JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 103, NO. E7, PAGES 16,841-16,853,JULY 25, 1998
Tectonic evolution of Bell Regio, Venus: Regional stress,
lithospheric flexure, and edifice stresses
Patricia
G. Rogers
l
RAND, Washington,D.C.
Maria
T. Zuber
Department
of Earth,Atmospheric,
andPlanetary
Sciences,
Massachusetts
Instituteof Technology,
Cambridge
Abstract. In orderto understand
therelationship
betweenvolcanicandtectonicprocesses
andthe
stressstatein the lithosphere
of Venus,we analyzedthestress
environments
andresulting
tectonic
featuresassociated
withthemajorvolcanicedificesin Bell Regio,usingMagellansynthetic
apertureradar(SAR) images
andaltimeter
measurements
of topography.
Themajorvolcanoes
of Bell
Regio,TepevMonsandNyx Mons,exhibittectoniccharacteristics
thatareuniquerelativeto
othervolcanicedificeson Venus. The mostprominentdistinction
is the lackof largerift zones
withintheoverallhighlanduplift,whichcharacterize
manyotherhighlandrisesonVenus.Also,
previousstudies
havedetermined
thatmanylargeVenusvolcanoes
exhibitradialtectonicstructuresontheirflanksbutgenerallylackthecircumferential
grabenwhichsurround
volcanoes
on
EarthandMars. TepevandNyx Montesexhibitboththeradialtectonicfeatures
associated
with
otherVenusJan
edificesandnumerous
concentric
graben.
Nyx Monsimpliesa moredistributed
magmaticsystemby itsbroadshape,radialchainsof pit craters,
andexpansive
flow fields,
whereasTepevMonsis a morecentralized
volcanicsystem,withlimitedassociated
longflows.
We investigate
theregionalstresses
associated
withBellRegioandstructural
features
believed
to
bea consequence
of lithospheric
flexuredueto volcanicloading,modeling
bothNyx Monsand
TepevMonsasaxisymmetric
loadswithGaussian
massdistributions
onanelasticplate.Therelationship
betweenthetectonicfeatures
surrounding
TepevMonsandstresses
associated
with
magmachamber
inflationarealsoexamined
through
finiteelement
analysis.
Usingtopography
datato modeltheshapeof thevolcano,we determine
thata horizontally
ellipsoidal
or tabularreservoirat a rangeof depthsfromapproximately
20 to 40 km cansatisfythelocations
of graben
formation
observed
in Magellanimages.Theseresultsimplya shiftin volcanicstylewithinBell
Regiofromanearlyphaseof broad,lowshieldformation
to latersteep-sided,
morecentralized
edificedevelopment.
Suchchanges
areconsistent
withanincrease
in thethickness
of thelithosphereovertime.
lithospheric flexure [Comer et al., 1985; McGovern and
Solomon, 1992]. Tepev Mons and Nyx Mons (provisional
Geophysicalanalysesof the tectonicfeaturesassociated name) exhibit both the radial tectonicfeaturesassociatedwith
with the Venushighlandsand major volcanoesprovideimpor- other venusJanedifices and numerousdistinct concentric gratant insight into the relationship between volcanic and ben [Campbell and Rogers, 1994].
To understandthe geophysicalevolution of Bell Regio,
tectonicprocessesand the stressstate of the venusJancrust
overtime. Bell Regio is unique relative to manyof the other this studyexaminesthe structural
featuresassociatedwith the
volcanichighland regionson Venus,suchas WesternEistla major volcanoesusing Magellan synthetic apertureradar
or Dione Regiones[Senske
et al., 1992],in its apparentlack of (SAR) imagesandaltimetermeasurements
of topography.
First,
rift zonesdissectingthe topographicswell. Most large Venus we analyzethe regionalstressfield in Bell Regiobasedon the
volcanoes also exhibit radial tectonic structures on their
style and distributionof tectonicfeaturesin the region. Next
flanks,and typically lack the circumferential
grabenwhich we examinestructuralfeatureswe believe to be a consequence
surround volcanoes on Earth and Mars, indicating
of lithosphericflexuredue to volcanic loading. Analytical
1.
Introduction
models for the formation of similar features on Earth and other
planetarysurfacesareexamined,and a modelfor the stressregimeandformationof tectonicstructures
within Bell Regiois
• Currently
at Center
for EarthandPlanetary
Studies,
Smithsonian
Institution,Washington,D.C.
developed. This analysisof lithosphericflexureand associCopyright1998 by the AmericanGeophysicalUnion.
PaperNumber 98JE00585.
0148-0227/98/98JE-00585
$09.00
ated deformationmodelsthe volcano as an axisymmetricload
with a Gaussianmassdistribution on an elastic plate of variable thickness,and incorporatescriteriafor tensile and shear
failure. Finally, the relationship
betweenthe tectonicfeatures
16,841
16,842
ROGERSAND ZUBER: TECTONICEVOLUTIONOF BELL REGIO,VENUS
ons
Figure1. Magellan
SARimageof BellRegio.Resolution
isapproximately
1.2km. Forscale,thelargecaldera
on TepevMons,the prominentcentraledificein the image,is approximately
30 km.
tesseraplateausarethoughtto
associatedwith the TepevMons edificeand stressesassoci- trendSW-NE. The preexisting
crust[Bindschadler
and Head, 1991]
atedwithmagmachamberinflationis examined
throughfinite be regionsof thickened
element analysis.
ß
2.
Regional Stress Regime
Analysisof regionalstresses
providesa framework
for understanding smaller-scaletectonic features within the
highland. As indicatedabove,this regionlacksrift zones;
however,large-scaletectonic deformationis exhibited by
andmayhaveinhibitedlateralspreading
andthe formation
of
majorrift zonesduringtheearlyperiodof highlandformation.
