JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 97, NO. El0, PAGES 16,069-16,083, OCTOBER 25, 1992

Flexural Ridges, Trenches,and Outer RisesAround Coronaeon Venus

DAVID T. SANDWELL

GeologicalResearch Division, Scripps Institution of Oceanography,Za Jol• California

GERALD SCHUBERT

Departmentof Earthand SpaceSciences, Institute of Geophysicsand Planetary Physics, University of California,Los Angeles

High-resolutionaltimetry collected by the Magellan spacecraftreveals trench and outerrise topographic signaturesaround major coronae(e.g. Eithinoha,Heng-O, Artemis, and Latona). In addition,Magellan syntheticaperature radar images show circumferential fractures in areaswhere the platesare curveddownward. Both observationssuggest that the lithospherearound coronae is flexed downwardby the weight of the overridingcoronal rim or by the negativebuoyancy of subductedlithosphere. We havemodelled the trenchand outerrise topography as a thin elasticplate subjected to a line load andbending moment beneath the coronarim. The approachwas testedat northernFreyja Montes where the bestfit elasticthickness is 18 km, in agreement with previouslypublished results. The elasticthicknesses determined by modellingnumerous profiles at Eithinoha,Heng-O, Artemis,and Latonaare 15, 40, 37, and 35 km, respectively.At Eithinoha,Artemis, and Latona where the platesappear to be yielding, the maximumbending moments and elasticthicknesses are similar to thosefound at the Middle America,Mariana, and Aleutiantrenches on Earth, respectively.Estimates of effectiveelastic thickness and plate curvature are usedwith a yield strengthenvelope model of the lithosphere to estimatelithospheric temperature gradients. At Heng-O,Artemis, and Latona, temperature gradients are less than 10 K/km, which correspondto conductiveheat losses of lessthan one half the expectedaverage planetary value. We proposetwo scenariosfor the creationof the ridge,trench, and outerrise topography:differential thermalsubsidence and lithospheric subduction. The topographyof Heng-O is well matchedby the differential thermal subsidencemodel. However, at Artemis and Latona the amplitudesof the trench and outer rise signaturesare a factorof 5 too largeto be explainedby thermalsubsidence alone. In thesecases we favor the lithosphericsubduction model wherein the lithosphere outboard of thecorona perimeter subducts (rolls back) and the corona diameter increases.

INTRODUCTION severalprominent coronae which display clear trench and outer rise The lithospheresof Earth and Mars are known to have elastic signatures.Using a thin elasticplate flexure model to characterize upper layers that undergoflexural deformation[Walcott, 1970; the shape of the trench and outer rise, we find that Venusian Comeret al., 1985]. These flexures are commonlycaused by flexures are similar in both amplitude and wavelength to largevolcanic loads on the lithospherewhich producea moat and lithospheric flexures seaward of subduction zones on Earth. outer rise. On Earth, flexures are also associatedwith subduction Moreover, we show that circumferential fractures are concentrated zones; the cold subductedplate appliesa bendingmoment to the in areas where the topographyis curved downward in good not yet subductedlithosphere creating a trench and outer rise agreementwith the high tensile stresspredicted by the flexure [Caldwellet al., 1976]. Despiteits high surfacetemperature (730 models. Finally, we presenttwo scenariosfor the developmentof K), Venusmay alsopossess an upperelastic lithospheric layer that the ridge-trench-outerrise flexuraltopography and circumferential could deform flexurally. A possible example of flexural fracturesof coronae. The first scenarioinvolves reheating and deformationon Venus occurs on the North Polar Plains just thermalsubsidence of the lithosphereinterior to the coronawhile northwardof Freyja Monteswhere the topographyis reminiscent the first scenarioinvolves expansion of the coronainterior and roll of the outerrise andforedeep of a plate underthrustinga terrestrial backof the subductinglithosphere exterior to the corona. mountainrange [Solomon and Head, 1990]. The high-resolution radar images and topographicdata of Venus obtained by the FLEXURAL CHARAUFERISTICS OF CORONAE orbitingMagellan spacecrafthave revealed numerous additional examples of possible flexural deformation of the Venusian The peripheriesof manycoronae consist of a relativelynarrow lithosphere.Prominent among these are the downwarpedtrenches annularridge surroundedby a trench or moat [Barsukovet al., andouter rises around some coronae as well as interiorslopes of 1986; Basilevskyet al., 1986; Pronin and Stofan,1990; Stofan large calderalike structures [Sandwell and Schubert, 1991; and Head, 1990;Solomon eta/., 1991;Squyres et al., this issue]. Solomonet al., 1991;Squyres et al., this issue]. Circumferentiallyoriented fractures (indicative of radialextension) In this paper we focus on flexural signaturesoutboard of are oftenfound within the trenchand on its exteriorwall [Squyres coronalrims with the purposeof inferring the thicknessof the et al., this issue]. Two prominentexamples of this ridge/trench Venusianelastic lithosphere.We presenttopographic profiles signatureare Eithinoha and the northernperimeter of Heng-O [Pettengillet al., 1991;Ford andPettengill, this issue] outboard of (Plate 1, top andbottom, respectively). In theseimages, discrete color changesrepresent changes in elevation (200 m per color change)and variations in graylevel represent the intensity of radar Copyright1992 by the AmedcanGeophysical Union. backscatter. This combination enables one to correlate the Papernumber 92JE01274. fractures,apparent in the syntheticaperture radar (SAR) images, 0148-0227/92/92JE-01274505.00 with the elevation,slope, and curvatureof the surface.

16,069 Plate1. Superposition ofSAR image (brightness variations) andtopography (colorchanges each200 m). Eithinoha (top) is a 400- km-diameterplateau surrounded byridges and deep trenches. Heng-O isa 1200-km-diametercorona;its northern perimeter (bottom)consists ofa ridge,a trench,and an outer rise; circumferential fractures occur in the trench. Dashed line marks locations of profilesin Figure1. SANDWELLAND SCHUBERT: RIDGES, TRENCHES, AND OUTER RISES AROUND CORONAE ON VENUS 16,071

3.0- 2.5 2. O Eithinoha

101.5 0.5 0.0

•-0.5 i i -60 -59 -58 -5F -56 -55 -54 -53 -52

3.0 - 2.5 2.0 Heng-O 1.5 1 0

0.0 J -0.5 0.5I • I I • I I •_ 4 5 6 7 8 9 10 11 12 Latitude (deg)

Fig. 1. Topographicprofiles across Eithinoha (top) and northern Heng-O (bottom). Track locations are shown in Plate1. The ridge,treaeh, aad outer rise topography at northeraHeng-O is characteristicof lithospheric flexure under a lineload. Theheavy line above each treaeh marks the loeatioa of the circumferential fractures.

