Modeling the provenance of the Apollo 16 regolith

N. E. Petro1 and C. M. Pieters1

Received 17 August 2005; revised 1 June 2006; accepted 12 June 2006; published 7 September 2006.

[1] The regolith at the Apollo 16 landing site, the only Apollo landing site in the centrallunar highlands, contains material derived from a number of sources. A model thataccounts for the introduction of basin ejecta and mixing of the megaregolith is used toestimate the abundance of basin material in the Apollo 16 regolith. Megaregolith mixingmodel estimates of the abundance of primary ejecta from the Imbrium, Serenitatis, andNectaris basins are found to be present in roughly equal (8–10%) proportions.Additionally, the presence of mare-derived material in the Apollo 16 regolith suggests thata significant component of the regolith (15–23%) is derived from lateral transport.There are inherent difficulties in directly comparing model results with ground truth atApollo 16. Results suggest shallower mixing during ejecta emplacement than predicted byOberbeck et al. (1975).

Citation: Petro, N. E., and C. M. Pieters (2006), Modeling the provenance of the Apollo 16 regolith, J. Geophys. Res., 111, E09005,

doi:10.1029/2005JE002559.

1. Introduction and Background

[2] The lunar surface is marked by impact craters of allsizes, ranging from submillimeters to several thousandkilometers in diameter. Although impacts that form cratershave occurred throughout lunar history, the formation of thelargest of these craters, known as basins, is believed to belimited to the early history of the Moon (before 3.85 Ga)[e.g., Wilhelms, 1987; Ryder, 2002]. During this earlyperiod, basins ejected a large amount of material thatwas distributed across the Moon and mixed with surround-ing surface materials. This repetitive process created a zoneof mixed material at the surface of the Moon ranging from afew meters to several kilometers deep [Arvidson et al.,1975; Horz et al., 1991]. This mixed zone, created earlyin lunar history and continuously modified by subsequentsmaller impacts, is known collectively as the megaregolith.Concurrent with and following the formation of the basins,smaller impacts modified the megaregolith, creating a fine-scale, meters-deep mixed zone known as the regolith. Ourprimary motivation for the study presented here is toevaluate a basin ejecta and megaregolith mixing model ata location in the lunar highlands that has been sampled sothat the constraints of the model can be understood withmore confidence. This work will then allow the model to beused to describe the origin of megaregolith elsewhere on theMoon.[3] Starting in the late 1960s, planetary scientists devel-

oped quantitative models describing the effects of thecratering process on the lunar surface. Early models werebased on measurements of terrestrial impact and explosioncraters and on remote observations of lunar impact craters.

For instance, models were developed to predict the thick-ness of ejecta surrounding lunar craters and were used toestimate how much material had been introduced to theApollo landing sites by specific nearby basins [McGetchinet al., 1973; Pike, 1974]. Additionally, Oberbeck et al.[1975] developed a model to describe the mixing thatoccurs during ejecta emplacement. The Oberbeck mixingmodel provided a means for estimating the proportion oflocally derived material relative to the amount of foreignmaterial introduced to any given location by a crater orbasin. The Oberbeck model was initially used to describenumerically the character of the deposits from craters andthe large nearside basins [Head, 1974]. Subsequently, theOberbeck model has been utilized to estimate the proportionof foreign to local material in the regolith at severallocations on the lunar surface [Pieters et al., 1985; Headet al., 1993; Blewett et al., 1995].[4] Each of the Apollo missions to the Moon sampled a

wide range of materials derived locally from the immediatesurroundings as well as foreign material derived from moredistal regions. For example, in their analysis of Apollo 11samples, Wood et al. [1970] identified anorthositic materialin the predominately mare regolith. Analysis of theApollo 11 site using remote sensing techniques [Staid etal., 1996] and geochemical analysis of regolith sampleswith particle sizes less than 1 mm [Korotev and Gillis,2001] indicate that some portion of this anorthositic materialwas introduced to the site via lateral transport. The presenceof material foreign to the local geology illustrates thesignificant role of impact cratering in lunar surface modifi-cation through the lateral redistribution of material. Addi-tionally, the ubiquitous presence of impact breccia in theregolith at the Apollo 16 site led many to conclude that themegaregolith had been significantly modified by materialsfrom an impact basin or basins [e.g., Hodges et al., 1973;Head, 1974; Ulrich et al., 1981; Spudis, 1989].

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1Department of Geological Sciences, Brown University, Providence,Rhode Island, USA.

