JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 97, NO. El0, PAGES 16,069-16,083, OCTOBER 25, 1992
Flexural Ridges,Trenches,and Outer RisesAround Coronaeon Venus
DAVID T. SANDWELL
GeologicalResearch
Division,ScrippsInstitutionof Oceanography,
Za Jol• California
GERALD SCHUBERT
Departmentof EarthandSpaceSciences,
Instituteof Geophysics
andPlanetaryPhysics,Universityof California,LosAngeles
High-resolutionaltimetrycollectedby the Magellanspacecraftrevealstrenchand outerrise topographic
signaturesaroundmajor coronae(e.g. Eithinoha,Heng-O, Artemis, and Latona). In addition,Magellan
syntheticaperatureradarimagesshowcircumferential
fracturesin areaswherethe platesare curveddownward.
Both observationssuggestthat the lithospherearoundcoronaeis flexed downwardby the weight of the
overridingcoronalrim or by the negativebuoyancyof subducted
lithosphere.
We havemodelledthe trenchand
outerrisetopographyasa thin elasticplatesubjectedto a line load andbendingmomentbeneaththe coronarim.
The approachwastestedat northernFreyjaMonteswherethe bestfit elasticthicknessis 18 km, in agreement
with previouslypublishedresults. The elasticthicknesses
determinedby modellingnumerousprofilesat
Eithinoha,Heng-O, Artemis,andLatonaare 15, 40, 37, and 35 km, respectively.At Eithinoha,Artemis,and
Latonawhere the platesappearto be yielding, the maximumbendingmomentsand elasticthicknessesare
similar to thosefound at the Middle America,Mariana,and Aleutiantrencheson Earth, respectively.Estimates
of effectiveelasticthicknessandplatecurvatureareusedwith a yield strengthenvelopemodelof the lithosphere
to estimatelithospherictemperature
gradients.At Heng-O,Artemis,andLatona,temperature
gradientsareless
than 10 K/km, whichcorrespond
to conductiveheatlossesof lessthanonehalf the expectedaverageplanetary
value. We proposetwo scenarios
for the creationof the ridge,trench,andouterrise topography:differential
thermalsubsidence
andlithosphericsubduction.The topographyof Heng-Ois well matchedby the differential
thermal subsidencemodel. However, at Artemis and Latona the amplitudesof the trench and outer rise
signatures
are a factorof 5 toolargeto be explainedby thermalsubsidence
alone. In thesecaseswe favor the
lithospheric
subduction
modelwhereinthelithosphere
outboard
of thecoronaperimetersubducts
(rollsback)and
the corona diameter increases.
INTRODUCTION
The lithospheresof Earth and Mars are known to have elastic
upper layers that undergoflexural deformation[Walcott, 1970;
Comeret al., 1985]. Theseflexuresare commonlycausedby
largevolcanicloadson the lithospherewhichproducea moat and
severalprominentcoronaewhichdisplaycleartrenchandouterrise
signatures.Usinga thin elasticplateflexuremodelto characterize
the shape of the trench and outer rise, we find that Venusian
flexures are similar in both amplitude and wavelength to
lithospheric flexures seaward of subduction zones on Earth.
outer rise. On Earth, flexures are also associatedwith subduction
Moreover, we show that circumferential fractures are concentrated
zones; the cold subductedplate appliesa bendingmomentto the
not yet subductedlithospherecreating a trench and outer rise
[Caldwellet al., 1976]. Despiteits highsurfacetemperature
(730
K), Venusmay alsopossess
an upperelasticlithospheric
layerthat
could deform flexurally. A possible example of flexural
deformationon Venus occurs on the North Polar Plains just
northwardof Freyja Monteswhere the topographyis reminiscent
of the outerrise andforedeepof a plateunderthrusting
a terrestrial
mountainrange[Solomonand Head, 1990]. The high-resolution
radar images and topographicdata of Venus obtained by the
orbitingMagellan spacecrafthaverevealednumerousadditional
examples of possible flexural deformation of the Venusian
lithosphere.Prominentamongtheseare the downwarpedtrenches
andouterrisesaroundsomecoronaeas well as interiorslopesof
large calderalike structures [Sandwell and Schubert, 1991;
Solomonet al., 1991;Squyreset al., thisissue].
In this paper we focus on flexural signaturesoutboardof
coronalrims with the purposeof inferring the thicknessof the
Venusianelastic lithosphere.We presenttopographicprofiles
[Pettengillet al., 1991;Ford andPettengill,thisissue]outboardof
in areaswhere the topographyis curved downward in good
agreementwith the high tensile stresspredictedby the flexure
models.Finally,we presenttwo scenarios
for the developmentof
theridge-trench-outer
rise flexuraltopographyandcircumferential
fracturesof coronae. The first scenarioinvolvesreheatingand
thermalsubsidence
of the lithosphereinteriorto the coronawhile
the first scenarioinvolvesexpansionof the coronainteriorandroll
backof the subducting
lithosphereexteriorto the corona.
Copyright1992by theAmedcanGeophysical
Union.
Papernumber92JE01274.
0148-0227/92/92JE-01274505.00
FLEXURAL
CHARAUFERISTICS
OF CORONAE
The peripheries
of manycoronaeconsistof a relativelynarrow
annularridge surroundedby a trenchor moat [Barsukovet al.,
1986; Basilevskyet al., 1986; Pronin and Stofan,1990; Stofan
and Head, 1990;Solomoneta/., 1991;Squyreset al., this issue].
Circumferentially
orientedfractures(indicativeof radialextension)
areoftenfoundwithin the trenchandon its exteriorwall [Squyres
et al., this issue]. Two prominentexamplesof this ridge/trench
signatureare Eithinoha and the northernperimeterof Heng-O
(Plate 1, top andbottom,respectively). In theseimages,discrete
color changesrepresentchangesin elevation (200 m per color
change)andvariationsin graylevelrepresent
theintensityof radar
backscatter.
This
combination
enables
one to correlate
the
fractures,apparentin the syntheticapertureradar(SAR) images,
with theelevation,slope,andcurvatureof the surface.
16,069
Plate
1.Superposition
ofSAR
image
(brightness
variations)
and
topography
(color
changes
each
200m).Eithinoha
(top)
isa400km-diameter
plateau
surrounded
byridges
anddeep
trenches.
Heng-O
isa 1200-km-diameter
corona;
itsnorthern
perimeter
(bottom)
consists
ofaridge,
atrench,
andanouter
rise;circumferential
fractures
occur
inthetrench.
Dashed
linemarks
locations
of
profilesin Figure1.
SANDWELL
ANDSCHUBERT:
RIDGES,
TRENCHES,
ANDOUTER
RISES
AROUND
CORONAE
ONVENUS
16,071
3.02.5
Eithinoha
2. O
1.5
10
0.5
0.0
•-0.5
-60
3.0
-59
-58
-5F
-56
-55
i
i
-54
-53
-52
-
2.5
2.0
Heng-O
1.5
1 0
0.5 •
0.0
-0.5
4
J
I
I
I
5
6
7
•
I
I
8
9
10
Latitude
(deg)
•_
11
12
Fig. 1. Topographic
profilesacross
Eithinoha(top)andnorthern
Heng-O(bottom).Tracklocations
areshownin Plate1. The
ridge,treaeh,aadouterrisetopography
at northera
Heng-Ois characteristic
oflithospheric
flexureundera lineload. Theheavyline
above each treaeh marks the loeatioa of the circumferential fractures.
represents
400 m of elevationchange.The interiorof Artemisis
elevatedby about1.5 km with respectto the southeastern
plains.
A topographicprofile crossingthe southernrim (Figure 2, top,
orbit 1191) revealsthe elevatedinterior,a low-broadridge, a 2.5coronaand cover someof the fractureson the surroundingplains. kin-deeptrenchand~l.O-km-highouterrise. The heightof the
A southto north topographicprofile (orbit 519) crossingthe outerrise was measuredwith respectto the regionaltopographic
whichslopesdownwardto thesouth.Thecircumferential
easternside of Eithinoha (Figure 1, top) reveals its peripheral gradient
fractures,which dominatethe SAR images,are confinedto the
ridgesandtrenches.In thiscasethetrenches
areverynarrow(-50
km) andtheridgessagtowardthe centerof thecorona. The thick trench and do not extend to the crest of the outer rise. The interior
horizontal lines above the trenches(Figure 1, top) mark the of Artemiscontainsimpactcratersandcomplexfracturepatterns
locationsof circumferentialfracturesapparentin theSAR images. [Stofanet 02.,thisissue;McKenzieet al., thisissue].