If the stressesthat governedthe formationof the SW-NE
tessera blocks still existed at the time the volcanic edifices
formed,similartrendsin the subsequent
volcanicand tectonic
features
mightbe observed.However,althoughsomeof the
Nyx MonslavaflowstrendSW-NE,little directevidenceof
significantSW-NE fracture
patternsexists.This impliesthat
tesserablocks which surround the major volcanic edifices the formationof TepevMons andNyx Mons postdatethe re(Figure 1) [Campbelland Rogers,1994]. Tesseraare gener- gional stressregimewhich producedthe tesseraor that
in the regionsthat lack fractures
did not exceedthe
ally the stratigraphically
oldestunits in this region and stresses
preserve
a recordof periodsof intensetectonicdeformation. lithosphericfailure criteria.
Plains regionssurrounding
Bell Regio are next in the
The fractureswithin someblocks are irregularlyoriented,but
sequence
afterthe tesseraand maybe divided
the prevailingfracturepatternswithin the tesseraregions stratigraphic
ROGERS AND ZUBER:
TECTONIC EVOLUTION
OF BELL REGIO, VENUS
16,843
ß
i:'
Figure2. MagellanSARimageof Nyx Monswith concentric
fracture
mapoverlay,centered
at approximately
29.9øN,48.5øE.Notetheradialchains
of pitcraters
andconcentric
fractures
surrounding
theedificeoutlined
in the image.
into at leastthreedistinctunits: bright plains, dark plains,
and ridgedplains[Campbelland Rogers,1994]. Theridged
plains arethe oldestof theseunits and recordan intenseperiod of deformationwith ridgesand grabenorientedSE-NW
topography
of Nyx Mons and surroundingregions. This edifice risesapproximately
I km abovethe surroundingapronof
flows; the centralbulge and wishbone ridges contain the
highestelevationsof the featureat approximately
6053.5 kin.
and SW-NE. The brightand darkplainsare lessdeformedthan Slopes
on the southernflanksof the edificearegenerally1ø the ridged plains or the tessera,with deformationprimarily 2ø, grading
intoslopes
lessthan0.5ø continuing
southward,
representedby SE-NW trending fractures. Since the lava corresponding
to the flow apronthat typically surroundsvolflowsfromthemajorvolcanicedificesin thisregionembaythe canoeson Venus [McGovern and Solomon, 1995]. It is in
tessera,superposemost of the plainsunits,and do not contain this gently slopingregionthat the mostprominentconcentric
majordeformationpatterns,it is reasonableto concludethat grabenoccur. Detailed structuralmappingof thesefeatures
grabenoccurat a radial
the last largevolcaniceventsin this regionpostdatethe re- indicatesthat the innermostconcentric
280 km fromthe centerof the edifice,
gionalstressregimewhich producedthe tesseraand ridged distanceof approximately
plains. These volcanicunitsthus recordmore recent localized while the outerradiusof thesefeatureslies at approximately
stresses
in the regionandare the subjectof the next sections. 470 kin. A 500-m changein elevation occursbetween these
two radii. The mostprominentvolcanic flow fields in the region (the youngest flows of Nyx Mons) emanatefromthese
3. Lithospheric Flexure and Nyx Mons
concentricfractures[Campbelland Rogers,1994].
The oldest volcanic edifice within Bell Regio is Nyx
Mons, a featurecharacterizedby a wishbone pattern of ridges
and gentle flank slopes. The inner region contains a central
bulge and radial chains of pit craters[Campbell and Rogers,
1994]. Surroundingthe edificeto the east,south,and northwest are large sets of circumferentialfractures,which are the
mainfocusof this section (Figure 2). Figure 3 illustrates the
3.1. Models of Lithospheric Flexure
The distributionof fracturesaroundlargevolcanicloadsis
an important indicator of the stressstate and effectivethickness of the elastic lithosphere. Comparing the tectonic
featuresformedin response
to largevolcanicloadson various
16,844
ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS
6055 ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' '
6054
6053
_
I
605
0
I
I
I
100
I
I
I
800
300
I
I
I
400
DISTANCE(KM)
Figure3. Topographic
profilethrough
Nyx Monstrending
approximately
westto east.Note the higherelevatedridgesand centralregions.
planetarysurfaceshas provided importantconstraintson the
relative lithospheric thicknesseson Venus, Earth, Mars. and
the Moon [e.g., Melosh, 1976, 1978; Comeret al., 1985; Hall
et al., 1986; McGovern and Solomon, 1993]. In these analyses,grabenformconcentricto a load as a result of surficial
extensionalbending stressesassociatedwith lithospheric
flexure. If the lithosphereis extremelythick or rigid, then the
stressfield is dominatedby compressionalforcesdue to the
volcano [Artyushkov,1973;Fleitout and Froidevaux,1983].
This analysisof lithosphericflexureand associateddeformationmodelsthe two majorvolcanoeswithin Bell Regio as
axisymmetricloads with Gaussian massdistributions on an
elastic plate, following the analysisof Melosh [1978] of the
mechanicsof lunar masconloading. Deviations of the actual
loadfrom axisymmetryare a second-ordereffect[Comeret al.,
1985]. Melosh [1978] analyzed load-relatedstressesand deformationand determinedthat the tectonic pattern predicted
by this model, with increasingradial distancefromthe center
of the load, includeda proximalzoneof radial thrust faults followed by strike-slip faults, all surrounded by concentric
normalfaults. Althoughthe zoneof strike-slip faulting is not
readily observedsurroundingthe lunar mascons,they suggestedthat someof the ridges surroundinglunar mariamight
be evidenceof strike-slipmotion. Golombek[1985] proposed
that the lack of observedstrike-slipfaultscan be explainedby
tribute the absence of topographic moats and concentric
normalfaulting surroundinglarge Venusvolcanoesto masking by lava flows fromthe centraledifice. In their model,the
the fact that fault nucleation occurs at subsurface interfaces,
though this does not account for the absenceof such features
3.2 Modeling Volcanic Loads
in regionsthat most likely lack discretesubsurface
layering.
