JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 96, NO. BI, PAGES 301-315, JANUARY 10, 1991
Comparisonof Observed and Predicted Gravity Profiles Over Aphrodite Terra, Venus
MARTIN T. BLACK
AstronomyProgram, University of Maryland, College Park
MARIA T. ZUBER
GeodynamicsBranch, NASA GoddardSpace Flight Center,Greenbelt, Maryland
DAVID C. MCADOO
NationalGeodetic Survey, Charting and Geodetic Services, National Ocean Service, NOAA, Rockville, Maryland
We compareobserved Pioneer Venus orbiter (PVO) gravityprofiles over Aphrodite Terra to profilespredicted frommodels of thermalisostasy, mantle convection, and Airy compensation.Similar approaches are usedin orderto investigatehow well the modelscan be distinguishedwith the PVO data. Topographyprofiles acrossAphrodite are comparedto model spreadingridge profilesin order to further assessthis model. Airy compensationdepths and convection layer thicknesses are greaterunder eastem Aphrodite than western Aphrodite.Compensation depths in theeast are greater than most estimates of lithosphericthickness, suggesting thatthis part of the ridgeis dynamicallysupported. In partsof westemAphrodite, the spreadingridge model gravityprovides a betterfit to the datathan either Airy compensationor manfie convection.Best-fit spreading ratesare between0.3 and 1.6 cm/yr. Airy compensationand mantleconvection cannot be distinguished in most places using only PVO data.
INTRODUCTION Venus.Others [Crumpier et al., 1987;Head andCrumpier, 1987] AphroditeTerra is thelargest highland area on Venus.It is a have arguedthat Aphroditedisplays morphological characteristics longlinear topographic feature running approximately east-west consistent with the divergentplate boundaryhypothesis. in theequatorial region from about 60 ø eastlongitude to 210ø In thispaper we developan approachto the modellingof Pio- eastlongitude and reaching a heightof over4 km abovethe mean neerVenus orbiter (PVO) gravityprofiles which allows us to test planetaryradius [Pettengill et al., 1980].Within Aphrodite are severalmodels of isostaticcompensation in Aphroditein a uni- severaldistinct uplands, including Ovda Regio (spanning therange form way. Our objective is to determinewhether we can distin- 80ø < longitude< 110ø), Thetis Regio (120 ø < longitude< 140ø), guish between the modelsusing the PVO gravityand topography andAtla Regio (195 ø < longitude< 210 ø) (Figure 2). Becauseof data and, if so, to determine which model best fits the data. We itssize and distinctive morphological character, anunderstanding present the resultsof modelling96 orbital arcsover Aphrodite of thetectonics ofAphrodite isessential for an understanding of using models of crustalspreading, mantle convection, and local the global tectonicsof Venus. compensation.It is foundthat in partsof westernAphrodite the Twohypotheses for the origin and nature of Aphroditehave spreadingridge modelprovides a betterfit to the PVO gravity beenput forward in theliterature. The first, that Aphrodite isthe datathan the othermodels do, thoughmost topographic profiles surfaceexpression ofrising mantle plumes, has been advanced by acrossAphrodite do not resemblethose expected for a spreading severalworkers [Phillips et al., 1981;Phillips and Malin, 1983; ridge like the Mid-AtlanticRidge. Elsewherein Aphroditethe Kieferetal., 1986; Kiefer and Hager, 1988 ]. Thehigh degree three models cannot be distinguishedusing only the PVO gravity of correlationbetween gravity and topography on Venusis un- and topographydata. We find evidencefor dynamicsupport of likethe terrestrial case, where the long-wavelength geoid(spher- topography east of 140o . icalharmonic degrees 4-9) is highlycorrelated with subduction [Hager,1984]. Isostaticcompensation models cannot account DATA forthe observed relationship between the long-wavelength grav- ityand topography onVenus [Kiefer et al., 1986], suggesting that The topographydata were taken from the ProjectMagellan mantleconvection isresponsible fordynamically maintaining the TopographyModel (PMTM), Version 3.0, a 1/8ø x 1/8ø gridof anomalies.It hasalso been proposed that Aphrodite is a diver- thePVO radaraltimeter data. This gridspacing, which is about gentplate boundary, analogous to terrestrialoceanic rises. Kaula 13km at theequator, is smallerthan the altimeter footprint size at andPhillips [1981] examined this hypothesis and concluded that all latitudes[Pettengill eta/., 1980], sothe horizontalresolution of platetectonics is not an importantheat transfer mechanism on theunderlying altimetry data is everywhereless than the PMTM gridspacing. The vertical uncertainty in the altimetry data is about Copyright1991 by theAmerican Geophysical Union. 200 m, takinginto account both statistical errors and systematic orbitdetermination errors [Pettengill et al., 1980]. Papernumber 90JB01853. The gravitydata were derived from PVO line-of-sight(LOS) 0148-0227/91790JB-01853505.00 velocitymeasurements. The instantaneousvelocity of PVO rela-