Finally, one of the most strikingexamplesof a ridge-trenchBasedon the height of the coronae,its fracturedinterior, its
numerous
lava flows, andits lack of impactcraters,we speculate outer rise signatureoccursat Latona which is a semicircular
thatEithinohais in a relativelyearlystageof its thermomechanical structure(-600 km diameter) located on the southernside of
Aphrodite(center22øS,172øE).The southern
partof Latonais
and/ortectonicdevelopment
[Squyres
et 02.,thisissue].
400
Heng-O(-IøN, 355øE)is a muchlargercorona(-1200 km shownin Plate2 (bottom)whereeachcolorchangerepresents
diameter)with a pronouncedridge-trench-outer
rise signature m of elevationchange.The interiorof Latonais not a flat plateau
ridgesthat have
alongits northernperimeteras shownin Plate 1 (bottom). The but insteadconsistsof two or more topographic
interiorof Heng-Olies at approximately
thesameelevationasthe the morphologyof thrust sheets. On average,the interior of
plains. A topographic
surrounding
plains. A topographic
profile(orbit501) crossing
its Latonalies -1.5 km abovethe southeastern
rim towardthesouth(Figure2,
northernrim (Figure 1, bottom),reveals a 1.0-kin-tall ridge profilecrossingthesouthernmost
followedby a 0.5-km-deeptrenchthatis about80 km wide anda bottom,orbit 1376) revealsa 1.5-kin-highridge, a 2.5-kin-deep
broad outer rise to the north. The circumferential fractures are
trench,and ~0.5-kin-highouter rise. Again, the outer rise was
most intenseat the baseof the trenchand diminish in frequency measuredwith respectto the regionaltopographicgradientto the
andintensitymovingup outof thetrench.Basedon thelackof an south. Circumferentialfracturesare very intensein the deeppart
elevated center, the lack of radar-bright lava flows, and a of the trenchbut decreasein intensityand frequencymovingup
prominent
impactcraterin itsinterior,we speculate
thatHeng-Ois ontothe outerrise wherethey terminateat the crestof the outer
relatively old and has reached a mature stage in its rise. Impactcratersarenot apparentin theinteriorof Latona,and
sinceits interioris bothelevatedandhighlyfractured,we speculate
thermomeehanical
and/ortectonicdevelopment.
The largestcorona-type
featurediscovered
to dateis Artemis that Latonais in a relativelyearly stageof its thermomechanical
[Stofanet 02.,thisissue],locatedto thesouthof AphroditeTerra(at and/ortectonicdevelopment.
32øS,132øE). The dominantcharacteristic
of Artemisis its ridge,
A majorhypothesis
of thispaperis thatthesetrenches,
outer
trench, and outer rise which form a nearly circular structure rises, and circumferential fractures (and perhaps the annular
of theVenusianlithosphere.
approximately2600 km in diameter. The southeastern
part of ridges)reflectflexuraldeformation
Artemis is shown in Plate 2 (top) where each color change We test the flexural hypothesisby comparing53 topographic
Eithinoha(Plate1, top),locatedat 57øS,8øE,is a plateaulike
structure
approximately
400 km in diameter.The highlyfractured
interiorof this coronais elevated0.6-1.0 km with respectto the
surrounding
plains. Lavaflowsemanatefromtheperimeterof the
Plate2. Superposition
of SAR imageandtopography(400 m per colorchange)for southeastern
Artemis(-2600 km diameter)and
southeastern
Latona(-600 km diameter).In eachcase,the edgeof theplateauhasa ridgesurrounded
by a deeptrench. Outerrises
occur -150 km outboard of the trench axis and the trenches contain circumferential
profilesin Figure2.
fractures.
Dashed line marks locations of
SANDWELL
ANDSCHUBERT:RIDGES,TRENCHES,
ANDOUTERRISESAROUNDCORONAE
ONVENUS
16,073
3.0_
25
2O
Artemis
_
15
O5
O0
-05
-48
-47
-46
-45
-44
-43
-42
-41
-40
3.5
3.0
Latona
2,.5
2,.0
1.5
1.0
0.5
0.0
-0.5
-29
-28
-27
-26
-25
-24
-23
Latitude (deg)
Fig. 2. Topographic
profilesacrosssouthernArtemis(top) andsouthernLatona(bouom). Tracklocationsareshownin Plate2.
Theheavylineaboveeachtrenchmarksthelocationof thecircumferential
fractures.Notethelargeamplitude
ridge,trenchand
outerrisesignatures
towardthe south.
profiles with the predictions of a simple flexural model.
Moreover,thesignandamplitude
of thesurfacestress
predicted
by
the modelsaxe comparedwith the location and intensityof
circumferential
fractures.We discusstwo possiblemodelsfor the
physicalcausesof the flexure. Other models,e.g., a viscous
gravitational
relaxationmodel[Bindschadler
andParmentier,1990;
Stofanet al., 1991;Stofanet al., thisissue],may alsobe ableto
explainthe existenceof trenches,outerrisesand circumferential
fractures.
ESTIMATES OF EFFECtiVE ELASTIC THICKNESS
OUTBOARD OF CORONAE
The flexuremodelconsistsof two components:a bending
momentappliedto theendof a brokenelasticplateanda line load
on a continuous
elasticplate. A morecomplicated
cylindrically
symmetricmodel was not usedbecausethe radii of thesefeatures
aresufficiently
largethattheflexuralradialtopography
across
the
quasi-circular
moatof eachcoronacanbe approximated
by the
flexural topographyacrossa linear moat. In addition to the
flexural componentsof the model, a regionaltrend and mean
radiuswereused.The completemodelis
W(X)--C
1exp
{•}cos
{•)+c2exp
(•)[cos
{•)+sin
(a•)](1)
+ C3X + C4
To matchthe trenchand outerrise topographyof Eithinoha,
Heng-O,Artemis,andLatona,we modeltheVenusianlithosphere wherex is horizontaldistanceperpendicularto the strikeof the
as a thin elasticplate floating on a fluid mantle [Turcotte and trench,Cl (kin) is the coefficientof thebendingmomentterm, c2
Schubert,1982,pp. 125-131]. The intensityof thecircumferential (km) is the coefficientof the line load term, c3 (km/km)is the
fracturesat bothArtemisandLatonasuggests
thatthe platesare regionaltopographic
gradient,c4(kin) is theradius,anda (km) is
behaving
inelastically
nearthetrenchaxes,andthusa purelyelastic theflexuralparametergivenby
model may be inappropriate. Here we follow the procedures
applied to Eaxth trencheswhich are also believed to be flexed
beyondtheir elasticlimits [seeGoetzeand Evans, 1979; McNutt,
1984]. First, the trench/outer
risetopography
is fit usinga thin
Ot
=[3pgE{1h3
Ve)]
]1/4
elastic plate model. Then the effective elastic thickness and
curvature(derivedfrom the elasticmodel) are usedto estimatethe
(2)
In (2), E is Young'smodulus,v is Poisson's
ratio,p is mantle
density, g is accelerationof gravity, and h is the unknown
inelasticrheologyof thelithosphere.For example,on Earthwhere thickness
of the elasticplate. Valuesof constant
parameters
are
subduetinglithosphereis flexed beyond its elastic limit, the givenin Table1. After fittingthetopographic
profilesusing(1),
thickness
determined
fromtheelasticmodelis usuallyonly about we calculate the bending moment M and surface stress(rxx
75%of thethickness
determined
usinga realistic,layeredrheology (positiveis tension)along the flexed lithosphere. Thesetwo
[McAdooet al., 1985]. The parameters
derivedfrom the elastic quantitiesaregivenby
model can also be reinterpretedin termsof a purely viscous
M(x)=-Ddx
dew
(3)
lithosphere
that is subducting
at a constantrate [De Brernaecker,
2
1977;Melosh,1978]. Thus,whiletheparameters
will be derived
from a purely elasticmodel,they can easilybe reinterpretedin
or== 6__M_M
(4)
he
termsof nonlinearandviscousrheologies.
