Remelting mechanisms for shallow source regions of mare basalts

Physicsof/heEarth andPlanetaryInteriors, 68(1991)9—31 9Elsevier SciencePublishersB.V., Amsterdam

Remeltingmechanismsfor shallowsourceregionsof marebasalts

Michael Manga and JafarArkani-Hamed

Departmentof GeologicalSciences,McGill University,3450 University Street, Montreal, Que.H3A LI 7, Canada

(Received3 September1990;revision accepted7 March1991)

ABSTRACT

Manga, M. and Arkani-Hamed, J., 1991. Remelting mechanismsfor shallow source regionsof mare basalts. Phys. Earth

Planet. Inter., 68: 9—31.

Two mechanismsarestudiedwhich could induceremeltingat shallowdepthswithin the Moon: a radioactiveheatingmodel

in which remelting is the result of lateral variations of the heat source concentrationemplacedby the end of the initialdifferentiation event, and a thermal insulation model in which remelting is induced by lateral variations of near-surface

conductivity as a result of a high-porosityejectablanketcreatedby basin-formingimpacts.The effectsof theseperturbations

are studied by evaluating the thermal evolution of an otherwise radially symmetric lunar model. The radioactive heating

models predict extensivepre-basinvolcanism, which would probablyremovefrom the sourceregion manyof the heat-produc-ing elementspotentially responsiblefor melting. Therefore,localizedhigh concentrationsof heat-producingelementsemplaced

earlywould mostprobably not be heat sourcesfor the basin-filling marebasalts;however, they areplausible heatsourcesfor

pre-basin marebasalts.The thermal insulation model predicts a delay of about 200 m.y. betweenimpact and volcanism.

Thermal insulation may also allow for the persistenceof source regions for youngbasaltsat shallowdepths. If greaterbasin

agesarecorrect, from 4.2 to 3.9 Ga, and mostvolcanismoccurred between3.8 and 3.6 Ga, then the thermal insulation model

may explain thedelay betweenimpact and basin filling. If thebasinsformed during a terminal cataclysmicevent at about3.9Ga, then the earliest stagesof basin filling at about 3.8 Ga may havebeen a result of melting beneaththe basinas a result of

mantle uplift. Basinfilling may have beencharacterizedby a migration of the sourceregion from beneaththe basinto beneath

the adjacent highlands.Cooling of the top 200 km beneaththe basinafter 200 m.y. becauseof its high surfaceconductivity is

consistent with the masconsupport requirement.

I. Infroduction (Urey, 1952) or deeppools of dust (Gold, 1956)were rejectedwhen it was realized that the maria

Lunar mare basaltscover 17% of the Moon’s are compositionally distinct from the highlandssurface,filling low-lying regionsandimpactbasins. (e.g. Ringwood and Essene,1970), and areseveralThey accountfor lessthan 1% of the massof the hundred million years younger than the basinscrust (Head, 1976), yet their origins have im- (e.g. Baldwin, 1963). Mare basaltsare thought toportant implications for thecompositionandther- havebeen derived from the partial remelting ofmal history of theMoon. Theorigin andpetrogen- mantle sourceregions,although they may be dueesis of thesebasalts has beena widely disputed to the persistenceof intercumulus liquids (Hub-topic for the past 20 years, and no single model bardandMinear, 1975). Severalremeltingmecha-for their origin has been widely accepted.Early nisms havebeenproposed:viscousenergydissipa-suggestionsthat the lunar maria areimpact melts tion during rebound after impact (Hulme, 1974),

pressurereleaseby the rapid reboundof the lunar

mantle after impact (Kunze, 1974) tidal energyPresentaddress:Departmentof Earth and PlanetaryScien-ces, Harvard University, 20 Oxford Street, Cambridge,MA dissipation (Wones and Shaw, 1975), magma as-02138, USA. similation and hybridization involving melt that

0031-9201/91/$03.50 ~) 1991 — Elsevier SciencePublishersB.V.

10 M. MANGA AND J. ARKANI-HAMED

originated from an initially cold deep interior incompatibleelementsin the deep interior, mak-(RingwoodandKesson,1976;TurcotteandAhern, ing the deepinterior an unlikely ultimate source1978), melting in the upwellings of early convec- region for marebasalts.tion in the deep interior (Chacko and Dc- Becauseof the uncertaintyof the early thermalBremaeker, 1982), heating causedby local con- stateof the Moon, mechanismswhich could in-centrationsof heat-producingelements(Hollister, duce remelting at shallow depths,within the top1975; Taylor, 1978), and thermal insulation by 400 km, will bestudied.Two remeltingmodelsareejectablankets(Arkani-Hamed, 1973c,1974). considered:a radioactiveheating model in which

Neither viscous dissipation (Hulme, 1974) nor heterogeneitiesin the concentrationof heat-pro-pressurereleaseinducedmelting (Kunze, 1974) is ducing elementsare emplacedby the end of theconsistent with the extended duration of mare initial differentiation event, and a thermal insula-volcanism as most basin rebound occurs nearly tion model in which lateral variations of near-instantaneouslyon geological time-scales.If tidal surface thermal conductivity, a result of a high-

energy dissipation(WonesandShaw,1975)wasto porosity ejectablanket, are createdby basin-for-provide sufficient energy to melt the source re- ming impacts. Both modelsapplyto either aMoongions, the Moon would have had to havebeen with an initially cold interior coveredby a magmavery close to the Earth; this may havebeen the ocean or to an initially totally molten Moon.

caseearly in lunar history, but the Moon would These two models are studied by looking at thehave recededquickly if tidal dissipation was sig- thermal evolution of an otherwiseradially sym-nificant (Kaula, 1971). Models involving heatpro- metric Moon. The feasibility of eachmodel can bevided by early convection (Chacko and De- evaluatedwith respectto constraintsimposedbyBremaeker,1982)or melt that originated from the observationsof lunarvolcanismin spaceandtime.deep interior (e.g. Ringwood and Kesson, 1976;Turcotteand Ahern, 1978) apply only to a Moonwith an initially cold interior; in thesemodels the 2 Modelsundifferentiateddeepinterior warmsup by radio-active heatingandconvection is initiated, or meltis removed upwardsby diapirism or melt migra- 2.1. Radially symmetricmodeltion. A Moon formed after the impact of a Mars-

sized body with theEarth (Stevenson,1987)or by The two models studied, radioactive heatingbinary fission (Binder and Lange, 1980) would and thermal insulation, involve the perturbationprobablybe initially totally molten. Evidencethat of a radially symmetricMoon. Therefore, a sym-the entire Moon was initially totally molten comes metric Moon is consideredfirst in detail to obtainfrom the magnitude of shallow moonquakes a plausible model to be later disturbed by either(Binder and Oberst, 1985) andthepresenceof 10 heterogeneitiesof heatsourcesor lateralvariationskm-scalethrust faults (Binder and Gunga, 1985), of thermalconductivity. The initial conditions forconsistent with estimatedcompressionalstresses the radially symmetricmodel,at time 4.4 Ga,after

causedby significant thermal contraction,and a an initial differentiation event, are basedon thepossible paleomagneticrequirementof an early cumulatesourcemodel in which the molten partiron core to account for the observed surface of the Moon differentiated quickly by fractionalmagnetization (Runcorn, 1977). However, the crystallization to producea plagioclase-richcrustpresenceof volatile-rich regions in the Moon in- and a compositionally stratified Moon (Taylorferred from very large Ge enrichments in and Jakes, 1974). The initial temperature, im-aluminousmarebasaltsand KREEP suggest that mediately after the solidification of the magmathe Moon was never totally molten (Dickinson et ocean,follows a peridotite solidus to the baseofal., 1989). An initially totally molten Moon would thecrust at 60 km, and decreaseslinearly to 0°Chavebeenlargelydifferentiated,leaving only small at the surface (Fig. la). This initial condition isamounts of heat-producingelements and other similar to thoseused for the initially molten part