301 302 BLACKET AL.: GRAVITY PROFILES OVER APHRODITE TERRA
rive to a receivingantenna on Earth, projectedonto the Earth-PVO compensation;and (3) convectionin the mantle. A model line- direction, was obtained from Doppler tracking of a radio signal of-sightgravity profile is producedfor each of thesemodels betweenPVO andthe groundstation [Sjogren et al., 1980]. Resid- andfit to the observedgravity profile by adjustingparameters, ual LOS velocitieswere obtainedby removingthe effectsof the as described below. Table I summarizes the models and their orbital motionsof Earth and Venus,the rotationof Earth, gravity adjustableparameters. Figure 1 presentsschematic drawings of of the Sun and other planets,and the centralmass component of the three models tested. the orbital motion of PVO [Phillips et al., 1979; Sjogrenet al., 1983]. Time derivativesof the velocityresiduals give the residual LOS accelerations,which are attributedto local variationsin grav- ity alongthe spacecraftorbit. A velocitydetermination was made every5 s duringthe 30 min beforeand afterperiapsis [Sjogren et al., 1980], which correspondsto a maximum along-groundtrack spacingbetween data points of about45 km. Bills et al. [1987] concludedthat althoughthe accelerationmeasurements in adja- cent orbits are consistentat a 1-2 mgal level, a formal error of 3 mgal more accuratelyreflects the accuracyof eachmeasurement when errorsin the determinationof the spacecraftorbit are taken Crustal Spreading (b) into account. The limiting noise sourcein the individualveloc- ity determinationsis the modulationof the radio signalsby the interplanetaryplasma, which can introduceuncertainties in the Reference Level gravity determinationsof up to about3 mgal, thoughthe noise alongindividual orbital arcs is often muchless than this [Phillips et al., 1979]. We have subtracteda harmonic background gravity field of degreeand order4 [Bills et al., 1987], correspondingto a wave- lengthof about9500 km, from theobserved LOS accelerationsin Airy Compensation orderto removeunmodelled dynamic orbit effectsfrom the data. Theseeffects are largestat long wavelengths,i.e., on the orderof (c) Upper Boundary theplanetary circumference, and less important for shorterwave- lengths.Orbit errors are small for wavelengthsof a fewthousand kilometersand less,which are of interestfor this study. In order to checkwhether any unmodelleddynamic effects remained in thedata, several of thepasses were analyzed using the ORBSIM orbitalsimulation program [Phillips et al., 1978] and a simple Lower Boundary modelof localcompensation. These results were compared with theresults of ourAiry compensationmodel (discussed in thenext Mantle Convection section)for thesame passes and found to beconsistent within the Fig. 1. Thethree models of isostaticcompensation tested in thisanalysis: data uncertainty. (a) Crustalspreading, where v, is thehalf-spreading velocity and w is the ridgewidth. (b) Local compensation, where t is the depth of compensation. MODEI• (c) Mantleconvection, where d is the convectionlayer thickness. In thissection we presentthe tectonicmodels used to produce the predictedLOS gravityprofiles over Aphrodite Terra. We Crustal Spreading considerthree modelsfor the relationshipbetween gravity and topography:(1) crustalspreading (thermal isostasy); (2) local In a platetectonic environment, new, hot materialis addedto lithosphericplates at spreadingridges and moves away from the
TABLE 1. Isostatic Models ridge as the crustspreads outward. The lithospherecools and contractsas it moves,causing the plateto subsidewith age.This Model Input Adjustable producesa relationshipbetween topography and age as well as Parameters betweengeoid height and age. If the ridgemaintains a constant Thermal isostasy Locationof ridge Spreadingrate, ridge spreadingrate, distance from the ridge is equivalentto age.For a axis, distancefrom half-width (vs, w) ridgedescribed by thesimple half-space cooling model [Turcotte ridge axis and Oxburgh,1967; Parker and Oldenburg,1973; Davis and Lister, 1974], the topography,b(x), and the geoidheight, h(x), are givenby [Haxbyand Turcotte, 1978] Airy compensation PVO topography Depthof compensation(t)