Eithinoha(Plate 1, top), locatedat 57øS,8øE, is a plateaulike represents400 m of elevationchange. The interiorof Artemisis structureapproximately 400 km in diameter.The highlyfractured elevatedby about1.5 km with respectto the southeasternplains. interiorof this coronais elevated0.6-1.0 km with respectto the A topographicprofile crossingthe southernrim (Figure 2, top, surroundingplains. Lava flowsemanate from theperimeter of the orbit 1191) revealsthe elevatedinterior, a low-broadridge, a 2.5- coronaand cover someof the fractureson the surroundingplains. kin-deeptrench and ~l.O-km-highouter rise. The heightof the A southto north topographicprofile (orbit 519) crossingthe outerrise was measuredwith respectto the regionaltopographic easternside of Eithinoha (Figure 1, top) reveals its peripheral gradientwhich slopes downward to thesouth. The circumferential ridgesand trenches. In thiscase the trenches are very narrow(-50 fractures,which dominatethe SAR images,are confined to the km) andthe ridges sag toward the centerof the corona. The thick trench and do not extend to the crest of the outer rise. The interior horizontal lines above the trenches(Figure 1, top) mark the of Artemiscontains impact craters and complex fracture patterns locationsof circumferentialfractures apparent in the SAR images. [Stofanet 02.,this issue; McKenzie et al., thisissue]. Basedon the height of the coronae,its fracturedinterior, its Finally, one of the most strikingexamples of a ridge-trench- numerouslava flows, andits lack of impactcraters, we speculate outer rise signatureoccurs at Latona which is a semicircular thatEithinoha is in a relativelyearly stage of its thermomechanical structure(-600 km diameter) located on the southern side of and/ortectonic development [Squyres et 02.,this issue]. Aphrodite(center 22øS, 172øE). The southernpart of Latonais Heng-O(-IøN, 355øE)is a muchlarger corona (-1200 km shownin Plate 2 (bottom)where each color change represents 400 diameter)with a pronouncedridge-trench-outer rise signature m of elevationchange. The interiorof Latonais not a flat plateau alongits northernperimeter as shownin Plate 1 (bottom). The but insteadconsists of two or more topographicridges that have interiorof Heng-Olies at approximatelythe sameelevation as the the morphologyof thrust sheets. On average,the interior of surroundingplains. A topographicprofile (orbit 501) crossingits Latonalies -1.5 km abovethe southeasternplains. A topographic northernrim (Figure 1, bottom), reveals a 1.0-kin-tall ridge profilecrossing the southernmostrim towardthe south(Figure 2, followedby a 0.5-km-deeptrench that is about80 km wide anda bottom,orbit 1376) reveals a 1.5-kin-highridge, a 2.5-kin-deep broad outer rise to the north. The circumferential fractures are trench,and ~0.5-kin-highouter rise. Again, the outer rise was most intenseat the baseof the trench and diminish in frequency measuredwith respectto the regionaltopographic gradient to the andintensity moving up outof thetrench. Based on thelack of an south. Circumferentialfractures are very intensein the deeppart elevated center, the lack of radar-bright lava flows, and a of the trenchbut decreasein intensityand frequencymoving up prominentimpact crater in its interior,we speculatethat Heng-O is ontothe outerrise where they terminateat the crestof the outer relatively old and has reached a mature stage in its rise. Impactcraters are not apparentin theinterior of Latona,and thermomeehanicaland/or tectonic development. sinceits interioris bothelevated and highly fractured, we speculate The largestcorona-type feature discovered to dateis Artemis that Latonais in a relativelyearly stageof its thermomechanical [Stofanet 02.,thisissue], located to thesouth of AphroditeTerra (at and/ortectonic development. 32øS,132øE). The dominantcharacteristic of Artemisis its ridge, A majorhypothesis of thispaper is thatthese trenches, outer trench, and outer rise which form a nearly circular structure rises, and circumferential fractures (and perhaps the annular approximately2600 km in diameter. The southeasternpart of ridges)reflect flexural deformation of theVenusian lithosphere. Artemis is shown in Plate 2 (top) where each color change We test the flexural hypothesisby comparing53 topographic Plate2. Superpositionof SAR imageand topography(400 m per colorchange) for southeasternArtemis (-2600 km diameter)and southeasternLatona (-600 km diameter).In eachcase, the edgeof the plateauhas a ridgesurrounded by a deeptrench. Outerrises occur -150 km outboard of the trench axis and the trenches contain circumferential fractures. Dashed line marks locations of profilesin Figure2. SANDWELLAND SCHUBERT: RIDGES, TRENCHES, AND OUTER RISES AROUND CORONAE ON VENUS 16,073

3.0- 25 _ Artemis 2O _ 15

O5 O0 -05 -48 -47 -46 -45 -44 -43 -42 -41 -40

3.5 3.0 2,.5 Latona 2,.0 1.5 1.0 0.5 0.0 -0.5 -29 -28 -27 -26 -25 -24 -23 Latitude (deg)

Fig. 2. Topographicprofiles across southern Artemis (top) andsouthern Latona (bouom). Tracklocations are shownin Plate2. Theheavy line aboveeach trench marks the location of thecircumferential fractures. Note the large amplitude ridge, trench and outerrise signatures toward the south. profiles with the predictions of a simple flexural model. The flexuremodel consists of two components:a bending Moreover,the sign and amplitude of thesurface stress predicted by momentapplied to theend of a brokenelastic plate and a line load the models axe comparedwith the location and intensityof on a continuouselastic plate. A morecomplicated cylindrically circumferentialfractures. We discusstwo possiblemodels for the symmetricmodel was not usedbecause the radii of thesefeatures physicalcauses of the flexure. Other models,e.g., a viscous aresufficiently large that the flexural radial topography across the gravitationalrelaxation model [Bindschadler and Parmentier, 1990; quasi-circularmoat of eachcorona can be approximatedby the Stofanet al., 1991; Stofanet al., thisissue], may alsobe ableto flexural topographyacross a linear moat. In addition to the explainthe existenceof trenches,outer rises and circumferential flexural componentsof the model, a regionaltrend and mean fractures. radiuswere used. The completemodel is