In an analysis of the formationof large volcanic loads on
Mars by McGovern and Solomon [ 1993], time-dependenteffectson the predictedfailure mechanisms
of the growing load
were considered.They determinedthat the zone of strike-slip
faulting is not observedbecauseit either occursin a region
that had previouslyformed normalfaults (the normal faults are
reactivated),or that they formand are buried by subsequent
deposits. The fracturesconsideredin our analysis occur on
the youngestvolcanicflows; thereforethis analysisconsiders
their formationas a late stageeventand is not concernedwith
the growing load. However, our treatmentof the lithosphere
as an elasticplate inherentlysupposes
that stresses
due to the
growing edificedid not pervasivelyfracturethe lithosphere.
In amore recentanalysis,McGovern and Solomon [1997] at-
This study analyzesthe volcanicedificesand associated
stressesin Bell Regio by modelingthe two majorloads as
Gaussiandistributions on an elastic plate lbllowing Melosh
[1978]. The generalsolution to the stressfield is given by
stresses in this moat fill are too low to induce failure.
Schultzand Zuber [1994] addressed
the paradoxof the existence of an annular zone of strike-slip faults around
prominentloads predictedin previousmodels,evidencefor
whichis rarelyfoundon planetarysurfaces.In theirmodel,the
discrepancies
betweenthe observations
and the modelpredictions result from other considerationssignificant in fault
analysis: the neglectof stressmagnitudesand relianceonly
on stresstrajectories,and the identificationof first failure.
When rock strength,stressdifferences,
stressgeometriesor
stress state at the onset of failure and load evolution
are taken
into account,their modelpredictsthat concentricnormalfaults
andjoints (as opposedto strike-slip faults)occur at or near
the surfacesurrounding
loads. Rockstrengthis significantin
determiningthe stresslevel when the first fracturesoccur.
Their model,which examinesthe importanceof failure mechanisms such as tensile cracking near surface regions and
varyingvaluesof Young'smodulus,was experimentally
verified by Williamsand Zuber [1995]. The analysisbelow uses
the generalsolutionsdescribedin the Melosh [1978] model
but also incorporatesthese failure criteria.
Melosh [ 1978] as
Ozz= +PcgZ+ J0(kr)[(A + Cz) coshkz + (B + Dz) sinhkz]
(1)
Or•
=+}CpcgZ
+(J0(kr)
+Jl(kr)'
kr /I [(A+Cz)
cosh
kz+(B+Dz)sinh
kz]
+_}(J0(kr
)+(l+v)
J,(kr)
)[Dcosh
kz+Csinh
kz]
kr
(2)
o0•:+}Cpcgz
+J•(kr)
kr [(A+ Cz)cosh
kz+ (B+ Dz)sinh
kz]
+•(vJ0(kr
)+(1
+v)
j•(kr))[D
cosh
kz+Csinh
kz] (3)
kr
ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS
•rz
16,845
=J•(kr)
[(A+Cz+•) sinh
kz+(B+Dz+-•)cosh
kz] (4)
o• = Oz•= 0
(5)
whereJ{(k0 andJ0(kr)areBesselfunctions,
(J= is the vertical
stress, (Jrr is the radial stress, (J• is the hoop (tangential)
stress,(Jrzis the shear stress, On is the normal stress, r is the
radiusfrom the centerof the load,z is the depth in the plate, k
is the wave number, and v is Poisson'sratio. Because the total
-5O
stressis soughtin this analysis,a termfor the confining pres-
sure(•pcgz)is addedto the abovestresseswhere• is the
{
ratio of horizontal to vertical overburden [Banerdt, 1988].
The vertical stressat the surface, and the lack of shear stress at
the surfac.
e or baseare indicated by the following boundary
conditions:
o= (z = 0, r) = bJ0(kr)
(Jrz(Z= 0, r) = (Jrz(Z= H, r) = o= (z = H, r) = 0
-100
0
1
2
3
(6)
Figure 4. Plot of elastic surfacestressesresultingfromthe
Nyx Monsloadwith a lithospheric
thickness
of 50 km. Nega-
(7)
tive stressesare compressional and positive stresses are
extensional.
The bar represents
the zoneof fracturingobserved
in the imagesandcorresponds
well to the R/A rangeof 1.5-2.7
resultingfrom the model.
In this analysis,the verticalload is represented
by
w= pmgT
I
(8)
wherePmis equalto its density,T is its height at r = 0, and g 3.3. Nyx Mons Modeling Results
is gravitational
acceleration.Accordingto Anderson[1951],
In this analysis,an analytic modelwas usedto determine
concentricnormalfaultingwill occurin the region definedby
the
stressfield and predictthe spatial distribution of faulting
positive(Jrrando** andmaximum(Jrr.
In order to distinguish the likely mechanism
for initial on the lithospheresurroundingNyx Mons. The predictions
lithospheric
failure, we haveincorporated
into this formalism were then comparedto the observed fault distributions,
the followingrockfailurecriteria: a Griffithcriterionforten- thereby constrainingthe propertiesof the lithospherethat
the volcano.Fifteencases,with varying lithospheric
silefailureand the Byericecriterionfor shearfailure[Schultz supports
and Zuber,1994]. Specifically,applyingstressto a fractured thicknessand Young's modulus,were consideredin this
rock will causefrictionalsliding along the fracturesprior to analysisofNyx Mons to determinewhich mostclosely correreaching
the level requiredto causebrittle failureof the rock spondsto the observedfracturepatterns.The fixedparameters
mass.Thisrelationship,
referredto as Byerlee'slaw, is given are given in Table 1.
In the first seven cases, the effects of varying the
by [Brace and Kohlstedt,1980]
lithospheric thickness between 30 and 70 km were examined.
'r = 0.85 o,
x = 60 -t- 10 + 0.6 o,,
The diameter of the feature was defined to be the distance at
3 < o, < 200 MPa
o,,> 200 Mpa
(9)
The Griffith criteria for brittle failure states that fracture occurs
at a givenstressaccordingto
o, = (2AE/ xc)"2.