Dynamic PVO topography Convectinglayer 2•rGp,•a (T,,• - T.) n compensation thickness(z; y) = (free-freeand (2) free-rigid boundary conditions) X 1+ (pm--Pa)a' BLACK ET AL.: GRAVITY PROFILESOVER APHRODITE TERRA 303 where p,,, (=3330 kg m-a) is the densityof the mantle,a (=3.1x10-5 øC-a) is the volumecoefficient of thermalexpan- sion,T,,, (=1365 øC) is the temperatureof the manfie,T• (=464 (6) øC)is thesurface temperature, p• (=63 kg m-a) is thedensity of theatmosphere, n (=8.0x10 -7 m2 s-•) is thethermal diffusiv- ity of thelithosphere, G is theuniversal gravitational constant, g (=8.87m s-2) isthe acceleration of gravity at thesurface, v., is the half-spreadingrate of theridge, w is theridge width, and x is the = _4ap - + distancefrom the ridge axis. We haveintroduced the parameter 2pma(Tm-T•)] w in orderthat the Fourier integrals converge. The ridge width is thedistance from the spreading ridge axis to theoldest crust that x[tan_• (x)• -]tan- 1 •(w+x)+•tanI _•(w-x) formedat theridge axis; i.e., wherethe topographicexpression (7) of theridge is definedto be zero. The ridgewidth is indepen- The adjustablep•ameters for thismodel •e v,, the half-spreading dentof the lengthof the gravityprofile used in the parameter velocity, •d w, •e •dge width. estimationand may be muchlarger than the profile. The sur- facetemperature and atmospheric density are averages of in situ Local compensation measurementsfrom the Venera7-12 spacecraft[Avduevskiy et al., To modelthe gravitydue to locallycompensated topography we 1983]. The Venussurface gravity is calculatedfrom the known haveused the modelof simpleAiry compensationas presented by physicalparameters of the planet. We have adoptedthe terres- McKenzie and Bowin [1976]. In this model the mass anomalies trial valuesfor the otherparameters under the assumptionthat the dueto topographyvariations are compensated by variationsin the compositionof the Venusianlithosphere and the temperatureof thicknessof a constantdensity crust in sucha way that the mass the mantleare similar to Earth. Increasingthe mantletemperature per unit area is constanteverywhere. The frequencyresponse by 125 øC, as is suggestedby someconvection and mantleflow (or admittance)between gravity and topographyfor this model, models[Turcotte et al., 1979; Kaula andPhillips, 1981; Stevenson upwardcontinued to an elevationa, is et al., 1983; Phillips and Malin, 1983; Sotin et al., 1989b], has a negligible effect on our model results. On Earth the depth of oceaniccrust older than about 70 Myr divergesfrom that given Z(k)= 2a'G (pc - p,)e-k• (1- e-kt) (8) by (1) and is better describedby the plate model [Parsonsand Sclater, 1977], which assumesan isothermalbottom boundary, wherepc (=2800 kg m-z) is thecrustal density and t is thedepth though there are regional variationsin the subsidencerate. We of compensation.The adjustableparameter in this modelis t. have usedthe half-spacemodel in our analysisbecause its formu- lation is simplerthan that for the plate model and our resultsare not significantlychanged by consideringonly data from young Mantle Convection lithosphere(as determinedby our spreadingvelocity estimates). McKenzie [1977] and Parsonsand Daly [1983] used a sim- In order to find the LOS gravity at spacecraftelevations, h(x) ple model of mantle convectionto predict admittancesbetween must be upward continuedand convertedto an expressionfor gravityand topography.Their modelassumed uniformly viscous gravityrather than geoid height. This is accomplishedmost easily Newtonianconvection in a mantlelayer of thicknessd. Effectsof by workingin the frequencydomain. The Fourier transformsof inertia,self-gravitation, and sphericitywere ignored. The model the verticalgravity go (z) andthe geoidheight h(x) are simply is useful becauseit yields analyticsolutions which are readily relatedby [Chapman,1979] appliedto calculationsof gravity anomalies,while avoidingthe complicationsof numericalmodelling. Parsons and Daly [1983] = allH() (3) derivedadmittances by convolvingtopographic and gravityker- nels with simplestructure functions for temperature.By using an assumedtemperature structure rather than solving the coupled where uppercaseletters indicate the Fourier transform of the heattransport equation, they were able to deriveanalytic expres- correspondinglower casefunction and k=2a-/A is the wave number sionsfor admittance. They found that the admittancesare most correspondingto a wavelengthA. Upward continuationto an sensitiveto the temperaturestructure of the upperthermal bound- elevationa is accomplishedby multiplicationby an exponential ary layer. The actualtemperature structure of Venusis not known, term so this simple approachis appropriatefor our study. While the model admittancescalculated here are probablyoverestimated at (4) long wavelengths,the discrepanciesare on the order of 10% or lessfor wavelengthsshorter than the convectionlayer thickness [Parsonsand