
'' ' • ...........
'
topography
can
bemaintained
insteady
state
aslong
asFp--Fs •'. / ..........
as
noted
byKiefer
and
Hager
(1991b).
For
this
case
the•
equilibrium
topographic
gradient
is:
•w
•
•x =6up
•gpcH2 .
•
•
--
(5)
-4.
13. Mantle LithosphericStrength
Calculations
showthatmostof theflowdriven
bypressure
gradients
inalayer
withadepth
dependent
viscosity
occurs
in •
the
region
where
theviscosity
iswithin
tentimes
thelayer •
minimum
(Buck,
1991).Thus,
thelower
crustal
channel
is •
taken
tobetheregionwitha temperature
within50øCof TM. •
Theaverage
viscosity
of thechannel
istakento betheviscosity
10.
o.f•e baseof thecrust.
In this model the highlandsare supportedby stress
23.
Tectonic Force, G
' I
i
I
.... i
- --
transmitted
laterally
bythecrust
and
mantle.
Themagnitude
of •
this
stress
canbeestimated
byintegrating
theshear
stress
atthe •
baseof the crust with horizontaldistance. For a mantle
'•
lithospheric
plate
moving
atavelocity
Uprelative
tocrust
which --•
hasa lowviscosity
layerof thickness
H andviscosity
)t, the
shear
stress
•c isHug//-/.Themaximum
tectonic
forceG per
10.
unitlength
maintained
bya mantleplateandtheuppercrustdue
to theshearbetweenthem is just the integral of Vc over
100.
Heat Flow
•'
horizontal
distance
fromwhere
theplate
originates
(i.e.atan •
upwelling).
This
interaction
willcause
thecrust
tobein •:
compression
andthemantle
in extension.
50O0
Results
Resultsfrom two model calculationsfor a 5000 km plate
moving
at5 cm/yrarepresented
here. The crustalthickness
on
Venus
is generallyestimatedto be lessthan30 km (Zuberand
Parmentier,
1990). Resultsare givenfor crustalthicknesses
of
both20 and30 kin. The bottompanelof Figure4 showsthat
-
•
Distance
(kin)
Fig. 4. Calculationresultsfor two crustalthickness,20 and
30 kin, as labeled. See text for discussion.
Discussion
surface
heatflow variesfrom over 100 mW/m2 within 200 km
ofacenter
ofplatespreading
downtolessthan25mW/m
2.
These simplified model calculationsshow that the lower
crustalviscositymustaverage1018Pa s or lessto allow
Themostimportant
resultof thesecalculations
concerns
the
equilibrium
topographic
slopeasa functionof position(seetop
ofFigure4). In the areawherethe plateis old the slopesare
largeandin theareaof mantledivergence
theslopesaresmall.
Thisis a resultof the topographic
gradientdepending
on the
lowercrustalthickness
andviscosity,asgivenby Equation6.
Inanareaof mantleplatedivergence
thelowercrustis thicker,
decouplingof crustand mantle. In the flattestlowland regions
the viscosityof the lower crust must be at least severaltimes
smallerthanthis. At temperatures
thatallow the mantleto retain
considerable
strength,flow lawsfor crustalrockspredicthigher
viscosities
thanassumed
here. Partialmeltingor the formation
of shearzonesmightleadto a local reductionin viscosityat the
hotterandweakerthan in an area of mantledownwelling. The
base of the crust.
longwavelength
slopeof thesurfacein thelowlandsof Venusis
Numerical
calculation
of equilibrium
topog?aphic
profilesare
generally
lessthan10-3m/m. Thevalueof/.toin equation
4 had beyondthescopeof this paper. However,it shouldbe clearthat
tobesetto3x1017
Pas to giveaboutthisslope.In thecoldest highlands
arepredicted
to occuroverareaswheremantleplates
areafor a 20 km thickcrust,the lower crustalviscosityis about convergeand downwell. The lowest lowlands occur where
1019Pa s.
mantleupwells.Thermalbuoyancyshouldelevatethemantleat
Thenextto thebottompanelshowsthecalculated
valuesof a siteof platespreading,
butthecrustshouldbe thinnedthereso
tl'•tectonic
forceG(x)forthese
calculations.
Theshear
stress
is thattheelevation
islowerthantheaverage
(Figure1). Themain
greater
wheretheheatflowis small,thusmostof thetectonic thickening
of thecrustin highlands
wouldbeaccomplished
by
force
builds
upoverthecoldpartofthemantle
plate.A value
of
(7= 5x !012N m-1isabout
theforcerequired
tosupport
the
highest
elevations
onVenus
if theaverage
crustal
thickness
is20
kin.Thisis theamount
of tectonic
forceresulting
froman
thetransport
of lowercrust,in muchthesamewaythatis
discussed
by KieferandHager(1991b).The spacing
of
lowlands
andhighlands
isontheorderof 1000's
ofkmwhichis
thereason
fortaking
L=5000kmasa representative
sizein the
average
stress
Vcof 1 MPa integrated
overa 5000km plate,or 5 exampleshownin Figure4.
MPa
over
thelast!000kmoftheplate.
Decoupling
ona globalscalecanexplain
thelowrateof
TheIbrce
thatcanbetransmitted
bythemantle
platewithoutsurface
deformation
inferred
for Venus(e.g.Solomon
et al.,
large
magnitude
deformation,
thelithospheric
strength,
isthe 1991).Thestrongest
crustal
deformation
should
beinthesame
integral
oftheyieldstrength
overdepth.
