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

PatriciaG. Rogersl RAND, Washington,D.C.

Maria T. Zuber

Departmentof Earth,Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology,Cambridge

Abstract. In orderto understandthe relationship between volcanic and tectonic processes and the stressstate in the lithosphereof Venus,we analyzedthe stress environments and resulting tectonic featuresassociated with the major volcanic edifices in Bell Regio,using Magellan synthetic aper- tureradar (SAR) imagesand altimeter measurements of topography. The major volcanoes of Bell Regio,Tepev Mons and Nyx Mons,exhibit tectonic characteristics that are unique relative to othervolcanic edifices on Venus. The mostprominent distinction is the lackof largerift zones withinthe overall highland uplift, which characterize many other highland rises on Venus. Also, previousstudies have determined that many large Venus volcanoes exhibit radial tectonic struc- tureson their flanks but generally lack the circumferential graben which surround volcanoes on Earthand Mars. Tepevand Nyx Montesexhibit both the radial tectonic features associated with otherVenusJan edifices and numerous concentric graben. Nyx Monsimplies a moredistributed magmaticsystem by itsbroad shape, radial chains of pit craters,and expansive flow fields, whereasTepev Mons is a morecentralized volcanic system, with limitedassociated long flows. We investigatethe regional stresses associated with Bell Regio and structural features believed to be a consequenceof lithospheric flexure due to volcanicloading, modeling both Nyx Monsand TepevMons as axisymmetric loads with Gaussianmass distributions on an elasticplate. The re- lationshipbetween the tectonic features surrounding Tepev Mons and stresses associated with magmachamber inflation are also examined through finite element analysis. Using topography datato modelthe shape of thevolcano, we determinethat a horizontallyellipsoidal or tabularres- ervoirat a rangeof depthsfrom approximately 20 to 40 km cansatisfy the locations of graben formationobserved in Magellanimages. These results imply a shiftin volcanicstyle within Bell Regiofrom an early phase of broad,low shield formation to latersteep-sided, more centralized edificedevelopment. Such changes are consistent with an increase in thethickness of thelitho- sphereover time.

1. Introduction lithospheric flexure [Comer et al., 1985; McGovern and Solomon, 1992]. Tepev Mons and Nyx Mons (provisional Geophysicalanalyses of the tectonicfeatures associated name) exhibit both the radial tectonicfeatures associated with with the Venus highlandsand major volcanoesprovide impor- other venusJanedifices and numerousdistinct concentric gra- tant insight into the relationship between volcanic and ben [Campbell and Rogers, 1994]. tectonicprocesses and the stressstate of the venusJancrust To understandthe geophysicalevolution of Bell Regio, overtime. Bell Regio is unique relative to manyof the other this studyexamines the structuralfeatures associated with the volcanichighland regionson Venus,such as WesternEistla major volcanoesusing Magellan synthetic apertureradar or Dione Regiones[Senske et al., 1992],in its apparentlack of (SAR) imagesand altimetermeasurements of topography.First, rift zonesdissecting the topographicswell. Most large Venus we analyzethe regionalstress field in Bell Regiobased on the volcanoes also exhibit radial tectonic structures on their style and distributionof tectonicfeatures in the region. Next flanks, and typically lack the circumferentialgraben which we examine structuralfeatures we believe to be a consequence surround volcanoes on Earth and Mars, indicating of lithosphericflexure due to volcanic loading. Analytical models for the formation of similar features on Earth and other planetarysurfaces are examined,and a modelfor the stressre- • Currentlyat Centerfor Earthand Planetary Studies, Smithsonian gime and formation of tectonicstructures within Bell Regio is Institution,Washington, D.C. developed. This analysisof lithosphericflexure and associ- ated deformationmodels the volcano as an axisymmetricload Copyright1998 by the AmericanGeophysical Union. with a Gaussianmass distribution on an elastic plate of vari- Paper Number 98JE00585. able thickness,and incorporatescriteria for tensile and shear 0148-0227/98/98JE-00585 $09.00 failure. Finally, the relationshipbetween the tectonicfeatures

16,841 16,842 ROGERSAND ZUBER: TECTONICEVOLUTION OF BELL REGIO,VENUS

ons

Figure1. MagellanSAR image of BellRegio. Resolution isapproximately 1.2km. Forscale, the large caldera on TepevMons, the prominentcentral edifice in the image,is approximately30 km.

associatedwith the Tepev Mons edifice and stressesassoci- trendS W-NE. The preexistingtessera plateaus are thought to atedwith magmachamber inflation is examinedthrough finite be regionsof thickenedcrust [Bindschadler and Head, 1991] element analysis. andmay have inhibited lateral spreading and the formationof

ß majorrift zonesduring the earlyperiod of highlandformation. 2. Regional Stress Regime If the stressesthat governedthe formationof the SW-NE tessera blocks still existed at the time the volcanic edifices Analysisof regionalstresses provides a frameworkfor un- formed,similar trends in the subsequentvolcanic and tectonic derstanding smaller-scaletectonic features within the featuresmight be observed.However, although some of the highland. As indicatedabove, this regionlacks rift zones; Nyx Mons lava flowstrend SW-NE, little directevidence of however,large-scale tectonic deformationis exhibited by significantSW-NE fracturepatterns exists. This impliesthat tesserablocks which surround the major volcanic edifices the formationof TepevMons andNyx Mons postdatethe re- (Figure 1) [Campbelland Rogers,1994]. Tesseraare gener- gional stressregime which producedthe tesseraor that ally the stratigraphicallyoldest units in this region and stressesin the regionsthat lack fracturesdid not exceedthe preservea recordof periodsof intensetectonic deformation. lithosphericfailure criteria. The fractureswithin someblocks are irregularlyoriented, but Plains regionssurrounding Bell Regio are next in the the prevailingfracture patterns within the tesseraregions stratigraphicsequence after the tesseraand maybe divided ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS 16,843 ß

i:'