Daly, 1983, Figure7], showingthat the analytic The Fourier transformof the horizontalcomponent of gravity, formulationadequately reproduces the effects of the topboundary gn(x, a), is theHilbert transform of Go (k, a) [Chapman,19791 layer on the admittance. Modelling of the terrestrialgeoid indicatesthat Earth's lower G•,(k, a) = i sgn(k) g (5) mantleis about300 times more viscousthan the upper mantle [Kieferet al., 1986]. In contrast,Kiefer et al. [1986] can match the observedadmittances on Venus with whole-mantle, uniform The inversetransforms then yield expressionsfor vertical and viscosityconvection, though the modelsallow the lower mantle horizontalgravity at an elevationa. For the half-spacecooling to be up to about 10 times more viscousthan the uppermantle model we find [Kieferand Hager, 1988]. Constantviscosity convection results 304 BLACKET At,.: GRAVITYPROFILES OVER APHRODITE ]"ERRA inhigher admittances than convection inwhich viscosity increases boundary condition corresponds to a no-slipboundary. Both withdepth. The model used here will thustend to overestimatefree and rigid boundary conditions are considered for thelower theadmittance if viscosity in Venus'smantle does increase with boundary.For free-freeboundary conditions, A=B=0. For free- depth,resulting in an underestimationof the convection layer rigid boundaryconditions, thickness.Since the change in viscosityappears to be small,the a'cosh kd assumptionof uniform viscosity does not introduce large errors A = (13) into our analysis. (sinhkd coshkd - kd) Fora temperaturedistribution T(k,s) which varies with depth s in a convectinglayer of thicknessd as B = (14) (sinhkd coshkd - kd) (9) The resultsfor a model with a rigid upperboundary were found to be intermediateto thoseof the free-free and free-rigid models, whereTi is a constant,the admittanceis [Parsonsand Daly, 1983, so they are not presentedhere. The adjustableparameter for the equation(C7)] convectionmodel is d, the thicknessof the convectinglayer. In what follows, the free-free convectivelayer thicknessis denoted by z and the free-rigid convectivelayer thicknessby y. • - i• +/c•75 (10) Z(k) =2a'G (p,•-p,•) [•+ (.e-•a •r(l+e-•a)] METHOD OF ANALYSIS where In a study of PVO and Arecibo radar data, Crumpier et •r3 + 3a'k2d2 _ 2k3daA al. [1987] divided westernAphrodite Terra into eight domains •'= (71'2 '"[-k2fl•2) 2 (11)bounded by topographicand radar backscatterlinearions which a-a + 3a'k2d2 _ 2kadaB .theycalled cross-strike discontinuities (CSDs). Within the frame- work of theseCSDs, Crumplerand Head [1988] reporteda trend ½'-- (•I"2 '"[-k2a2)2 (12)of bilateraltopographic symmetry parallel to the CSDs. The cen- The constantsA andB are determinedby the boundaryconditions ters of bilateral symmetryare linear ridge segments,interpreted at s=0 and s=d. A "free" boundarycondition corresponds to a by Crumplerand Head [1988] to be analogousto terrestrialmid- free-slipboundary on whichshear stresses vanish, and a "rigid" oceanridge axes. The centersof bilateral symmetryare offset
CSD DOMAINS--APHRODITE TERRA, VENUS
30
15
-3
-45 60 90 120 150 180
LongRude(Degrees)
Fig. 2. The nineCSD domainssuperimposed on a contourmap of AphroditeTerra [after Crumpier and Ilcad, 1988]. The solidlines (domains 1-8) are the CSDsand centers of bilateralsymmeuy selected by Crumpier and Head [1988]. The dashedline marksthe positionof the ridgeaxis chosenby us for domain9. The groundtracks of orbits437 and 475 are alsomarked. Only thosedata which fell wilhin domains3 and 8, respectively,were used in the analysisof thesetwo orbits.The CSDstrend roughly NW-SE and the centers of bilateral symmetrytrend roughlySW-NE. BLACK ET AL.: GRAVITYPROFILES OVER APHRODITETERRA 30_5
TABLE 2. Location of PVO Orbits correspondingsubspacecraft point. A regularlyspaced topography , , sequence,with a sampling interval of 20 km in the direction Domain Numberof LongitudeRange PVO Orbits normalto the ridge axis, was createdby projectingeach of these topographyvalues onto the nearestpoint in this ridge-normal West East series.The positionerrors introduced by thisapproximate method 1 12 59.9 71.3 of assigningtopography values are smaller than the footprint size of the PVO altimeter [Pettengillet al., 1980], so are not 2 3 73.5 75.7 significant. Projecting the gravity and topographydata onto a 3 18 76.6 92.0 line perpendicularto the ridge axis compensatesfor the fact that the orbital trackscross Aphrodite at an oblique angle. After the 4 4 94.3 98.O LOS gravity profile and correspondingtopography profile were 5 8 99.7 106.4 constructed,each model was fit to the data by one of two least