(10)
whichthe topographyof the edificemergedwith the surrounding plateau. Since Nyx Mons is an irregularly shaped
"wishbone"feature, minimum and maximumvalues for the load
extentwerealsoexamined.The maximumdiameter,corresponding to the feature'sN-S extent, is 350 km, and the minimum
diameter,correspondingto the edifice'sE-W extent and an
idealized circular shapefor the feature,is 270 km. These di-
where2c is the lengthof the pre-existingcrack,A is the sur- ameters correspond to halfwidths of 175 and 135 km,
faceenergy,E is the Young'smodulus,
ando, is the applied respectively.The deviationof the load froma Gaussianshape
tensilestress[Price and Cosgrove,1990].
is not significant.
The next casesexaminedthe effectsof varying Young's
modulus.In-situmeasurements
of elasticmoduli can be up to
an order of magnitudelower than laboratory measurements
[Cullen et al., 1987], so we examinedthe effectof reducing
Table 1. FixedParameters
Usedin Modelin•N7x Mons
Parameter
Description
Value
Young's
modulus
byanorder
ofmagnitude
(from
1011
to 10rø
-2
g
gravitationalacceleration
8.6 m s
-3
Pm
T
loaddensity
3000kg m
load height
horizontal/vertical
1 km
overburden
Poisson's ratio
Pc
lithosphere
density
0.5
0.33
3300
kgm'3
Pa) while varying the load halfwidth and the lithospheric
thickness.
Next
we examined the effect of an increase in
Young's
modulus
(to1012
Pa).Thissituation
mayrepresent
the effectiveYoung's modulusof a rock containingclosed
cracks[Jaeger and Cook, 1979] although it's uncertain that
this effectwould increaseE by an order of magnitude. We
considerthis value to be an upperlimit on E.
The effectof increasingthe lithospheric thickness shifts
the rangeof concentricnormalfaulting to slightly higher val-
16,846
ROGERSAND ZUBER: TECTONICEVOLUTIONOF BELLREGIO,VENUS
..
.........
.....
•,•
-.:
•:•
•:•:•..
:•?•
....
,.......
::&• .:
'-'•,•
.......
:•:•.•
:-4•'
•:.. •
.........
•
"'•:•::•.•:.•.•
............
•½•;,
....
•........
..... .&•-::•
.......•
ß
•:-..
:•
••
...........
•:.-•:•.•..•.:.:.•..
•½•
• ...
.........
.,•:•.....
•,•<.-•...•..:....•.•:..•:•
•::•:•:-•::•
.•,:•
.... • ,.•
..............................................................
......................
......
Figur••. Magellan
SARimageofTcpcvMonswith fracture
mapoverlay.Notetheprominent
fiattumsconcentrio
to thevolcano.
Forscale,
thelargest
caldera
onTcpcvMonsis approximately
30 kmin diameter.
uesof R/A (normalized
radialposition,
whereA is the Monsdiscussed
above
[Campbell
andRogers,
1994].It rises
halfwidth
oftheload),
whiledecreasing
thesizeoftheload approximately
:5kmabove
thesurrounding
plains
andischarcauses
a smallincrease
in themaximum6,and
therangeof acterized
byrelatively
steep
slopes
(20ø- 40ø)nearthesummit
R/Aforgraben
formation.
Decreasing
Young's
modulus
de- region.Thesteepest
slopes
occur
alongtheeastern
flankof
creases6rr and the R/A range for graben formation,while
increasingE has the oppositeeffect.
The innerandouterradii for the concentric
faults(280 and
470 km) correspond
to an R/A rangeof approximately
2.0 - 3.5
ifA = 135kmandanR/Arange
of 1.6-2.7ifA = 175km.Figure 4 illustrates
the resultsof the bestsolutionthat produces
concentricnormal faulting in the range of 1.5 -2.7. Total
stress(MPa)is plotted againstR/A. Individual points are
plottedonthe O'rrcurve. Theseresultsindicatethatfor the parametersused in this analysis,a lithosphericthicknessof 50
km,E-'10•, andloadhalfwidth
of 175kmbestdescribes
the
conditionsat Nyx Mons at the time of the formationof the concentric grab.
en.
the volcano(Figure5). Two large(11 and 31 km diameter)
calderassuperpose
the summitregion. The northernflank is
characterizedby prominentfracturesand coalescedchains of
pit cratersconcentrically
distributedaroundthe mainpeak
andcalderas.In thissection
we consider
theoriginof tectonic
featureson Tepev Mons, beginning with a test of the
lithospheric
flexuremodelusedaboveandconcluding
with a
comparison
betweenterrestrialvolcanicdeformation
patterns
and the Venus observations.
4.1. Modelingof Tepev Mons ConcentricFractures
In preliminary
analyses
by Solomonet al. [1992] it was
postulated
that the concentric
grabennorthof TepevMons
4. Edifice Stressesand Tepev Mons
mayhaveresulted
fromlithospheric
flexuredueto the volcanic
load. To testthis hypothesis,
an analysissimilarto the one
TepevMons is a prominentvolcanicshieldwithin Bell
Regio thoughtto be youngerthan the large volcanoNyx
described
abovefortheformation
of theconcentric
graben
surrounding
Nyx Monswasperformed
fortheTepevMonsload.
ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS
16,847
ing an accuratesurfaceresponse,which could result in
spurious
rangemeasurements.
Hencetheminimumelevation
of
this potentialmoatis difficultto constrain.
Assumingthe flow
"•-200
is containedwithin the lowest region, the approximatecenter
of the moatwouldcorrespond
to an R/A valueof 1.8, almostat
the centerof the rangeofmaximumextension
predictedin our
modelsusinga lithospheric
thickness
of 30 - 50 km. This re-
m -400
sult is supportedby recentstudiesof gravity-topography
relationshipswhich yield elasticthicknessestimates
for this
regionin the rangeof 30-50 km [Smrekar,1994].
There is thus evidencefor lithosphericbending associated
with Tepev Mons, but the results of our model indicate that
this flexure is not the likely causeof the prominentconcentric
grabenwhich occuron the steep northern flanks, close to the
-600
0
1
2
3
center of the load.