ESTIMATES OF EFFECtiVE ELASTIC THICKNESS W(X)--C1exp {•} cos {•)+ c2 exp (•)[cos {•)+ sin (a•)] OUTBOARD OF CORONAE (1) + C3X + C4 To matchthe trenchand outerrise topographyof Eithinoha, Heng-O,Artemis, and Latona, we modelthe Venusian lithosphere wherex is horizontaldistance perpendicular to the strike of the as a thin elasticplate floating on a fluid mantle [Turcotte and trench,Cl (kin) is the coefficientof the bendingmoment term, c2 Schubert,1982, pp. 125-131]. The intensityof thecircumferential (km) is the coefficientof the line load term, c3 (km/km)is the fracturesat bothArtemis and Latona suggests that the platesare regionaltopographic gradient, c4 (kin) is theradius, and a (km) is behavinginelastically near the trench axes, and thus a purelyelastic theflexural parameter given by model may be inappropriate. Here we follow the procedures applied to Eaxth trencheswhich are also believed to be flexed beyondtheir elasticlimits [seeGoetze and Evans, 1979; McNutt, Ot=[3p gE{1- h3 Ve)] ]1/4 (2) 1984]. First, the trench/outerrise topographyis fit usinga thin elastic plate model. Then the effective elastic thickness and In (2), E is Young'smodulus, v is Poisson'sratio, p is mantle curvature(derived from the elasticmodel) are usedto estimatethe density, g is accelerationof gravity, and h is the unknown inelasticrheology of thelithosphere. For example,on Earthwhere thicknessof the elasticplate. Valuesof constantparameters are subduetinglithosphere is flexed beyond its elastic limit, the givenin Table 1. After fittingthe topographic profiles using (1), thicknessdetermined from the elasticmodel is usuallyonly about we calculate the bending moment M and surface stress(rxx 75% of thethickness determined using a realistic,layered rheology (positiveis tension)along the flexed lithosphere. These two [McAdooet al., 1985]. The parametersderived from the elastic quantitiesare given by model can also be reinterpretedin terms of a purely viscous lithospherethat is subductingat a constantrate [De Brernaecker, M(x)= - Ddew (3) dx 2 1977;Melosh, 1978]. Thus,while theparameters will be derived from a purely elasticmodel, they can easily be reinterpretedin or== 6__M_M (4) termsof nonlinearand viscous rheologies. h e 16,074 SANDWELLAND SCHUBERT: RIDGES, TRENCHES, AND OUTER RISES AROUND CORONAE ON VENUS

TABLE 1. Thermal and Mechanical Parameter Values to the trench axis, the best coefficients of the end moment and line for VenusJanLithosphere load (cl andc2) would act in oppositedirections to createa nicefit to the observationsin the 100 to 600 km distance range. Parameter Value However, at the origin, the model topographywould have an Tin,manfie temperature 1673K unrealisticvalue (> +100 kin). To suppressthis instability,we Te.temperature at baseof elasticlithosphere 1023K forced both cl and c2 to be be negative [Lawson and Hanson, To, surface temperature 728 K 1974]; physically,this constrainsboth the end momentand line a, thermalexpansivity 3.1x 10'5 K 'l load to flex the platedownward at the origin. E, Young'smodulus 65 GPa Pm,mantle density 3000kg m '3 • thermaldiffusivity 8 x 10'7 m 2 s 'l Freyja Montes v, Poisson'sratio 0.25 We testedthe procedureusing sevenprofiles (even numbered g, accelerationof gravity 8.87m s'2 orbits500-512) acrossnorthern Freyja Montes (80øN, 335øE) whereSolomon and Head [1990] modelleda trenchand outerrise signatureusing three Venera 15 and 16 altimeterprofiles. An whereD is theflexural rigidity given by exampleof the fits of modelshaving five elasticthicknesses (0, 10, 20, 30, and 40 kin) to profile 506 are shownin Figure 3 12(1- v2lJ (bottom). The 0 kin elastic thicknesscorresponds to a model D=[ l•h3 .] (5)consisting of only a linear trend (i.e., only c3 and c4 in (1)). The To comparethe flexure models of Venusian lithospherewith model with the 10-kin-thickelastic plate flexes too sharplyto match the outer rise while the 40-kin flexure model does not bend flexure modelsof subductinglithosphere on Earth, the bending moment Mo and plate curvatureKo at the first zero crossing sharpenough. A 20-kin-thick plate providesthe best fit. The seaward of the trench axis Xo are calculated. The first zero surfacestress (positive tension) predicted by the bestmodel is also crossingis foundby settingthe flexurepart of (1) equalto zeroand shownin Figure3 (top). The surfacetensile stress is greatestat solvingfor thefirst nonnegativeposition about 60 km from the origin where the plate curvature is maximum. The best fitting modelsfor all sevenprofiles are shownin x._•.oo• =tan.,[-(c, t C2+ c2)] +Jr (6) Figure4, andthe misfits and coefficients cl - ca are givenin Table The objectiveis to estimatethe flexural parameter{z and the 2. The bendingmoment Mo andplate curvature Ko at thefirst zero flexuralcoefficients Cl and c2 by varying all of the parameters cl, c2, ca, c4 ) such that the root-mean-square(RMS) misfit between the model and the observations is minimum. After Freyja Montes, Profile 506

determining{z, cl, andc2 we estimatethe elastic plate thickness 600 using(2) andthe maximumbending moment which occursat the baseof the trenchusing (3). 500 While this is the standardleast squaresapproach, there are a 400 numberof complicationsarising from this application.First, one 3OO may noticethat there is no obviousadjustable parameter to specify 200 the locationof the origin in (1). The approximateposition of the 100 originwas chosen as the highestpoint alongthe ridge just inboard 2o krn of the trenchaxis sincethis is where the line load and bending • -100 i momentare acting; in fact, the highestpoint was selectedafter the 0 œ00 400 profile was low-pass-filtered(~160-km cutoff wavelength)in 3.5 orderto smoothout local maxima/minimasuperimposed on the broaderridge. In additionto havingthe origin coincidewith the 3.0 peakin thetopographic load, the locationof theorigin was allowed 40 krn to vary to achieve a "best fit" to the observations. These minor •2.5 variationsare accommodated by varyingthe relativeamplitudes of •2.0 30 km cl andc2 whichcontain cosine and sinetenns that shift the phase of the flexureprofile. 20 krn 1.5 After specifyingthe origin, the latitude and longitudeof the prof'dewere converted to distanceperpendicular to the trenchaxis. •1.0 lO kra To focuson thetrench and outer rise flexure, only theobservations at distancesof ~100 to -600 km were usedin the leastsquares fit. 0.5 .... 0 kra As seenin (1), the model dependslinearly on the parametersCl - 0.0 c4 but nonlinearly on {z. To determine the model with the 0 200 400 minimumRMS misfit, we set {z and found the bestset of cl - c4 ß Thisprocedure was repeated for a wide rangeof {z corresponding Distance to elasticthicknesses of 5 to 80 kin. One morecomplication arose Fig. 3. Fits of plateflexure models to profile 506 acrossnorthern Freyja becausethe observationsdo not continueall the way to the origin Montes(bottom). The 20-km-thickelastic plate providesthe minimum (i.e., the topographicridge adjacentto the trench). When the RMS fit as well as the best visual fit. Model surface stress is tensile flexuralparameter was much less than the distance from the origin betweenthe trench axis and ~170 km (top). SANDWELLAND SCHUBERT: RIDGES, TRENCHES, AND OUTER RISES AROUND CORONAE ON VENUS 16,075