6 16 114.3 131.1 squaresmethods. The half-spacecooling model was fit to the data for each 7 7 130.7 137.5 pass by calculatingthe model vertical and horizontalgravity 8 6 139.9 146.5 componentsat each data point position along the PVO gravity profile using (6) and (7). The two componentswere projected 9 22 161.3 194.7 onto the LOS direction and summed to give the model LOS gravity at this point. A model gravity profile was produced for all combinationsof the two adjustableparameters within the ranges0.1 cmyr -1 _ 'FABLE 3. ParameterFits for Aphrodite . i , , Domain Airy Free-Free Free-Rigid SpreadingRidge Compensation Convection Convection t• 6t, z, 6z, y, rs, 6rs, w, km km km km km cm/yr cm/yr km km 1 101 12 415 45 940 54 1.2 0.1 7769 554 2 175 18 583 60 1208 101 1.1 0.1 8467 993 3 82 5 342 15 907 23 0.5 0.1 3011 93 4 70 6 288 19 775 38 0.9 0,1 6975 557 5 56 6 303 21 906 36 3.6 0.5 6125 761 6 25 6 128 27 464 37 5.8 1.7 1444 236 7 63 19 282 48 811 99 3.8 1.2 3629 788 8 139 30 467 70 1071 121 1.1 0.8 7033 959 9 153 18 481 46 1095 77 3.0 0.6 886 198 , 306 BLACKET AL.:GRAVITY PROFILES OVER APHRODITE TERRA than this is included, given the estimatedspreading velocities. nine domainsshown in Figure 2. Table 2 lists the locationsof The fits are not significantlychanged by truncatingthose passes thesepasses, grouped by domain. Column 2 lists the numberof with longer profiles. passesin eachdomain. Columns3 and 4 list the longituderanges The Airy and convectionmodels were fit to the data for each of the ridge-crossingpoints of the orbits in each domain. passusing digital finite impulse response (FIR) filters[Oppenheim Table 3 containsa summary of the parameterfits. For each andSchafer, 1975, p. 237ff]. For eachmodel, the appropriatead- model the averageof the best-fitvalues of the adjustableparam- mittance((8) or (10)) was low-passfiltered and sampledat each eter(s) in each domain is listed along with the associateduncer- data point positionalong the PVO gravity profile to createa dis- hainties. creterepresentation of the frequencyresponse. A complexfast The best-fit Airy depths of compensationfor each pass are Fouriertransform (FlaT) algorithm was used to calculatethe dig- plottedversus the ridge-crossing longitude of thepass in Figure3. ital FIR filter coefficients. This filter was convolvedwith the The fits for which S(t)<3.0 mgal are denotedby filled circlesand topographydata seriesto producethe model gravity at this data the fits for which for which S(t)>3.0 mgal are denotedby open point position. The model gravity was projectedonto the LOS circles. The 3.0 mgal demarcationvalue was chosenbecause directionto give the model LOS gravity at this point. This proce- it representsthe degreeof uncertaintyin the data, as explained dure was carried out at each point along the data profile to create in the next paragraph. The maximum upper bound on t is 500 a model LOS gravity profile. A standarderror of estimatewas km becauseparameter space was only searchedthis far to find calculated for the fit of each model profile to the data profile. the best-fitvalue, with the rationalethat any compensationdepth The standarderrors of estimate for the Airy, free-free convec- larger than this would not be physicallymeaningful. The best-fit tion,and free-rigid convection models are given by S(t), S(z), and flee-freeconvection layer depths are shown in Figure4 andthe S(y),respectively. The best-fit parameters foreach model for each bestfits for free-rigid convection layer depth are given in Figure passare those that minimize the standard errors of estimate.The 5. In Figures4 and5, asin Figure3, filledcircles denote fits adjustableparameters for each model were varied over the fol- with standarderrors less than 3.0 mgal and open circles denote lowing ranges(for reasonsdiscussed later): 5 km _< t _<500 km, fits with standarderrors greater than 3.0 mgal. The maximum 25 km_< z _< 1000 km, 25 km <_ •t _< 2000 km. upperbounds on z and y are 1000 km and 2000 km, respectively, with the exception of the one or two passeson each plot for which the best-fit value was larger than this limit. The best fits RESULTS for half-spreadingvelocity and ridge width are shownin Figure The analysisdescribed above was carried out on 96 passesof 6. Again,the fits for which$ (v, w)<3.0 mgalare denotedby PVO gravitydata that crossed Aphrodite Terra through one of the filledcircles and those for which$ (v, w)>3.0 mgalare denoted I ! I I I I 500 - o S(t)>3.0 mgal - ß S(t)<3.0 regal 400 :300 200 100 T 0 60 80 100 120 140 160 180 200 longitude Fig. 3. Airy depthof compensationversus longitude. Filled circles are fits with S(t)<3.0 mgal; open circles are fits with S(t)>3.0 mgal. I I I o S(z)>3.0 mgal 1000• ß S(z)<3.0 mgal 8OO 6OO 400 2OO , I , 60 80 