Similar features are observed on the flanks
of Pavonis and Arsia Mons, two large shield volcanoes on
Figure 6. Plotof elasticsurfacestresses
resultingfrommodel- Mars [Comer et al., 1985]. Comer et al. studied the tectonic
ingtheTepevMons loadwith a lithosphericthicknessof 30 featuresassociatedwith large volcanic loads on Mars and dekm.The bar represents
the zoneof fracturingobservedin the termined that the concentric graben on Pavonis and Arsia
images.UnliketheNyx Mons case,this regiondoesnot corwhich lie closeto the centerof the load may be concentricexrespond
to theR/A rangeof 1.5-2.5resulting
fromthemodel.
tensionalfracturesformedduring the evolution of the caldera
rim as magmawas withdrawnor solidified,producingan annular ring of faults. Another causemay have been topographic
Five caseswere examinedin which the lithosphericthickness stressesand gravitationaIspreading,which resultedin extenvaried from 20 to 60 km. The resultsof the model for the caseof
sional faults on the flanks of the shield [McGovern and
a 30-km-thicklithosphere
are illustratedin Figure6.
Solomon,1993]. The concentricgrabenmay also reflect zones
Structuralmappingof concentricgrabenaroundTepev of weakness inherited from flexural stressesduring an early
Mons indicates that these features occur at inner and outer rastageof volcanogrowth. In the next sectionwe examinesome
dial distances
of 65 and90 km, respectively.With a halfwidth of thesemechanismsin more detail and discusspossibleterresfor theloadof 80 km basedon topographicprofilesacrossthe trial analogsto understandif stresseswithin the Tepev Mons
edifice(Figure7), thiscorresponds
to R/A valuesranging
from edifice may have produced the observedcircumferentialfrac-
0.8 to 1.1. However,resultsof the modelindicatethat maxi-
tures.
mum extensionalstressoccursat R/A of 1.5 to 2.5. This region
corresponds
to the approximate
locationof a possibletopo- 4.2. Models of Edifice Deformation
graphic
moatnorthof TepevMons(R/A= 1.8)whichhasbeen
As discussedabove, the free surfaceof a volcanic edifice
discussed
by severalauthors[Janleet al., 1988;Solomonand
tectonicdeformation
asa resultof severalmechaHead, 1990; McGovernand Solomon,1992; Campbelland mayundergo
Rogers,
1994](Figure8). Theeffective
elastic
thickness
based nisms: inflation and doming due to subsurfaceinjection of
with calderacollapse,
andgravitaon the location of this volcanicallyfloodedmoatyielded a magma,deflationassociated
tional
relaxation
which
may
lead
to
slumping
of
material
along
preliminary
valueof approximately
10 km [McGovernand
Solomon,1992]. However,the lavaflow whichfills this moat the flanks. The mechanicalbehavior and overall morphology
of all
hasa highsurface
roughness
[Campbelland Rogers,1994] of a volcanicshieldgenerallyresultsfromthe interaction
whichmayhaveprevented
theMagellanaltimeter
fromacquit- theseprocesses.However,gravitationalcollapseandslump-
6056
6054
6052
,,,l[,,,l,,,,I,,,,I
0
50
100
150
200
250
300
DISTANCE
Figure 7. Topographic
profilethroughTepev Mons trendingapproximately
NW to SE. The two peakscenteredat approximately
200 and250 km represent
small,steepvolcanoes
on the SE flanksof TepevMons.
16,848
ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS
Figure 8. MagellanSAR imageof lavaflow northof TepevMons,thoughtto be confinedwithin a topographicmoat. TepevMonsis off the imageto the southeast.
ing of the flanks may be lesssignificantfor venusianedifices examinedthe tectonicresponses
associated
with the evolution
due to their relatively gentle profilesand limited verticalex- of the calderaon OlympusMons, Mars. They used a linear
tent [Head and Wilson, 1992]. Thereforethe major forces elastic finite elementmodel to determinethe range of magma
affectingthe overallmorphology
of Venusvolcanoesmaybe chambergeometriesand pressuresthat could producethe obrelatedto stressesassociated
with the evolutionof a magma servedtectonic pattern. Specifically,the ridges and graben
reservoirand internaldike propagation.Severalauthorshave which formedfrom subsidence
of the calderafloor duringdeflaexamined the surface deformation associated with stresses that
tion of the magmachamberwere usedto provideconstraints
on
arisefromthe inflationand deflationof a subsurface
magma the dimensions,depthand pressuresassociatedwith the subchamber.A periodof upliftandswellingof theedificemayoc- surfacereservoir. They determinedthat the surfacestress
cur due to the inflation of such a magmachamberand the distribution is relatively insensitive to the details of the
associated
injectionof dikes and sills. Deflation,which may shapeof the magmachamberand is very sensitiveto its depth.
leadto /•aldera
collapse,
results
asrifteruptions
occuralong
the flanksor as intrusionsoccurinto new regionswithin the
volcano [Dieterich and Decker, 1975; Marsh, 1984].
In earlymodelsof magmachamberdetbrmationthe chamber
was represented
by a point sourcein an elastichalf space,or
by magmareservoirs
thatweresphericaland smallin comparisonto their depth [Anderson,1935; Mogi, 1958]. However,
thesepoint sourcemodelsapplied accuratelyonly to stresses
at largedistances
from the chamber.Later modelsrepresented
the magmareservoiras a finite sourceandwere ableto more accuratelydeterminenearfield (shallow source)stresses[Ryan,
1988]. Dieterichand Decker [1975] determined
thatthe early
analyticalapproachespredictedgenerally similar surfacedeformation,regardlessof the actual model used and that these
modelsdid not predict the ratio of horizontal to vertical sur-
facemovementsobservednear summitregions. They were
amongthe first to usea finite elementmethod,enablingthemto
modelsummitdeformations
and rift zone intrusionsusinga variety of shapesand depthsfor the magmareservoir. Dieterich
and Decker [1975] also observeda relationshipbetweenflank
4.3. Numerical Modeling of Edifice Deformation
Inthissection
weexamine
whether'
theconcentric
graben
observedon the flanksof TepevMonscouldbe dueto stresses
within the edifice. To understand the nature of the stress state
of the edifice,we constructedan axisymmetric
finite element
model to calculate the elastic stresses within
the volcano and
to examinethe relationshipbetweenthesestresses
and the observed tectonic features. Following a model previously
employed in the study of caldera subsidence[Zuber and
Mouginis-Mark, 1992] we analyzed the stressesassociated
with variations in a magmareservoir. However, while the
Zuber and Mouginis-Mark[1992] analysismodeledthe deflation of the magmachamberandthe resultingcalderastructures,
this modelis concerned
with the inflationof the magmachamber and the associated stresses on the flanks of the volcano.