Figure2. MagellanSAR image of Nyx Monswith concentricfracture map overlay, centered at approximately 29.9øN,48.5øE. Note the radial chains of pit cratersand concentric fractures surrounding the edificeoutlined in the image.

into at leastthree distinct units: bright plains, dark plains, topographyof Nyx Mons and surroundingregions. This edi- and ridgedplains [Campbell and Rogers,1994]. The ridged fice risesapproximately I km abovethe surroundingapron of plains arethe oldestof theseunits and recordan intensepe- flows; the central bulge and wishbone ridges contain the riod of deformationwith ridgesand grabenoriented SE-NW highestelevations of the featureat approximately6053.5 kin. and SW-NE. The brightand dark plainsare lessdeformed than Slopeson the southernflanks of the edificeare generally 1ø - the ridged plains or the tessera,with deformationprimarily 2ø , gradinginto slopes less than 0.5 ø continuingsouthward, representedby SE-NW trending fractures. Since the lava correspondingto the flow apronthat typically surroundsvol- flowsfrom the majorvolcanic edifices in thisregion embay the canoeson Venus [McGovern and Solomon, 1995]. It is in tessera,superpose most of the plainsunits, and do not contain this gently slopingregion that the mostprominent concentric majordeformation patterns, it is reasonableto concludethat grabenoccur. Detailed structuralmapping of these features the last largevolcanic events in this regionpostdate the re- indicatesthat the innermostconcentric graben occur at a radial gional stressregime which producedthe tesseraand ridged distanceof approximately280 km from the centerof the edifice, plains. These volcanicunits thus recordmore recent localized while the outerradius of thesefeatures lies at approximately stressesin the regionand are the subjectof the next sections. 470 kin. A 500-m change in elevation occursbetween these two radii. The most prominentvolcanic flow fields in the re- 3. Lithospheric Flexure and Nyx Mons gion (the youngest flows of Nyx Mons) emanatefrom these concentricfractures [Campbell and Rogers,1994]. The oldest volcanic edifice within Bell Regio is Nyx Mons, a featurecharacterized by a wishbone pattern of ridges 3.1. Models of Lithospheric Flexure and gentle flank slopes. The inner region contains a central bulge and radial chains of pit craters[Campbell and Rogers, The distributionof fracturesaround large volcanic loads is 1994]. Surroundingthe edificeto the east,south, and north- an important indicator of the stressstate and effectivethick- west are large sets of circumferentialfractures, which are the ness of the elastic lithosphere. Comparing the tectonic main focusof this section (Figure 2). Figure 3 illustrates the featuresformed in responseto large volcanic loads on various 16,844 ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS

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605 I I I I I I I I I I 0 100 800 300 400 DISTANCE(KM) Figure3. Topographicprofile through Nyx Monstrending approximately west to east.Note the higherele- vatedridges and centralregions.

planetary surfaceshas provided importantconstraints on the tribute the absence of topographic moats and concentric relative lithospheric thicknesseson Venus, Earth, Mars. and normalfaulting surroundinglarge Venus volcanoesto mask- the Moon [e.g., Melosh, 1976, 1978; Comeret al., 1985; Hall ing by lava flows fromthe centraledifice. In their model,the et al., 1986; McGovern and Solomon, 1993]. In these analy- stresses in this moat fill are too low to induce failure. ses,graben form concentric to a load as a result of surficial Schultzand Zuber [1994] addressedthe paradoxof the ex- extensional bending stressesassociated with lithospheric istence of an annular zone of strike-slip faults around flexure. If the lithosphereis extremelythick or rigid, then the prominentloads predictedin previousmodels, evidence for stressfield is dominatedby compressionalforces due to the whichis rarelyfound on planetarysurfaces. In their model,the volcano [Artyushkov,1973; Fleitout and Froidevaux,1983]. discrepanciesbetween the observationsand the modelpredic- This analysisof lithosphericflexure and associateddefor- tions result from other considerations significant in fault mationmodels the two major volcanoeswithin Bell Regio as analysis: the neglectof stressmagnitudes and relianceonly axisymmetricloads with Gaussian massdistributions on an on stresstrajectories, and the identificationof first failure. elastic plate, following the analysisof Melosh [1978] of the When rock strength, stressdifferences, stress geometries or mechanicsof lunar masconloading. Deviations of the actual stress state at the onset of failure and load evolution are taken loadfrom axisymmetryare a second-ordereffect [Comer et al., into account,their modelpredicts that concentricnormal faults 1985]. Melosh [1978] analyzed load-relatedstresses and de- and joints (as opposedto strike-slip faults) occur at or near formationand determinedthat the tectonic pattern predicted the surfacesurrounding loads. Rock strengthis significantin by this model, with increasing radial distance from the center determiningthe stress level when the first fracturesoccur. of the load, includeda proximalzone of radial thrust faults fol- Their model,which examinesthe importanceof failure mecha- lowed by strike-slip faults, all surrounded by concentric nisms such as tensile cracking near surface regions and normalfaults. Althoughthe zoneof strike-slip faulting is not varyingvalues of Young's modulus,was experimentallyveri- readily observedsurrounding the lunar mascons,they sug- fied by Williamsand Zuber [1995]. The analysisbelow uses gestedthat someof the ridges surroundinglunar mariamight the generalsolutions described in the Melosh [1978] model be evidenceof strike-slipmotion. Golombek[1985] proposed but also incorporatesthese failure criteria. that the lack of observedstrike-slip faults can be explainedby the fact that fault nucleation occurs at subsurface interfaces, 3.2 Modeling Volcanic Loads though this does not account for the absenceof such features in regionsthat most likely lack discretesubsurface layering. This study analyzesthe volcanicedifices and associated In an analysis of the formationof large volcanic loads on stressesin Bell Regio by modelingthe two major loads as Mars by McGovern and Solomon [ 1993], time-dependentef- Gaussiandistributions on an elastic plate lbllowing Melosh fectson the predictedfailure mechanismsof the growing load [1978]. The generalsolution to the stressfield is given by were considered.They determinedthat the zone of strike-slip Melosh [ 1978] as faulting is not observedbecause it either occurs in a region that had previouslyformed normal faults (the normal faults are Ozz= +PcgZ+ J0(kr)[(A + Cz) coshkz + (B + Dz) sinhkz] (1) reactivated),or that they formand are buried by subsequent Jl(kr)'I deposits. The fracturesconsidered in our analysis occur on Or•=+}CpcgZ +(J0(kr) + kr / [(A+ Cz) cosh kz+ (B + Dz) sinh kz] the youngestvolcanic flows; thereforethis analysisconsiders their formationas a late stageevent and is not concernedwith +_}(J0(kr )+ (l+v) kr J,(kr) )[Dcosh kz+C sinh kz] (2) the growing load. However, our treatmentof the lithosphere as an elasticplate inherentlysupposes that stressesdue to the o0•:+}Cpcgz +J•(kr) kr [(A + Cz)cosh kz + (B+ Dz)sinh kz] growing edificedid not pervasivelyfracture the lithosphere. In amore recentanalysis, McGovern and Solomon [1997] at- +•(vJ0(kr )+ (1 kr+v) j• (kr))[D coshkz +C sinh kz] (3) ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS 16,845