Theplots
inFigure
4 regions
where
largetopographic
slopes
couldbemaintained:
show
thatthemantle
lithospheric
strength
isgreater
than
the namely,
where
theplate
iscoldandsothelower
crust
isstrong.
forces
due
tocoupling
between
crust
andmantle.
Therefore,
the However,
simple
predictions
ofpatterns
ofdeformation
maybe
plate
should
notbedisrupted.
difficult
tomakesince
stress
canbetransmitted
bothbythe
2114
Buck: GlobalDecoupling
of Crustand'Mantle
onVenus
uppercrust and the mantle lithosphere. The tesseraterrain
indicatethat manypartsof the uppercrusthavefailed and
thickness
andthermalgradient,
J. Geophys.
Res.,93,
11,911-11,929, 1988.
Hager,B.H., Subducted
slabsandthegeoid:Constraints
on
mantlerheologyand flow, J. Geophys.Res.,89, 6003Variabilityin platesizeandspeedmayexplainthevariability
6015, 1984.
in topographyand deformationpatternsseenin different
highlands. The crustabovea largerplate wouldbe cooler, Head,J.W.L.S.Crumpier,J. C. Aubele,J.E.GuestandR.S.
Saunders,Venusvolcanism: Classificationof volcanic
higher viscosityand so better coupledto the plate. Better
features and structures,associations,and global
couplingshouldleadto strongcompressional
deformation
asis
distributionfrom Magellandata, J. Geophys.Res.,
seenin plateau-shaped
highlands
suchasIshtarTerraandThetis
Regio.A smallfast-moving
platemightnotresultin significant 97,13,495-13,532, 1992.
deformationof the surfaceof the crust. This might produce Kaula,W.M., Venus: A contrast
in evolutionto Earth.,
deformed.
Science,247, 1191-1196, 1990.
domalhighlandssuchasBetaandAria Regiowhichshowmore
evidenceof extensionthancompression
(Bindscharier
et al., Kiefer,W.S., andB.H. Hager,A mantleplumemodelforthe
1992). The extension
wouldbe drivenby thecollapseof the
equatorialhighlandsof Venus,J. Geophys.Res.,96,
20,947-20,966, 199la.
hightopography.
Predictingthe regionalstylesof volcanism
associated
with Kiefer, W.S., andB.H. Hager,Mantle Downwelling
and
CrustalConvergence:A Model for Istar Terra,Venus,J.
thismodelrequiresassumptions
regarding
thecomposition
of
Geophys.Res.,96, 20,967-20,980,199lb.
themantleandcrust.Withoutmakingthoseassumptions
I can
Kiefer,
W.S., M.A. Richards,B.H. Hager,andB.G. Bills,A
saythatmeltingof theupwelling
mantleshould
begreatest
in the
dynamicmodelof Venus'sgravityfield, Geophys.Res.
regionsof mantleplate divergencein the lowlands. Many
Lett., 13, 14-17, 1986.
topographicallylow regions are coveredwith relatively
undeformedvolcanics,thoughthe mostobvioussourcesare at Kirby, S.H. and A.K. Kronenberg, Rheology of the
lithosphere: Selectedtopics,Rev. Geophys.,25, 1219higherelevations(Headet al., 1992). Crustalmeltingmight
1244, 1987.
occurin thehighlands
wherethickcrustcouldbeveryhot.
The highestheat flow is predictedto occurin the lowest Koch,P.S.,Rheology
andmicrostructures
of experimentally
lowlands of Venus and the lowest heat flow should occur in
deformed
quartzaggregates,
Ph.D. thesis,Univ.Calif.Los
topographically
elevatedareas.Thisis qualitatively
consistent 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 Planet. Sci.. 12.411-44q
l o•zt
amplitudeof the topographicstep acrosscompressionalSjogren,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.
Phillips, Venus gravity anomaliesand their correlations
to the thicknessof the brittle layer of uppercrust. The data
with topography,
J. Geophys.
Res.,88, 1119-1128,1983.
cannotbe explainedsolelyby thelapseratein theatmosphere,Smrekar,S.E., andR.I. Phillips,Gravity-drivendeformation
butrequires
thatheatflowbeinversely
correlated
withelevation of the cruston Venus, Geophys.Res. Lett., 15, 693-696,
belt. Theyarguethatthetopographic
stepis roughly
equivalent
1988.
(SuppeandConnors,1992). Whetherthepresent
modelcan
quantitatively
matchtheseobservations
canonlybe addressedSolomon,S.C., J.W. Head, W.M. Kaula, D.P. McKenzie,B.
with numericalmodelsof decoupling.
Parsons,R.J. Phillips, G.Schubert,and M.Talwani, Venus
tectonics: Initial analysisfrom Magellan, Science,252,
297-312, 1991.
Acknowledgments.
Thanksto JohnSuppeandMaria Zuber
for helpfuldiscussions
andto WalterKiefer,JohnHopperand Solomon,
S.C.andJ.W. Head,Mechanisms
for Lithospheric
two anonymous
reviewersfor comments
on the manuscript. HeatTransporton Venus: Implications
for TectonicStyle
Supportcame from NSF grant OCE-91-04076. Lamontand Volcanism,J. of Geophys.Res., Vol. 87, No. B1I,
9236-9246, November 10, 1982.
DohertyGeological
Observatory
contribution
4999.
Suppe,J. andC. Connors,CriticalTaperWedgeMechanics
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(Received:June9, 1992;
revised:August24, 1992;
accepted:
September
9, 1992)