REMELTING MECHANISMS FOR SHALLOW SOURCE REGIONS OF MARE BASALTS 11

of the Moon by other investigators(e.g. Toksözet the averageconcentrationin mare basalts,240al., 1978; Binder and Lange, 1980). The liquidus ppb(Brown, 1977). For thecalculationspresentedand solidus used are those for a dry peridotite herethe Moon wasassumedto havebeeninitially(MilIhollen et al., 1974). As themolten part of the totally molten; this assumption affects only theMoon solidifies, thereis an upward concentration distribution of heat-producingelements.Assum-of incompatibleelementstowardsthe baseof the ing insteadthe differentiation of a magmaoceancrust, producing the KREEP layer, rich in REE 500 km deep would reduce the concentrationofand incompatibleelements.The radially symmet- heat-producing elements by 36%; the thermaltic distribution of heat-producingelementshasa evolution of a model assumingwhole-Moon dif-maximum concentration in this layer, at depths ferentiation and20 ppb uraniumis approximatelyfrom 60 to 80 km; the concentrationdecreases equivalent to a model with a 500 km deepmagmaexponentiallywith depth,with a skin depthof 60 oceanand27 ppb uranium.km (Fig. ib), identical to that used by Hubbard Heat generationis provided by the long-lived

238 235 232 40and Minear (1975), i.e. the relative abundanceof isotopes U, U, Th, and K. The present-heat-producingelementsdecreasesby a factor of day bulk uraniumabundanceis assumedto be 201/e of its value every60 km. This skin depthwas ppb. This value is lower than an initial estimateofchosenso that basalts originating at a depth of 60 ppb(Toksöz andSolomon,1973)anda revised150 km from a region of 15% melt would havea estimateof 46 ppb (Langsethet al., 1976) basedconcentrationof uranium approximatelyequal to on two heat flow measurements,because these

Temperature °C u/u~0 500 1000 1500 o 25 50 75

0 ‘I

100

C2.

E a a

~ 200

a)0

300

a b400 _______________________________

Fig. 1. (a) Initial temperaturedistribution at 4.4 Ga. Thesolidus and liquidus are for dry peridotite (Milihollen et al., 1974). (b)Normalized heat-producingelement distribution basedon Taylor and Jakes(1974),with a maximumat depthsfrom 60 to 80 km, and

decayingexponentiallywith depth with a skin depth of 60 km. Whole-Moon differentiation is assumed.


1 Thermal Conductivity (W/mK) conductivity of porous rocks, but the difference6 betweenatmosphericand vacuum conditions de-

creasesas temperatureincreasesbecauseof radia-tive effects(Fujii and Osako, 1973); conductivity

500 / was found to decreasewith pressureuntil iO~// Torr (Bernett et al., 1963; Mitzutam and Osako,

I s 1974). Thus, it is expectedthat the highly frac-1000 tured breccias in the megaregolith, a layer of

I high-porosity, impact-fracturedrocks, would havea significantly reducedconductivity and, hence,it

1500 would act as a thermal blanket. Highland rock

\ 77017with K = 0.2 W mK1 (Horai andWinkler,\ 1976) is thought to be representativeof highland

2000 breccias,although it appears to be more highlyFig. 2. Thermal conductivity model used in this paper. Con- sinteredthan most breccias(Warrenand Rasmus-ductivity is for olivine (Roy et al., 1981) modified to account ..sen, 1987). This is the thermal conductivity as-for radiation effects at high temperatures(curve R). Alsoshownis the conductivity modelof Schatzand Simmons(1972) sumedfor themegaregolithin this study,although(curve S). theactualconductivity may differ by asmuchasa

factor of two (Warrenand Rasmussen,1987).The radially symmetricMoon is assumedto be

estimatesneglected the effects of global cooling coveredby a uniform thicknessmegaregolith.The

(Schubertet al., 1980) and heat flow focusing at megaregolith,assumedto be 1 km thick, basedonmareedges(Conel andMorton, 1975; Warrenand seismic studies(WarrenandTrice, 1977), is under-Rasmussen,1987). The valueof 20 ppbis equalto lain by a fractured zoneextendingto the seismicestimatesof the bulk uranium abundancein the discontinuity at 20 km (Toksöz et al., 1974). AEarth’s crust anduppermantle (Ringwood,1979) megaregolith 1 km thick, thinner than other esti-and only 3 ppb larger than the most recentesti- mates of 2—4 km (e.g. Golombek and McGill,matefor theMoon (WarrenandRasmussen,1987). 1983), is chosen to be representativeof the ra-

The temperature-dependentthermalconductiv- dially symmetric,unperturbedMoon. Thepresent-ity model used in this paperis themeanconduc- daythicknessincludesejectaandfracturingcausedtivity for olivine (Roy et al., 1981) to which an by the basin-forming impacts, effects which areestimateof thecontribution of radiationat higher not included in the radially symmetric Moontemperatureshas been added (Fig. 2). Thermal model and the radioactiveheating model, only inconductivity, K, dependsmore stronglyon poros- the thermal insulationmodel. The conductivity ofity than composition—the conductivity of the upper20 km is assumedto be 1.5 W mK~,inanorthite is about one-half the conductivity of accordancewith Keihm and Langseth(1977). Thepyroxene and olivine (Horai, 1971) whereasthe conductivities of the megaregolith and the un-high-porosity lunar soils haveconductivitiesmore denying fractured zone are approximatedby an

than two ordersof magnitudesmaller(Langsethet effective conductivity of 1.0 W mK— for theal., 1976). Although the measuredconductivity of outer 10 km usinglunar rocks correlatesstronglywith their porosity(Fig. 1, Warren and Rasmussen,1987) thenature ‘total = ~1of theporosity is more important than thedegree Keffectjve ~ K.of porosity; microcracks, i.e. pores with a highaspectratio, havea very significanteffect on con- whereI, and K

1 arethe thicknessand thethermalductivity but contribute little to porosity (Francl conductivity of the ith layer respectively,and N isand Kingery, 1954; WalshandDecker, 1966). The the total number of layers. The effect of a veryeffect of vacuum conditions further reducesthe low conductivity regolith of a few meters thick-


TABLE 1 dent rate of heat-production.At the outer surface

Model properties and parametersused in thermal evolution of theshell (thesurfaceof theMoon) the tempera-calculations tune is taken to be 0 ° C, and at the inner surface

Radius 1740 km of theshell (at a depthof 400 km) the temperatureDensity 3340 kg m

3 is equal to the solidus temperatureat that depth.Specificheat 1200Jkg~0C_i The inner surfacewas assumedto be at constantHeatof fusion 400 kJkg -

U 20 ppb temperatureover the entire time interval consid-Th/U 3.~/ ered, from 4.4 to 3.0 Ga, as most thermal evolu-K/U 2000 lion models, regardlessof their choice of parame-

ters, initial conditions, and heat transfer mecha-nism, show a nearly constanttemperatureat this

depth over this time interval (e.g. Toksöz and

ness, with K=0.01 W mK~ (Langseth et al., Solomon, 1973; Hubbard and Minear, 1975;1976), is negligible. Other model parametersare Solomonand Chaiken, 1976; Toksöz et al., 1978;listed in Table 1. Arkani-Hamed, 1979; Binder and Lange, 1980;

During the initial differentiation event, com- Chacko and DeBremaeker,1982); thus, the mod-positional stratification causedby the sinking of els studiedhereshould apply equally well to bothdensecumulatesleadsto a densitystratification. It a Moon initially coveredby a magmaocean, andis expectedthat the inverteddensitystructureof a an initially totally molten Moon. The latent heatmagmaoceansolidifying by fractional crystalliza- of fusion and percentageof melt are assumedtotion, calculatedby Herbert (1980), is a transient be distributed linearly between the solidus andcondition, as the low viscosity of this region be- liquidus temperatures(Bottinga andAllégre, 1978).

causeof its near-solidustemperatureandresidual This model may underestimatethedegreeof par-melt would quickly produce a stable density tial melting as melting may increaserapidly nearstratification. This would not changethedistribu- the solidus and more slowly at higher tempera-tion of heat-producingelementswhich remain in tunes(Bickle, 1986).the residual liquids and they will still be con- Lunar selenothermsfor the radially symmetriccentrated upwards. The intrinsically different model areshownin Fig. 3. Small amountsof meltsourceregions requiredto explain the wide range areproduced,with a maximum of 10% melt from

of marebasaltcompositionsimply that little or no 4.2 to 4.0 Ga. By 3.3 Ga the outer 320 km hasmixing has occurred in these regions (Tuncotte completely solidified and below this depth theand Kellogg, 1986; Papikeet al., 1990). This den- amountof melting is less than 2%.sity stratification is expectedto preventconvective The effectsof changingthe bulk uraniumcon-overturn in the outer layers of the Moon that are tent, the temperature-dependentthermal conduc-consideredin this paper, andheat transferin this tivity model,andtheskin depthof theheatsourceregion is by conduction.Radiativeheat transferis distribution on the Moon’s temperaturedistribu-accounted for by increasing the temperature-de- tion at 3.4 Ga are shown in Fig. 4. The tempera-pendent thermal conductivity (Fig. 2). The heat tune changeshown is relative to a model with aconductionequation bulk uranium content of 20 ppb, a heat source