•rz =J•(kr) [(A+ Cz + •) sinhkz+ (B + Dz + -•) cosh kz] (4) o• = Oz•= 0 (5) whereJ{(k0 andJ0(kr) are Bessel functions, (J= is the vertical stress, (Jrr is the radial stress, (J• is the hoop (tangential) stress,(Jrz is the shear stress, On is the normal stress, r is the radiusfrom the centerof the load,z is the depth in the plate, k -5O is the wave number, and v is Poisson'sratio. Because the total stressis soughtin this analysis,a term for the confining pres- sure(•pcgz)is addedto the abovestresses where • is the ratio of horizontal to vertical overburden [Banerdt, 1988]. { I The vertical stressat the surface, and the lack of shear stress at -100 the surfac.e or base are indicated by the following boundary 0 1 2 3 conditions:

o= (z = 0, r) = bJ0(kr) (6) Figure 4. Plot of elastic surfacestresses resulting from the Nyx Monsload with a lithosphericthickness of 50 km. Nega- tive stresses are compressional and positive stresses are (Jrz(Z = 0, r) = (Jrz(Z = H, r) = o= (z = H, r) = 0 (7) extensional.The bar representsthe zoneof fracturingobserved in the imagesand correspondswell to the R/A rangeof 1.5-2.7 In this analysis,the verticalload is representedby resultingfrom the model. w= pmgT (8) wherePm is equalto its density,T is its height at r = 0, and g 3.3. Nyx Mons Modeling Results is gravitationalacceleration. According to Anderson[1951], concentricnormal faulting will occurin the region definedby In this analysis,an analytic modelwas usedto determine positive(Jrr and o** andmaximum (Jrr. the stressfield and predict the spatial distribution of faulting In order to distinguish the likely mechanismfor initial on the lithospheresurrounding Nyx Mons. The predictions lithosphericfailure, we have incorporatedinto this formalism were then comparedto the observed fault distributions, the followingrock failure criteria: a Griffithcriterion for ten- thereby constrainingthe propertiesof the lithospherethat sile failure and the Byericecriterion for shearfailure [Schultz supportsthe volcano.Fifteen cases, with varying lithospheric and Zuber,1994]. Specifically,applying stress to a fractured thicknessand Young's modulus, were consideredin this rock will causefrictional sliding along the fracturesprior to analysisofNyx Mons to determinewhich mostclosely corre- reachingthe level requiredto causebrittle failureof the rock spondsto the observedfracture patterns. The fixedparameters mass.This relationship,referred to as Byerlee'slaw, is given are given in Table 1. by [Brace and Kohlstedt,1980] In the first seven cases, the effects of varying the lithospheric thickness between 30 and 70 km were examined. The diameter of the feature was defined to be the distance at 'r = 0.85 o, 3 < o, < 200 MPa x = 60 -t- 10 + 0.6 o,, o,,> 200 Mpa (9) which the topographyof the edificemerged with the surround- ing plateau. Since Nyx Mons is an irregularly shaped The Griffith criteria for brittle failure states that fracture occurs "wishbone"feature, minimum and maximumvalues for the load at a given stressaccording to extentwere also examined. The maximumdiameter, correspond- ing to the feature'sN-S extent, is 350 km, and the minimum o, = (2AE/ xc)"2. (10) diameter,corresponding to the edifice's E-W extent and an idealized circular shapefor the feature,is 270 km. These di- where2c is the length of the pre-existingcrack, A is the sur- ameters correspond to halfwidths of 175 and 135 km, faceenergy, E is the Young's modulus,and o, is the applied respectively.The deviationof the load froma Gaussianshape tensilestress [Price and Cosgrove,1990]. is not significant. The next casesexamined the effectsof varying Young's Table 1. FixedParameters Used in Modelin•N7x Mons modulus.In-situ measurements of elasticmoduli can be up to an order of magnitude lower than laboratory measurements Parameter Description Value [Cullen et al., 1987], so we examinedthe effectof reducing -2 Young'smodulus by an orderof magnitude (from 1011 to 10rø g gravitationalacceleration 8.6 m s Pa) while varying the load halfwidth and the lithospheric -3 Pm loaddensity 3000kg m thickness. Next we examined the effect of an increase in Young'smodulus (to 1012Pa). This situation may represent T load height 1 km the effectiveYoung's modulusof a rock containing closed horizontal/vertical overburden 0.5 cracks[Jaeger and Cook, 1979] although it's uncertain that this effectwould increaseE by an order of magnitude. We Poisson's ratio 0.33 considerthis value to be an upperlimit on E. The effectof increasing the lithospheric thickness shifts Pc lithospheredensity 3300kg m '3 the rangeof concentricnormal faulting to slightly higher val- 16,846 ROGERSAND ZUBER: TECTONICEVOLUTION OF BELL REGIO,VENUS