16,074
SANDWELL
ANDSCHUBERT:
RIDGES,
TRENCHES,
ANDOUTERRISESAROUND
CORONAE
ONVENUS
TABLE
to the trench axis, the best coefficients of the end moment and line
1. Thermal and Mechanical Parameter Values
for VenusJan
Lithosphere
Parameter
load (cl andc2) would actin oppositedirectionsto createa nicefit
to the observationsin the 100 to 600 km distance range.
However, at the origin, the model topographywould have an
unrealisticvalue (> +100 kin). To suppressthis instability,we
forced both cl and c2 to be be negative[Lawson and Hanson,
1974]; physically,this constrainsboth the end momentandline
loadto flex theplatedownwardat the origin.
Value
Tin,manfietemperature
Te.temperature
atbaseof elasticlithosphere
To,surface
temperature
1673K
1023K
728 K
a, thermal
expansivity
3.1x 10'5K'l
E, Young'smodulus
65 GPa
Pm,mantle
density
• thermal
diffusivity
3000kgm'3
8 x 10'7m2s'l
v, Poisson'sratio
0.25
g,acceleration
ofgravity
8.87m s'2
Freyja Montes
We testedthe procedureusing sevenprofiles (even numbered
orbits500-512) acrossnorthernFreyja Montes (80øN, 335øE)
whereD is theflexuralrigiditygivenby
D=[12l•h3
(1- v2lJ
.]
(5)
To comparethe flexure models of Venusian lithospherewith
flexure modelsof subductinglithosphereon Earth, the bending
moment Mo and plate curvatureKo at the first zero crossing
seaward of the trench axis Xo are calculated. The first zero
crossing
is foundby settingtheflexurepartof (1) equalto zeroand
solvingfor thefirst nonnegative
position
x._•.o
=tan.,[-(c,
+c2)]
+Jr
o•
t
C2
the model
and the observations
is minimum.
match the outer rise while the 40-kin flexure model does not bend
sharpenough. A 20-kin-thick plate providesthe bestfit. The
surfacestress(positivetension)predictedby thebestmodelis also
shownin Figure3 (top). The surfacetensilestressis greatestat
about 60 km from the origin where the plate curvature is
maximum.
The best fitting modelsfor all sevenprofiles are shownin
(6) Figure
4, andthemisfitsandcoefficientscl - ca are givenin Table
The objectiveis to estimatethe flexural parameter{z and the
flexuralcoefficientsCl andc2by varyingall of theparameters
cl, c2, ca, c4 ) such that the root-mean-square(RMS) misfit
between
whereSolomonand Head [1990] modelleda trenchandouterrise
signatureusingthree Venera 15 and 16 altimeterprofiles. An
exampleof the fits of modelshaving five elasticthicknesses
(0,
10, 20, 30, and 40 kin) to profile 506 are shownin Figure 3
(bottom). The 0 kin elastic thicknesscorrespondsto a model
consistingof only a linear trend (i.e., only c3 andc4 in (1)). The
model with the 10-kin-thickelasticplate flexes too sharplyto
2. The bendingmomentMo andplatecurvatureKo at thefirstzero
Freyja
After
determining
{z,cl, andc2 we estimatetheelasticplatethickness
Montes,
Profile
506
600
using(2) andthe maximumbendingmomentwhich occursat the
baseof the trenchusing(3).
400
While this is the standardleast squaresapproach,there are a
3OO
numberof complicationsarisingfrom this application.First, one
maynoticethatthereis no obviousadjustable
parameterto specify
200
the locationof the originin (1). The approximatepositionof the
100
originwaschosenasthehighestpointalongtheridgejust inboard
2o krn
of the trenchaxis sincethis is where the line load and bending
i
momentare acting; in fact, the highestpointwas selectedafterthe
0
œ00
400
profile was low-pass-filtered(~160-km cutoff wavelength)in
3.5
orderto smoothout local maxima/minimasuperimposed
on the
broaderridge. In additionto havingthe origincoincidewith the
3.0
peakin thetopographic
load,thelocationof theoriginwasallowed
40
krn
•2.5
to vary to achieve a "best fit" to the observations. These minor
variationsareaccommodated
by varyingtherelativeamplitudes
of
30
km
•2.0
cl andc2 whichcontaincosineand sinetennsthatshift the phase
of the flexureprofile.
20
krn
1.5
After specifyingthe origin, the latitude and longitudeof the
lO kra
prof'dewereconvertedto distanceperpendicular
to thetrenchaxis.
•1.0
To focuson thetrenchandouterriseflexure,only theobservations
.... 0 kra
0.5
at distancesof ~100 to -600 km were usedin the leastsquaresfit.
As seenin (1), the modeldependslinearly on the parametersCl 0.0
c4 but nonlinearly on {z. To determine the model with the
0
200
400
minimumRMS misfit, we set {zand foundthe bestsetof cl - c4 ß
Distance
Thisprocedure
wasrepeatedfor a widerangeof {zcorresponding
to elasticthicknesses
of 5 to 80 kin. Onemorecomplication
arose
Fig. 3. Fits of plateflexuremodelsto profile506 acrossnorthernFreyja
becausethe observations
do not continueall the way to the origin Montes(bottom). The 20-km-thickelasticplate providesthe minimum
(i.e., the topographicridge adjacentto the trench). When the RMS fit as well as the best visual fit. Model surface stress is tensile
500
• -100
flexuralparameter
wasmuchlessthanthedistance
fromtheorigin
betweenthetrenchaxisand~170km (top).
SANDWELL
ANDSCHUBERT:
RIDGES,
TRENCHES,
ANDOUTER
RISES
AROUND
CORONAE
ONVENUS
16,075
RMS misfit doesnot decreasesignificantlyfor platesthickerthan
40 km (Figure5) so we have adoptedthis as the bestplausible
value.
7
•
508
•
5o•
•./o•_•_•.._•
•
5o•
-----" 500
_
0
200
400
600
D•s • c•c e
Fig. 4. Bestfits of flexuremodelto sevenprofilesacrossnorthernFreyja
Montes(evennumberedorbits500-512). Best fit modelparameters
are
givenin Table2.
The
tensile
surface
stress for the 40-kin-thick
model
(Figure 8, top) is moderatebetween50 km and 200 km from the
origin. Circumferentialfracturesoccurfrom the originout to about
110 km (thickline) in fair agreementwith themodel.
The bestfittingmodelsfor all 15 profriesacrossnorthernHengO are shown in Figure 9. In contrastto Freyja and Eithinoha
whichrequireelasticplatethicknesses
greaterthan 10 km, Heng-O
requiresan elasticplatethicknessthatis greaterthan30 km (Figure
5). This canbe seenin Figure8 wherethe fit of the 20-kin-thick
model is quite poor on the outer trenchwall. It is interestingto
notethatthe amplitudeandshapeof the flexure at Heng-O do not
placetight constraintson themaximumelasticplatethickness.In
fact, for mostof the profiles,the minimum RMS misfit occurred
for an elasticplatethicknessof 80 km. A visualexaminationof the
fits of theseprofiles,however,showeda poormatchat the baseof
the trench. Therefore,the resultsshownin Figure9 and given in
Table 2 arebestfittingmodelshavingelasticthicknesslessthanor
equalto 40 km.
Artemis
The amplitudeof theflexureat Artemisis extremelylarge. This
highamplitudecombinedwith a peakedouterrise providesa tight
crossingoutboardof the trenchaxis are alsogivenin Table 2 for
constrainton the acceptablevalues of elastic thickness. For
latercomparison
with trencheson Earth. A plot of RMS misfitfor
example,the large-amplitudeflexure along profile 1191 is well
all sevenprofilesversuselasticthickness
(Figure5) revealsa sharp
matchedby a 30-kin-thickelasticplate,while platethicknesses
of
decrease in misfit between thicknesses of 0 and 10 kin. The
20 km and50 km are unacceptable(Figure 10, bottom). The fits
minimum misfit occurs at an elastic thickness of about 18 km,
to all 12 profilesat Artemisareremarkablyconsistent(Figure11).
althoughmodelswith elasticthicknesses
rangingfrom about10 to
The best overall model has an elastic thicknessof 37 km, while the
25 km fit thedatafairly well. This is in goodagreementwith the
rangeof acceptableelasticthicknesses
lies between30 km and45
11-18 km elasticthicknessrange found by Solomonand Head
km (Figure5). Models with elasticthicknessesof 25 km or less
[ 1990] usinga differentdatasetanda differentmethod.
areincompatiblewith the observations.