100 120 140 160 180 200 longitude Fig. 4. Free-freelayer thicknessversus longitude. Filled circles are fits with S(z)<3.0 regal' open circles are fits with S(z)>3.0 mgal. -1 i I I I I [ -- 2OO0 o S(y)>3.0 mgal ß S(y)<3.0 mgal -•1500 1000 500 6O 80 100 120 140 160 180 200 longitude Fig. 5. Free-rigidlayer thickness versus longitude. Filled circles are fits with S(y)<3.0 mgal; open circles are fits with S(y)>3.0 mgal. 308 BLACK ET AL.: GRAVITY PROHLES OVER APHRODITETERRA I 1 ' I ' I I i 2O '1 - o StY,w)>3.0 mgal - ß Sty,w)<3.0 mgal 80 100 120 140 160 180 200 longitude I I I I I t t 10000 o S(v,w)>3.0 mgal ß S(v,w)<3.0 mgal SO00 6000 •)4000 2000 o 60 80 100 120 140 160 180 200 longitude Fig. 6. (a) Half-spreadingvelocity versus longitude. Filled circles are fits with S (l•, w)<3.0mgal; open circles arefits with ,5'(v, zv)>3.0mgal. (b) Ridgewidth versus longitude. Filled circles are fits with $ (v, w)<3.0 mgal; opencircles are fits with S (v, iv)>3.0 mgal. BLACK ET AL.: GRAVrrY PROHt.ESOVER APHRODITETERRA 309 1111111111111111111111111111 _ 15 _ _ o 0 0 - _ o _ 0 0 - o o 10-- o o -- 10 o o o _ 0 0 -- Oq• o o ooJ o• o - o f 15 (d)- - o o o o - _ o - - o o - 10 oOO o o _ o o øø - -- o o - _ o o øo o - _ o Ooo o o o o o o_ - o o o o _0•0 0 J 0 0 _ _ •) o o _ - 0 0 o o 0 O 0 0 0 -- 0 __ co C9ooO -- 0 0 (b Oo o ø co o - o o o o ., Oo o _• o _ o o f o o o oo _ ...... •,. .... 0o_,.e-oo• O0 ...... 0 9.•0..... o-.o ...... 0 - 9..... • ...... - øo o d• • 'ø•o - _ o• o _ _- OoTM OOoøo 0 o •ø•Oo•_fo• •od o•oo•u -_ I, ,,-,•1, ,o•ø?•o,, [•-,, t,,,, I,,, I , , , 60 80 1DO 120 140 160 180 200 60 80 100 120 140 160 180 200 longitude longitude Fig. 7. Standarderrors of estimateof (a) Airy depth, (b) free-free depth, (c) free-rigid depth, and (d) the spreadingmodel versus longitude. The dottedline in eachplot marksthe 3 mgal errorlevel (seetext). by open circles. The upper limits on v• and w were taken to be passeswhose topography profiles, within the accuracyof the data, 20 cm/yr and 10000 km, respectively. fit the spreadingmodel as well as profilesacross the Mid-Atlantic The standard errors of estimate for the best fit of all four models Ridge. It can be seenthat, in general,the topographydoes not fit to eachpass over Aphroditeare plottedversus the ridge-crossing the spreadingmodel as well as profiles acrossthe Atlantic. Sotin longitudeof eachpass in Figures7a-7d. The horizontaldotted line et al. [1989b]suggest that the failureof the observedtopography marks the 3 mgal error level. Error values below this line indicate to fall off as age-m couldbe due to crustalthickness variations model gravity profileswhich differ from the observedprofile, in of about 15 km as a functionof age with the thickercrust in the an rms sense,by an amountless than the inherentuncertainty of centralpart of the ridge, a ridgejump [Mammerickxand Sandwell, the data. Figure 8 showsS(b) versuslongitude for the best fit of 1986], or tectonicprocesses unrelated to crustalspreading. Head modelspreading ridge topographyto the observedtopography of andCrumpler [1990] suggestthat Ovda andThetis Regiones are eachpass. The horizontaldotted line marksthe 200 m errorlevel. plateaussimilar to Icelandresulting from the presenceof elevated Valuesof S(b) below this line indicatepasses whose topography uppermantle temperature, which producesthicker crust and thus profilesdiffer by an amountless than the data uncertaintyfrom increasedisostatic topography. Our analysishas not allowedfor the profileexpected for the spreadingridge producingthe bestfit crustal thickness variations. to the observedgravity profile for that pass. A spreadingridge The resultsfor two representativePVO passesover Aphrodite would be expectedto show somevariation from an ideal profile are shownin Figures9 through11. The ORBSIM model results due to contributionsto the topographyfrom other sources,such for pass475 (in domain8) are shownin Figure 9 alongwith as crustalthickness variations. Grimm and Solomon[1989] found both the filtered(degree and order 4 gravityfield subtractedfrom thatprofiles across the Mid-Atlantic Ridge extending to an average the data) and unfiltered PVO LOS accelerations for the same distanceof 1500km fromthe ridge axis, comparable to thelengths pass.The groundtrack for pass475 is shownin Figure2. The of our Aphroditeprofiles, show an rms variationfrom the best- modelprofiles are consistentwith eachother within the 3 mgal fittingspreading ridge profiles of up to about800 m, thoughmost uncertaintyin the data. The removal of the backgroundfield of their profilesshowed variations of lessthan 600 m. If we take from this passhas removed almost 10 mgal from the signaland a variationof 600 m to be applicableto