..

...... ,...... •,• ::&• .: •:• •:-.. -.: •:•:•.. '-'•,•...... :• :•?• ...... •:•:•.• :-4•'"'•:•::•.•:.•.••:...... •½•;, • .... ••...... ,•:••...... •,•<.-•...•..:....•.•:..•:• ...... &•-::•...... •::•:•:-•::•• ß .•,:• •:.-•:•.•..•.:.:.•...... ••½• ,.•• ...... Figur••. MagellanSAR image of TcpcvMons with fracturemap overlay. Note the prominentfiattums con- centrioto thevolcano. For scale, the largest caldera on Tcpcv Mons is approximately30 km in diameter. uesof R/A (normalizedradial position, where A is the Monsdiscussed above [Campbell and Rogers, 1994]. It rises halfwidthofthe load), while decreasing thesize of the load approximately:5km above the surrounding plains and is char- causesa small increase in themaximum6,and the range of acterizedby relativelysteep slopes (20 ø- 40ø) near the summit R/Afor graben formation. Decreasing Young's modulus de- region.The steepest slopes occur along the eastern flank of creases6rr and the R/A range for graben formation,while the volcano(Figure 5). Two large(11 and 31 km diameter) increasingE has the oppositeeffect. calderassuperpose the summitregion. The northernflank is The innerand outer radii for the concentricfaults (280 and characterizedby prominentfractures and coalescedchains of 470 km) correspondto an R/A rangeof approximately2.0 - 3.5 pit cratersconcentrically distributed around the mainpeak ifA = 135km and an R/A range of 1.6-2.7 ifA = 175km. Fig- andcalderas. In thissection we considerthe originof tectonic ure 4 illustratesthe resultsof the bestsolution that produces featureson Tepev Mons, beginning with a test of the concentricnormal faulting in the range of 1.5 -2.7. Total lithosphericflexure model used above and concluding with a stress(MPa)is plotted againstR/A. Individual points are comparisonbetween terrestrial volcanic deformation patterns plottedon the O'rrcurve. Theseresults indicate that for the pa- and the Venus observations. rametersused in this analysis,a lithosphericthickness of 50 km,E-'10 •, andload halfwidth of 175km best describes the 4.1. Modelingof Tepev Mons ConcentricFractures conditionsat Nyx Mons at the time of the formationof the con- centric grab.en. In preliminaryanalyses by Solomonet al. [1992] it was postulatedthat the concentricgraben north of TepevMons 4. Edifice Stressesand Tepev Mons mayhave resulted from lithospheric flexure due to the volcanic load. To testthis hypothesis,an analysissimilar to the one TepevMons is a prominentvolcanic shield within Bell describedabove for the formation of theconcentric graben sur- Regio thought to be youngerthan the large volcanoNyx roundingNyx Monswas performed for the TepevMons load. ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS 16,847

ing an accuratesurface response, which could result in spuriousrange measurements. Hence the minimum elevation of this potentialmoat is difficultto constrain.Assuming the flow is containedwithin the lowest region, the approximatecenter of the moatwould correspondto an R/A valueof 1.8, almostat the centerof the rangeofmaximumextension predicted in our "•-200 modelsusing a lithosphericthickness of 30 - 50 km. This re- sult is supportedby recent studies of gravity-topography relationshipswhich yield elasticthickness estimates for this m -400 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 -600 grabenwhich occuron the steep northern flanks, close to the 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 elasticsurface stresses resulting from model- Mars [Comer et al., 1985]. Comer et al. studied the tectonic ing the TepevMons load with a lithosphericthickness of 30 featuresassociated with large volcanic loads on Mars and de- km. The bar representsthe zoneof fracturingobserved in the termined that the concentric graben on Pavonis and Arsia images.Unlike the Nyx Mons case,this region doesnot cor- which lie closeto the centerof the load may be concentricex- respondto the R/A rangeof 1.5-2.5resulting from the model. tensionalfractures formed during the evolution of the caldera rim as magma was withdrawn or solidified,producing an annu- lar ring of faults. Another causemay have been topographic Five caseswere examinedin which the lithosphericthickness stressesand gravitationaIspreading, which resultedin exten- varied 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 concentricgraben may also reflect zones Structuralmapping of concentricgraben around Tepev of weakness inherited from flexural stressesduring an early Mons indicates that these features occur at inner and outer ra- stageof volcanogrowth. In the next section we examinesome dial distancesof 65 and90 km, respectively.With a halfwidth of thesemechanisms in more detail and discusspossible terres- for theload of 80 km basedon topographicprofiles across the trial analogsto understandif stresseswithin the Tepev Mons edifice(Figure 7), thiscorresponds to R/A valuesranging from edifice may have produced the observed circumferentialfrac- 0.8 to 1.1. However, resultsof the modelindicate that maxi- tures. mum extensionalstress occurs at R/A of 1.5 to 2.5. This region correspondsto the approximatelocation of a possibletopo- 4.2. Models of Edifice Deformation graphicmoat north of TepevMons (R/A = 1.8)which has been discussedby severalauthors [Janle et al., 1988;Solomon and As discussedabove, the free surfaceof a volcanic edifice Head, 1990; McGovernand Solomon,1992; Campbelland may undergotectonic deformation as a resultof severalmecha- Rogers,1994] (Figure 8). Theeffective elastic thickness based nisms: inflation and doming due to subsurfaceinjection of on the location of this volcanically floodedmoat yielded a magma,deflation associated with calderacollapse, and gravita- preliminaryvalue of approximately10 km [McGovernand tionalrelaxation which may leadto slumpingof materialalong Solomon,1992]. However,the lavaflow whichfills this moat the flanks. The mechanicalbehavior and overall morphology hasa high surfaceroughness [Campbell and Rogers,1994] of a volcanicshield generally results from the interactionof all whichmay have prevented the Magellan altimeter from acquit- theseprocesses. However, gravitational collapse and slump-