3T 1 II / aT\ skin depthof 60 km, and the modified Roy et al.C~-~j-

1= ~—~(~r2K-~_-) +A (2) (1981) conductivity (Fig. 2). The bulk uranium

content waschangedfrom 20 to 15 ppb (closer towas solved inside a radially symmetric shell 400 chondritic values), to 30 ppb (Arkani-Hamed,km thick by a finite difference method. In eqn. 1979), andto 60 ppb (ToksözandSolomon,1973).(2), C is specific heat (assumedconstant), T is The temperature-dependentconductivity of the

temperature, l is time, r is radial distancefrom modified Roy et al. (1981) model used in thisthe centerof the Moon, K is temperatune-depen- paper was changed to the higher-conductivitydent thermal conductivity, and A is time-depen- model of Schatzand Simmons (1972). The fairly


________ arbitrarily chosen heat source distribution skin4 4 depthwaschangedfrom 60 to 40 km andto 100

3.6 4 4 2 km. Changing the bulk uranium content has thelargest effect on temperature,up to 800°Cat a

.—1 000o depthof 120 km when it is increasedto 60 ppb.

Even changesof only 5 ppb can changethe tem-0) peratureby up to 120°C.Increasingthe thermal

conductivity, i.e. using the Schatzand SimmonsC (1972)model, increasesthe temperatureat shallow11) 500ci depthsby up to 40°C and decreasesthe tempera-E ture at greater depthsby up to 20°C.The effecta)

H- of decreasingtheheatsourceskin depthresultsinhighertemperaturesat shallowdepths,up to 30°Chigher, whereasincreasing the skin depth results

° in lower temperaturesat shallow depths, up to400 300 200~ 100 0

Depth (km) 30°C lower, and higher temperaturesat greatendepths,up to 20°Chigher.

Fig. 3. Lunar selenothermsat five times (4.4, 4.2, 4.0, 3.6, and The two nemelting modelsstudied in this paper3.0 Ga), for the radially symmetric unperturbed model.

result from perturbationsof a radially symmetricSelenothermlabelled 4.4 Ga is the initial condition.

model with the model parameterslisted in Table1. In the radioactive heating model nemelting is

due to heating by local enrichmentof heat-pro-ducing elements,whereasin the thermal insulation

____________________ ______ model nemelting is inducedby thermalblanketing1000

causedby a low thermalconductivity ejectablan-

00 ket.800 60

ci)C0.) 600

It hascommonly beenassumedin manebasalt

petrogenesismodels that radioactiveheating pro-~ 400- ducedthe required remelting(e.g. Hollisten, 1975;o /\ 2.2. Radioactiveheatingmodel

ci) Brown, 1977; Taylor, 1978; Binder, 1982, 1985).C

200 - Remeltingis assumedto result from local enrich-0 ments of heat-producingelements emplaced byci)ci — — the end of the initial differentiation event. TheseE — — — heterogeneitiesmay be related to convectionpat-11)

H-15 terns in the magma ocean(Brown, 1977), asym-

-20C metrical fractionation of the magmaocean(War-100 300 200 100 0

Depth (km) ren andWasson,1980), locally trappedinterstitialFig. 4. The effectsof thechoiceof parameterson a selenotherm late-stageresidualliquid (Taylor, 1978), on the lateat 3.4 Ga. Curveslabelled 15, 30, and 60 arefor bulk uranium accretionof largeplanetessimals(Hartmann, 1980;contentsof 15, 30, and 60 ppb. Curveslabelled 40 and 100 are Shervaisand Taylor, 1986). Convectivemotionsfor models with a uranium distnbution skin depthof 40 and within the cumulates would very efficiently re-100 km. The short-dashedline is for a model with theconduc- move inter-cumulusliquids into overlying regionstivity model of Schatz and Simmons (1972) (Fig. 2). Thechange in temperatureis relative to a model with a bulk (Ringwood and Kesson, 1976) and regions ofuranium abundanceof 20 ppb, a skin depth of 60 km, and heat-producingelementenrichment would be atmodified Roy et al. (1981) conductivity (Fig. 2). shallowdepths,probablyin the latest-stageresid-


ual liquids. Later enrichmentsmight be due to the initial differentiation eventat 4.4 Ga. Anoma-diapirism or the migration of melt from deepen lies of this size can produce excess amountsofpreviouslyundifferentiatedregions(Ringwoodand melt approximatelyequal to thevolume of basaltKesson, 1976; Turcotte and Ahern, 1978; in the Imbrium basin.Ringwood, 1979) or to the sinking of cumulates The effect of radioactive element enrichment

and convective overturn becauseof the gravita- was studied quantitatively. The heat conductiontional instability of an inverted density structure equationfor axi-symmetnicgeometryin sphericalpossibly createdby a magmaoceanwhich solidi- coordinates,fied by fractional crystallization(Herbert, 1980). 8T i a / ar

Figure 5 shows thegeometryusedin the radio- Cp—ã~-= —~ ~j—~r2K-~—

active heating models. Many models were runwith different sizesand depthsof the heatsource + 2 ~ (K sin ~-~-~)+ A (3)

anomaly. Only two of the models are presented T Stfl 0here; in one model the region of enrichmentwas was solved by the alternatingdirection finite dif-placed from 60 to 80 km (shallowmodel), and in ferencemethod (Douglas, 1961). In eqn. (3), 0 isthe othermodel from 180 to 200 km (deepmodel), the colatitude. At the surfaceand at a depth ofThe heat source anomalywas assumedto be a 400 km, the boundaryconditionsare the sameas

disk-shapedregion with a radius of 75 km (0 = thoseof the radially symmetricmodel.At a colati-2.5°)and thickness of 20 km in an otherwise tude of 50° a zeroheat flux boundaryconditionradially symmetricMoon, emplacedby theendof wasimposed,i.e. 8T/~0= 0 at 0 = 50°.

0

RADIOACTIVE HEATING MODELFig. 5. (a) Radioactiveheatingmodel in which partialmelting results from regionsof enrichmentof heat-producingelements.(b) The

dimensions,boundaryconditions,and propertiesof the model.Thezone of enrichmentis a disk-shapedregion with a thicknessof 20km and a radiusof 75 km.


Figure 6 shows the temperaturechangealong the time interval considered. However, as timethe axisof symmetryasa resultof theenrichment progresses,deeperregions warm up for the shal-of heat-producingelements(called hereafterthe low anomalies, and both deeper and shalloweranomaly),relative to the radially symmetricMoon. regions warm up for the deepanomalies,relativeModel temperaturesshown are for a shallow to the radially symmetricmodel.anomaly (60—80 km depth) with two and three The effect of heat source anomalies on thetimes enrichment (Figs. 6a and b respectively), distribution of melt in the lunar mantle is dis-andfor a deepanomaly(180—200km depth)with played in Fig. 7. Figs. 7a—d correspond to thetwo and five times enrichment (Figs. 6c and d models shown in Figs. 6a—d respectively. Eachrespectively).The samedegreeof heat-producing figure consistsof sevenpanelsshowinga verticalelement enrichmentat shallow and great depths cross-sectionthrough theupper mantle and crustdoes not have the same effect on temperature at different times for the thermalevolution begin-becausethe amount of anomalousheat-producing ning at 4.2 Ga,andat every200 m.y. until 3.0 Ga.elementsdiffers owing to theassumedexponential The dimensionsof eachpanel shownare1200 kmdistribution of theseelementsin the radially sym- horizontally (0 = 20°)and400 km vertically. The

metric model.Thetempenatu’-eanomalyis created top of eachprofile correspondsto the surfaceofquickly, andits amplitude changesvery little over the Moon, and thebottom to a depthof 400 km.

120 25C

a b100

200

I ~42 ~42

40i 300 200 100 0 400 300 200 lOi 0

21,

c d

15

10 A 40 AN0A2~L442~400 300 200 100 0 ~ 300 200 100 0Depth (km)

Fig. 6. Temperaturedifferences(°-C)betweentemperaturesalonga radiuspassing through the middle of the region of enrichmentin

the radioactiveheatingmodel,and theradially symmetricmodel.Models shownarefor a shallowanomalywith two timesenrichment

(a) and three times enrichment(b), and a deep anomaly with two times enrichment(c) and five times enrichment (d). The labelsonthe curvesaretimes in Ga.