RMS misfit doesnot decreasesignificantly for platesthicker than 40 km (Figure 5) so we have adoptedthis as the bestplausible value. The tensile surface stress for the 40-kin-thick model (Figure 8, top) is moderatebetween 50 km and 200 km from the 7 origin. Circumferentialfractures occur from the originout to about 110 km (thickline) in fair agreementwith the model. The bestfitting models for all 15 profriesacross northern Heng- O are shown in Figure 9. In contrastto Freyja and Eithinoha • 508 whichrequire elastic plate thicknesses greater than 10 km, Heng-O • 5o• requiresan elasticplate thickness that is greaterthan 30 km (Figure 5). This can be seenin Figure 8 wherethe fit of the 20-kin-thick model is quite poor on the outer trenchwall. It is interestingto •./o•_•_•.._• 5o• note that the amplitudeand shape of the flexure at Heng-O do not • -----" 500 placetight constraintson the maximumelastic plate thickness.In _ fact, for most of the profiles, the minimum RMS misfit occurred for an elasticplate thickness of 80 km. A visualexamination of the 0 200 400 600 fits of theseprofiles, however, showed a poormatch at the baseof D•s • c•c e the trench. Therefore,the resultsshown in Figure 9 and given in Table 2 are bestfitting modelshaving elastic thickness less than or Fig. 4. Bestfits of flexuremodel to sevenprofiles across northern Freyja equalto 40 km. Montes(even numbered orbits 500-512). Best fit modelparameters are givenin Table2. Artemis

The amplitudeof the flexureat Artemisis extremelylarge. This high amplitudecombined with a peakedouter rise providesa tight crossingoutboard of the trenchaxis are alsogiven in Table 2 for constrainton the acceptablevalues of elastic thickness. For latercomparison with trencheson Earth. A plot of RMS misfit for example, the large-amplitudeflexure along profile 1191 is well all sevenprofiles versus elastic thickness (Figure 5) revealsa sharp matchedby a 30-kin-thickelastic plate, while platethicknesses of decrease in misfit between thicknesses of 0 and 10 kin. The 20 km and 50 km are unacceptable(Figure 10, bottom). The fits minimum misfit occurs at an elastic thickness of about 18 km, to all 12 profilesat Artemisare remarkably consistent (Figure 11). althoughmodels with elasticthicknesses ranging from about10 to The best overall model has an elastic thicknessof 37 km, while the 25 km fit the datafairly well. This is in goodagreement with the rangeof acceptableelastic thicknesses lies between30 km and 45 11-18 km elasticthickness range found by Solomonand Head km (Figure 5). Models with elasticthicknesses of 25 km or less [ 1990] usinga differentdata set and a differentmethod. are incompatiblewith the observations. The surfacestress predicted by the 30-km-thick elasticplate Eithinoha model (Figure 8, top) exceeds1.0 GPa. This stressis too large to The same modelling procedureswere applied at Eithinoha, be sustained by even the strongestrocks at high confining Heng-O, Artemis,and Latona. An exampleof the fits of models pressures(40 km deep) [Goetze and Evans, 1979]. The havingfive elasticthicknesses (0, 4, 12, 20, and 28 kin) to profile implicationis that the lithospherebetween the origin and200 km 519 crossingthe northernperimeter of Eithinoha is shownin has undergonecomplete failure. The plate is bent beyondits Figure6 (bottom). In this case,an 8-kin-thickelastic plate flexes elastic limit, and the magnitude of the stressis limited by the too sharply,while platesthicker than 28 km do not bendsharply strengthof the rock. Note that this zoneof extremelyhigh stress enough; a 12-kin-thickplate providesthe bestfit to this profile. approximatelycoincides with the locationof the intensesurface The tensile surfacestress for the 12-kin-thick model (Figure 6, fractures(thick line). The flexuremodel alsopredicts less intense top) is moderatebetween 50 km and 100 km from the origin. surface fractures on the crest of the outer rise where circumferential Circumferentialfractures occur from the origin out to about75 km fractures are not seen. This combination of tall outer rise and lack (thickline) in fair agreementwith the model. of evidencefor tensilestress on theouter rise can also be explained The best fitting models for all four profiles acrossnorthern by a flexuremodel that incorporatesa significantcomponent of Eithinoha are shown in Figure 7. Models having elastic radial compression.However, sincea bendingmoment and an thicknessesbetween 10 and 30 km all fit the data fairly well end load producesimilar topographicsignatures [Parsons and althoughthe best fitting model has an elasticthickness of about15 Molnar, 1976],evidence for compressionis inconclusive. km. While Eithinohadoes not providethe strongestevidence for lithosphericflexure, it doesprovide an exampleof a relativelythin Latona elasticplate to contrastwith otherareas having thick plates. The amplitudeof theflexure at the southernperimeter of Latona is alsoquite large and placesa tight constrainton the rangeof Heng-O acceptableelastic thicknesses. For example,profile 1376 is best An exampleof the fits of modelshaving five elasticthicknesses modelledusing a 30-kin-thickelastic plate while platethicknesses (0, 20, 30, 40, and 50 kin) to profile 501 crossingthe northern of 20 km and50 km are unacceptable(Figure 12, bottom). Indeed perimeterof Heng-O is shownin Figure 8 (bottom). In thiscase a the best solutionfor the 20-kin-thick plate is just a straightline. 20-kin-thickplate flexes too sharply,while all plate thicknesses The fits to all 15 profriesat Latonaare againremarkably consistent greaterthan 30 km matchthe profile fairly well. For Heng-O, the (Figure13). The bestoverall model has an elasticthickness of 35 16,076 SANDWELLAND SCHUBERT:RIDGES, TRENCHES, AND OUTER I•SES AROUND CORONAEON VENUS

TABLE 2. Trench Profile Models

Best Line Orbit h, RMS, RMS, cl c2, c3, Mo, Ko km m m km km 10'3 1016N 10'amq

Freyja 0500 20 35.8 131.1 -0.866 -1.465 0.63 13.66 Freyja 0502 20 35.6 144.7 -0.972 -1.401 0.70 15.34 Freyja 0504 20 44.3 139.9 -0.656 -0.142 -1.402 0.49 0.72 Freyja 0506 20 39.5 140.8 -0.562 -0.326 -1.456 0.48 10.50 Freyja 0508 25 55.1 145.5 -0.825 -1.441 0.84 9.31 Freyja 0510 20 44.7 77.6 -0.901 -0.019 -1.309 0.65 14.22 Freyja 0512 15 33.9 83.1 -0.729 -0.278 -1.287 0.37 19.39

Eithinoha 0515 24 100.8 162.2 -1.332 -0.133 -2.602 1.28 16.12 Eithinoha 0517 20 72.2 209.2 -0.414 -1.406 -2.021 0.86 18.80 Eithinoha 0519 16 109.0 227.0 -1.399 -1.418 -1.608 1.03 43.61 Eithinoha 0521 12 91.6 165.4 -2.081 -1.296 0.45 45.53