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6052 ,,,l[,,,l,,,,I,,,,I 0 50 100 150 200 250 300 DISTANCE Figure 7. Topographicprofile through Tepev Mons trendingapproximately NW to SE. The two peakscen- teredat approximately200 and 250 km representsmall, steep volcanoes on the SE flanksof TepevMons. 16,848 ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS

Figure 8. MagellanSAR imageof lava flow northof TepevMons, thought to be confinedwithin a topo- graphicmoat. TepevMons is off the imageto the southeast.

ing of the flanks may be less significantfor venusianedifices examinedthe tectonicresponses associated with the evolution due to their relatively gentle profilesand limited vertical ex- of the calderaon Olympus Mons, Mars. They used a linear tent [Head and Wilson, 1992]. Thereforethe major forces elastic finite elementmodel to determinethe range of magma affectingthe overallmorphology of Venusvolcanoes may be chambergeometries and pressuresthat could producethe ob- relatedto stressesassociated with the evolution of a magma servedtectonic pattern. Specifically,the ridges and graben reservoirand internaldike propagation. Severalauthors have which formedfrom subsidenceof the calderafloor duringdefla- examined the surface deformation associated with stresses that tion of the magmachamber were usedto provideconstraints on arisefrom the inflation and deflationof a subsurfacemagma the dimensions,depth and pressuresassociated with the sub- chamber.A periodof upliftand swelling of the edificemay oc- surfacereservoir. They determinedthat the surfacestress cur due to the inflation of such a magmachamber and the distribution is relatively insensitive to the details of the associatedinjection of dikes and sills. Deflation,which may shapeof the magmachamber and is very sensitiveto its depth. leadto /•alderacollapse, results as rift eruptions occur along the flanksor as intrusionsoccur into new regionswithin the volcano [Dieterich and Decker, 1975; Marsh, 1984]. 4.3. Numerical Modeling of Edifice Deformation In earlymodels of magmachamber detbrmation the chamber was representedby a point sourcein an elastichalf space,or Inthis section we examine whether' the concentric graben by magmareservoirs that were spherical and smallin compari- observedon the flanksof TepevMons couldbe dueto stresses sonto their depth [Anderson,1935; Mogi, 1958]. However, within the edifice. To understand the nature of the stress state thesepoint sourcemodels applied accuratelyonly to stresses of the edifice,we constructedan axisymmetricfinite element at largedistances from the chamber.Later modelsrepresented model to calculate the elastic stresses within the volcano and the magmareservoir as a finite sourceand were able to more ac- to examinethe relationshipbetween these stresses and the ob- curatelydetermine near field (shallow source)stresses [Ryan, served tectonic features. Following a model previously 1988]. Dieterichand Decker [1975] determinedthat the early employed in the study of caldera subsidence[Zuber and analytical approachespredicted generally similar surfacede- Mouginis-Mark, 1992] we analyzed the stressesassociated formation,regardless of the actual model used and that these with variations in a magmareservoir. However, while the modelsdid not predict the ratio of horizontal to vertical sur- Zuber and Mouginis-Mark[1992] analysismodeled the defla- facemovements observed near summitregions. They were tion of the magmachamber and the resultingcaldera structures, amongthe first to usea finite elementmethod, enabling them to this modelis concernedwith the inflation of the magmacham- model summitdeformations and rift zone intrusionsusing a va- ber and the associated stresses on the flanks of the volcano. riety of shapesand depthsfor the magmareservoir. Dieterich Deflation and resultingdeformation within the Tepev Mons and Decker [1975] also observeda relationshipbetween flank calderasmay have also occurredduring its history, however eruptions and the systematicinflation and deflation of the structureswithin the calderasof Tepev Mons can not be re- summitreservoir; flank eruptions occur as magmais trans- solved, most likely due to the presenceof a fine grained portedvertically to a shallowstorage zone beneaththe summit surficial deposit [Campbell and Rogers, 1994]. We used the followed by lateral transportof magmafrom the summitreser- finite elementprogram TECTON [Melosh and RaeJ3ky,1981] voir to the flanks by dikes. Zuber and Mouginis-Mark[1992] to developa linear elastic model of the stressesand displace- ROGERSAND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS 16,849