Deflationand resultingdeformationwithin the Tepev Mons
calderasmay have also occurredduring its history, however
eruptions and the systematicinflation and deflation of the structureswithin the calderasof Tepev Mons can not be resummitreservoir; flank eruptions occur as magmais trans- solved, most likely due to the presenceof a fine grained
portedverticallyto a shallowstoragezone beneaththe summit surficialdeposit [Campbell and Rogers, 1994]. We usedthe
followed by lateral transportof magmafromthe summitreser- finite elementprogramTECTON [Melosh and RaeJ3ky,1981]
voir to the flanksby dikes. Zuber and Mouginis-Mark[1992] to developa linear elastic modelof the stressesand displace-
ROGERSAND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS
16,849
Table 2. ParametersUsed in Finite ElementModeling of
ofRx = Ry = 16km. Theleftboundary
is a symmetry
axis
TepevMons
along which horizontaldisplacements
vanish. At the bottom
boundaryof the grid, at depthsmuchlargerthanthe level of
Parameter
Value
the chamber,
verticaldisplacements
vanish,whileat largera-
.3
3000kg m
c•ialdistances
(rightboundary)
bothhorizontal
andvertical
Young's
Modulus
(within
chamber)
10
9Pa
displacementsvanish. Figure 10 illustrates the surface
stressesresultingfrom this analysis.
Young's
Modulus
(outside
chamber)
10• Pa
Density
Poisson's ratio
The resulting variations in the stressfield were examined
and the modelresultswere comparedwith our observations
fromMagellan images.Specifically,the innermostlocation of
0.33
predicted
concentric
grabenformation
is definedby thepoint
at which•Jrrcrosses
fromnegative(compression)
to positive
(extension)in the finite elementresults,followingmethods
mentsassociatedwith the edifice and underlying crust and
mantle.
In orderto improvethe accuracyof the finite elementrepresentation of the volcano, we extracted a representative
topographic
profilefor Tepev Mons from the Magellan globalaverage(5.4-kin resolution)data set. The modelgrid was then
constructedto conformto this profile shapealong the upper
surface.Given that Tepev Mons has significant changes in
slope along its flanks,this methodpermitteda morerealistic
assessment
of the role of local topographyon the final stress
field. The profile we used for the Tepev Mons volcano was
takenfromthe approximatecenterof the larger easterncaldera
(29.6øN, 45.6øE)and extendedto the northwest. Fromthe
start of this profile, the zone of concentricgraben formation
begins at approximately40 km and extendsto approximately
115 km. Any additionalgrabenat greaterdistancesmay have
been obscuredby later lava flows.
The magmareservoir was modeledas a simplechamberin
which
inflation
occurs as a distribution
of outward
directed
radial forces
at specified
nodes,with the force magnitudeequal
9
2
to 1 x 10 kg m s- (1000 MPa). Varying the forcemagnitude
affectedthe magnitude, but not the distribution, of surface
stresses.The modelallowsanalysisof varyingmagmachamber
depth,size,and shape,as well as the density, Poisson's ratio,
and Young's modulusof the magmaand countryrock. The parametersmost typically usedare listed in Table 2.
Figure 9 illustrates an exampleof the axisymmetricfinite
elementgrid used in this analysiscontaining8238 nodes and
8181 elements,with a grid size of 100 km by 300 km. This
casemodelsa spherical magmachamberwhich has 107 elements,lies at a center depth, D, of 30 km, and has dimensions
I
I
I
used in previous studies [Comer et al., 1979; Zuber and
Mouginis-Mark, 1992]. We also considereda case with no
magmachamber
to analyzestresses
due solelyto the volcano,
and found relativelysmall load-induced
surfacestressesin the
vicinityof thesummitthatwereeasilyoverwhelmed
by the effectsof evena smallmagma
chamber.However,this analysis
does not account for edifice stressesfrom other sourcessuch as
lithosphericflexure, which would tend to add horizontal com-
pression in the upper lithosphereand may inhibit the
transmission
of extensional
stresses
to the surface[McGovern
andSolomon,1993]. Thusthe depthof burialforanygiven
magmachambermustbe shallowerto producethe observed
grabenthanfor a scenariowithoutflexuralstresses.Likewise,
the observable
distribution
of fractures
mayhavebeenaltered
due to burial by superposing
flows [McGovernand Solomon,
1997]. Specifically,the burial of the innermostfracturesnear
the summitregionwould increasethe horizontal radius of the
ch•crossover,
and biasthe predictionof the magmachamberra-
diusto largervalues. Burial of innermostgrabenwould also
biasthe depthprediction
to largervalues,sincegrabenformation movesoutward with increasingdepth to the chamber.
Neglecting theseadditional potential factorsthus biasesour
predictionstoward largerchamberdepths,so our analysis
placesan upperboundon the depthof burial.
4.4
Results
In orderto constrainthe likely magma
chamber
geometry,
we variedalternatelythe depth,size,andshapeof the model
reservoir. Numerouschambergeometrieswere examined
(approximately
90 totalvariations),
froma spheroid
with vary-
I
-2O
-4O
-60
-8O
-10o
0
50
10o
150
2o0
250
300
R (km)
Figure9. An axisymmetric
finiteelement
gridusedin theanalysis
of TepevMons,containing
8238nodesand
8181elements,
witha gridsizeof 100kmby300km.Themagma
chamber
in thisexample
liesat a centerdepth
(D) of 30 km,andhasdimensions
of Rx= 16km(horizontal
radius),
andRy= 16km(vertical
radius).