a venusianspreading gives a residualprofile very similar to that obtainedusing the ridge and add it quadraticallyto the 200 m data uncertainty,we ORBSIM program.The observedtopography profile for pass475 find thatthis variation dominates the measurementuncertainty, so is plottedalong with the model spreadingridge topographyin the total uncertaintyis about 600 m, marked by the horizontal Figure10a. The observedand model gravity profiles for pass475 dashedline in Figure 8. Valuesof S(b) below this line indicate areplotted in Figure10b. Topographyand gravity profiles for pass 310 BLACKET AL.: GRAVITY PROFILES OVER APHRODrrE TERRA o o o o o - o o0(•) o o o o o•b oo øo o • o o o o • o - Ooo o - o o o oo o oO o00 - oOo øo o •o oo• o o• •o oo o o ooo oøo _Q•o___ • ¸ 0 0 ...... t...... ,...... i...... i...... t...... i...... i...... i...... t...... i...... i...... i...... t...... i...... i...... :...... t...... i...... i...... i...... t...... i...... :...... i...... t...... i...... ,...... i...... 60 80 100 120 140 t60 180 200 longitude Fig. 8. Standarderror of estimateof topographyversus longitude for fits of spreadingridge topographyto data. The dotted line marks the 200 m error level and the dashedline marks the 600 m error level (see text). 437 (domain3) areplotted in Figures1l a and1 lb, respectively,with the topographyhere. Thiseffect is alsopresent with the andits groundtrack is markedin Figure2. Notethat both the removalof a degreeand order 2 field. verticaland horizontal scales are different in Figures10b and 1 lb. In the centralpart of Ovda Regio (88ø < longitude< 106ø) The verticalscales are the samein Figures10a and 11a, but the thereis a discrepancyin the fits for t, z, andy betweenthe lower- horizontalscales are different. The observedtopography does not numberedPVO orbits and the higher-numberedorbits that crossed resemblethe modelspreading ridge topography in eithercase. All the ridge with almostthe same groundtracks about a year later. the compensationmodels fit the datafor pass475 with standard This discrepancyhas been identified in otherstudies of Aphrodite errorsless than 3.0 mgal; none of the modelsdo for pass437. gravity[Sotin et al., 1989a], but hasnot beenexplained. It could There is no significantdifference between the fits for pass475. be due to a systematicproblem in the reductionof the raw LOS The differencein standarderrors of fit betweenthe best-fitting data. The discrepancydoes not affect any of our conclusions. model(Airy compensation)and the worst-fitting model (free-rigid Thereis a sharpincrease in Airy compensationdepths in Thetis convection)is only about0.8 mgal. The spreadingmodel fits Regio between130 ø and 140ø (Figure3). Compensationdepths the pass437 data significantlybetter than do the othermodels, eastof 140ø, the easternedge of Thetis, are generallydeeper than thoughit doesnot fit well. S (v, w)=3.41 mgal,more than 3 compensationdepths to thewest. West of 140ø Airy compensation mgal lessthan the standarderror for the next-best-fittingmodel depthsvary with longitudein a mannersimilar to that found by (Airy compensation). Herrick et al. [1989], who derived Airy compensationdepths Severalaspects of theresults bear mention. None of themodels usinga three-dimensionalpoint massmodel. Both free-freeand fit thedata east of 180ø (Figures3-8). It is probablethat both Atla free-rigid convectionlayer thicknessesshow the same patternof Regio(the topographic high lying on theequator between 195 ø greaterdepths east of 140ø (Figures4-5) and follow a pattern and210ø; Figure 2) andthe rolling uplands to thenorth of thispart roughlyparallel to thatfor Airy depthswest of 140ø. of theridge, which are morphologically different from Aphrodite Half-spreadingvelocity is low (most values of rs<2.0 cm/yr) [Ehmannand Head, 1983], are contributingsignificantly to the everywherethe fits are well-constrained(Figure 6a). This is con- gravityhere in sucha way that the gravitysignal cannot be sistentwith the conclusionof Kaula and Phillips [1981] that if ascribedto a single simple process. Venushas terrestrial-styleplate tectonicsthe spreadingvelocities In thelongitude range 121ø-131 ø in ThetisRegio, the removal are between0.5 cm/yr and 5.0 cm/yr. Sotinet al. [1989b]com- of the degreeand order4 field from the datahas reduced the bined data from many PVO passesover a narrow zone of western magnitudesof the gravityanomalies to closeto zero,indicating Aphroditeto producea syntheticgravity profile perpendicularto that the sourcesof theseanomalies are long-wavelength(of order the ridge at about88 ø. They useda staticmass model of the 10000km), andpresumably deep, processes not closely correlated topographyunder this profile to model the gravity and obtained Bt,^cI• ET AL.: GRAVITY PROFILESOVER APHRODITETERRA 311 2O o , ß ß ß o _ /' 0...4•---0--(• 10 /'/a' • • ,•..