Table 2. ParametersUsed in Finite ElementModeling of ofRx = Ry = 16km. Theleft boundary is a symmetryaxis Tepev Mons along which horizontaldisplacements vanish. At the bottom

Parameter Value boundaryof the grid, at depthsmuch larger than the level of the chamber,vertical displacements vanish, while at largera- .3 Density 3000kg m c•ialdistances (right boundary) both horizontal and vertical displacementsvanish. Figure 10 illustrates the surface Young'sModulus (within chamber) 109Pa stressesresulting from this analysis. Young'sModulus (outside chamber) 10• Pa The resulting variations in the stressfield were examined and the modelresults were comparedwith our observations Poisson's ratio 0.33 fromMagellan images.Specifically, the innermostlocation of predictedconcentric graben formation is definedby the point at which•Jrr crosses from negative (compression) to positive mentsassociated with the edifice and underlying crust and (extension)in the finite elementresults, following methods mantle. used in previous studies [Comer et al., 1979; Zuber and Mouginis-Mark, 1992]. We also considereda case with no In orderto improvethe accuracyof the finite elementrepre- magmachamber to analyzestresses due solely to the volcano, sentation of the volcano, we extracted a representative and found relativelysmall load-inducedsurface stresses in the topographicprofile for Tepev Mons from the Magellan global- vicinityof the summitthat were easily overwhelmed by the ef- average(5.4-kin resolution)data set. The modelgrid was then fectsof evena smallmagma chamber. However, this analysis constructedto conformto this profile shapealong the upper does not account for edifice stressesfrom other sourcessuch as surface.Given that Tepev Mons has significant changes in lithosphericflexure, which would tend to add horizontal com- slope along its flanks, this methodpermitted a more realistic pression in the upper lithosphereand may inhibit the assessmentof the role of local topography on the final stress transmissionof extensionalstresses to the surface[McGovern field. The profile we used for the Tepev Mons volcano was and Solomon,1993]. Thusthe depthof burialfor any given takenfrom the approximatecenter of the larger easterncaldera magmachamber must be shallowerto producethe observed (29.6øN, 45.6øE)and extendedto the northwest. From the grabenthan for a scenariowithout flexural stresses. Likewise, start of this profile, the zone of concentric graben formation the observabledistribution of fracturesmay have been altered begins at approximately40 km and extendsto approximately due to burial by superposingflows [McGovernand Solomon, 115 km. Any additionalgraben at greaterdistances may have 1997]. Specifically,the burial of the innermostfractures near been obscuredby later lava flows. the summitregion would increasethe horizontal radius of the The magmareservoir was modeledas a simple chamberin which inflation occurs as a distribution of outward directed ch•crossover, and biasthe predictionof the magmachamber ra- diusto largervalues. Burial of innermostgraben would also radial forcesat specifiednodes, with the force magnitudeequal 9 2 biasthe depthprediction to largervalues, since graben forma- to 1 x 10 kg m s- (1000 MPa). Varying the forcemagnitude tion movesoutward with increasingdepth to the chamber. affectedthe magnitude, but not the distribution, of surface Neglecting theseadditional potential factorsthus biasesour stresses.The model allows analysisof varyingmagma chamber predictionstoward larger chamberdepths, so our analysis depth,size, and shape,as well as the density, Poisson's ratio, placesan upperbound on the depthof burial. and Young's modulusof the magmaand country rock. The pa- rametersmost typically usedare listed in Table 2. 4.4 Results Figure 9 illustrates an exampleof the axisymmetricfinite elementgrid used in this analysiscontaining 8238 nodes and In orderto constrainthe likely magmachamber geometry, 8181 elements,with a grid size of 100 km by 300 km. This we variedalternately the depth,size, and shapeof the model casemodels a spherical magmachamber which has 107 ele- reservoir. Numerous chambergeometries were examined ments,lies at a center depth, D, of 30 km, and has dimensions (approximately90 totalvariations), from a spheroidwith vary-

I I I I

-2O

-4O

-60

-8O

-10o 0 50 10o 150 2o0 250 300 R (km) Figure9. An axisymmetricfinite element grid used in theanalysis of TepevMons, containing 8238 nodes and 8181elements, with a gridsize of 100km by 300km. The magma chamber in thisexample lies at a centerdepth (D) of 30 km,and has dimensions of Rx = 16km (horizontal radius), and Ry = 16km (verticalradius). 16,850 ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS

ing radii to ellipsoids with varying horizontal and vertical axes. Table 3 illustrates results from several of these models. 2xlOs • Asthe vertical dimension (Ry) of the chamber increases rela- tive to the horizontal dimension (Rx) (a vertically elongate ellipsoid),or the depthto the chamberbecomes shallower, the stresses become more concentrated towards the center of the load and the zone of extension(graben formation) moves in- ward. It is obvious from Table 3 that neither spherical chambersnor ellipsoidal magmabodies comparablein size to the summit calderacan producethe requiredstress field within a range of reasonabledepths. The 40-km crossoverpoint can be accommodatedmost eas- ily by a tabular magma chamber 44-52 km in radius, -4x10S• • 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) depth are illustratedin Table 3. The thickness of the chamber Figure 10. Elasticsurface stresses resulting from the inflation has less of an impact on the location of the crossoverpoint of a sphericalmagma chamber beneath Tepev Mons, illustrated than the width and depth of burial. The small changes in in Figure 9. crossoverpoint with changing thickness reflect the varying