Heng-O 0495 40 36.7 109.9 -0.652 -0.242 * 1.46 3.96 Heng-O 0496 40 34.7 139.8 -0.539 * 0.71 1.93 Heng-O 0497 40 51.6 144.8 -0.622 * 0.82 2.23 Heng-O 0498 40 67.7 128.8 -0.789 * 1.04 2.83 Heng-O 0499 40 85.5 126.4 -0.755 * 1.00 2.71 Heng-O 0500 35 46.4 113.1 -0.918 * 1.00 4.03 Heng-O 0501 35 34.9 118.1 -0.931 * 1.01 4.09 Heng-O 0502 35 39.3 125.9 -0.806 * 0.87 3.54 Heng-O 0503 40 31.9 115.2 -0.738 * 0.98 2.65 Heng-O 0504 40 40.2 102.7 -0.693 * 0.92 2.49 Heng-O 0505 40 45.5 118.1 -0.613 * 0.81 2.20 Heng-O 0506 40 38.8 132.6 -0.548 * 0.72 1.97 Heng-O 0507 40 34.9 148.9 -0.061 -0.696 * 1.00 2.72 Heng-O 0508 40 31.5 230.6 -0.911 * 1.21 3.27 Heng-O 0509 40 40.1 215.1 -0.999 * 1.32 3.59

Artemis 1183 35 137.1 221.3 -10.936 -2.264 -0.860 19.07 76.99 Artemis 1185 30 109.2 222.0 -8.851 -5.058 -1.221 13.98 89.65 Artemis 1187 30 113.5 243.3 -6.774 -7.934 -1.359 13.64 87.49 Artemis 1189 30 109.9 253.2 -7.798 -10.177 -1.323 16.52 105.95 Artemis 1191 30 78.5 249.1 -7.301 -15.404 -1.182 20.24 129.78 Artemis 1193 30 86.3 260.6 -2.863 -19.236 -1.258 19.17 122.90 Artemis 1195 35 61.2 284.7 -12.910 -8.267 -1.082 26.44 106.75 Artemis 1197 35 40.2 289.9 -16.189 -4.513 -0.925 28.85 116.47 Artemis 1199 35 55.6 267.4 -18.003 -3.147 -0.894 31.13 125.68 Artemis 1201 40 65.6 290.5 - 17.869 -5.769 -0.868 39.49 106.80 Artemis 1203 45 60.9 167.9 -16.455 -5.867 -0.994 43.92 83.41 Artemis 1205 40 58.4 221.6 -6.766 -16.952 -1.234 32.32 87.41

Latona 1370 30 95.0 236.6 -0.933 -5.153 -2.137 5.29 33.91 Latona 1371 35 102.5 270.6 -0.439 -5.434 -2.491 6.40 25.84 Latona 1372 35 99.1 278.4 -0.466 -5.132 -2.241 6.10 24.64 Latona 1373 30 102.9 252.6 -9.109 -1.996 7.86 50.43 Latona 1374 30 129.9 327.8 -8.369 -1.965 7.22 46.33 Latona 1375 30 102.5 242.4 -7.775 -2.062 6.71 43.04 Latona 1376 30 162.0 200.2 -9.004 - 1.795 7.77 49.84 Latona 1377 30 138.9 214.2 -6.144 -2.022 5.30 34.01 Latona 1378 30 125.6 295.4 -5.711 -2.189 4.93 31.61 Latona 1379 35 96.5 190.6 -0.477 -3.586 -2.238 4.43 17.92 Latona 1380 35 126.3 264.1 -5.881 -2.109 6.40 25.83 Latona 1381 40 92.0 230.6 -0.549 -2.967 -2.160 4.70 12.73 Latona 1382 40 86.1 309.2 -4.186 -2.100 5.56 15.05 Latona 1383 40 82.7 230.6 -0.454 -3.714 -2.060 5.56 15.03 Latona 1384 45 126.4 325.7 -4.142 -1.972 6.57 12.48

Maximumelastic thickness for Heng-Owas set to 40 km. Line RMS correspondsto 0-km elasticthickness. *The gradientparameter was not included in fits to Heng-O. km, while the rangeof acceptableelastic thicknesses lies between stressis greatestin the deeppart of the trenchand diminishes 27 km and 60 km (Figure 5). As in the caseof Artemis,models movingup ontothe crestof theouter rise (Figure 2). Thereis an with elasticthicknesses of 25 km or lessare incompatiblewith the excellent correlation between stress intensity and surface observations.For profile 1376 (Figure 12, top) the surfacetensile fracturing. SANDWELLAND SCHUBERT: RIDGES, TRENCHES, AND OLrrER RISES AROUND CORONAE ON VENUS 16,077

250

/ • 200 ..•• / Artemis /// '%150

, \ / lOO ',.. Freyja

5o ...... ?7_g__:_o___

10 20 30 40 50 60 70 80 Elastic Thickness

Fig. 5. RMS misfit of flexuremodel versus elastic plate thickness for sevenprofiles across northern Freyja Montes, four profiles acrossnorthern Eithinoha, 15 profilesacross northern Heng-O, 12 profilesacross southern Artemis, and 15 profilesacross southernLatona. Zero elasticthickness corresponds to a linear trend modelwith no flexure. The minimumof eachmisfit curve providesan estimateof the elasticplate thickness (-18 km, Freyja;-15 km, Eithinoha;-37km, Artemis;35 km, Latona;Heng-O hasno minimum).

Eithonoha Profile 519 Eithinoha

6

•,•..800600 400 -• -' • ------'-•'•-•--•-XZ--- 521 200

o -- __ 12 k• 0 200 400 , , 5 o 200 400 600 Distance , ; 28 km Fig.7. Bestfits of flexuremodel to four profiles across northern Eithinoha 20 km (oddorbits 515-521). Best fit modelparameters are given in Table2. 1. 12 km canalso be calculated.However, the estimatesof the depthto the 1. baseof the elasticlayer are highly dependenton the rheological ...... 4 km propertiesof the ductile lower lithosphere. Without a good o. knowledgeof lithosphericrheology on Venus,one can only adopt 0 km characteristicvalues used for Earth'soceanic lithosphere [Goetze O. and Evans, 1979]. Here we follow Solomonand Head [1990]

• I i wherethey characterized the strengthof the upperbrittle portion of -0'50 200 400 the lithosphereusing a frictionalsliding law [Byedee, 1978] and Dis t ance the strengthof the lower lithosphereusing a ductileflow law for dryolivine (10 -16 s -1 strainrate). Thesetwo failure criteria define Fig.6. Fitsof plate flexure models toprofile 519 across northern Eithinoha a yieldstrength envelope (YSE) [Goetzeand Evans, 1979] where (bouom).The12-km-thick elasticplate provides theminimum RMS fit as thebase of theYSE is approximatelydefined by the 740 K well as thebest visual fit. Model surfacestress is tensilebetween the trench isotherm[McAdoo et al., 1985] andthe thicknessof the YSE is the axisand -150 km (top). Circumferential fractures (thick line, top) occur out to a distance of 75 km. mechanicalthickness of thelithosphere. When the lithosphereis flexed, the largestdeviatoric stresses occur at the top and bottom of the layer. For moderateplate LITHOSPHERICTitERMAL GRADIENT curvatures(-10 -7 m-l), significantyielding occurs in boththe uppermostand lowermost part of themechanical lithosphere which Theparameters of thebest fitting thin elastic plate models can areweak. This yieldingcauses the effective elastic thickness of the be usedto estimatethe depth to thebase of theelastic layer. lithosphere(i.e., derivedfrom flexuremodelling) to be lessthan Assumingthis corresponds toan isotherm, the geothermal gradient the actualmechanical thickness of thelithosphere McNutt [ 1984]. Heng-O, P•o•i•e 501 A•temis, P•o•i•e 1191