The degreeof melting hasmaxima of 14%, 22%, effect on the depthof melting for smalldegreesof13%, and 25% in Figs. 7a—d, respectively. Al- enrichment. For both sets of models, the maxi-though the degreesof melting are similar for a mum degreeof melting occursearly, at about4.0given degreeof enrichment,thechangein temper- Ga. The degree of melting decreaseswith timeature, asseenin Fig. 6, differs significantly; this is becauseof theglobal cooling of theMoon andthebecauseat greaterdepthsthe temperatureis closer decayof the heat-producingelements(by a factorto thesolidusandsmaller temperaturechangesare of two oven the time interval considered).By 3.0required for melting, compared with shallow Ga thereis no melt at any depthin all the models.depths, where temperaturesare well below the For the models with two times enrichment the

solidus. As the depth of the anomaly increases, degreeof melting is less than 5% everywherebysmaller and smaller amounts of heat-producing 3.4 Ga and 3.5 Ga for modelswith a shallow andelementsarerequiredto producethesameamount deep anomaly, respectively.If extraction of meltof melt. For shallow anomalies, the region of from thesourceregionrequiresmore than 5% meltenrichment does not itself melt but instead the (Turcotte andAhern, 1978; Binder, 1985)radioac-region beneathit melts, whereasfor deepanoma- tive heating models with degreesof enrichmentlies the region of enrichmentmelts.Thedifference greater than three or four times are required toin the depth of theshallowestpart of the magma accountfor the younger3.2 b.y.-old basalts.

chamberinducedby shallow and deep anomaliesis only about20 km eventhough thedifferencein 2.3. Thermal insulation model

thedepthof the regionsof enrichmentis 120 km.The effect of changing the depth of the heat The importanteffect of megaregolithinsulationsourceanomalywithin theupper200 km has little on the thermal evolution of asteroids(e.g. Haack

20° a 0° 20° b 00 200 C 0° 20° d ~ 2O~

4.2 Ga ~---~ ~ ____ -~ _____ _____ ~ ~Ei:ii:~~I000km

4.0Ga/~ ~ __ ___ ~i~I ~T~I~-=

3.8 Ga ~ ~ ___ ____ ___ ~

400km

0 km

3.6 Ga ==~ -~C~== ~ ~~== _____ ~—~--- =~ ~ - -

400 km

0km

3.4 Ga —-----—~ ~—-~-- —----~ ~— —~ ~ —~ ~—-- --

3.2 Ga

3.0 Ga_____________ _____________ _____________ _____________ _____________ _____________ ____________ _____________ 4~km

contour Interval 3% melt Contour Interval 3% melt contour Interval 3% melt contour Interval 3% melt

Fig. 7. Distribution of melt for the radioactive heating model. Each figure consistsof sevenpanelsat different times in the thermal

evolution beginningat 4.2 Ga, and at every 200 m.y. until 3.0 Ga.The horizontal dimension of eachpanelshownis 1200 km. The top

of eachpanelcorrespondsto the Moon’s surface,and the bottomto a depthof 400 km. Thecenter-lineis the axis of symmetry.The

figures correspond to modelswith a shallow anomaly with two times enrichment (a) and three times enrichment (b), and a deep

anomalywith two times enrichment(c) and five times enrichment(d). The contour interval is 3% melt.

18 M. MANGA AND i ARKANI-HAMED

et al., 1990) andthe Moon (Arkani-Hamed,1973c, where4 is the porosity,G is the effectivestress,G1974; Warrenand Rasmussen,1987) is the basis is the grain size (cm), R is the gasconstant(kcalfor the thermal insulation model. Large basin- K -‘ mol— i) A = (2—10) x iO~is a ponosity-de-forming impacts would result in the ejection of pendentconstant,and Q = —85 ±29 kcal mol~largevolumesof blocks, loosematerial, and dust, is the apparentactivationenergy.The valuesof Awhich would be distributedcircumferential to the and Q were determined experimentally bybasin.The high porosity of this material reduces Schwennand Goetze(1978) for grain boundaryits thermal conductivity, and thus, the impact diffusion of olivine crystals for temperaturesejectablanket actsas a thermal insulator. In the greaterthan about0.7 of the melting temperature.thermal insulation model, impact-createdlateral If the extrapolationof theseparametersis valid atheterogeneitiesin the thicknessof the high-poros- lower temperatures,sinteningon time-scalesof 1ity surfacelayer combinedwith impact fracturing b.y. becomesimportantat temperaturesof aboutresult in lateralvariationsof thermalconductivity. 600°C. To reachthis temperatureat the baseofThe modelingprocedureandthe radially symmet- the ejectablanket,a conductivity less than 0.2 Wtic Moon in which theseperturbationsare intro- mK1 is required for a surface layer of 10 kmduced are identical to those for the radioactive thickness. The effect of pressuremay limit theheatingmodel, thickness of the ejecta blanket by reducing its

Assumingan ejectablanket of uniform thick- porosity. At pressuresfrom 0.1 to 0.2 kbar, fromnesswhich extendsan additional 300 km beyond 2.5 to 5 km depths in the Moon, the tensilethe edge of a basinwith a radius of 300 km, and strength of rocksis exceededand fracturesmayvolumes of ejecta transportedbeyond an Im- begin to close. Porosity should disappearbelowbrium-sizebasin of (1—8) x 10~km3 (McGetchin about20 km as the compressivestrengthof rockset al., 1973; Head et al., 1975), ejecta blanket is exceeded.The seismic discontinuity at 20 kmthicknessesrange from 1 to 8 km. The thermal (Toksözet al., 1974) is often interpretedas theconductivity of the ejectablanket is taken to be depthat which porosityis eliminated.Shock-fnac-the sameas that of the homogeneoushigh-ponos- tuned lunar rocks differ significantly from shock-ity surface layer of 1 km thicknessused in the fractured terrestrial rocks in the range of crackradioactiveheatingmodel. Becauseits thicknessis closurepressures,theseare up to 2 kbar for lunargreaten,the effectiveconductivity of thetop 10 km rocks,comparedwith 0.5 kbar for terrestrialrocksbeneath and including the ejecta blanket is as- (Simmonset al., 1975). If higherestimatesof earlysumedto rangefrom 0.5 to 0.1 W mK~i.e. 2—10 meganegoliththickness,greatenthan 5 km (Hönzettimessmallerthan the effectiveconductivityof the al., 1983) and 10 km (Hantmann,1980; Spudis,top 10 km of the radially symmetric model. Be- 1984) and as high as 30—40 km (Cashore andcauseof the large uncertaintyin the thermalcon- Woronow, 1985), are correct, then the basin-for-ductivity and thicknessof the ejectablanket,re- ming impactswould havelittle effecton the thick-sults were also calculated for models with an nessof themeganegolithasthemegaregolithwouldejectablanket effectiveconductivity, Keff, of 0.5 be reducedeverywhereby compactionand sinter-W mK (onehalf the conductivity of the radially ing to its maximum possiblethicknesswithin asymmetric model) and 0.1 W mK~ (10 times few hundredmillion years.smaller conductivity than the radially symmetric The geometry,boundaryconditions,and near-model). The thicknessof the ejectablanket and surfaceconductivitiesused in the thermal insula-megaregolithis limited by sintering (temperature tion modelare shownin Fig. 8. Thebasinradiusisrelated) and compaction(pressurerelated). The taken to be 300 km, correspondingto an Im-changeof porosity due to sintering is given by brium-sizebasin,and a continuousejectadeposit(YomogidaandMatsui, 1984) with uniform thicknessand thermal propertiesis

assumedto extendan additional 300 km beyondthe basin(Croft, 1985). The reboundof the basin

8 ln(1 — ~)/8t = Aa/G3 ‘exp( — Q/RT) (4) floor after excavation is assumedto be 40 km