•.... •'• ....•,...,• o c• o t• _ - ,, ?• • filtered pvo los accelerations . •' ---•--.unfilLered pro los acceleraLions - _ -...... e ...... airy compensaLion model, L=155 _ • orbsira compensaLion model, L=155 km -10 2 0 -2 -4 -6 -8 -10 latitude Fig. 9. Comparisonof the fits obtained for simpletopographic compensation by ORBSIM and in thiswork for PVO pass475. Also shownare the filteredand unfiltered PVO LOS data. lower and upperbounds on the half-spreadingrate of 0.3 cm/yr for only one of the passesin this part of Aphrodite. Aphrodite and 0.5 cm/yr, in agreementwith our half-spreadingrate of 0.4 doesnot have the shapeof spreadingridge like the Mid-Atlantic cm/yr at 88ø. Ridge, thoughthe gravity data can be fit very well over part The fits for ridge width (Figure 6b) showquite a bit of scatter, of the ridge by the spreadingridge model. The modelscannot but all of the well-constrained fits are at values of w less than be distinguishedanywhere else in Aphrodite, i.e., there is no about4000 km. This corresponds,for 0.3 cm/yr DISCUSSION unlessthe topographyis very young, sinceboth thermalmodels [Phillips eta!., 1981] and the widths of Dali and Diana chas- A comparisonof Figures 7a-7d shows that for most of the mam in central Aphrodite [Zuber, 1987; Banerdt and Golombek, passesbetween 68 ø and 107ø the spreadingmodel fits the data 1988] imply that the baseof the lithospherein this regionis no significantlybetter than the other models. However, S(b)<600 m deeperthan about 50-100 km. Mantlematerial below this depth 312 BLACKET AL.: GRAvrrY PROFreES OVER APHRODITE TERRA PVO Pass 475 [] observed topography -2 ...... e...... model topography, rms diff.=0.763 km -4 0 -2 -4 -6 -8 -10 latitude PVO Pass 475 20 o o filtered pvo los accelerations ...... o ...... airy model, t=155 km --h--free-free model, z=550 km , free-rigid model, y=1250 km (b) ---•---spreading model, vs=0.6 cm/sec, w=1100 km -lo -2 -4 -6 -10 latitude Fig. 10. (a) Observedand modeltopography profiles for PVO pass475. (b) Model gravityfits for pass475 plotted along with the observedPioneer Venus LOS accelerations. BLACKET AL.:GRAvrr¾ PROFILES OVER APHRODITE TERRA 313 PV0 Pass 437 - •'00-000ra.' - - [] observed topography - -2 ...... •>...... model topography, rms diff.=l.288 km -- _ (a) -4 5 0 -5 -10 -15 latitude PVO Pass 437 2O -- .0.0.1•'0'0' _ _ 10 __ - - ' % - - • ;oo - -10 [] filtered pvo los accelerations ...... <• ...... airy model, t=75 km - --•---free-free model, z=325 km - ,. free-rigid model, y=950 km - (b) ---•--spreading model, vs=0.4 cm/sec, w=1600 km - -20 5 0 -5 -10 -15 latitude Fig. 11. (a) Observedand model topography profiles for PVO pass437. (b) Modelgravity fits for pass437 plottedalong with the observedPioneer Venus LOS accelerations. 314 BLACKET AL.:GRAVITY PROHLES OVER APHRODITE TERRA would not be resistantto viscousdeformation on geologicaltime 5. Deep Airy compensationdepths and convectionlayer thick- scales.Turcotte [1989] hasproposed a heatpipe mechanism for nessesindicate there must be some dynamic componentto the the lithospherictransfer of heaton Venusthat would allow the supportof topographyin Aphroditeeast of 140ø . lithospheretobe greater than 150 km thick, but east of 140ø Airy 6. The model fits indicate that it is likely that more than one compensationdepths are up to 250km andit is unlikelythat the mechanismis responsiblefor the formationof Aphrodite. mechanicallithosphere could be thisthick. The depths of convec- tionimplied by thefits here are quite deep (about 600-1000 km Acknowledgments.Thanks to PeterFord for providingPVO datatapes, for free-free convectionand about 1500-2000 km for free-rigid especiallythe PMTM data set, as well as muchhelp with the data and convection).The core-manfieboundary is expectedto be at about many useful discussionsof them. We thank the Magellan project for 2800km depth[Phillips and Malin, 1983],so theselayer thick- supplyingtheir digital topographymodel. We alsothank Bruce Bills for nessesimply convection extending down through a large fraction helpfuldiscussion and suggestionsfor improvingthis work. The Lunar of the mantle. Convectionin a mantlein whichviscosity increases andPlanetary Institute generously provided computer time and accessto withdepth requires deeper convection to producegravity anom- theirGeophysical Data Facility,through which ORBSIM wasused. This aliesof the samemagnitude as the constant-viscositymodel we work was takenfrom a thesissubmitted to the graduateschool, University haveused. 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