6OO 500- 20001500 400- 300- 1000 200- 100- 500 __ 40 km o o 30 km I I I I i i i i -1000 200 400 200 400 600 800 3.0 4.0

2.5 3.5 2.0 '•",. '"' _50km 1.5

1 0 •2.0 . •1.5 0.5 o 1.0

0.0 0.5

0.0 -0'50 200 400 200 400 600 800 Distance (kin) Distance (kin)

Fig. 8. Fitsof plateflexure models to profile501 acrossnorthern Heng-O Fig. 10. Fits of plate flexure modelsto profile 1191 acrosssouthern (bottom).The 40-km-thickelastic plate provides the minimum RMS fit as Artemis(bottom). The 30-km-thickelastic plate provides the minimum well as the best visual fit. Model surface stressis tensile between the trench RMS fit as well as the best visual fit. Model surface stress is tensile axisand -300 km (top). Circunfferentialfractures (thick line, top) occur out betweenthe trench axis and -280 km (top). Circumferentialfractures (thick to a distance of 160 km. line,top) occur out to a distanceof 180 km.

Heng-O Artemis

14 • .....---.--•-•-'•- 509508 12 f..•.._•.• • 507 .•----• •--•'--"----"-•506 _•/•.•...... 505 --• 504 _• 503 ...... 502 • ...... 501 ...... 500 - ...... 499 • ...... 498 --• 497 0K i i -• 496 200 •00 600 800 • ...... 495

200 400 600 Fi•. 1l. Bestfits of fi•xum mo•cl to (o• •umbem•otbi• Distance (kin) T•lc Z Fig. 9. Bestfits of flexuremodel to 15 profilesacross northern Heng-O (orbits495-512). Best fit modelparameters are given in Table2. SANDWELLAND SCHUBERT: RIDGF•, TRENCHES, AND OUTER RISES AROUND CORONAE ON VENUS 16,079

Latona, Profile !376 Latona

16

14 800

4OO 12 30 km o 200 400 600

4.0

377

o

•2, o0

0.5 200 400 600

Distance o Fig. 12. Fitsof plateflexure models to profile1376 across southern Latona o 200 400 600 (bottom).The 30-km-thickelastic plate provides the minimum RMS fit as well as the best visual fit. Model surface stressis tensile between the trench Distance (kin) axisand ~300 km (top).Circumferential fractures (thick line, top) occur out to a distance of 230 km. Fig. 13. Bestfits of theflexure model to 15profiles across southern Latona (orbits1370-1384). Best fit modelparameters are given in Table2.

Completelithospheric failure occurswhen the plate curvature conductivityused in the abovecalculation is too low. (3) The exceedsabout 10 -6 m-1. (Notethat Artemis has an average plate areasthat we haveinvestigated have anomalously thick and strong curvatureof 10-6 m-1, suggestingthat the lithosphere has failed.) lithosphereswith respectto the averagelithospheric thickness on Solomonand Head [1990] adapted this YSE model for the Venus. (4) The heat productionin the interior of Venus is parametersappropriate to Venusand provide a diagramto map the substantiallylower than the heat productioninside Earth. (5) elasticthickness into mechanicalthickness by using the plate Venuslooses a substantialfraction of itsheat by extrusionof large curvature(Figure 4 of their paper). We haveused their diagram quantitiesof lava. (6) Heatloss on Venusis episodicand global with ourestimates of elasticthickness and plate curvature (Table 2) with a time scale> 200 m.y. Over the nextfew yearsit will be to estimatethe mechanical thickness of thelithosphere outboard of importantto eliminateas many of theseexplanations as possible to Freyja, Heng-O, Artemis, and Latona; the resultsare given in arriveat a betterunderstanding of theVenusian heat loss budget. Table 3. At thistime it wouldbe prematureto speculateon themost likely At FreyjaMontes, we find the bestrange of elasticthicknesses explanation,however. isbetween l0 and25 km andthe plate curvature is 13x l0-8 m-l; this agreeswell with Solomonand Head's [ 1990] estimatesbased TECTONIC AND TIIERMAL MODELS FOR THE DEVELOPMENT onVenera 15 and 16 altimeterprofiles. These parameters map into OF A RIDGE, TRENCH, AND OUTER RISE thermalgradients of between9.5 and26 K/km. A similarrange of thermalgradient is inferredat Eithinoha(6.8-24 K/km). For the We proposetwo models(scenarios) for the developmentof other three areas, however, we estimate that the mechanical ridge,trench, and outer rise flexural topography on theperimeters thicknessof the lithosphereis greaterthan 30 km (Table 3) which of the largestcoronae. In the first model (Figure 14, tectonic mapsinto much lower thermal gradients (< 10 K/km). scenario),a mantleplume reaches the base of thelithosphere and Assumingthe Venusian lithosphere has a thermalconductivity spreadshorizontally (i.e., radially) outwardbeneath the underside of3.3 W m-1 K' 1,the temperature gradients estimated atHeng-O, of thelithosphere. The hot, light plume forms an inverted pancake Artemis,and Latona correspond to a surfaceheat flow of lessthan thatis heldup againstthe bottom of thelithosphere by virtueof its 33mW m -2. Thisis less than one half of theexpected planetary buoyancy.Over time this hot plumehead thins and weakens the average heat flow for Venus. There are many possible lithosphere.Melt penetratesthe lithosphere providing a routefor explanationsfor this low estimate:(1) The lithosphereon Venus furtherescape of hot mantlematerial. A largevolume of mantle remainsstrong at temperaturesexceeding 1013 K (740øC)or the materialspreads over the top surface of thelithosphere causing it to strainrates are much higherthan on the Earth. (2) The thermal depressand ultimately to fractureand fall. Thecold lithosphere on 16,080 SANDWELLAND SCHUBERT: RIDGES, TRENCHES, AND OUq•R RISES AROUND CORONAE ON VENUS

TABLE 3. LithosphericThickness and Temperature Gradient

Elastic Curvature, Mechanical Temperature ]hickhess,km 10-$ m -1 Thickness,*km Gradient,+ K km-1

Freyja# 11- 18 15 12-21 24- 14 Freyja 10- 25 13 11- 30 26- 9.5 Eithinoha 10- 30 29 12-42 24- 6.8 Heng-O 30 - 45 3 32- 49 8.9 - 5.8 Artemis 30- 45 103 60- 90 4.8 - 3.2 Latona 27 - 60 29 37- 82 7.7 - 3.5

*Mechanicalthickness derived from Figure 4. of Solomonand Head [1990]. +Temperaturegradient based on 1013K (740øC)temperature atbase of elasticlayer. # Publishedresults, Solomon and Head [1990].