(Taylor, 1982). The reboundof the lithosphere canbe incorporatedinto the effectivesurfacecon-results in the rise of a mantle plug (the region ductivity. Three basin ages,4.4, 4.2, and 4.0 Ga,between 40 and 100 km is shifted upwards to are modeledafter the endof the initial differentia-betweenthe surfaceand60 km) anda correspond- tion eventat 4.4 Ga. Theseagesare greaterthaning upward displacementof heat-producingele- the Imbrium event (3.86 Ga) but the two lowerments.All of the impact energy is assumedto go agesare more typical of some estimatesof basininto heating the basin ejectawhich cools quickly excavationages(e.g. Baldwin, 1987a,b). The 4.4by radiation before resettlingon the surface,al- Ga eventwasmodeledto studythe effect of earlythoughthe effect of impactheatingof non-ejected impacts,subsequentlycoveredby more recentim-targetmaterialcanbe very significant (Bratt et al., pacts. The absolute time of the basin-forming1985).The high thermal conductivity of the basin event±100 m.y. is not critical to the relativefloor is due to temperature-inducedsintering of timing of basalticvolcanism with respectto thefractured and porous surfacematerial by basin timeof impact.rebound, impact heating and early basin-filling The effectsof the thermal blanket on the tern-basalts,and the inclusionof a 5 km post-rebound peraturebeneaththe centerof the ejectablanketbasin depth in eqn. (1) to calculateits effective (at 0 = 15°) relative to the radially symmetricconductivity. As radioactiveheattransfer is much Moon are shown in Figs. 9a, b and c, for anmore efficient than heat conduction,the 5 km effectiveconductivity, ~ of the ejectablanketdeepbasinis assumedto haveinfinite conductiv- of 0.5 W mK~,0.25 W mK~,and0.1 W mK~,ity, and thus, the effect of a non-sphericalsurface respectively,and for a basin formedat 4.0 Ga. It

aejecta blanket

.~‘ 1’,’ ‘ , - mantle ~

400 km’~’~~

K,5=O.25 K,5=2.O 100

Okrn~ !~I~antcrus:0i32~c5O0~c

THERMAL INSULATION MODELFig. 8. (a) Thermalinsulationmodel in which partial melting is incluccuby theblanketingeffectof impact ejecta.(b) Thedimensions,

boundary conditions,and propertiesof the model. Thebasin has a radius of 300 km. correspondingto an Imbrium-sizebasin,and a

uniform ejecta blanket extendsan additional 300 km beyond the basin.


should be noted that the temperaturesfor the for the radially symmetric model becauseof themodel with K

0~1= 0.1 W mK’ for the ejecta high-conductivitysurfacelayeroven the basin andblanketwould lead to sintering at the baseof the the uplift of heat-producingelements.The warm-layerandhencean increasein Keti. The effective- ing beneaththe basin at depthsgreaterthan 200nessof thermal insulation varies almost linearly km after 3.4 Ga is due to the diffusion of heatwith the ejectablanket’sconductivity at shallow laterally from beneaththe adjacentejectablanket.depths.The insulating effect occurs very quickly The distribution of melt for the model withnearthe surface;however,the penetrationof the Keit = 0.25 W mK - is shownin Figs. lOa, b andtemperatureanomaly is slow. For longer times, c at seven time intervals of 200 m.y., after anthe boundarycondition at 400 km has the effect impactat 4.0 Ga, 4.2 Ga, and4.4 Ga, respectively.of reducingand limiting the temperaturechange. Eachfigure consistsof sevenpanelssimilar to Fig.The temperaturebeneaththe centerof the basin 7 for the radioactiveheatingmodel; however,therelative to the radially symmetricMoon is shown horizontal dimension of eachpanel is 1800 kmin Fig. 9d. Initially, at depthsof about100 km the (0 = 30°). Perturbationsbeyond 0 = 30° aretemperatureis higher than for the radially sym- negligible. The maximum percentagemelt occursmetric model becauseof the reboundof hotter between3.6 and3.2Ga. The maximumdegreesofmantle material, but the temperaturedecreases partial melting are 13%, 19%, and 26% for basinswithin 400 m.y. andthe temperatureis lower than formedat 4.0, 4.2, and4.4 Ga, respectively.Oven

20~1 400 — ___________________________________

a

400 300 200 100 0 400 300 200 100 0

800 4~ —cj)c , d 3.8

~

400 300 200 100 0 400 300 200 100 0

Depth (km)Fig. 9. Temperaturedifference(°C) alonga radiuspassingthroughthe middle of the thermalejectablanket in the thermal insulation

model, and the radially symmetric model for conductivities of 0.5 W mK~ (a), 0.25 W mK

1 (b), and 0.1 W mK~ (c). Thetemperaturedifference beneaththebasinis shownin (d). The labels on the curvesarethe times in Ga.


the first 200 m.y. after impact, for basinsformed higher near-surfacetemperaturessurroundingtheat 4.2and4.0 Ga, the regionbeneaththebasinhas Serenitatisbasin inferred from electrical conduc-the highestdegreeof melting; this is the result of tivity measurements,which werepreviously inter-mantle uplift beneaththe basin, whereasthe re- pretedas being a result of the removalof heatandgion beneaththe ejectablanket is only beginning heat-producingelementsby basaltextrusion(Dyalto heatup. However, as the impactageincreases, and Daily, 1979; Vanyanet a!., 1979). The effectthe effect of mantle uplift becomesrelatively of basalt removal is much smaller than the ther-smaller, and for a basin formed at 4.4 Ga the mal insulationeffect.highestdegreeof melting after200 m.y. is beneath The motivation for developingthe thermal in-the ejecta blanket. Qualitatively, the effects of sulationmodel is that it relatesthe spatial distri-changingthe conductivityof the ejectablanketare bution of the mariato the causeof remelting.Theidentical; however,the degreeof melting changes heterogeneitiesresponsiblefor remelting in thisto a maximumof 7%, 13%,and35% at 3.2 Ga for model are impact induced, and the remelting ismodelswith K

0~~of 0.5 W mK~,0.25 W mK’, indirectly impact triggered.The thermalinsulationand 0.1 W mK 1, respectively(seeFigs. ha and model used is similar to those used by Arkani-b). Thehigh near-surfacetemperaturesinducedby Hamed(1973c, 1974),but the distribution of heata blanket with a conductivity of 0.1 W mK

1 sourceshas been revised in accordancewith thewould probably lead to sinteningand to a come- qualitativemodel of Taylor andJakes(1974)—in-spondingincreasein conductivity.The volumesof stead of being distributed exponentially to theexcessmelt inducedby thermalblanketingare, in surface,the maximumabundanceoccursat depthsgeneral,more thanone orderof magnitudelarger from 60 to 80 km. This hasthe effectof increasingthan the volume of basaltsin an Imbrium-sized the temperaturesbeneaththe ejectablanket morebasin.Thetemperatureanomaliespredictedby the than in the earlier modelspresentedby Arkani-thermal insulation model are consistentwith the Hamed (1973c, 1974). The melting anomaliesin

30° a ~. ~. b 30° 0• 30°

4.2 Ga -~ ___________

4~bu

4.0 Ga ________ ____ ~ _____

3.8 Ga ~ ____ ~ ~~m0m~ ~ e~

3.6 Ga ~ ~1~== ~ ~~1==r ~ =~~=

3.4 Ga

3.2 Ga ~ ~

3.0 Gacontour Intorvel 3% melt Contour Interval 3% melt contour Interval 3% melt

Fig. 10. Distribution of melt for the thermal insulation model.Each figure consistsof sevenpanelsat different times in the thermal

evolution beginningat 4.2 Ga,and at every200 m.y. until 3.0 Ga.The horizontal dimensionof eachpanelshownis 1800 km. The topof eachpanel correspondsto the Moon’s surface,and the bottom, to a depth of 400 km. The center line is the axis of symmetry.