16,850
ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS
ing radii to ellipsoids with varying horizontal and vertical
2xlO
s
axes. Table 3 illustrates
•
results from several of these models.
Asthevertical
dimension
(Ry)ofthechamber
increases
relative to the horizontal dimension (Rx) (a vertically elongate
ellipsoid),or the depthto the chamberbecomesshallower,the
stresses become more concentrated
towards
the center of the
load and the zone of extension(graben formation)moves inward. It is obvious from Table 3 that neither spherical
chambersnor ellipsoidal magmabodies comparablein size to
the summitcalderacan producethe requiredstressfield within
a range of reasonabledepths.
The 40-km crossoverpoint can be accommodated
most easily by a tabular magma chamber 44-52 km in radius,
approximately8 km in maximumthickness,over a range of
0
20
40
60
80
100
120
depths from 18 to 36 km. The tradeoffsbetween shape and
R (kin)
depthare illustratedin Table 3. The thickness of the chamber
Figure 10. Elasticsurfacestresses
resultingfromthe inflation has less of an impact on the location of the crossoverpoint
of a sphericalmagmachamberbeneathTepev Mons, illustrated than the width and depth of burial. The small changes in
crossoverpoint with changing thickness reflect the varying
in Figure 9.
-4x10S
•
•
Table 3. Variationsin o• CrossoverPoint (From Compressional
to ExtensionalRegime) With Changes
in D (Depth to Center of Chamber),Rx (Horizontal Radius),and Ry (Vertical Radius)
!
r
Rx, km
Ry, km
-15
16
16
16
-30
16
16
22
-50
16
16
26
Dcenter,
km
Crossover{Jrr.km
SphericalQhambers:
EllipsoidalChambers:
-20
10
20
16
-50
10
20
19
-40
20
30
27
-50
20
30
3l
-18
45
4
35
-18
52
4
40
- !8
60
4
46
-18
66
4
49
-28
56
4
45
-28
48
4
40
-36
48
4
42
-36
44
4
40
-22
62
2
46
-22
62
4
48
-22
62
6
47
-22
62
8
45
Tabular Chambers:
Shallow:
Intermediate:
Deep:
SensitivitytoThickness:
ROGERSAND ZUBER: TECTONICEVOLUTIONOF BELL REGIO,VENUS
16,851
-2O
-40
-60
-8O
-10o
0
50
100
150
200
250
300
R (km)
Figure 11. Axisymmetricfinite elementgrid for a solutionof TepevMons edifice stresseswith a magmachamber at an intermediatedepth.The magmachamber,representing
a sill-like intrusion,lies at a centerdepth(D) of
28 km, andhasdimensions
of Rx= 48, andRy= 4.
distance
to the surfacefromthe upperboundary
of the chamber.
The width of the reservoiris inversely correlatedwith the
depth,suchthat morenarrow"sills"may producethe required
stressfield as the centerlinedepth increases.Note, however,
that the surfacestress magnitudedeclines with increased
chamberdepth,so a shallow chambermay be morelikely to
create observable
5.
Discussion
and
Conclusions
In thisstudy,thenatureof thestress
stateandlithospheric
structure
of Bell Regiohavebeenexamined.Thestyleanddistribution of tectonic features associated with the volcanic
loadsin Bell Regiowereanalyzed
in an attemptto understand
the regionalstresseswhich producedthesetbatures.A com-
fractures.
is illustratedthroughthe variOur resultsindicatethat the circumt•rrential
grabenoccur- plexhistoryof stressregimes
ring on the flanksof Tepev Mons couldbe the result of edifice ous structural features associated with several different
stressescausedby a sheet-like or tabular magmareservoir. geologicterrains. The oldestunits in the region,SW-NE
Figures 11 and 12 illustrate the results of this solution for an
intermediatechamberdepth(28 km) with a horizontalradiusof
trendingtessera
blocks,provideconstraints
on the earlyre-
gional stresstrajectories. These regional stressesdo not
appearto haveaffected
the emplacement
of the largevolcanic
may possibly have fed smaller magmachambersat shallower edifices,TepevMonsandNyx Mons.
48 km and a vertical radius of 4 km. This sill-like
intrusion
depths. However, without better resolution of the structure
To quantifythe stressregimein Bell Regiowe haveap-
within the calderas,furtheranalysis is not possible. Our plied analytical modelsfor the formationof similar structures
analysisof Tepev Mons showsthat the observedspatial dis- on Earth and other planetarysurfaces. We have identified
of
tribution ofgraben may be attributedto stressescausedby structuralpatternsthat we believeto be a consequence
magma chamber inflation, and therefore no inference of
lithospheric
flexuredueto volcanicloadingand otherfeatures
with inflationof a magma
reservoirbelithosphericthicknesscan be madefromthese grabenloca- thatmaybe associated
fractures
surrounding
Nyx
tions. However, our earlier analyticalmodelof Tepev Mons neathTepevMons. Concentric
andtheirdistributions
examined.By modflexurebasedon the possiblelocation of a topographicmoat Monsweremapped
may provide constraintson the thickness of the elastic lithosphere.
elingNyx Monsasa surfaceloadon an elasticplate,we used
the concentricgrabento provide a constrainton the effective
elasticthicknessat the timethe volcanowasemplaced.Our
analysisindicatesthat,foran assumed
Young'smodulusfor
theplate
of 10IIPa anda loaddiameter
ofapproximately
350
km, a lithosphericthicknessof 50 km bestdescribesthe condi-
tions at Nyx Mons at the time the concentricgrabenwere
formed.Thispredicted
elasticthickness
is in goodagreement
with Magellangravity analyses.Smrekar [1994] indicates
thattheeffectiveelasticthicknessat shortwavelengths
is 30
-lOS •_'•
_ 5 km, and 50 _ 5 at long wavelengths,wherethe 30 km
valuereflectsa thinnedelasticplate at the timethe volcanoes
__ wereemplacedandthe 50 km valuerepresentspresentday
elastic thicknesses. It should be noted that Smrekarwas ana-
lyzing the overallhighlandswell, whereasthis analysis
modelsthe individualvolcanicloadsin the region.