Tectonic Scenario Thermal Scenario

f

Fig. 14. (Left)Tectonic scenario: plume head approaches the lithosphere and spreads radially, causing it to thinand weaken; melt andhot mantle material pond on the surface of thelithosphere causing it to fail underthe load; the old and dense lithosphere sinks intothe mantle forming a circularsubduction zone that increases in radiuswith time; the interior spreads radially to fill thegrowing void;a prominenttrench and outer rise develop. (Right) Thermal scenario: plume head approaches the lithosphere and spreads radially;thermal conduction and/or advection thins the lower lithosphere in a circulararea with sharp edges; the hot interior cools andsubsides relative to the coolexterior forming ridge, trench, and outer rise topography. the perimeterof the flow sinks into the mantle forming a bottomof thelithosphere by virtueof its buoyancy.However, this subduction zone and circumferential fractures (i.e., a corona). timeonly a smallervolume of meltescapes to thesurface. The hot Continued subduction causes the trench to roll back so the radius material in the plume thins the lithosphereand creates an of thecorona increases and the interiorof thecorona expands to fill isostaticallycompensated plateau at thesurface. As shownbelow, the void. This type of subductionand back arc spreadingis the transition from the hot-thin interior to the cold-thick exterior commonlyfound behind subduction zones on Earth. mustbe quite sharp(<50 kin) for a ridge/trenchsignature to In the secondmodel (Figure 14, thermalscenario) a mantle develop.The interiorlithosphere then cools to the surface,while plumehead also reaches the base of the lithosphereand spreads theexterior lithosphere maintains its temperatureprofile through a horizontally(i.e., radially) outward. As in thefirst model, the hot, balanceof heatsupply at its basewith heatloss at its surface.As a lightplume forms an invertedpancake that is heldup againstthe consequenceof the cooling,the interiorlithosphere increases in SANDWELLAND SCHUBERT: RIDGES, TRENCHES, AND OUTER RISES AROUND CORONAE ON VENUS 16,081

densityand it subsidesisostatically. During the subsidence,the 200 Ma lO Ma interiorlithosphere remains welded to the exteriorlithosphere. The differential subsidence causes upward flexure inside and elastic downward flexure outside, forming the ridge, trench, and outer rise topography. ductile It shouldbe notedthat thesemodels are not mutuallyexclusive. The main difference between the models is where the hot material fluid is emplaced,above or below the preexistinglithosphere. In the tectonic scenario when subduction ceases and the corona reaches Fig. 15. Diagramshowing the initial conditionsof the differentialthermal its final diameter, the interior lithospherewill be hot and thin, subsidencemodel. The base of the thermal boundary layer (i.e., while the exterior lithospherewill be cold and thick. At this point lithosphere)is definedby the Tmisotherm, while thebase of theelastic plate the corona must go through a phase of differential thermal is definedby the Te isotherm. The interiorlithosphere (fight side)is hot, subsidence.Another possibility in the tectonicscenario is thatthe thin, and elevated relative to the exterior lithosphere. The interior interior of the corona spreads radially but the preexisting lithospherecools and subsideswith time, while the exteriorlithosphere maintainsits temperatureprofile by a constantbackground mantle heat flux lithospheredoes not subduct. When the spreadingceases, the q. interior lithospherewill be hot relative to the exterior lithosphere and thus will undergo a final thermal subsidencephase. A becauseits geotherm is maintained by a constantbackground calculationof the differentialthermal subsidence is presentednext mantle heat flux q. As the interior lithospherecools and thickens to showthat it can explainthe smallamplitude flexures observed at with time, its averagedensity increases. (The thermalexpansivity Heng-O but cannot producethe large trenchesand outer rises at a is given in Table 1.) Far from the contactzone, the lithosphere Eithinoha, Artemis, and Latona. subsidesisostatically at a rate proportionalto the squareroot of time (Figure 16, dotted curves). After 200 m.y. of cooling, the DifferentialThermal Subsidence interior has reached the same level as the exterior. Within about The model incorporatestwo-dimensional cooling, thermal 150 km on either side of the contact zone, however, the subsidence,and flexureof weldedadjacent lithosphere of different lithosphere flexes to accommodate the differential thermal ages[Sandwell and Schubert,1982; Sandwell, 1984] (Figure 15). subsidence. The form of the flexure and the predicted surface As in the previoussection, it is assumedthat the coronaehave stress depend on both the subsidencehistory and the lateral sufficientlylarge radii that their circularity is unimportantin the variationsin elasticthickness. The flexuresolution is obtainedby evolution of the flexural topography. In the initial state, it is summing flexures that have accumulated over small time assumedthat 200-m.y.-old Venusian lithosphereoutside of the increments.At eachtime stepthe differentialequation is solvedby corona abuts younger lithosphereof age 10 m.y. inside of the an iterationmethod to accountfor the spatialvariations in flexural corona. The initial thermalprofiles far from the contactzone are rigidity. given by the classical error function solution of the one- The predictions of this simple thermal subsidencemodel dimensionalcooling half-spacemodel [Turcotte and Schubert, comparefavorably with topographicprofiles across Heng-O. For 1982] wherethe temperatureat the surfaceof the lithosphereis To example,outboard of the ridge (-400 km to 50 km, Figure 16) and the deepmantle temperature is Tm (seeTable 1 for values). profile501 matchesthe modeltopography curve corresponding to The rateof heatdiffusion is controlledby thethermal diffusivity completethermal subsidence (200 m.y.). Inboardof the ridge the The temperaturedistribution in the vicinity of the contactzone is model topographydies not match the observations.It shouldbe smoothedby allowing heat to diffuse acrossthe zone for 10 m.y. pointedout that the only adjustableparameters in the model are the The rheologyof the lithosphereis consideredto be perfectlyelastic initial ages of the interior and exterior lithospheres and the at depthsless than the elastic isotherm Te of 1023K (750øC)and sharpnessof the contactzone. Theseages set the amplitudeof the ductileor fluid at greaterdepths. The ductilematerial (Figure 15) initial step offset as well as the elasticthicknesses of the interior cansupport the smallbuoyancy forces due to thermalcontraction and exteriorlithospheres. In this case,the amplitudeof the final but cannot supportthe larger flexural stresses.Because of the ridge, trough,and outer rise flexure is aboutone half of the initial sharp temperaturecontrast, there is a large changein elastic stepamplitude. thickness across the contact zone. The initial elastic thickness of Noneof thethermal subsidence profiles match the topograph• the interiorlithosphere is 7km, while the initial elasticthickness of of Latonaas shownin Figure 16. Removalof a linear topographic the exteriorlithosphere is 42 km. The initial stateis assumedto be gradientwould improvethe fit on the exteriortopography, but the an unstressedconfiguration. model trench would be much too small (-400 km to -200 km, The relativesharpness of the initial thermaltransition across the Figure16). The modelalso does not fit anyof the Artemisprofiles contact zone is essentialfor the subsequentdevelopment of a becausethe amplitudeof the modelflexural topographyis abouta flexural moat and ridge topography.The model doesnot address factor of 5 too small. One could increasethe amplitude of the the physicsof how sucha sharpthermal transition is established. model topographyby increasing the age contrast between the The sketchin Figure 14 suggeststhat the initial stateis the product interior and exterior lithospheres. However, since thermal of the reheatingand thinning of the lithosphereabove a mantle subsidenceis proportionalto the squareroot of age,the modelage plume. However,the mathematicalmodel of the developmentof contrastmust be increasedto an absurd value of 5 b.y. which flexural moat and ridge topographyapplies no matter how the exceeds the age of the planet. These results suggest that "initial"plateaulike state is formed. differentialthermal subsidence may be an importantprocess for the The interior lithosphere(Figure 16, x > 0) is allowed to cool majority of coronaethat have relatively small amplitudeflexures, with time while the exterior lithospheredoes not cool with time but theycannot explain the larger flexures at Arte•nisand Latona. 16,082 SANDWELL AND SCHUBERT: RIDGES, TRENCHES, AND OUTER RISES AROUND CORONAE ON VENUS