Ejectablanket effective conductivity is0.25 W mK~. The figurescorrespondto basin formation agesof 4.0 Ga (a), 4.2 Ga (b), and

4.4 Ga (c). The contour interval is 3% melt.


30° a 0° 30° b 0° 30°0 Er

4.2 Ga — ____ _____ ~— _______

400km -0 km

4.0 Ga _____ ___ _____ ____ ___

400 km0 km

38 Ga ~ ~400 km0 km

36 Ga ~ ___ ___

400 km—- — 0km

34 Ga ~ ~ ~____________________________ ____________________________ _____________________________ 400 km

3.2 Ga ~ 0 km

_____________________________ ____________________________ ____________________________ ____________________________ 400 km

3.0 Ga km

_____________________________ ____________________________ _____________________________ ____________________________ 400 km

contour interval 3% melt contour interval 3% meltFig. 11. Distribution of melt at seventimes for the thermal insulationmodel for ejectablanketswith an effective conductivity of 0.5

W mK’ (a) and 0.1 W inK~ (b) (seeFig. 10 for descriptionand explanation).Contour interval is 3% melt.

the earlier modelsare due to perturbationsin the thermal evolution calculationswith observationsthicknessof the solid lithosphereoverlying a par- and measurements.Theseobservationsand mea-tially molteninterior which thickensabout100 km sunementsprovide constraintson the models. Asfrom 4.0to 3.0 Ga for a radially symmetricMoon; only shallow sourcesare consideredhere,in effect,this is largelya resultof the higherbulk uranium the constraintstestthe feasibility of shallow sourcecontentof 60 ppb (Ankani-Hamed,1973c) and 30 regionsin a static Moon.ppb (Arkani-Hamed,1974).Also, a simulatedcon-vection in the partially moltenregionwasused in 3.1. Chronologythe earlier models, which enhancesthe upwardheat transfer from the deeperinterior and thus The questionof whethertherewas a time delayreduces the cooling rate of the near-surfacere- between basin formation and basin filling orgions. In the models presentedhere, the melting whether mane volcanism has been a continuousanomaliesare magmachambersin a solid litho- processsince basin excavation, is an importantsphere. time constraint for thermal models. Based on

cratercounts (Baldwin, 1987b),viscous relaxationmodels of basins (Baldwin, 1987a), and K—An

3. Discussion nadiometnic ages of selected ejecta samples(Schaeffer,1977) the agesof the basinsare calcu-

The plausibilitiesof bothnemelting modelsare lated to rangefrom 4.3 to 3.83 Ga. However, theevaluatedby comparingthe consequencesof the absenceof impactmeltsolden than 3.9Ga (Ryder,


1990)andwidespreadshockmetamorphismof the magmachamber,suggestingadelay betweenbasinsurfaceat about 3.9 Ga (Wasserbenget al., h977) excavationand basin-filling. If the ages inferredsuggestthat the largeneansidebasinsmayhaveall from most of the returnedsamples(e.g. Geiss etbeenformed overa relatively shortperiodof time, al., 1977) and crater counts on surface flows andlasting about 50—100 m.y. It is now recognized pre-manecraters (e.g. Boyce, h976) are correct,that marevolcanismextendedto pre-basinforma- then there are delays of at least 50—100 m.y.tion times(e.g. Taylor et al., 1983). The extent of betweensignificantbasinfilling andbasinexcava-pre-basin mane volcanismcannot be determined tion, even if thebasins formed during a terminal(Ryder and Taylor, 1976), but its widespreadex- cataclysmic event at about 3.9 Ga (e.g. Ryder,tent, including the far side, is suggestedby the 1990). If basin agesare mucholder (e.g. Baldwin,distribution of dark-haloed craters (Schultz and 1987a, b), and mare agesare representativeofSpudis, 1979) and recent spectral images by the major basin filling, then possible delays rangeGalileo spacecraft(see EOS, 1991, p. 1). Most from 100 to 500m.y. Thethermalinsulationmodelreturned mare basaltagesrange from 3.8 to 3.2 is consistentwith a delay betweenvolcanismandb.y. (Geisset a!., 1977), andfrom cratercounting, basinformation. However, this delay might not bebasin filling is generally thought to have lasted observedin the agesof basin fill if the melt wasfrom 3.8 to 2.5 Ga (Boyce, 1976), andpossibly to induced by pre-existing thermal blankets fromas recently as 1 Ga (Schultz and Spudis, 1983), earlier impacts.If modelswhich ascribeolder ageswith most filling occurring from 3.8 to 3.6 Ga to thebasinsare correct, then the earliestflows in(Head, 1976). the Imbrium basin, for example,might be due to

The radioactive heating models produce the the thermal blanketing effect of olden nearbylargestamountof melt early, from about4.2 to 4.0 basins such as Serenitatis.This model also main-Ga, and the volume of melt decreasesover time tains a large degreeof melting until 3.0 Ga, whenbecauseof the decayof the heat-producingele- calculationswere stopped, andmight accountforments andthesecularcooling of theMoon. Thus, the extendedduration of volcanism in a coolingradioactiveanomaliesemplacedearly in lunar his- Moon.tory, by the endof the initial differentiationevent, The earlieststagesof volcanism in the thermalwould probablyresult in extensivepre-basinmane insulationmodel might notbe dueto the effect ofvolcanism. The prolonged production of melt theejectablanket,but ratherto the initial effect ofwould require very large degreesof heat-produc- the uplifted mantle, enhancedby impact heatinging element enrichment;enrichmentlargeenough (an effect not included here). Both uplift and

for morethan 50% melt to exist at about4.2 Ga. impact heating temperatureperturbationsessen-Such large amountsof melt early in the Moon’s tially disappearbeforeabout500m.y. after impacthistory would probablybe extrudedand muchof (Bratt et al., 1985). After aboutthe first 200 m.y.

the heat-producingelements responsiblefor the the effect of the insulating blanket may be moremelting, very efficiently reducing the enrichment, significant. Basin filling may have been char-Thus, evenwith substantialinitial enrichment,suf- acterizedby amigration of the sourceregion fromficient degreesof partial melting would probably beneath the basin as it cools, to beneath thenot extendpast3.8 Ga. Forenrichmentat shallow adjacentejectablanketas this regionwarmsup. Indepths,very little of the enrichedzone melts and Mane Orientale, the small volume of flows allowsthe extraction of basaltswould have less of an for a good mapping of the temporal history ofeffect on subsequentmelting than the extraction volcanism: the largest central basalts(volumetri-of melt producedby enrichmentsat greatendepths cally) areroughly 130 m.y. youngerthan thebasin,wheretheenrichedzoneitself melts. and the two smaller regions in the outer rings

The thermal insulation model inducesand en- (over the ejecta blanket), Lacus Autumni andhancesthe degreeof partial melting beneaththe LacusVenis,are about400—500m.y. youngerthanejectablanket. There is a period of time, about the basin(Greeley, 1976). The thermal insulation200 m.y., betweenan impact andthe creationof a effect would not result in the most volumetrically

24 M. MANGA AND £ ARKANi-HAMED

significant flows occurring so early, but rather sourcereaches25—30%melt. Lu—Hf, Sm—Nd, Sn—300—400m.y. later, andis entirely consistentwith Rb, and total REE data suggest less than 10%the later flows, both in time and in space.The melting of a cumulatesource(Unruh et al., 1984).smaller volume of basaltsin Onientalecompared Heat-producingelementswere assumedto panti-with Imbrium might be due to the young ageof tion entirely into the meltand the removalof meltthe Orientalebasin(3.83 Ga) andsmallersize, i.e. removesa correspondingproportion of heat-pro-

coolerMoon, and thinnerejectablanket(Arkani- ducing elementsfrom the source region to theHamed, 1974). Smaller basins should exhibit a Moon’s surface. For this simplified extrusiongreaterdelay betweenformation and the begin- model, melt is removedevenfor the radially sym-ning of volcanismbecauseof a smallerandthinner metric, unperturbedMoon. Allowing for melt ex-

ejectablanket, andyounger basinsshould induce traction, Figs. 12aand b show the distribution oflessmelting with a longer time delay(seeFig. 10). melt for two representativeradioactive heating

As it is unlikely that regions with largedegrees models, one with a shallow heat-sourceanomalyof partial melting can persist for a long time with threetimesenrichment,and a secondwith awithout the extractionof melt, the thermal evolu- deepheat-sourceanomalywith five times enrich-tion modelswere recalculated,and melt was re- ment;melt disappearsentirely by 3.7and 3.75 Gamoved whenever the degree of partial melting and extrusion ends by 4.1 and 4.15 Ga, respec-exceeded5%. Melt migration would probably ne- tively. For the thermal insulation model with anquine more than 5% melt on the Moon (Turcotte ejecta blanket effective conductivity of 0.25 Wand Ahern, 1978), but Binder (1985) suggested mK~(Fig. 12c), melt disappearsby 3.05 Ga andthat melt will leave the source region when the extrusionends by 3.4 Ga. Even for this simple

20° a 20° b 0° 20°30° C 0° 30°O km

4.2 Ga _______ _______ ~ _____ _______ -

400 km0 km

4.0 Ga =-~ ~ ____ ____ _________ ______

__________________ _________________ _________________ _________________ 400 km0 km

3.8 Ga ~ ~ ___ ____ _______

__________________ _________________ _________________ _________________ 400 km

3.6 Ga 0km

__________________ _________________ _________________ __________________ _____________________________ _____________________________ 400 km