The surfacestresspredictedby the 30-km-thickelasticplate
Eithinoha
model(Figure8, top) exceeds1.0 GPa. This stressis too largeto
The samemodelling procedureswere applied at Eithinoha, be sustainedby even the strongestrocks at high confining
Heng-O, Artemis,andLatona. An exampleof the fits of models pressures(40 km deep) [Goetze and Evans, 1979]. The
havingfive elasticthicknesses
(0, 4, 12, 20, and28 kin) to profile implicationis thatthe lithospherebetweenthe origin and200 km
519 crossingthe northernperimeterof Eithinohais shownin has undergonecompletefailure. The plate is bent beyondits
Figure6 (bottom). In thiscase,an 8-kin-thickelasticplateflexes elastic limit, and the magnitudeof the stressis limited by the
too sharply,while platesthickerthan28 km do not bendsharply strengthof the rock. Note that this zoneof extremelyhigh stress
enough; a 12-kin-thickplate providesthe bestfit to this profile. approximatelycoincideswith the locationof the intensesurface
fractures(thick line). The flexuremodelalsopredictslessintense
The tensilesurfacestressfor the 12-kin-thick model (Figure 6,
top) is moderatebetween50 km and 100 km from the origin. surface fractures on the crest of the outer rise where circumferential
fractures are not seen. This combination of tall outer rise and lack
Circumferentialfracturesoccurfrom the originout to about75 km
of evidencefor tensilestresson theouterrisecanalsobeexplained
(thickline) in fair agreement
with themodel.
The bestfitting modelsfor all four profiles acrossnorthern by a flexuremodel that incorporatesa significantcomponentof
Eithinoha are shown in Figure 7. Models having elastic radial compression.However, sincea bendingmomentand an
thicknessesbetween 10 and 30 km all fit the data fairly well end load producesimilar topographicsignatures[Parsons and
is inconclusive.
althoughthebestfittingmodelhasan elasticthickness
of about15 Molnar, 1976],evidencefor compression
km. While Eithinohadoesnot providethe strongestevidencefor
lithospheric
flexure,it doesprovidean exampleof a relativelythin Latona
elasticplatetocontrast
withotherareashavingthickplates.
The amplitudeof theflexureat thesouthern
perimeterof Latona
is alsoquite large andplacesa tight constrainton the rangeof
Heng-O
acceptable
elasticthicknesses.For example,profile 1376 is best
An exampleof thefits of modelshavingfive elasticthicknesses modelledusinga 30-kin-thickelasticplatewhile platethicknesses
(0, 20, 30, 40, and 50 kin) to profile 501 crossingthe northern of 20 km and50 km areunacceptable
(Figure12, bottom).Indeed
perimeterof Heng-O is shownin Figure8 (bottom). In thiscasea the bestsolutionfor the 20-kin-thick plate is just a straightline.
20-kin-thickplate flexes too sharply,while all plate thicknesses The fits to all 15 profriesat Latonaare againremarkablyconsistent
greaterthan30 km matchthe profile fairly well. For Heng-O, the (Figure13). The bestoverallmodelhasan elasticthickness
of 35
16,076
SANDWELLAND SCHUBERT:RIDGES,TRENCHES,AND OUTERI•SES AROUNDCORONAEON VENUS
TABLE
Freyja
Freyja
Freyja
Freyja
Freyja
Freyja
Freyja
2. Trench Profile Models
Best
Line
Orbit
h,
km
RMS,
m
RMS,
m
cl
km
0500
0502
0504
0506
0508
0510
0512
20
20
20
20
25
20
15
35.8
35.6
44.3
39.5
55.1
44.7
33.9
131.1
144.7
139.9
140.8
145.5
77.6
83.1
-0.866
-0.972
-0.656
-0.562
-0.825
-0.901
-0.729
162.2
209.2
227.0
165.4
109.9
139.8
144.8
128.8
126.4
113.1
118.1
125.9
115.2
102.7
118.1
132.6
148.9
230.6
215.1
100.8
72.2
109.0
91.6
Mo,
1016N
Ko
10'am
q
-0.019
-0.278
-1.465
-1.401
-1.402
-1.456
-1.441
-1.309
-1.287
0.63
0.70
0.49
0.48
0.84
0.65
0.37
13.66
15.34
0.72
10.50
9.31
14.22
19.39
-1.332
-0.414
-1.399
-0.133
-1.406
-1.418
-2.081
-2.602
-2.021
-1.608
-1.296
1.28
0.86
1.03
0.45
16.12
18.80
43.61
45.53
-0.652
-0.242
-0.539
-0.622
-0.789
-0.755
-0.918
-0.931
-0.806
-0.738
-0.693
-0.613
-0.548
-0.696
-0.911
-0.999
Eithinoha 0515
Eithinoha 0517
Eithinoha 0519
Eithinoha 0521
24
20
16
12
Heng-O 0495
Heng-O 0496
Heng-O 0497
Heng-O 0498
Heng-O 0499
Heng-O 0500
Heng-O 0501
Heng-O 0502
Heng-O 0503
Heng-O 0504
Heng-O 0505
Heng-O 0506
Heng-O 0507
Heng-O 0508
Heng-O 0509
40
40
40
40
40
35
35
35
40
40
40
40
40
40
40
Artemis
Artemis
Artemis
1183
1185
1187
35
30
30
137.1
109.2
113.5
221.3
222.0
243.3
-10.936
-8.851
-6.774
Artemis
Artemis
Artemis
Artemis
Artemis
Artemis
1189
1191
1193
1195
1197
1199
30
30
30
35
35
35
109.9
78.5
86.3
61.2
40.2
55.6
253.2
249.1
260.6
284.7
289.9
267.4
-7.798
-7.301
-2.863
-12.910
-16.189
-18.003
Artemis
Artemis
Artemis
1201
1203
1205
40
45
40
65.6
60.9
58.4
290.5
167.9
221.6
- 17.869
-16.455
-6.766
Latona
Latona
Latona
Latona
Latona
Latona
Latona
Latona
Latona
Latona
Latona
Latona
Latona
Latona
Latona
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
30
35
35
30
30
30
30
30
30
35
35
40
40
40
45
95.0
102.5
99.1
102.9
129.9
102.5
162.0
138.9
125.6
96.5
126.3
92.0
86.1
82.7
126.4
236.6
270.6
278.4
252.6
327.8
242.4
200.2
214.2
295.4
190.6
264.1
230.6
309.2
230.6
325.7
-0.933
-0.439
-0.466
36.7
34.7
51.6
67.7
85.5
46.4
34.9
39.3
31.9
40.2
45.5
38.8
34.9
31.5
40.1
-0.061
-0.477
-0.549
-0.454
c2,
km
-0.142
-0.326
c3,
10'3
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
1.46
0.71
0.82
1.04
1.00
1.00
1.01
0.87
0.98
0.92
0.81
0.72
1.00
1.21
1.32
3.96
1.93
2.23
2.83
2.71
4.03
4.09
3.54
2.65
2.49
2.20
1.97
2.72
3.27
3.59
-2.264
-5.058
-7.934
-10.177
-15.404
-19.236
-8.267
-4.513
-3.147
-5.769
-5.867
-16.952
-0.860
-1.221
-1.359
19.07
13.98
13.64
76.99
89.65
87.49
-1.323
-1.182
-1.258
-1.082
-0.925
-0.894
16.52
20.24
19.17
26.44
28.85
31.13
105.95
129.78
122.90
106.75
116.47
125.68
-0.868
-0.994
-1.234
39.49
43.92
32.32
106.80
83.41
87.41
-5.153
-5.434
-5.132
-9.109
-8.369
-7.775
-9.004
-6.144
-5.711
-3.586
-5.881
-2.967
-4.186
-3.714
-4.142
-2.137
-2.491
-2.241
-1.996
-1.965
-2.062
- 1.795
-2.022
-2.189
-2.238
-2.109
-2.160
-2.100
-2.060
-1.972
5.29
6.40
6.10
7.86
7.22
6.71
7.77
5.30
4.93
4.43
6.40
4.70
5.56
5.56
6.57
33.91
25.84
24.64
50.43
46.33
43.04
49.84
34.01
31.61
17.92
25.83
12.73
15.05
15.03
12.48
Maximumelasticthickness
for Heng-Owassetto 40 km.