Copyright 2006 by the American Geophysical Union.0148-0227/06/2005JE002559$09.00

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[5] The specific origin of the breccias at Apollo 16 wasnot obvious initially, and is still subject to debate. The earlyapplication of crater ejecta models generated several diversehypotheses. In estimating the contribution of basin materialto the Apollo 16 site McGetchin et al. [1973] employed acrater ejecta scaling equation and concluded that theImbrium basin contributed a small amount of materialrelative to that of the Nectaris basin. Head [1974] utilizedphotogeologic interpretation of the Apollo 16 region toconclude that the Nectaris basin was the dominant basinthat modified the region, and therefore that it must havecontributed a great deal of material to the surface. Incontrast, Oberbeck et al. [1974] utilized ejecta mixingequations in concluding that the Imbrium basin was thedominant basin that modified the Apollo 16 region.[6] Two recent integrated models have been used to

describe the nature of various components in the regolithdue to the redistribution of material by basin-formingimpacts [Haskin et al., 2003a; Petro and Pieters, 2004a].The Haskin et al. [2003a] model characterizes individualbasin-derived ejecta deposits within a given area or ‘‘squareof interest’’ (SOI). Haskin’s model contains a number ofsteps, each of which evaluates characteristics of a givenbasin’s ejecta deposit within a SOI. These attributes aremodeled in detail and include the mass of primary ejecta,the size, distribution, and excavation efficiency of second-ary craters, and the fraction of primary basin ejecta in eachdeposit. The model by Petro and Pieters [2004a] estimatesthe total amount of foreign and locally derived material inthe megaregolith at a single location on the lunar surfacefollowing the formation of all recognized basins. The modelutilizes several parameters, each of which can be variedsystematically in order to evaluate a range of possiblescenarios. The basin ejecta mixing (BEM) model of Petroand Pieters [2004a] can also be used to estimate the depthof the mixed zone as well as the amount of material derivedfrom any basin present in the megaregolith following thebasin formation period.[7] While the Haskin et al. [2003a] and Petro and Pieters

[2004a] models are similar in that they quantify the effectsof basin formation and describe the average properties ofbasin ejecta deposits, they are different in that they addressdistinct issues relating to basin ejecta emplacement and canbe used to serve independent purposes. For example, theHaskin model characterizes, in substantial detail, the natureof individual basin deposits within a SOI while the Petroand Pieters BEM model describes the bulk properties ofcomponents across the megaregolith. In modeling basinejecta emplacement, the BEM model utilizes simplifyingassumptions while the Haskin model quantifies severalaspects of the ejecta emplacement process. Both modelsmake the assumption that topography does not effect ejectaemplacement and that ejecta distribution is continuousabout the center of a basin.[8] Both Haskin et al. [2003a] and Petro and Pieters

[2004a] applied their respective models to evaluate theregolith components at roughly the same area in the centerof the South Pole-Aitken Basin (SPA). The Petro and Pietersstudy evaluated the effects of a range of parameters, whilethe Haskin study focused on a narrower range of scenarios.Despite the different approaches of the two models,they reached a similar conclusion, namely that the central

region of SPA is dominated by locally derived regolithcomponents.[9] In modeling the Apollo 16 regolith, we focus specif-

ically on estimates of the contributions from the Nectaris,Serenitatis, and Imbrium basins. We use the Petro andPieters [2004a] approach modified to include post-basin-formation regolith components. We present the approach inthis paper as a complement to the detailed work of Haskin etal. [2003a]. We seek to improve upon the simpler BEMmodel in order to better address global issues associatedwith the effects of basin formation on the Moon. Forindividual regions the interested reader is encouraged toapply the detailed approach of Haskin et al. [2003a] forcomparison. In improving upon the BEM model, we eval-uate different degrees of mixing during basin ejecta em-placement (Oberbeck m parameter) as well as the extremecase of no mixing (where ejecta is deposited as layers). Theresults of these calculations are then compared to geochem-ical estimates of the amount of Imbrium basin materialsampled at the Apollo 16 site. Lunar-wide effects ofbasin formation are discussed elsewhere [Petro and Pieters,2005, 2006; N. E. Petro and C. M. Pieters, The lunar-wideeffects of basin formation on the lunar crust, manuscriptin preparation, 2006].

2. Setting of the Apollo 16 Site

[10] The Apollo 16 mission landed in the Descartes High-lands, a region that was later determined both by sampleanalysis and by photogeologic interpretation to have beensignificantly modified by ejecta derived from surroundingbasins [Hodges et al., 1973; Wilhelms, 1987]. Amongst theApollo landing sites, Apollo 16 is the only mission to havelanded in the dominantly anorthositic highlands, and there-fore the landing site is the only Apollo site to have beenexposed to all of the �4.5Ga of lunar history. Previousresearch regarding the basin(s) that may have been respon-sible for the modification of the Descartes region focused onthe large, relatively young Imbrium basin [Morrison andOberbeck, 1975] and the older, closer Nectaris basin [Head,1974; James, 1981; Spudis, 1989]. Figure 1 illustrates themain topographic ring and distances to the Apollo 16 site forthe Nectaris, Serenitatis, and Imbrium basins.[11] The spatial relationship between the Apollo 16 site