3.4 Ga____________________ ___________________ ___________________ ____________________ ________________________________ ________________________________ 400 km

3.2 Ga 0km

__________________________________________ ___________________ ____________________ ________________________________ ________________________________ 400 kmcontour Interval 1% melt contour interval 1% melt contour interval 1% melt

Fig. 12. Distributionof melt for the melt extraction modelsfor theradioactiveheatingmodelwith a shallowanomalywith threetimes

enrichment(a) and a deep anomalywith five times enrichment(b), and the thermal insulationmodel with a basinageof 4.0 Ga andan ejectablanket with an effective conductivity of 0.25 W mK — (c). Melt is removedto the surface when the degreeof melting

exceeds5%. Each figure consistsof six panelsat different times in the thermal evolution beginningat 4.2 Ga, and at every 200 my.

until 3.2 Ga. The horizontal dimension of eachpanel is 1200 km (a, b) and 1800 km (c). The top of eachpanel correspondsto theMoon’s surface,and the bottom to a depth of 400 km. The center-lineis the axis of symmetry.The contour interval is 1% melt.


melt removal model, the difference between the gion beneaththe basin cools more quickly thantwo remelting models shown in Fig. 12 is signifi- the region beneaththe ejecta blanket and high-cant; melt extrusionstopsmorequickly for a deep lands,andthemasconwould be bestsupportedbyheat-sourceanomalythana shallow anomaly,and theuppermantle beneaththe basin.only the thermal insulation model allows for the The viscosities of both remelting models werepersistenceof melt for an extendedperiodof time. studiedquantitatively; theviscositiesof the mod-

els werecalculatedbasedon a power creeplaw for3.2. Masconsupport dry websterite(Ave Lallemont, 1978),

Large positive gravity anomaliesareassociated o~= -~ =Aa1~ exp(Q/RT) (5)

with thecircular marebasins.The thicknessof themarebasaltsrangesfrom a few hundredmetersin where s~is the viscosity, a is thedeviatoric stress,the irregular maria(Hörz, 1978)to up to 8 or 9 km ~ is thestrain rate, R is thegasconstant,A = 102

in the center of the large basins(Solomon and kbar” s, Q = 77.9 kcal/mol~ is the activationHead, 1979). The absenceof positive Bouguer energy,and n = 4.3. Dislocation creepdominatesanomaliesover thehighlandsandpositive free-air for stressesgreater than I bar whereasdiffusionanomaliesover unfilled basins (Bills and Ferrari, creep dominates for stressesless than 0.1 bar1980)imply that the mascons,themassconcentra- (Turcotte and Schubert,1982). A changein devia-tions responsible for the gravity anomaly, are toric stress from I bar to 1 kbar changesthelimited to the filled circular basins.Thesemascons viscosity by 10 orders of magnitude (fig. 3b ofare the result of rapid isostatic rebound after Solomonet al., 1982). However, becausethe devi-impact excavationand thesubsequentmarefilling atoric stressesin the Moon are not known, and(Phillips andLambeck,1980). Thesupportof these becauseof the uncertainty in extrapolating thedensity perturbationsfor 3.5 b.y. requiresa strong high temperaturemeasurementsto lower tempera-upper mantle beneath the mascons; estimated tures, the absolutevalues of viscosity were notviscosities during the period of basin formation calculated.As the temperaturedependenceof bothand mare filling are of theorder of 1025_1026 Pa diffusion anddislocationcreepvaries linearly withs~ (Arkani-Hamed,1973b; Baldwin, 1987a) and exp(Q/RT), and assumingthat the stressesat aof theorderof 1027_1028 Pa s~for the last 3 b.y. given depthdo not changesignificantly with time,(Arkani-Hamed, 1973a). thechangein viscosity can be calculatedby

The supportof masconsfor over 3 b.y. requiresa stronguppermantlebeneaththemascon.In the Q / 1 1 \

(6)radioactive heating models, a masconemplaced ln ~12— ln m = —

over the region of enrichmentmight not be verywell supported as a result of the temperature where the subscripts denote values at differentrelated decreasein viscosity. However, if the times or places.The secularchangein viscosity asbasaltsflowed into low lying areasand basins,and a function of depth from 4.0 to 3.0 Ga for thedid not accumulatedirectly abovetheir source,the radially symmetric model is shown in Fig. 13a.masconmay be better supported.This would re- Over theperiodfrom 4.0 to 3.0 Ga, the periodofquire significant lateral displacementof thebasalt mascon formation, the viscosity of the outer 200for a single source region as the source region km increasesby 1—4 orders of magnitude, inmust be largeenoughto accountfor thevolume of agreementwith the viscosity increaseestimatedbasalt. However,manysmall sourceregionswould from maresubsidenceduring this period(Arkani-not haveas large an effect on the viscosity. In Hamed, 1973b).The changein viscosity was alsoaddition, removal of melt to form the mascon calculatedfor the radioactiveheatingmodels andremovesheat and radioactiveelements,reducing thermal insulation models. Figure 13b shows thethe temperature anomaly and increasing the lateral viscosity variations as a result of tempera-viscosity. In the thermal insulation model the re- ture differences betweenthe radially symmetric


tion of the radial increasebecauseof the seculara 30 cooling of the Moon of Fig. 13a, a significant

3.2 increase(Baldwin, 1987a), and the lateral varia-tions shown in Fig. 13b. The height andjagged-

2 ness of the Onientale and Imbrium rims have

36 probablynot changedsignificantly sincetheir for-

mation (Baldwin, 1987b), implying that the secu-3.8 lan increasein viscosity since the formation of

0 older basinsmay havebeen comparablewith theviscosity decreasebeneaththe ejectablanket. The

> absence of positive free-air gravity anomalies400300 200 100 a aroundSerenitatisand Imbrium, and in fact, the

1 presenceof negativeanomalyrings (Fig. 5, Bills

b 0 and Ferrari, 1980), implies that the relaxationof0 D2 basin rim heights, despitetheir long wavelength,

05 would be determinedby the viscosity at shallowdepthsin the crust. The relaxationof jaggedness,

S2 becauseof its short wavelength, also would in-

volve only shallow depths. Thus, although Fig.

13b suggeststhat the viscosity decreasebeneathS3 the ejecta blanket dominatesoven the secularin-

-~ crease, rim height relaxation is controlled byH near-surfaceviscosity, which is always very large

-4 becauseof the low near-surfacetemperatures.If

400 300 200 100 this is thecase,thepreservationof rim height andDepth (km) jaggednessdoesnot provide a good constrainton

Fig. 13. (a) The changein viscosity with time for the radially lateral viscosity variations, and the decreaseinsymmetric model relative to the viscosity at 4.0 Ga. The viscosity beneaththe ejectablanket predicted bynumberson the curvesare the times (billions of yearsago). (b) the thermal insulation model is not inconsistentLateral viscosity variationsbecauseof temperaturedifferences with the observations. The viscosity decreasebetweenthe radially symmetric modeland the perturbedmod- . .

elsat 3.4 Ga.Curvesarefor the radioactiveheatingmodelwith shown in Fig. 13b is also the maximum decreasea shallow region of heat-sourceenrichment with two times and theviscositydecreasewould diminish neartheenrichment and three times enrichment (S2, S3) and a deep edgesof the ejectablanket. Only the region be-regionof enrichmentwith two times enrichmentand five times neaththe basin showsan increasein viscosity, byenrichment(D2 and D5), and the thermal insulationmodel (a a factor of aboutfive in theouter 150 km.basinageof 4.0 Ga and an ejectablanket effectiveconductivity .

of 0.25 W mK~) beneaththe ejectablanket(H) and beneath In the radioactive heating model, for the de-the basin(B). greesof enrichmentassumedat greatdepthsfrom

180 to 200 km (curves D2 and D5) the changein

viscosity is very small, whereastheviscosity for ashallow heat-sourcemodel (curves S2 and S3)

model andtheperturbedmodels at 3.4 Ga. In the decreasesby 1—4 orders of magnitudebecauseofradioactiveheatingmodels(curves S2,S3, D2, and the largertemperatureanomaly.Thus, the thermalD5) the temperaturesusedare along the axis of insulationmodel is themostlikely to be consistentthe anomaly.In the thermalinsulation model, the with the mascon support requirement,althoughtemperaturesusedare the maximum temperature the radioactive heating model is acceptablepro-increasesbeneaththeejectablanket (curveH) and vided that thebasaltsaredepositedat somelateralalongtheaxisof symmetryof thebasin(curve B). distance from their sourceregions, or the source

The viscositychangeover time is thecombina- depthis very large.