Line RMS corresponds
to 0-km elasticthickness.
*The gradientparameter
wasnotincludedin fits to Heng-O.
km, while the rangeof acceptableelasticthicknesses
lies between
27 km and 60 km (Figure5). As in the caseof Artemis,models
with elasticthicknesses
of 25 km or lessareincompatiblewith the
observations.For profile 1376 (Figure12, top) the surfacetensile
stressis greatestin the deeppart of the trenchanddiminishes
movingup ontothecrestof theouterrise(Figure2). Thereis an
excellent correlation between stress intensity and surface
fracturing.
SANDWELL
ANDSCHUBERT:
RIDGES,
TRENCHES,
ANDOLrrER
RISES
AROUND
CORONAE
ONVENUS
250
..••
• 200
16,077
Artemis
/
/
///
'%150
,
\
/
lOO
',..
Freyja
.....................................?7_g__:_o___
5o
10
20
30
40
50
60
70
80
Elastic Thickness
Fig.5. RMS misfit of flexuremodelversuselasticplatethickness
for sevenprofilesacross
northern
FreyjaMontes,fourprofiles
acrossnorthernEithinoha,15 profilesacrossnorthernHeng-O, 12 profilesacrosssouthernArtemis,and 15 profilesacross
southernLatona. Zero elasticthicknesscorresponds
to a linear trendmodelwith no flexure. The minimumof eachmisfit curve
providesan estimateof theelasticplatethickness
(-18 km, Freyja;-15 km, Eithinoha;-37km, Artemis;35 km, Latona;Heng-O
hasno minimum).
Eithonoha
Profile
Eithinoha
519
6
•,•..
800
600
-• -'•------'-•'•-•--•-XZ--521
400
200
o
--
__
0
200
12
k•
,
400
o
,
1.
28
km
20
km
12
km
............. 4 km
o.
0
km
O.
•
I
5
400
600
Distance
;
1.
-0'50
,
200
i
200
400
Dis t ance
Fig.7. Bestfitsofflexuremodeltofourprofiles
across
northern
Eithinoha
(oddorbits515-521).Bestfit modelparameters
aregivenin Table2.
canalsobe calculated.However,the estimates
of thedepthto the
baseof the elasticlayer are highly dependenton the rheological
propertiesof the ductile lower lithosphere. Without a good
knowledgeof lithospheric
rheologyonVenus,onecanonlyadopt
characteristic
valuesusedfor Earth'soceaniclithosphere[Goetze
and Evans, 1979]. Here we follow Solomonand Head [1990]
wheretheycharacterized
thestrengthof theupperbrittleportionof
the lithosphereusinga frictionalslidinglaw [Byedee,1978] and
the strengthof the lower lithosphereusinga ductileflow law for
dryolivine(10-16s-1strainrate).Thesetwofailurecriteriadefine
Fig.6. Fitsofplateflexure
models
toprofile
519across
northern
Eithinohaa yieldstrength
envelope
(YSE) [GoetzeandEvans,1979]where
(bouom).
The12-km-thick
elastic
plate
provides
theminimum
RMS
fitas thebase
of theYSEis approximately
defined
bythe740K
well asthebestvisualfit. Model surfacestressis tensilebetweenthe trench
axisand-150km(top).Circumferential
fractures
(thick
line,top)occur
out
to a distance of 75 km.
LITHOSPHERICTitERMAL GRADIENT
isotherm[McAdooet al., 1985] andthe thicknessof the YSE is the
mechanical
thickness
of thelithosphere.
When the lithosphereis flexed, the largestdeviatoricstresses
occur at the top and bottom of the layer. For moderateplate
curvatures
(-10-7m-l), significant
yieldingoccurs
in boththe
uppermost
andlowermostpartof themechanical
lithosphere
which
Theparameters
of thebestfittingthinelasticplatemodels
can areweak. Thisyieldingcausestheeffectiveelasticthicknessof the
be usedto estimate
thedepthto thebaseof theelasticlayer. lithosphere(i.e., derivedfrom flexuremodelling)to be lessthan
Assuming
thiscorresponds
toanisotherm,
thegeothermal
gradient theactualmechanicalthicknessof thelithosphere
McNutt[ 1984].
Heng-O,
P•o•i•e
501
A•temis,
6OO
P•o•i•e
1191
2000
500-
1500
400300-
1000
200-
500
100-
o
-1000
__
I
I
I
40
200
km
30
o
I
i
i
200
400
3.0
4.0
2.5
3.5
2.0
400
600
'•
",.'"'
1.5
i
km
i
800
_50
km
•2.0
1. 0
•1.5
0.5
o
1.0
0.0
0.5
-0'50
200
0.0
400
200
400
600
800
Distance (kin)
Distance (kin)
Fig. 8. Fitsof plateflexuremodelsto profile501 across
northern
Heng-O Fig. 10. Fits of plate flexure modelsto profile 1191 acrosssouthern
(bottom).The 40-km-thickelasticplateprovidestheminimumRMS fit as Artemis(bottom). The 30-km-thickelasticplateprovidesthe minimum
well as the best visual fit. Model surface stressis tensile between the trench
RMS fit as well as the best visual fit.
axisand-300 km (top). Circunfferential
fractures
(thickline,top)occurout
between
thetrenchaxisand-280 km (top). Circumferential
fractures
(thick
line,top)occuroutto a distance
of 180km.
to a distance of 160 km.
Heng-O
14
12
• f..•.._•.•
Model surface stress is tensile
Artemis
.....
509
• 507
---.--•-•-'•-
508
.•----• •--•'--"----"-•
506
_•/•.•.............
505
--•
504
_•
503
......... 502
•
...........
501
...........
500
- ................ 499
•
....... 498
--•
497
-•
496
•
0K
i
200
i
•00
......495
200
400
600
Distance (kin)
Fig. 9. Bestfits of flexuremodelto 15 profilesacrossnorthernHeng-O
(orbits495-512).Bestfit modelparameters
aregivenin Table2.
Fi•. 1l. Bestfitsof fi•xum mo•clto
(o• •umbem•otbi•
T•lc
Z
600
800
SANDWELL
ANDSCHUBERT:RIDGF•,TRENCHES,
ANDOUTERRISESAROUNDCORONAE
ONVENUS
Latona,
Profile
!376
16,079
Latona
16
14
800
4OO
12
30
o
200
400
km
600
4.0
377
o
•2,o0
0.5
200
400
600
Distance
Fig. 12. Fitsof plateflexuremodels
toprofile1376across
southern
Latona
(bottom).The30-km-thickelasticplateprovides
theminimumRMS fit as
o
o
200
to a distance of 230 km.
600
Distance (kin)
well as the best visual fit. Model surfacestressis tensile between the trench
axisand~300km (top).Circumferential
fractures
(thickline,top)occurout
400
Fig. 13. Bestfits of theflexuremodelto 15profilesacross
southern
Latona
(orbits1370-1384).Bestfit modelparameters
aregivenin Table2.