and these large and relatively close basins is clearly impor-tant for understanding the geologic history of the site.However, for completeness we must also consider theeffects of the other 40 basins on the regolith at theApollo 16 site. The location of the main topographic ringof all 43 recognized basins, as well as the location of theApollo 16 landing site (indicated with a star) are identified inFigure 2. Each of the 43 basins is assigned a numbercorresponding to its place in the stratigraphic sequence asdefined by Wilhelms [1987], where 0 corresponds to theoldest basin (SPA) and 42 represents the most recent basin(Orientale). The stratigraphic number and diameter of themain topographic ring for each basin is provided in Table 1.Given the number of basins and the complex cratering historyof the lunar surface, determining the source of specificmaterials in the Apollo 16 regolith presents an imposing task.[12] It is instructive to compare the site in the middle of the

southern farside (SPA-1) studied by both Haskin et al.

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[2003b] and Petro and Pieters [2004a] with the nearsidehighlands (Apollo 16). Both the SPA-1 andApollo 16 sites arelocated in broadly similar terranes. The SPA-1 site, likeApollo 16, is significantly cratered and situated in a region

that has not beenmodified by the emplacement ofmare basalt.However, on the basis of their spatial relationship to basins,the Apollo 16 site and SPA-1 have had distinctive geologichistories, and therefore themegaregolith produced at each sitedue to basin modification has most likely evolved quitedifferently. This relationship is illustrated in Figure 3, wherethe main topographic ring diameter as well as the distancefrom Apollo 16 and SPA-1 is identified for each basin. AtSPA-1, most of the large (>600 km diameter) basins arelocated greater than 90� from this site (i.e., they are in theopposite hemisphere). In comparison, the relationship be-tween the basins and the Apollo 16 site reveals that there aremany large, young basins close to the Apollo 16 site. Indeed,most of the basins greater than 600 km in diameter are within90� of the site. The proximity of the Imbrium, Nectaris, andSerenitatis basins to the Apollo 16 site (Figures 1 and 3a)suggests that contributions from these large basins played amajor role the evolution of the surface there.

3. Evolution of the Lunar Regolith: The Apollo16 Example

[13] Material contributed from several basins locatednear the Apollo 16 site should be found in the regolith.The question as to which basin(s) had the most significanteffect on the regional geology, and consequently on thesamples, has largely focused on two basin sources: Nec-taris and/or Imbrium. For example, Spudis [1989], usingEarth-based spectral measurements of the lunar surface,proposed a Nectaris component in the Apollo 16 landing siteregion. Sample analyses suggest several possible sourcesfor materials in the Apollo 16 regolith. On the basis of

Figure 2. Nearside centered, Mercator projection of Clementine albedo (750 nm) image with latitudesfrom 70�N to 70�S. The locations of the main topographic ring for each basin (as identified by Spudis[1993]). The number associated with each basin corresponds to a number listed in Table 1. A gray staridentifies the Apollo 16 landing site, and a white star identifies the SPA-1 site.

Figure 1. Apollo 16-centered, orthographic projection ofClementine albedo (750 nm) image. The diameter of themain topographic ring [Spudis, 1993] and distance to theApollo 16 site from the Imbrium, Serenitatis, and Nectarisbasins are given (in kilometers).

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petrographic and geochemical analysis of Apollo 16 samples,Stoffler et al. [1985] concluded that there are two distinctgeologic units at the Apollo 16 site. Each unit representsprimary basin ejecta materials, with one from the Nectarisbasin and one from the Imbrium basin. Ejecta from theNectaris basin were identified as being highly feldspathicand KREEP-free, while the Imbrium deposits were identi-fied as KREEP-bearing polymict-breccias. It is clear that theconsiderable debate regarding the modification history ofthe Apollo 16 site has generated several viable hypotheses.Our modeling of the Apollo 16 regolith is intended to placeconstraints on the likelihood of finding materials from anyof the nearby basins in the sample collection.

3.1. Basin Ejecta Mixing Model for Apollo 16

[14] The basin ejecta mixing (BEM) model by Petro andPieters [2004a] considered the effect of 42 basins identifiedby Wilhelms [1987] and Spudis [1993] on the developmentand composition of the megaregolith at a location inside the

South Pole-Aitken Basin. The model utilized several param-eters, namely the mixing parameter (m) of Oberbeck et al.[1975] and the ejecta thickness equation of Pike [1974]. Themodel assumes that the emplacement of basin ejecta createsa mixed zone where foreign material mixes homogeneouslywith the local surface. The ejecta scaling equation ofHousen et al. [1983] was not used in the initial model.Comparisons are made between the Pike [1974] and Housenet al. [1983] models in section 4.2. Different combinationsof BEM model parameters for basins result in variations inthe amount of foreign material introduced to a site, which inturn results in differing estimates of the composition of theregolith.[15] The transient crater size for each basin is integral in

determining the amount of basin ejecta introduced to a site.Petro and Pieters [2004a] evaluated three estimates oftransient crater size for each basin (a minimum, mean,maximum). The size estimates for all basins were derived