3.3. Sourceregion depth The constant-temperatureboundarycondition as-sumedat a depth of 400 km does not permit a

Oven 20 typesof marebasaltshavebeenidenti- study of the feasibility of the two remeltingmech-fied; however, they are generally grouped into anisms at greater depths. To consider greater

three categories: high-Al, high-Ti, and low-Ti depths,theeffectsof solid-stateconvectionshouldsuites. There is a general trend of decreasingTi be included unless the whole Moon was stablycontent with age, although the youngestflows in density stratified.Procellarumand Imbnium are high-Ti basalts. Ifthe melting depth, and hencebasaltsourceregion 3.4. Extrusiondepth, increaseswith time, asecondhigh-Ti sourceregion underlying the low-Ti sourceregionwould The extrusion history of marebasaltshasbeenbe required for the youngest flows. Proposed related to the Moon’s global stateof stress, suchdepthsfor the sampledhigh-Ti basaltsare of the that extrusionoccurredduring an initial periodoforder of 100—200 km (Hugheset al., 1989), and expansion,andextrusionendedby a changefromfrom 200—400 km (KessonandLindsley, 1976)to global expansion to global contraction (Solomonmore than 400 km (Hugheset al., 1988) for the and Chaiken, 1976; Solomon, 1978), with extru-low-Ti suite. sion beingenhancedby local stressesasa resultof

In thecumulatesourcemodel(Taylor andJakes, masconloading (Solomon and Head, 1979). Ten-1974), a decreasein melting depth over time re- sional stressesact to maintain open conduitsandsuIts in a decreasein Ti content (e.g. Brown, to accentuatestressat the propagatingcrack tip,1977). Radially symmetricmodels are consistent whereascompressionactsto closeconduits,accel-with a decreasein melting depth, but neither the eratemagmafreezing, andimpedecrack tip prop-radioactiveheatingmodel nor the thermal insula- agation(Solomon, 1978).tion model predicts significant change in the For a Moon initially covered by a magma

depthof the melting anomaly. In the radioactive ocean,the lithospherewould havebeendominatedheating model, different suites might originate by tensional stresses(Binder and Lange, 1980;from heat-producingelement enrichmentsat dif- Turcotte, 1983) becauseof the contractionof the

ferentdepths; however,therewould beno correla- outer few hundredkilometersas it cooled aroundtion of composition with age, as all suites would a relatively constant-volumeinner mantle. Thus,erupt early (before basin formation) if these en- although the Moon may havebeen contracting,richmentswereemplacedby the end of the initial extensionalstressesin the outermost layers, cou-differentiation at 4.4 Ga. In the thermalinsulation pled with additional local extensionalstressesfrommodel, different source depths might be due to regions of melting, would have facilitated magmaheterogeneitiesin the thicknessand thermal prop- extrusion for an extendedperiod. However, earlyertiesof the ejectablanket. For a thermal blanket impact gardeningmay have releasedstressesthatwith a thermal conductivity of 0.5 W mK’ corn- had built up before the end of basin formation

paredwith 0.25 W mK~, thedepth to the top of (Solomon,1986)thusreducingaccumulatedtensilethe magma chamberdiffers by about 100 km at stressesover the first 500 m.y. For the magma3.6 Ga. This differenceis at the lower limit of the ocean models studied by Kirk and Stevenson

100—250km differencebetweenestimatesof source (1989), constrainedby a maximum radius changedepths for the high-Ti and low-Ti basalts. The of ±1 km (Solomon and Chaiken, 1976), thepossible persistenceof melt at shallow depths Moon expandedfor the first 2 b.y. as a result of(about 150 km, a proposeddepth for high-Ti thecompetition betweenthermal contraction andbasalts) in the thermal insulation model makesit volume expansionproduced by chemical differ-an ideal model for the origin of the late Ti-rich entiation, resulting in extensionalstressesfor thisflows in OceanusProcellarumandImbrium. These period. Also, magma-drivenfracturing may be the

basaltshave not been sampled, so no petrologi- most important transfer mechanismin the crustcally inferred depth is available for comparison, and lithosphere (Spenceand Turcotte, 1990); if

28 M. MANGA AND 3. ARKANI-HAMED

this is the case,theexistenceof sufficient melt in the caseof deepregions of enrichment,the melt-the marebasaltsourceregionsmay be asufficient ing occurs in the region of enrichment and theprerequisitefor basaltextrusion, melt producedearly would probably be extruded

It has commonly been assumed that mare andwould carry with it manyof theheat-pnoduc-basaltsrosehydrostatically,andthus,as thesource ing elementsresponsiblefor melting. Thus, it isdeepened the basalts rose to higher levels unlikely that heat-producingelementenrichments(Solomon, 1975; Wilson and Head, 1981). How- emplacedby the endof the initial differentiationever, no systematicaltitude—age relationship of eventcould beresponsiblefor a significantamountthe lunar maria is observed(Lucchitta andBoyce, of thebasin-filling basalts,althoughthey maybe a1979),and theeruptionof melt mayhavedepended suitableheatsourcefor pre-basinmanebasalts.more on thevolume of magmaproduced,andthus In the thermal insulation model, nemelting is

on local pressures,than global hydrostaticeffects induced about 150—200 km beneath the ejecta(Muller and Muller, 1980; Whitfond-Stark, 1982). blanketby the low thermal conductivity of basinThe surfaces of many of the maria (notably ejectablankets.The extendedduration of melting

Senenitatis,Cnisium, Smythii, and Van de Graaff) beneaththeejectablanketmakesit an idealmodeldo not at presentlie on an equipotentialsurface, for theorigin of theyoungerhigh-Ti basalts,pos-and a best-fit ellipsoidal surfacewould require a sibly including the unsampledhigh-Ti basalts incenterof mass that is offset 2.7 km eastof the OceanusProcellanumand Imbrium which are be-present-daycenterof mass (Sjogren, 1977). Also, tween3.0 and2.5 b.y. old. The thermal insulationthe surfaces of Mare Tranquillitatis and Mane model also predicts a delay between the impactFecunditatislie 2 km abovethis best-fit ellipsoidal andejectablanket inducedremeltingof about200surface(Sjogren, 1977). This would suggest that m.y. Such a time lag is consistentwith someof thesignificant subsidenceof basinshasoccurreddun- older basin agesif most of the basin filling oc-ing mare filling andlater by viscous relaxationas curned between3.8 and 3.6 Ga; however, if thea result of mascon loading (Arkani-Hamed, basinsformed during a terminalcataclysmicevent1973a,b).Onthebasisof sucharguments,it would between3.9 and 3.8 Ga, any delay is likely to beappearthat the existenceof depressedregions is less than 100 m.y. Early basin filling might havenot sufficient for their filling, and some type of beendueto theuplift of deeperandhottermaterialheterogeneityis responsiblefor their filling, beneaththe basin, to impact heating, or to melt

inducedby olden ejectablankets.After about 200m.y., the region beneaththe basin is colder than

4. Conclusions the surroundingsbecauseof its higher surfaceconductivity and theuplift of heat-producingele-

Both models studied, a radioactive heating ments,andit is betterableto support themascons.

model and a thermal insulation model, result in The thermal insulation model explainsthe spatialremeltingat shallowdepths.The radioactiveheat- relation between the mania and basins, as theing model, in which enrichmentsof heat-produc- volcanism, although not directly triggered by im-ing elementsare the heat sources for remelting, pact, is due to impact-relatedthermal pertunba-

results in nemelting early in lunar history and tions.would result in extensivepre-basinvolcanism, iftheseenrichmentswere emplacedby the end ofthe initial differentiation event. The effect of Acknowledgmentschangingthe depth of the enrichmentwithin thetop 200 km hasa minor effect on the depth of This work was supportedby Natural Sciencesmelting. However, melting occursbeneathshallow and Engineering Council of Canada (NSERC)regionsof heat-producingelementenrichment,and grant no. 0GP0041245,and an NSERC under-

the extrusion of this melt may not affect the graduateaward to M. Manga. The authorsappre-concentrationof the heat-producingelements.In ciatea constructivereview by R.B. Baldwin.


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Remelting mechanisms for shallow source regions of mare basalts

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