Completelithosphericfailure occurswhen the plate curvature conductivityusedin the abovecalculationis too low. (3) The
exceeds
about10-6m-1. (NotethatArtemishasanaverage
plate areasthatwe haveinvestigated
haveanomalously
thickandstrong
curvature
of 10-6m-1,suggesting
thatthelithosphere
hasfailed.) lithospheres
with respectto the averagelithospheric
thickness
on
Solomonand Head [1990] adaptedthis YSE model for the Venus. (4) The heat productionin the interior of Venus is
parameters
appropriate
to Venusandprovidea diagramto mapthe substantially
lower than the heatproductioninsideEarth. (5)
elasticthicknessinto mechanicalthicknessby usingthe plate Venuslooses
a substantial
fractionof itsheatby extrusion
of large
curvature(Figure4 of theirpaper). We haveusedtheirdiagram quantities
of lava. (6) HeatlossonVenusis episodicandglobal
with ourestimates
of elasticthickness
andplatecurvature(Table2) with a time scale> 200 m.y. Overthenextfew yearsit will be
to estimatethemechanical
thickness
of thelithosphere
outboardof important
to eliminateasmanyof theseexplanations
aspossible
to
Freyja, Heng-O, Artemis,and Latona; the resultsare given in arriveat a betterunderstanding
of theVenusianheatlossbudget.
Table 3.
At thistimeit wouldbepremature
to speculate
onthemostlikely
At FreyjaMontes,we find the bestrangeof elasticthicknesses explanation,however.
isbetween
l0 and25km andtheplatecurvature
is 13x l0-8m-l;
thisagreeswell with Solomonand Head's [ 1990] estimatesbased
onVenera15and 16 altimeterprofiles.Theseparameters
mapinto
thermalgradients
of between9.5 and26 K/km. A similarrangeof
thermalgradientis inferredat Eithinoha(6.8-24 K/km). For the
TECTONIC AND TIIERMAL MODELS FOR THE DEVELOPMENT
OF A RIDGE, TRENCH, AND OUTER RISE
We proposetwo models(scenarios)for the developmentof
ridge,trench,andouterriseflexuraltopography
on theperimeters
thickness
of the lithosphereis greaterthan30 km (Table3) which of the largestcoronae. In the first model(Figure 14, tectonic
mapsintomuchlowerthermalgradients
(< 10 K/km).
scenario),
a mantleplumereachesthebaseof thelithosphere
and
Assuming
theVenusianlithosphere
hasa thermalconductivity spreadshorizontally(i.e., radially) outwardbeneaththe underside
of3.3W m-1K'1,thetemperature
gradients
estimated
atHeng-O, of thelithosphere.
Thehot,lightplumeformsaninverted
pancake
Artemis,andLatonacorrespond
to a surfaceheatflow of lessthan thatis heldup againstthebottomof thelithosphere
by virtueof its
33mWm-2. Thisislessthanonehalfof theexpected
planetary buoyancy.Over time thishot plumeheadthinsandweakensthe
average heat flow for Venus. There are many possible lithosphere.Melt penetrates
thelithosphere
providinga routefor
explanations
for thislow estimate:(1) The lithosphereon Venus furtherescapeof hotmantlematerial. A largevolumeof mantle
remainsstrongat temperatures
exceeding1013 K (740øC)or the materialspreads
overthetopsurface
of thelithosphere
causing
it to
strainratesare much higherthan on the Earth. (2) The thermal depress
andultimatelyto fractureandfall. Thecoldlithosphere
on
other three areas, however, we estimate that the mechanical
16,080
SANDWELL
ANDSCHUBERT:
RIDGES,
TRENCHES,
ANDOUq•RRISESAROUNDCORONAE
ONVENUS
TABLE 3. Lithospheric
Thickness
andTemperature
Gradient
Elastic
]hickhess,
km
Freyja
#
Freyja
Curvature,
10-$m-1
Mechanical
Temperature
Thickness,*
km
Gradient,
+ K km-1
12-21
11- 30
24- 14
26- 9.5
11- 18
10- 25
15
13
Eithinoha
10- 30
29
12-42
24- 6.8
Heng-O
30- 45
3
32- 49
8.9- 5.8
Artemis
Latona
30- 45
27 - 60
103
29
60- 90
37- 82
4.8 - 3.2
7.7 - 3.5
*Mechanical
thickness
derivedfromFigure4. of Solomon
andHead[1990].
+Temperature
gradient
basedon 1013K (740øC)temperature
atbaseof elastic
layer.
# Publishedresults,Solomonand Head [1990].
Tectonic Scenario
Thermal Scenario
f
Fig.14. (Left)Tectonic
scenario:
plumeheadapproaches
thelithosphere
andspreads
radially,causing
it to thinandweaken;
melt
andhotmantlematerialpondonthesurface
of thelithosphere
causing
it to fail undertheload;theoldanddenselithosphere
sinks
intothemantleforminga circularsubduction
zonethatincreases
in radiuswithtime;theinteriorspreads
radiallyto fill thegrowing
void;a prominent
trenchandouterrisedevelop.(Right)Thermalscenario:
plumeheadapproaches
thelithosphere
andspreads
radially;thermalconduction
and/oradvection
thinsthelowerlithosphere
in a circular
areawithsharpedges;thehotinteriorcools
andsubsides
relativeto thecoolexteriorformingridge,trench,andouterrisetopography.
of thecoronaincreases
andtheinteriorof thecoronaexpandsto fill
bottomof thelithosphere
by virtueof itsbuoyancy.However,this
timeonlya smallervolumeof meltescapes
to thesurface.Thehot
material in the plume thins the lithosphereand createsan
isostatically
compensated
plateauat thesurface.As shownbelow,
the void. This type of subductionand back arc spreadingis
commonly
foundbehindsubduction
zonesonEarth.
In the secondmodel (Figure 14, thermalscenario)a mantle
plumeheadalsoreaches
thebaseof thelithosphere
andspreads
horizontally
(i.e.,radially)outward.Asin thefirstmodel,thehot,
lightplumeformsaninvertedpancake
thatis heldupagainst
the
mustbe quite sharp(<50 kin) for a ridge/trenchsignatureto
develop.The interiorlithosphere
thencoolsto thesurface,while
theexteriorlithosphere
maintainsits temperature
profilethrougha
balanceof heatsupplyat its basewith heatlossat itssurface.As a
consequence
of thecooling,the interiorlithosphere
increases
in
the perimeterof the flow sinks into the mantle forming a
subduction zone and circumferential fractures (i.e., a corona).
Continued subduction causes the trench to roll back so the radius
the transition from the hot-thin interior to the cold-thick exterior
SANDWELL
ANDSCHUBERT:RIDGES,TRENCHES,
ANDOUTERRISESAROUNDCORONAE
ONVENUS
densityand it subsidesisostatically. During the subsidence,the
interiorlithosphereremainsweldedto theexteriorlithosphere.The
differential subsidence causes upward flexure inside and
downward flexure outside, forming the ridge, trench, and outer
rise topography.
It shouldbe notedthatthesemodelsarenot mutuallyexclusive.
The main difference
200 Ma
16,081
lO Ma
elastic
ductile
between the models is where the hot material
fluid
is emplaced,aboveor below the preexistinglithosphere.In the
tectonic scenario when subduction ceases and the corona reaches
its final diameter, the interior lithospherewill be hot and thin,
while the exteriorlithospherewill be cold and thick. At thispoint
the corona must go through a phase of differential thermal
subsidence.Anotherpossibilityin the tectonicscenariois thatthe
interior of the corona spreads radially but the preexisting
lithospheredoes not subduct. When the spreadingceases,the
interior lithospherewill be hot relative to the exterior lithosphere
and thus will undergo a final thermal subsidencephase. A
calculationof thedifferentialthermalsubsidence
is presented
next
to showthatit canexplainthesmallamplitudeflexuresobservedat
Heng-O but cannotproducethe large trenchesand outer rises at
Eithinoha, Artemis, and Latona.
DifferentialThermalSubsidence
Fig. 15. Diagramshowingthe initial conditionsof the differentialthermal
subsidencemodel. The base of the thermal boundary layer (i.e.,
lithosphere)
is definedby the Tmisotherm,while thebaseof theelasticplate
is definedby the Te isotherm. The interiorlithosphere(fight side)is hot,
thin, and elevated relative to the exterior lithosphere. The interior
lithospherecoolsand subsideswith time, while the exteriorlithosphere
maintainsits temperature
profileby a constantbackground
mantleheatflux
q.
becauseits geothermis maintained by a constantbackground
mantleheatflux q. As the interiorlithospherecoolsand thickens
with time, its averagedensityincreases.(The thermalexpansivity
a is givenin Table 1.) Far from the contactzone,the lithosphere
subsidesisostaticallyat a rate proportionalto the squareroot of
time (Figure 16, dotted curves). After 200 m.y. of cooling, the
interior has reached the same level as the exterior.