Table 1. Lunar Basinsa and Example Mixing Scenario

Basin Main Ring, km Ejecta Amount, m Mod. m/2 Mixing Depth, m FRC Nectaris RC Serenitatis RC Imbrium RC

0 SPA 26001 Tsiolkovsky-Stark 700 3.22 13.04 42.0 0.082 Insularum 600 17.34 6.71 116.3 0.173 Marginis 580 2.47 9.97 24.6 0.264 Flamsteed-Billy 570 3.70 8.76 32.4 0.325 Balmer 500 2.26 8.18 18.5 0.416 Werner-Airy 500 83.18 3.84 319.1 0.327 Pingre-Hausen 300 0.01 11.14 0.2 0.388 Al-Khwarizmi-King 590 1.50 11.99 18.0 0.389 Fecunditatis 690 41.83 6.58 275.3 0.4310 Australe 880 21.00 10.22 214.5 0.4811 Tranquillitatis 700 211.51 5.15 1089.4 0.3012 Mutus-Vlacq 690 27.82 7.12 198.2 0.4013 Nubium 690 63.06 6.10 384.9 0.4614 Lomonsov-Fleming 620 2.17 11.64 25.2 0.5015 Ingenii 315 0.01 14.55 0.2 0.5416 Poincare 325 0.02 12.97 0.3 0.5717 Keeler-Heaviside 500 0.42 15.75 6.6 0.5418 Coulomb-Sarton 440 0.18 14.41 2.6 0.5719 Smythii 740 10.28 9.80 100.8 0.5320 Lorentz 365 0.05 13.44 0.7 0.5621 Amundsen-Ganswindt 335 0.04 10.85 0.4 0.6022 Schiller-Zucchis 335 0.07 9.32 0.7 0.6323 Plank 325 0.02 12.09 0.29 0.6624 Birkhoff 325 0.02 14.65 0.26 0.6925 Freundlich-Sharanov 600 1.64 17.07 27.9 0.5626 Grimaldi 440 0.29 10.80 3.2 0.6027 Apollo 480 0.31 15.06 4.7 0.6128 Nectaris 860 305.47 4.69 1432.5 0.43 0.2129 Mendel-Rydberg 420 0.89 11.88 10.6 0.48 0.2030 Moscoviense 420 0.13 14.88 1.9 0.51 0.1831 Korolev 440 0.32 17.59 5.6 0.52 0.1832 Mendeleev 365 0.05 14.46 0.7 0.55 0.1733 Humboldtianum 650 2.01 11.24 22.6 0.51 0.1834 Humorum 425 8.78 5.67 49.8 0.56 0.1635 Crisium 740 37.78 7.86 296.9 0.52 0.1836 Serenitatis 920 311.80 6.54 2038.7 0.41 0.15 0.1537 Hertzsprung 570 0.94 15.89 14.9 0.44 0.14 0.1438 Sikorsky-Rittenhouse 310 0.02 10.88 0.23 0.50 0.13 0.1339 Bailly 300 0.02 10.49 0.18 0.54 0.12 0.1240 Imbrium 1160 178.76 8.11 1449.3 0.48 0.13 0.13 0.1241 Schrodinger 320 0.03 11.28 0.3 0.53 0.12 0.12 0.1142 Orientale 930 2.98 12.77 38.1 0.52 0.12 0.12 0.11

aLunar basins and their corresponding main ring diameters identified by Spudis [1993] given in stratigraphic order with oldest at the top [Wilhelms,1987]. Example of the calculation of the total non-indigenous or foreign regolith component (FRC) and the regolith component (RC) from specific basins inthe Apollo 16 regolith. This scenario used the Pike [1974] ejecta thickness equation, the modified m/2 parameter, and the mean* transient crater sizes for allbasins.

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from the size for transient craters of 10 basins described byWieczorek and Phillips [1999]. A fourth group (mean*) wasdefined as the mean transient crater size for the 32 basinsnot explicitly described by Wieczorek and Phillips [1999]along with the transient crater size for the 10 basins thatthey defined. The magnitude of the Oberbeck mixingparameter m was also varied systematically to examine theeffects of a reduced degree of mixing between the ejectedmaterial and the target. Each combination of the variousparameters produces three estimates: the total amount offoreign material introduced to the site from basin ejecta, the

maximum depth of the mixed zone due to the incomingejecta, and the proportions of basin-derived and original insitu material in the megaregolith. For each basin-formingevent, the depth of the mixed zone at a site is determined bythe product of the amount of ejecta introduced to the siteand the mixing value (m) used. These values are recalculatedafter each basin event so as to describe the nature of themegaregolith during its evolution.[16] We have applied the BEM model to the Apollo 16

site to evaluate the nature of the regolith at that site. Anexample of the mixing process with one set of parameters,

Figure 3. Comparison of the main ring diameters of all lunar basins [Spudis, 1993] and their distance to(a) the Apollo 16 site and (b) the SPA-1 site. Numbers refer to the basins listed in Table 1. After Petro andPieters [2004a].