-2xlO s
A concentric
zoneof weakness,
represented
by grabenand
0
20
40
60
80
100
1•0
coalesced
chainsof pit craters,surrounding
TepevMonswas
1t (krn)
alsoexamined.
Thesefeatures,
previouslyidentifiedaspossiFigure 12. Elasticsurfacestresses
resultingfromthe inflation bly dueto lithosphericflexure[Solomonet al., 1992], occur
of a horizontallyelongate(sill-like) magmachamberbeneath on the steepflanksof the volcano.Our analysisindicatesthat
TepevMons,illustratedin Figure11. The barrepresents
the they most likely formedas a result of extensionalstressesasregionof fracturing
observed
in the Magellanimages.
sociatedwith inflation and domingduring magmachamber
16,852
ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS
inflation. Reservoir-induced
stresseswere analyzedusing a finite elementmodel, and our results indicate that inflation of a
largesheet-likemagmareservoir,represented
by a horizontal
ellipsoid in our model,mostlikely generatedthe zoneof ex-
appearsto have occurredat both Tepev Mons (evidentfrom the
topographicmoat) and Nyx Mons (resulting in the concentric
graben). However, Tepev Mons appearsto have experienced
additional
deformation
due to the stresses associated
with
magmachamberinflation. Whereas the Tepev Mons load is
The tectonic deformation within the venusJan edifices exrelatively concentratedin a central region with a zone of fracturing surroundingthe edifice and flows which are relatively
amined above can be comparedand contrasted with two
limited in extent,Nyx Mons is muchbroader,with relatively
volcanic regions on Earth: Hawaii and the GalapagosIslands. These two volcanic areas differ markedly in their
expansiveflows and large radial chainsof pit craterspossibly
indicatinga more distributedmagmaticsystem. In the analysis
patternsof surfacedeformation.Kilauea volcano,locatedat
the southeastern end of the Hawaiian island chain, exhibits
by McGovern and Solomon [1995], a thick lithosphere is
two large rift zonesextendingeast and southwestfromthe proposedas a precursorto the growth of a large shield volcano on Venus. A thin lithosphere would lead to plainssummit.Rift zones,linearpatterns
of extensionon the scaleof
formingvolcanism,or smallershields. In our scenario,Nyx
the individual edifices,formperpendicularto the directionof
leastcompressive
stress.The southflank of Kilaueais driven Mons, which is stratigraphically older, could representthe
seawardover the downwardly flexed oceanic crust due to
transitionalstate between broad, effusiveplains volcanismto
gravitational
stresses
inherentin its shapeandby intrusions more shield-formingeruptionsrepresentedby Tepev Mons.
of highdensitymagmaalongtherift zones.Stressaccumulates
In addition, horizontal compressivestresseswould indueto repeatedintrusions
alongthe eastrift zone,producing
a creaseas the edifice grows, inhibiting the easy rise to the
net horizontal forcewithin Kilauea's south flank. Opposed surfaceandreleaseof magma[McGovernand Solomon, 1995].
Therefore,for volcanismto occurin a constructas large as Teby only water on its seawardside, seismicand aseismicslip
occurs at the interfacebetween the volcanic pile and sedipev Mons, a pressurized magmareservoir, which we have
mentedold ocean crust (a zone of weakness). The northern
postulatedis responsiblefor this volcano's concentricfracflank of Kilauea is buttressedby Mauna Loa, which prevents tures, would be needed. This pattern of increasingshield
northward displacementof the edificeduring dike intrusions height and steeperflank slopes with decreasingapparentage
[Thurber, 1988; Dieterich, 1988; Ryan, 1988].
is also supportedby the presenceof two very steepvolcanoes
In contrast to the Hawaiian volcanoes, the western Galaon the SE flank of Tepev Mons. The flows fromthese steep
pagos shield volcanoes lack prominent rift zones. The
edificespost-datethoseof TepevandNyx Montes,and arethe
Galapagosislands are dominatedby six largebasalticshield
likely sourceof the rough lava flow which tracesthe flexural
volcanoesbelievedto have formedover a hot spot now under moatnorthof Tepev Mons (Figure 1) [Campbell and Rogers,
Fernandinaand Isabela islands. Galapagosshield volcanoes 1994]. The trends in surfacedeformationand volcano morhavesteepslopes(15ø-35ø),
broadflatsummits
anddeepcal- phometryobservedwithin Bell Regiomay thus ofi•ra view of
deraswhich contribute to a distinct morphology relative to
the long-termhistoryof a Venushighlandrise,from early flood
other shield volcanoes (e.g., Hawaii). The morphology of
eruptions to late-stage centralized shield or dome-forming
volcanism.
these shields results from surfaceprocessessuch as gravitational relaxation, the emplacementof lava flow fields, and
Acknowledgments.We gratefullyac'knowledge
J. Melosh for proresponseto magmachamberstresses [Cullen et al., 1987].
vidingthe TECTON Code, B. Campbellfor insightfuldiscussions
and
Cullenet al. [1987] suggested
that the stressregimeof the Gasoftwaresupport,andP. McGovernandS. Smrekarfor extremelyhelplapagosshieldshinders lateral drainageof magmaandallows
ful reviews. This work was supportedin part by the NASA Planetary
large volumes of melt to solidify as intrusions. Most of the
GeologyandGeophysicsProgram.
eruptions on the Galapagosvolcanoes are from linear or arcuate fissures(circumferentialfissuresaround summitcalderas, References
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[1991] interpret to reflect patterns of underlying dikes froma
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P.G.Rogers,
MRC315, Smithsonian
Institution,
Washington,
DC
20560.(e-mail:[email protected])
M.T.Zuber,Department
of Earth,Atmospheric,
andPlanetary
Sciences,
Massachusetts
Institute
of Technology,
Cambridge,
MA 02139.
(e-mail:[email protected])
(Received
September
24, 1996;revised
February
17,1998;accepted
February19, 1998.)