Table 3. Variationsin o• CrossoverPoint (From Compressionalto ExtensionalRegime) With Changes in D (Depth to Center of Chamber),Rx (Horizontal Radius),and Ry (Vertical Radius)

! r Dcenter,km Rx, km Ry, km Crossover{Jrr. km

SphericalQhambers: -15 16 16 16

-30 16 16 22

-50 16 16 26

EllipsoidalChambers:

-20 10 20 16

-50 10 20 19

-40 20 30 27

-50 20 30 3l

Tabular Chambers:

Shallow:

-18 45 4 35

-18 52 4 40

- ! 8 60 4 46

-18 66 4 49

Intermediate:

-28 56 4 45

-28 48 4 40

Deep:

-36 48 4 42

-36 44 4 40

SensitivitytoThickness:

-22 62 2 46

-22 62 4 48

-22 62 6 47

-22 62 8 45 ROGERSAND ZUBER: TECTONICEVOLUTION OF 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 Tepev Mons edifice stresseswith a magmacham- ber at an intermediatedepth. The magmachamber, representing a sill-like intrusion,lies at a centerdepth (D) of 28 km, andhas dimensions of Rx= 48, andRy = 4.

distanceto the surfacefrom the upperboundary of the chamber. 5. Discussion and Conclusions The width of the reservoir is inversely correlatedwith the depth,such that morenarrow "sills" may producethe required In thisstudy, the nature of thestress state and lithospheric stressfield as the centerlinedepth increases.Note, however, structureof Bell Regiohave been examined. The style and dis- that the surfacestress magnitude declines with increased tribution of tectonic features associated with the volcanic chamberdepth, so a shallow chambermay be more likely to loadsin Bell Regiowere analyzed in an attemptto understand create observable fractures. the regionalstresses which producedthese tbatures. A com- Our resultsindicate that the circumt•rrentialgraben occur- plexhistory of stressregimes is illustratedthrough the vari- ring on the flanksof Tepev Mons couldbe the result of edifice ous structural features associated with several different stressescaused by 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 trendingtessera blocks, provide constraints on the earlyre- intermediatechamber depth (28 km) with a horizontalradius of gional stresstrajectories. These regional stressesdo not 48 km and a vertical radius of 4 km. This sill-like intrusion appearto haveaffected the emplacementof the largevolcanic may possibly have fed smaller magmachambers at shallower edifices,Tepev Mons and Nyx Mons. depths. However, without better resolution of the structure To quantifythe stressregime in Bell Regiowe haveap- within the calderas,further analysis is not possible. Our plied analytical modelsfor the formationof similar structures analysisof Tepev Mons shows that the observedspatial dis- on Earth and other planetarysurfaces. We have identified tribution ofgraben may be attributedto stressescaused by structuralpatterns that we believeto be a consequenceof magma chamber inflation, and therefore no inference of lithosphericflexure due to volcanicloading and otherfeatures lithosphericthickness can be madefrom these grabenloca- thatmay be associatedwith inflationof a magmareservoir be- tions. However, our earlier analyticalmodel of Tepev Mons neathTepev Mons. Concentricfractures surrounding Nyx flexurebased on the possiblelocation of a topographicmoat Monswere mapped and their distributions examined. By mod- may provide constraintson the thickness of the elastic litho- elingNyx Monsas a surfaceload on an elasticplate, we used sphere. the concentricgraben to provide a constrainton the effective elasticthickness at the timethe volcanowas emplaced. Our analysisindicates that, for an assumedYoung's modulus for theplate of 10IIPa anda loaddiameter ofapproximately 350 km, a lithosphericthickness of 50 km best describesthe condi- tions at Nyx Mons at the time the concentricgraben were formed.This predicted elastic thickness is in goodagreement with Magellangravity analyses.Smrekar [1994] indicates thatthe effective elastic thickness at shortwavelengths is 30 _ 5 km, and 50 _ 5 at long wavelengths,where the 30 km valuereflects a thinnedelastic plate at the timethe volcanoes wereemplaced and the 50 km value representspresent day -lOS •_'• __ elastic thicknesses. It should be noted that Smrekarwas ana- lyzing the overallhighland swell, whereasthis analysis modelsthe individualvolcanic loads in the region. -2xlO s A concentriczone of weakness,represented by grabenand 0 20 40 60 80 100 1•0 coalescedchains of pit craters,surrounding Tepev Mons was 1t (krn) alsoexamined. These features, previously identified as possi- Figure 12. Elasticsurface stresses resulting from the inflation bly due to lithosphericflexure [Solomon et al., 1992], occur of a horizontallyelongate (sill-like) magmachamber beneath on the steepflanks of the volcano.Our analysisindicates that TepevMons, illustrated in Figure 11. The bar representsthe they most likely formedas a result of extensionalstresses as- regionof fracturingobserved in the Magellanimages. sociatedwith inflation and domingduring magmachamber 16,852 ROGERS AND ZUBER: TECTONIC EVOLUTION OF BELL REGIO, VENUS inflation. Reservoir-inducedstresses were analyzedusing a fi- appearsto have occurredat both Tepev Mons (evidentfrom the nite elementmodel, and our results indicate that inflation of a topographicmoat) and Nyx Mons (resulting in the concentric largesheet-like magma reservoir, represented by a horizontal graben). However, Tepev Mons appearsto have experienced ellipsoid in our model,most likely generatedthe zoneof ex- additional deformation due to the stresses associated with tensionand fracturesobserved in Magellan images. magmachamber inflation. Whereas the Tepev Mons load is The tectonic deformation within the venusJan edifices ex- relatively concentratedin a central region with a zone of frac- amined above