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highlighting selected basin events, is illustrated in Figure 4.The scenario in Figure 4 utilized the Pike [1974] ejectascaling equation, mean* transient crater sizes, and a mod-ified (reduced) form of the Oberbeck et al. [1975] mixingratio called ‘‘m/2’’ (see section 4.1). The depth of mixing atthe Apollo 16 site and the amount of material in the regolithderived from each basin immediately following that basinevent are illustrated in Figure 4. It is important to note thatthe values given for each step in Figure 4 are for the periodimmediately following the specific basin event labeled andnot those of the final proportion of material in the regolith.Each mixed zone consists of the ejecta from that specificbasin mixed with preexisting material, which often consistsof mixed material from prior basins. For example, theSerenitatis mixed zone incorporates the material from allprior events such as Tranquillitatis and Nectaris as well ascrustal material not mixed by prior events. Subsequentevents such as Imbrium do not mix as deeply at the siteand thus incorporate and mix material only within theSerenitatis mixed zone (which contains material from allprevious events).[17] In subsequent sections we examine the depths of the

mixed zone and the amounts of primary basin ejecta in theregolith by systematically varying the parameters that areinvolved in the basin ejecta mixing model. The calculationsfor the Apollo 16 site allow us to estimate the total amountof local material derived from ancient preexisting crustalmaterial as well as the abundance of primary ejecta fromspecific basins, such as from Imbrium, in the presentregolith.

3.2. Post-Basin Contribution to the Apollo 16 Site:Constraints From the Samples

[18] Analysis of rock or breccia fragments in representa-tive soils allows the relative proportion of different types ofmaterial to be measured. Although most of the soil samplesfrom the Apollo 16 site are feldspathic, Korotev [1997]identifies as much as 6% mare basalt material in the <1 mmgrain size fraction of the regolith. While this proportion ofmare material is a function of the grain size investigated, weassume that it is generally representative of the bulkproportion of mare material in the Apollo 16 regolith. This

measurement allows us to estimate the net amount ofmaterial introduced to the Apollo 16 site following theperiod of basin formation [Petro and Pieters, 2004b]. It isimportant to remember that the amount of mare basalt at theApollo 16 site only represents a net accumulation ofmaterial after billions of years of impact history, duringwhich repeated impacts into the lunar surface both intro-duced material to the site and removed material from thesite. Since the closest mare to the Apollo 16 site is 220 km,Korotev’s sample data are in clear contrast to the theoreticalprediction of Arvidson et al. [1975], who estimated thatonly �1% of regolith would be derived from greater than10 km from any site on the lunar surface.[19] Even though the total amount of foreign material,

both highland and mare, introduced to the Apollo 16 siteafter the formation of the basins is not explicitly identifiedby Korotev [1997], the measurement of basalt abundanceallows the total to be derived. To estimate the total amountof post-basin-formation foreign material (both mare andhighland material), we assume that all mare material foundat Apollo 16 was introduced after the basins formed. Thisassumption is based on the fact that both McKay et al.[1986] and Simon et al. [1988] did not find any mare-derived material in the Apollo 16 ancient regolith breccias.The absence of basalt in ancient regolith breccias impliesthat mare material was introduced to Apollo 16 followingthe formation of the Cayley Plains (�3.9 Ga). Zeigler et al.[2003] identified potential source maria for the basalt frag-ments found at Apollo 16 based on their composition andremote sensing analyses of the surrounding region. TheZeigler et al. [2003] analysis places compositional limits onpotential sources and sets an outmost boundary at�1100 km. Additionally, Zellner et al. [2003], based onages of basaltic impact glasses from Apollo 16, suggestedthat the craters Theophilis and Cyrillus could be sources fora portion of the mare glasses at Apollo 16. The innermostboundary is set by the closest mare to the Apollo 16 site,which is �220 km to the east. The two craters identified byZellner et al. [2003] are in the source region set by theZeigler data. This range of source regions is illustrated in

Figure 4. Illustration of example homogeneous mixing scenario illustrating the evolution of themegaregolith with time. Given is the depth of the mixed zone associated with the Tranquillitatis, Nectaris,Serenitatis, Imbrium, and Orientale basin events as well as the amount of primary basin ejecta in themixed zone immediately following that event. White areas represent the pre-Nectarian crust following theSPA event. The example illustrated here utilized the Pike [1974] ejecta thickness equation, the modifiedm/2 mixing ratio, and the mean* transient crater size for the basins.