The model incorporatestwo-dimensionalcooling, thermal
subsidence,
andflexureof weldedadjacentlithosphereof different
ages[Sandwelland Schubert,1982;Sandwell,1984] (Figure 15).
As in the previoussection,it is assumedthat the coronaehave
sufficientlylarge radii that their circularityis unimportantin the
evolutionof the flexural topography. In the initial state,it is
assumedthat 200-m.y.-old Venusian lithosphereoutside of the
corona abuts younger lithosphereof age 10 m.y. inside of the
corona. The initial thermalprofiles far from the contactzone are
given by the classical error function solution of the onedimensionalcooling half-spacemodel [Turcotteand Schubert,
1982] wherethe temperatureat the surfaceof the lithosphereis To
andthe deepmantletemperature
is Tm (seeTable 1 for values).
The rateof heatdiffusionis controlledby thethermaldiffusivity
The temperaturedistributionin the vicinity of the contactzoneis
smoothedby allowing heatto diffuseacrossthe zone for 10 m.y.
The rheologyof thelithosphere
is considered
to be perfectlyelastic
Within
150 km on either side of the contact zone, however,
about
the
lithosphere flexes to accommodate the differential thermal
subsidence. The form of the flexure and the predicted surface
stressdepend on both the subsidencehistory and the lateral
variationsin elasticthickness.The flexuresolutionis obtainedby
summing flexures that have accumulated over small time
increments.At eachtime stepthe differentialequationis solvedby
an iterationmethodto accountfor the spatialvariationsin flexural
rigidity.
The predictions of this simple thermal subsidencemodel
comparefavorablywith topographicprofilesacrossHeng-O. For
example,outboardof the ridge (-400 km to 50 km, Figure 16)
profile501 matchesthemodeltopography
curvecorresponding
to
completethermalsubsidence
(200 m.y.). Inboardof the ridgethe
model topographydies not match the observations.It shouldbe
pointedout thatthe only adjustableparametersin themodel are the
initial ages of the interior and exterior lithospheres and the
at depthslessthantheelasticisothermTe of 1023K (750øC)and sharpness
of the contactzone. Theseagessetthe amplitudeof the
ductileor fluid at greaterdepths.The ductilematerial(Figure 15)
initial stepoffset as well as the elasticthicknesses
of the interior
cansupportthe smallbuoyancyforcesdueto thermalcontraction and exteriorlithospheres.In this case,the amplitudeof the final
but cannotsupportthe larger flexural stresses.Becauseof the
ridge, trough,and outerrise flexure is aboutone half of the initial
sharp temperaturecontrast,there is a large changein elastic stepamplitude.
thickness across the contact zone.
The initial
elastic thickness of
theinteriorlithosphereis 7km, while the initial elasticthicknessof
theexteriorlithosphereis 42 km. The initial stateis assumedto be
an unstressed
configuration.
The relativesharpness
of theinitial thermaltransitionacrossthe
contactzone is essentialfor the subsequentdevelopmentof a
flexuralmoat and ridge topography.The model doesnot address
thephysicsof how sucha sharpthermaltransitionis established.
The sketchin Figure 14 suggests
thattheinitial stateis the product
of the reheatingand thinningof the lithosphereabove a mantle
plume. However,the mathematicalmodelof the developmentof
flexural moat and ridge topographyappliesno matter how the
"initial"plateaulikestateis formed.
The interior lithosphere(Figure 16, x > 0) is allowed to cool
with time while the exterior lithospheredoesnot cool with time
Noneof thethermalsubsidence
profilesmatchthetopograph•
of Latonaasshownin Figure 16. Removalof a lineartopographic
gradientwouldimprovethe fit on the exteriortopography,but the
model trench would be much too small (-400 km to -200 km,
Figure16). The modelalsodoesnotfit anyof theArtemisprofiles
becausethe amplitudeof the modelflexuraltopographyis abouta
factor of 5 too small. One could increasethe amplitudeof the
model topographyby increasingthe age contrastbetween the
interior and exterior lithospheres. However, since thermal
subsidence
is proportionalto the squareroot of age,the modelage
contrastmust be increasedto an absurd value of 5 b.y. which
exceeds the age of the planet. These results suggest that
differentialthermalsubsidence
may be an importantprocessfor the
majorityof coronaethathave relativelysmall amplitudeflexures,
buttheycannotexplainthelargerflexuresat Arte•nisandLatona.
16,082
SANDWELL AND SCHUBERT: RIDGES, TRENCHES, AND OUTER RISES AROUND CORONAE ON VENUS
0.0
-0.5
'? -1.0
..;c
"-
Latona
-1.5
E
P.. -2.0
tl
;...
"
,....,..........
,.~u.
~ -2.5
...
\
H eng - 0
.............,,/'..... ,
70
........ , ... .-" .... \, ... \
... \
\
,rrrnnrn ::.:;;;; ...... · .. ·,,~:t.",
n
200
§<
E-...
-3.0
-3.5
-4J500
-400
-300
-200
-100
o
100
Distance (krn)
Fig. 16. Evolution of the topography for the differential thermal subsidence model (dotted curves). The thermal perturbation has
decayed after 200 m.y. of cooling. The topography of Heng-O is well matched by the 200-m.y. model, while the topography of
Latona cannot be fit by the model.
Subduction Model
The flexural trench and outer rise topography observed at
Eithinoha, Artemis, and Latona is similar to flexural topography
observed on the seaward side of subduction zones on Earth. For
example, at Eithinoha the elastic plate is relatively thin (-15 kIn)
and the bending moment at the trench axis is small (0.9 x 10 16 N).
This compares favorably with the thin plate (-12 kIn) and small
moment (0.6 x 10 16 N) observed at the Middle America Trench.
In contrast, at Artemis the elastic plate is relatively thick (-37 kIn)
and the bending moment is relatively large (25 x 10 16 N). This
compares favorably with an elastic thickness of 29 kIn and a
maximum bending moment of 13 x 10 16 N found at the Mariana
Trench [Caldwell et al., 1976]. Similarly, at Latona the elastic
thickness and bending moment are 35 kIn and -6.0 x 10 16 N,
respectively which compares favorably with the Aleutian Trench
(28 kIn and 8.9 x 10 16 N). On the Earth, the bending moment is
primarily supplied by the negative buoyancy of the subducted
lithosphere. The overriding plate is almost locally compensated so
that it exerts almost no downward force on the subducting plate.
Moreover, in many cases, the overriding plate is in a state of
tension which results in back-arc spreading that is nearly parallel to
the subduction zone [Barker and Hill, 1981]. As a final analogy,
McKenzie et al. [this issue] have noticed that many of the arclike
topographic structures in eastern Aphrodite Terra (including Latona
and northern Artemis) have similar morphology and scale to
subduction zones in the East Indies on Earth. In both cases, the
subduction zones are curved with the high topography on the
concave side.
On Earth, the negative buoyancy of the subducted lithosphere
acts as a stress guide that draws the not yet subducted lithosphere
into the trench. This effect (slab pull) is believed to be the major
driving force of plate tectonics [Schubert, 1980]. An unusual
feature of some coronae including Eithinoha, Artemis and Latona
is that the trench wraps around the corona by more than 180·.
Thus if the trench axis were to remain stationary, the entire
lithosphere would have to compress and thicken as it moved into
the trench. Because this seems physically implausible and there
are no indications of circumferential compression outboard of the
trench, we prefer the model where the trench axis rolls back and
the corona increases in diameter.
SUMMARY
1. High-resolution altimetry collected by the Magellan
spacecraft has revealed trench and outer rise topographic signatures
around many major coronae [Sto/an et al., this issue]. In addition,
Magellan SAR images show circumferential fractures in areas
where the plates are curved downward. These observations
suggest that the lithosphere arl;lUnd coronae is flexed downward
either by the weight of the overriding coronal rim or by the
negative buoyancy of subducted lithosphere.