can be comparedand contrasted with two turing surroundingthe edifice and flows which are relatively volcanic regions on Earth: Hawaii and the GalapagosIs- limited in extent,Nyx Mons is muchbroader, with relatively lands. These two volcanic areas differ markedly in their expansiveflows and large radial chainsof pit craterspossibly patternsof surfacedeformation. Kilauea volcano,located at indicatinga more distributedmagmatic system. In the analysis the southeastern end of the Hawaiian island chain, exhibits by McGovern and Solomon [1995], a thick lithosphere is two large rift zonesextending east and southwestfrom the proposedas a precursorto the growth of a large shield vol- summit. Rift zones,linear patterns of extensionon the scaleof cano on Venus. A thin lithosphere would lead to plains- the individual edifices,form perpendicular to the directionof formingvolcanism, or smaller shields. In our scenario,Nyx leastcompressive stress. The southflank of Kilauea is driven Mons, which is stratigraphically older, could representthe seaward over the downwardly flexed oceanic crust due to transitionalstate between broad, effusiveplains volcanismto gravitationalstresses inherent in its shapeand by intrusions more shield-formingeruptions represented by Tepev Mons. of highdensity magma along the rift zones.Stress accumulates In addition, horizontal compressivestresses would in- due to repeatedintrusions along the eastrift zone,producing a creaseas the edifice grows, inhibiting the easy rise to the net horizontal force within Kilauea's south flank. Opposed surfaceand release of magma[McGovern and Solomon, 1995]. by only water on its seawardside, seismicand aseismicslip Therefore,for volcanismto occurin a constructas large as Te- occurs at the interface between the volcanic pile and sedi- pev Mons, a pressurized magmareservoir, which we have mentedold ocean crust (a zone of weakness). The northern postulated is responsiblefor this volcano's concentricfrac- flank of Kilauea is buttressedby Mauna Loa, which prevents tures, would be needed. This pattern of increasing shield northward displacementof the edifice during dike intrusions height and steeperflank slopes with decreasingapparent age [Thurber, 1988; Dieterich, 1988; Ryan, 1988]. is also supportedby the presenceof two very steep volcanoes In contrast to the Hawaiian volcanoes, the western Gala- on the SE flank of Tepev Mons. The flows from these steep pagos shield volcanoes lack prominent rift zones. The edificespost-date those of Tepev andNyx Montes,and are the Galapagosislands are dominatedby six large basalticshield likely sourceof the rough lava flow which tracesthe flexural volcanoesbelieved to have formedover a hot spot now under moatnorth of Tepev Mons (Figure 1) [Campbell and Rogers, Fernandinaand Isabela islands. Galapagosshield volcanoes 1994]. The trends in surfacedeformation and volcano mor- havesteep slopes (15ø-35ø), broad flat summitsand deep cal- phometryobserved within Bell Regio may thus ofi•ra view of deras which contribute to a distinct morphology relative to the long-termhistory of a Venushighland rise, from early flood other shield volcanoes (e.g., Hawaii). The morphology of eruptions to late-stage centralized shield or dome-forming these shields results from surfaceprocesses such as gravita- volcanism. tional relaxation, the emplacementof lava flow fields, and responseto magmachamber stresses [Cullen et al., 1987]. Acknowledgments.We gratefullyac'knowledge J. Melosh for pro- Cullenet al. [1987] suggestedthat the stressregime of the Ga- vidingthe TECTON Code, B. Campbellfor insightfuldiscussions and softwaresupport, and P. McGovernand S. Smrekarfor extremelyhelp- lapagosshields hinders 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 Geologyand GeophysicsProgram. eruptions on the Galapagosvolcanoes are from linear or ar- cuate fissures(circumferential fissures around summit calderas, References radial fissureslower on flanks) which Chadwick and Howard Anderson,E. M., The dynamicsof the formationof cone-sheets,ring [1991] interpret to reflect patterns of underlying dikes froma dykes,and cauldronsubsidence, Proc. R. Soc.Edinburgh, 56, 128- subsurfacemagma chamber. The circumferentialand radial dik- 157, 1935. ing has been attributedto episodesof broad volcano inflation Anderson,E. M., The Dynamicsof Faulting,206 pp., Oliver and Boyd, and subsidence[Chadwick and Howard, 1991; Sirekin, 1972] London, 1951. where dikes are eraplacedperpendicular to the least compres- Artyushkov,E. V., Stressesin the lithospherecaused by crustalthickness inhomogeneities,d. Geophys.Res., 78, 7675-7708,1973. sive stresses. Banerdt,W. B., Globaldynamic stress modeling on Venus,Lunar Planet. Tepev Mons appearsmorphologically similar to the Gala- Sci. XI• 25-26, 1988. pagos volcanoes (steep flanks, broad summits,large calderas, Bindschadler,D. L., and J. W. Head, Tessera terrain, Venus: Charac- ßand lack of rift zone deformation). Basedon these discussions, terizationand models tbr originand evolution,d. Geophys.Res., 96, 5889-5907, 1991. the Galapagos islands may be the better terrestrial analog to Borgia, A., J. Burr, W. Montero, L. D. Morales and G. E. Alvarado, Tepev Mons than typical Hawaiian volcanoes. As discussed Faultpropagation/bids induced by gravitational/•ilure and slumping above, there are no large regions of thru-going extensionor ot'theCentral Costa Rica volcanic range: Implicationstbr largeter- rifting at Bell Regio, nor is thereany indicationof the more lo- restrialand Martian volcanicedifices, d. Geophys.Res., 95, 14357- 14382, 1990. calized rifting that is evident on Kilauea. 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