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Figure 5, with additional intermediate rings drawn at 220 kmintervals.[20] Assuming that the source of the Apollo 16 mare

basalt is within the rings illustrated in Figure 5, a propor-tional amount of surrounding highland material introducedto Apollo 16 over the same period can also be estimatedfrom the areal coverage. Between the 220 and 1100 kmrings mare basalt covers �40% of the possible sourceregion. We assume lateral transport operates in a statisticallyrandom manner over this entire region for the last �3.9 Gaperiod. The observed 6% mare basalt thus suggests a totalamount of �15% foreign material (derived from 1100 to220 km) in the present Apollo 16 regolith. A benefit of thismethod of quantifying cumulative lateral transport is that weare automatically accounting for all craters without specif-ically having to identify and calculate the contribution fromeach crater. Note, however, that a small portion (�5%) ofthe large source region overlies the KREEP-rich terraneidentified by Jolliff et al. [2000], suggesting that post-heavy-bombardment cratering may have also introduced anet amount of �1% KREEP-bearing material to the Apollo16 site unrelated to primary Imbrium ejecta. Furthermore,55% of the area between 1100 and 220 km from Apollo 16contains highland material, suggesting that additionalKREEP-bearing material (i.e., Imbrium ejecta) could alsobe introduced to the Apollo 16 site.

[21] On the other hand, if the source of the mare is limitedto a smaller closer region (e.g., the region between 220 and440 km that contains Sinus Asperitatis and the southwesternregion of Mare Tranquillitatis) the areal coverage by mareis only 26% and the total amount of foreign materialintroduced following the formation of the basins could beas great as 23%. In the case of the potentially smaller sourceregions, almost none of the PKT is covered, suggesting thatno post-heavy-bombardment KREEP material would beintroduced to the Apollo 16 site. Thus the range of foreignmaterial from distances >220 km introduced to the Apollo16 site after the formation of the basins is estimated to be�15 to 23%.

4. Modified Parameters of the Basin EjectaMixing Model

[22] Modification of the initial BEM model in order tomore accurately bound estimates of the amount of foreignand local material in the regolith is discussed here. We focuson the two parameters that are most important to estimatingthe amount of foreign and locally derived material in theregolith at the Apollo 16 site: the ejecta mixing ratioparameter and the ejecta scaling model used.

4.1. Modified Mixing Ratio

[23] Oberbeck et al. [1975] defined a ratio of locallyderived to foreign-derived material in the ejecta fromcraters. The original mixing ratio is defined by

m ¼ 0:0183� R0:87s ; ð1Þ

where Rs is the range from the center of the crater to thelocation of interest. This original equation and severalscaled forms of it were initially utilized by Petro and Pieters[2004a]. However, the strict use of this equation may not bethe most accurate description for basin ejecta emplacement.Schultz and Gault [1985] found from laboratory-scalecratering experiments that a larger amount of primary ejectais preserved at the surface than predicted by the Oberbeck etal. [1975] mixing model. This strongly suggested that themixing values predicted by Oberbeck were too large. On theother hand, remote sensing observations of Copernicusanorthositic ejecta mixed with mare basalt [Pieters et al.,1985] and Orientale anorthositic ejecta on surrounding marebasalt [Head et al., 1993; Blewett et al., 1995] appear to beconsistent with predictions from the Oberbeck ratio up to am value of �5.00.[24] To address these concerns, we compare two series of

scenarios of basin ejecta mixing for Apollo 16 megaregolith,one that strictly utilizes the Oberbeck et al. [1975] defined mvalues and one that uses a modified (lower) value. The twoforms of the mixing ratio compared and used here are thosethat provided model results for SPA-1 in the work of Petroand Pieters [2004a] most similar to the alternate modelingresults of Haskin et al. [2003b]. The modified mixing valueutilizes the Oberbeck values of m up to 5.00, and valuesgreater than 5.00 are modified by roughly half to address theuncertainty in mixing values. We call this modified mixingratio ‘‘m/2.’’ The modification defined here specificallydecreases by half the difference between the Oberbeckcalculated m value (from equation (1)) and 5.00 for thosemixing values greater than 5.00. For example, if m is 25, ‘‘m/

Figure 5. Clementine 750 nm albedo image centered onthe Apollo 16 landing site. Innermost ring (at 220 km fromApollo 16 site) marks nearest mare basalt deposit. Theoutermost ring (at 1100 km) marks outermost potentialsource of mare in Apollo 16 regolith as determined byZeigler et al. [2003]. Intermediate rings are spaced at 220 kmintervals.

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2’’ is 15. This has the effect of decreasing the mixingefficiency of the ejected material, resulting in a greaterconcentration of primary ejecta in the regolith as the ejectedmaterial is mixed to shallower depths (see section 4.3 for thedepth of mixing calculation). Haskin et al. [2003a] alsoidentified the need to modify the Oberbeck mixing param-eter in order to account for a reduced mixing efficiency. Itshould be noted that several basins located near the Apollo16 landing site, including the Nectaris basin, have mixingvalues less than the Oberbeck m value of 5.00 and are notvaried in any of the scenarios discussed below.