0.0

-0.5

-1.0 Latona '?..;c "- -1.5 " ...... , ... .-" .... \, ... \ 70 E ,.... ,...... \ ... \ P.. -2.0 ...... ,,/'..... , H eng - 0 \ tl ;... ,.~u. ... n ,rrrnnrn ::.:;;;; ...... · .. ·,,~:t.", 200 ~ -2.5 §< E-... -3.0

-3.5

-4J500 -400 -300 -200 -100 o 100 Distance (krn) Fig. 16. Evolution of the topography for the differential thermal subsidence model (dotted curves). The thermal perturbation has decayed after 200 m.y. of cooling. The topography of Heng-O is well matched by the 200-m.y. model, while the topography of Latona cannot be fit by the model.

Subduction Model SUMMARY The flexural trench and outer rise topography observed at Eithinoha, Artemis, and Latona is similar to flexural topography 1. High-resolution altimetry collected by the Magellan observed on the seaward side of subduction zones on Earth. For spacecraft has revealed trench and outer rise topographic signatures example, at Eithinoha the elastic plate is relatively thin (-15 kIn) around many major coronae [Sto/an et al., this issue]. In addition, and the bending moment at the trench axis is small (0.9 x 1016 N). Magellan SAR images show circumferential fractures in areas This compares favorably with the thin plate (-12 kIn) and small where the plates are curved downward. These observations moment (0.6 x 1016 N) observed at the Middle America Trench. suggest that the lithosphere arl;lUnd coronae is flexed downward In contrast, at Artemis the elastic plate is relatively thick (-37 kIn) either by the weight of the overriding coronal rim or by the and the bending moment is relatively large (25 x 1016 N). This negative buoyancy of subducted lithosphere. compares favorably with an elastic thickness of 29 kIn and a 2. We have selected four of the largest coronae (Eithinoha, maximum bending moment of 13 x 1016 N found at the Mariana Heng-O, Artemis, and Latona) which display these flexural Trench [Caldwell et al., 1976]. Similarly, at Latona the elastic characteristics and have modelled the trench and outer rise thickness and bending moment are 35 kIn and -6.0 x 10 16 N, topography as a thin elastic plate subjected to a line load and respectively which compares favorably with the Aleutian Trench bending moment beneath the corona rim. The elastic thicknesses (28 kIn and 8.9 x 1016 N). On the Earth, the bending moment is determined by modelling numerous profiles at Eithinoha, Heng-O, primarily supplied by the negative buoyancy of the subducted Artemis, and Latona are 15, 40, 37, and 35 kIn, respectively. At lithosphere. The overriding plate is almost locally compensated so Eithinoha, Artemis, and Latona where the plates appear to be that it exerts almost no downward force on the subducting plate. yielding, the maximum bending moments and elastic thicknesses Moreover, in many cases, the overriding plate is in a state of are similar to those found at the Middle America, Mariana, and tension which results in back-arc spreading that is nearly parallel to Aleutian trenches on Earth, respectively. the subduction zone [Barker and Hill, 1981]. As a final analogy, 3. Estimates of effective elastic thickness and plate curvature McKenzie et al. [this issue] have noticed that many of the arclike are used with a yield strength envelope model of the lithosphere to topographic structures in eastern Aphrodite Terra (including Latona estimate lithospheric temperature gradients. At Heng-O, Artemis, and northern Artemis) have similar morphology and scale to and Latona, temperature gradients are less than 10 KIkm which subduction zones in the East Indies on Earth. In both cases, the correspond to conductive heat losses of less than one half the subduction zones are curved with the high topography on the expected average planetary value. There are many possible concave side. explanations for the low estimated heat flows. However, On Earth, the negative buoyancy of the subducted lithosphere modelling of many more areas is needed to establish a planetary acts as a stress guide that draws the not yet subducted lithosphere average. into the trench. This effect (slab pull) is believed to be the major 4. We propose two scenarios for the creation of the ridge, driving force of plate tectonics [Schubert, 1980]. An unusual trench and outer rise topography: differential thermal subsidence feature of some coronae including Eithinoha, Artemis and Latona and lithospheric subduction. The topography of Heng-O is well is that the trench wraps around the corona by more than 180·. matched by the differential thermal subsidence model. However at Thus if the trench axis were to remain stationary, the entire Artemis and Latona, the amplitudes of the trench and outer rise lithosphere would have to compress and thicken as it moved into signatures are a factor of 5 too large to be explained by thermal the trench. Because this seems physically implausible and there subsidence alone. In these cases we favor the lithospheric are no indications of circumferential compression outboard of the subduction model wherein the lithosphere outboard of the corona trench, we prefer the model where the trench axis rolls back and perimeter subducts (rolls back) and the corona diameter increases. the corona increases in diameter. SANDWELLAND SCHUBERT: RIDGES, TRENCHES, AND OUTER RISES AROUND CORONALS ONVENUS 16,083

Acknowledgments. We thank Peter Ford for providingan updated Parsons,B., andP. Molnar, The originof outertopographic rises versionof the altimeterprofiles and many techniciansat Jet Propulsion associatedwith trenches,Geophys. J. R. Astron.Soc., 45, 707-712, Laboratory for processingof the SAR images. Ellen Stofan, Duane 1976. Bindschadler,Buck Janes,and StephenSquyres organized the coronae Pettengill,G. H., P. G. Ford, W. T. K. Johnson,R. K. Raney, and L. SAR data into a very usable format. Barry Parsonsprovided helpful A. Soderblom, Magellan: Radar performanceand data products, suggestionson modelling the trench/outerrise flexure. Dan McKenzie Science,252, 260-265, 1991. contributedto manyof the ideasrelated to the subductionzone hypothesis Pronin,A. A., and E. R. Stofan,Coronae on Venus: Morphologyand andprovided feedback on manyaspects of theresearch. The researchwas distribution,Icarus, 87, 452-474, 1990. partiallysupported by theMagellan Project (JPL 958950 and JPL 958496). 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