2. We have selected four of the largest coronae (Eithinoha,
Heng-O, Artemis, and Latona) which display these flexural
characteristics and have modelled the trench and outer rise
topography as a thin elastic plate subjected to a line load and
bending moment beneath the corona rim. The elastic thicknesses
determined by modelling numerous profiles at Eithinoha, Heng-O,
Artemis, and Latona are 15, 40, 37, and 35 kIn, respectively. At
Eithinoha, Artemis, and Latona where the plates appear to be
yielding, the maximum bending moments and elastic thicknesses
are similar to those found at the Middle America, Mariana, and
Aleutian trenches on Earth, respectively.
3. Estimates of effective elastic thickness and plate curvature
are used with a yield strength envelope model of the lithosphere to
estimate lithospheric temperature gradients. At Heng-O, Artemis,
and Latona, temperature gradients are less than 10 KIkm which
correspond to conductive heat losses of less than one half the
expected average planetary value. There are many possible
explanations for the low estimated heat flows. However,
modelling of many more areas is needed to establish a planetary
average.
4. We propose two scenarios for the creation of the ridge,
trench and outer rise topography: differential thermal subsidence
and lithospheric subduction. The topography of Heng-O is well
matched by the differential thermal subsidence model. However at
Artemis and Latona, the amplitudes of the trench and outer rise
signatures are a factor of 5 too large to be explained by thermal
subsidence alone. In these cases we favor the lithospheric
subduction model wherein the lithosphere outboard of the corona
perimeter subducts (rolls back) and the corona diameter increases.
SANDWELL
ANDSCHUBERT:
RIDGES,
TRENCHES,
ANDOUTER
RISES
AROUND
CORONALS
ONVENUS
16,083
Acknowledgments. We thank Peter Ford for providingan updated Parsons,
B., andP. Molnar,The originof outertopographic
rises
versionof the altimeterprofiles and many techniciansat Jet Propulsion
associatedwith trenches,Geophys.J. R. Astron.Soc.,45, 707-712,
1976.
Laboratory for processingof the SAR images. Ellen Stofan, Duane
Bindschadler,Buck Janes,and StephenSquyresorganizedthe coronae Pettengill,G. H., P. G. Ford, W. T. K. Johnson,R. K. Raney,and L.
SAR data into a very usableformat. Barry Parsonsprovidedhelpful
A. Soderblom,Magellan: Radar performanceand data products,
Science,252, 260-265, 1991.
suggestionson modelling the trench/outerrise flexure. Dan McKenzie
contributedto manyof theideasrelatedto the subduction
zonehypothesis Pronin,A. A., and E. R. Stofan,Coronaeon Venus: Morphologyand
distribution,Icarus, 87, 452-474, 1990.
andprovidedfeedbackon manyaspectsof theresearch.The researchwas
partiallysupported
by theMagellanProject(JPL958950andJPL958496). Sandwell,D. T., Thermomechanicalevolutionof oceanicfracturezones,
J. Geophys.Res., 89, 11,401-11,413, 1984.
REFERENCES
Sandwell,D., and G. Schubert,Lithosphericflexureat fracturezones,J.
Geophys.Res.,87, 4657-4667, 1982.
Barker, P. F., and I. A. Hill, Back-arc extension in the Scotia Sea,
Sandwell,D. T., and G. Schubert,Lithosphericflexure due to thermal
Philos. Trans. R. Soc. London Ser. A, 300, 249-262, 1981.
subsidenceof coronae(abstract),Eos Trans.A GU, 72(17), Spring
Barsukov,V. L., et al., The geologyand geomorphology
of the Venus
Meeting Suppl., 174, 1991.
surfaceasrevealedby theradarimagesobtainedby Veneras15 and16,
Schubert,G., Self-drivenmotionsof platesanddescending
slabs,in Plate
J. Geophys.Res.,91, 378-398, 1986.
Tectonics
andMechanisms
of Continental
Drift, editedby P. A. Davies
Basilevsky,A. T., A. A. Pronin, L. B. Ronca,V. P. Kryuchkov,A. L.
andS. K. Runcorn,pp. 151-158,Academic,San Diego, Calif., 1980.
Sukhanov,and M. S. Markov, Styles of tectonic deformationon
Solomon,S.C., andJ. W. Head,Lithospheric
flexurebeneaththe Freyja
Venus: Analysisof Veneras 15 and 16 data,J. Geophys.Res., 91,
Montesforedeep,Venus: Constraintson lithosphericthermalgradient
399-411, 1986.
andheatflow, Geophys.Res.Lett., 17, 1393-1396, 1990.
Bindschadler,D. L., and E. M. Parmentier,Mantle flow tectonicsand a
Solomon, S.C., J. W. Head, W. M. Kaula, D. McKenzie, B. Parsons,
ductile lower crust: Implications for the formation of large-scale
R. J. Plfillips, G. Schubert,and M. Talwani, Venus tectonics: Initial
featureson Venus,J. Geophys.Res.,95, 21329-21344, 1990.
analysisfrom Magellan,Science,252, 297-312, 1991.
Byeflee,J. D., Frictionof rocks,PureAppl. Geophys.,116, 615-626,
Squyres,S. W., D. M. Jones,G. Baer, D. L. Bindschadler,G. Schubert,
1978.
V. L. Sharpton,and E. R. Stofan,The morphologyand evolutionof
Caldwell, J. G., W. F. Haxby, D. E. Karig, and D. L. Turcotte,On the
coronaeon Venus,in press J. Geophys.Res.,thisissue.
applicabilityof a universalelastictrenchprofile, Earth Planet. ScL Stofan,E. R., and J. W. Head, Coronaeof MnemosyneRegio, Venus:
Lett., 31, 239-246, 1976.
Morphologyand origin,Icarus, 83, 216-243, 1990.
Comer, R. P., S.C. Solomon, and J. W. Head, Mars: Thicknessof the
Stofan, E. R., D. L. Bindschadler, J. W. Head, and E. M. Parmentier,
lithosphere from the tectonic response to volcanic loads, Rev.
Coronastructureson Venus: Models of origin,J. Geophys.Res.,96,
Geophys.,23, 61-92, 1985.
20,933-20,946, 1991.
De Bremaecker,J. C., Is the oceaniclithosphereelasticor viscous?,J.
Stofan, E. R., V. L. Sharpton, G. Schubert, G. Baer, D. L.
Geophys.Res., 82, 2001-2004, 1977.
Bindschadler,
B. M. JanesandS. W. Squyres,Globaldistributionand
Ford,P. G., andG. H. Pettengill,Venustopographyand kilometer-scale
characteristics
of coronaeandrelatedstructures
onVenus:Implications
slopes,J. Geophys.Res.,this issue.
for origin and relationto mantleprocesses,
J. Geophys.Res., this
Goetze, C., and B. Evans, Stress and temperature in the bending
issue.
lithosphere
as constrained
by experimental
rock mechanics,
Geophys. Turcotte,D. L., andG. Schubert,Geodynamics,
JohnWiley, New York,
J. R. Astron. Soc., 59, 463-478, 1979.
Lawson, C. L., and R.J. Hanson,Solving Least SquaresProblems,
PrenticeHall, EnglewoodCliffs, N.J., 1974.
McAdoo, D.C., C. F. Martin and S. Poulouse, Seasat observationsof
flexure:Evidencefor a stronglithosphere,Tectonophysics,
116, 209222, 1985.
McKenzie, D., P. G. Ford, C. Johnson, B. Parsons, D. Sandwell, S.
Saunders,and S.C. Solomon,Featuresof Venus generatedby plate
boundaryprocesses,
J. Geophys.Res.,thisissue.
McNutt, M. K., Lithosphericflexureand thermalanomalies,J. Geophys.
Res., 89, 11,180-11,194, 1984.
Melosh,H. J., Dynamicsupportof outerrise topography,Geophys.Res.
Lett., 5, 321-324, 1978.
1982.
Walcott,R. I., Flexureof thelithosphere
at Hawaii, Tectonophysics,
9,
435-446, 1970.
D. T. Sandwell,GeologicalResearchDivision, ScrippsInstitutionof
Oceanography,
SanDiego, La Jolla,CA 92093-0220.
G. Schubert,Departmentof EarthSpaceSciences,IGPP, Universityof
California,Los Angeles,CA 90024.
(ReceivedOctober15, 1991;
revised June 4, 1992;
acceptedJune4, 1992.)