4.2. Amount of Basin Ejecta

[25] For our evaluation of the Apollo 16 site we alsocompare the Pike [1974] estimate of ejecta thickness to theHousen et al. [1983] ejecta thickness estimate in severalscenarios. The Pike [1974] equation in the BEM model usedby Petro and Pieters [2004a] is

t ¼ 0:033r

R

� ��3:0; ð2Þ

where t is the amount of basin ejecta introduced to a site, Ris the radius of the transient crater, and r is the distance tothe center of the basin. The Housen et al. equation producesa non-dimensional estimate of the amount of basin ejecta(t*), scaled to crater size, that is introduced to a site. TheHousen et al. equation used for comparison is

t� ¼ A er � 2ð Þ2p

sin 2qð Þer�2r��er ; ð3Þ

where A is a coefficient of value 0.08 as advocated byWieczorek and Zuber [2001], er is the range exponent in thedebris profile and has a value of 2.61 (representative ofimpact into Ottawa Sand) [see Housen et al., 1983], q is theangle at which the ejecta leave the transient crater (assumedto be 45�), and r* the a nondimensional distance from thecrater center. Haskin et al. [2003a] used a different value ofA (0.2) and for er (2.83, representative of impact into water)but used the same q value. Incorporating the constants wehave selected into the equation and solving for thedimensional case, the Housen et al. equation simplifies to

t ¼ 0:0078Rr

R

� ��2:61; ð4Þ

where the variables are the same as in the Pike equation (2).Values of the amount of basin ejecta introduced to a sitedetermined using the Housen et al. equation are on averageless than those predicted by the Pike equation. It isimportant to note that for both ejecta models, the finalestimates of the amount of basin ejecta introduced to theApollo 16 site are corrected in our calculations to accountfor the curvature of the Moon. This correction has the effectof increasing the estimated amount of material introduced toApollo 16 when compared to equations (2) and (4).

4.3. Depth of Mixing and Proportion of Basin Materialin the Megaregolith

[26] In the BEM model, the depth of the mixed zone iscalculated for each event and is created by the emplacementof basin ejecta. The depth of mixing (DoM) was initiallydefined by Petro and Pieters [2004a] as the depth to whichforeign material is mixed with the locally derived material.

It was assumed that the mixing occurs homogenouslythroughout the mixed zone for each basin. In section 5 wewill discuss the implications of such an assumption on theconcentration of material at and near the surface. The valuefor the depth of mixing is the product of the mixingparameter used, either m or m/2, and the amount of ejectaintroduced to the location (from equations (2) or (4)). Theeffect of modifying the mixing parameter decreases thedepth of mixing but since the amount of material remainsthe same, the BEM model predicts a greater concentrationof foreign material near the surface for the scenarios thatutilize the m/2 parameter.[27] The calculation of the proportion of basin material

follows from the method described in Petro and Pieters[2004a]. At the location of interest on the lunar surface, theDoM and the proportion of foreign and locally derivedmaterial involved in the mixing are calculated for each basinevent. The effects of all 42 basin events are calculated in thestratigraphic sequence defined by Wilhelms [1987], with theproportion of locally derived material in the megaregolithbeing continuously updated after each event. Following theyoungest basin, the total amount of foreign material in themegaregolith is calculated (e.g., foreign regolith component,FRC, in Table 1). In a similar fashion, the resultingproportion of material in the megaregolith derived from aspecific basin is calculated after each subsequent event.

5. Results of BEM Model for Apollo 16

[28] Using the BEM model with the parameters discussedabove, we estimated the proportion of various componentsin the regolith at the Apollo 16 site. The specific contribu-tion from the Nectaris, Serenitatis, and Imbrium basins wereestimated in addition to the contribution of material fromthe remaining 39 basins. We first assess the character of theregolith assuming basin ejecta mixes homogeneously withlocal material during emplacement. This is the approachtaken by Petro and Pieters [2004a] for SPA-1. We thenassess the case when no mixing occurs during emplacement.These two end-member cases should bound what happensin reality. The specific effects of the SPA basin are excludedfrom these analyses because the scale of the basin formingevent is so much greater than the other events that itdominates pre-Nectarian history.

5.1. Regolith Model With Homogeneous Mixing

[29] We calculated 12 scenarios for the Apollo 16 sitefor all basins using three estimates of transient crater size,two sets of mixing values, and two models for the amountof crater ejecta introduced to the site. In each of the 12scenarios, we calculated the abundance of primary Necta-ris, Serenitatis, and Imbrium ejecta, the amount of materialfrom all other basins, and the amount of ancient crustalmaterial present in the regolith immediately following theformation of the basins. The abundances of these fivecomponents at the end of the basin-forming period areillustrated in Figure 6 for each of the 12 scenarios. Theabundances illustrated in Figure 6 are only for basin eventsand do not include the lateral transport effects of smallercratering events that occurred following the period of basinformation. The numerical results of four representativescenarios are given in Table 2. Detailed results for one

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sequence (indicated with an arrow in Figure 6) are listed inTable 1.[30] The percentages of material from the Nectaris,

Serenitatis, and Imbrium basins are generally self-consis-tent throughout all scenarios regardless of which ejectathickness model is used, particularly amongst the scenarioswith the same mixing values. The largest variation (�3%)in the estimates of basin material present occurs betweencomparisons of models using different mixing values. Theestimates of the relative amount of Imbrium and Serenita-tis material among all scenarios are generally very similarto each other. The calculations for Nectaris are a specialcase. The Nectaris basin is the oldest of the three basinsspecifically examined here [Wilhelms, 1987; Spudis, 1993]that leads to basin ejecta from Nectaris being modified tothe greatest degree by all subsequent basin-mixing events.Additionally, Nectaris is located close to the Apollo 16 site(Figure 1), which results in a mixing value less than 5.00(as determined from equation (1)). Because the mixingvalue is less than the Oberbeck m value of 5.00, the samevalue is used throughout all scenarios. The lack ofvariation of the mixing parameter for Nectaris in theseexamples means that any variation in the final amount inthe regolith is due to modification by later basins. Con-versely, because Imbrium received little modification bysubsequent basins, the only variation in the estimate of theamount of Imbrium ejecta is due to the mixing valuesused.

5.2. Regolith Model With No Mixing

[31] We also explore the end-member in which no mixingoccurs during the emplacement process. Such a scenariorepresents the opposite end of the mixing spectrum whencompared to homogenous mixing. Sample data can then beused to constrain the approximate magnitude of mixing thatoccurs. When no mixing occurs during emplacement, basinmaterial is deposited as individual discrete units. A com-parison of simple layered basin ejecta emplacement (nomixing) with the homogeneous mixing example presentedin Table 1 is illustrated in Figure 7. For the no mixing end-member (Figure 7, left), basins that contributed more than50 m of material to the Apollo 16 site are labeled and otherbasins whose contribution is less than 50 m are groupedtogether. To the right of this illustration is a similar scenariothat assumes homogenous mixing (which follows from theexample in Figure 4). The values for the cumulative amountof ejecta involved in Figure 7 are the same for both end-members and are given in Table 1. Any dilution of surfacematerials that occurs in the no mixing case is a result ofsubsequent regolith gardening and the formation of craters.In the no mixing end-member case, Imbrium-derived ma-terial is concentrated in the near surface and would be onlydiluted by materials from other basins that underlies theImbrium deposit by post-Imbrium cratering. The thicknessof the ejecta is dependant on the ejecta model used and sizeof the transient crater.

6. Geochemical Components in the Apollo 16Regolith

[32] An analysis of lunar soil from the Apollo 16 siteby Korotev [1997] presents specific estimates for the

Figure 6. Pie charts illustrating the different componentsestimated to be in the Apollo 16 megaregolith as determinedby the various scenarios discussed here. Ancient crustalmaterials are defined as being material derived from theancient crust plus material introduced to the site by theSouth Pole-Aitken Basin. Other represents ejected materialfrom the other 39 basins not otherwise specificallyaddressed. Arrow indicates scenario described in Table 1and featured in Figure 4 and Figure 7, left.

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relative abundance of identifiable components sampledthere. Of particular relevance to this study of basin ejectamixing is Korotev’s estimate of the abundance of ejectaassumed to be derived from the Imbrium basin. Korotev[1997] analyzed soil and regolith particles sampled byApollo 16 to determine the relative proportions andprovenances of the various components in the regolith.He concluded that between 25 and 32% of the regolith isderived from primary Imbrium ejecta based on theproportion of KREEP-bearing mafic impact-melt brecciasin the samples. Imbrium basin-derived materials arebelieved to be readily identifiable because of the uniquegeochemical signature of the Imbrium region and there-fore Imbrium ejecta [Haskin, 1998; Haskin et al., 1998;Jolliff et al., 2000]. Korotev classified all KREEP-bearingmafic impact-melt breccias in the Apollo 16 regolith asbeing derived from Imbrium ejecta. These mafic impact-melt breccias are the most enriched in both Th and Sm ofall the materials sampled at the Apollo 16 site, which isregarded to be a consequence of the composition of thetarget material at the Imbrium basin.[33] Korotev [1997, p. 471] described the remaining

components in the regolith, concluding that 64% of theregolith at Apollo 16 is composed of ‘‘prebasin surfacematerials’’ and �6% is mare basalt material. Korotevdefines the prebasin surface material to be ‘‘lithologiesthat existed at or near the surface of the Moon �4.0 Gaago and their brecciated derivatives.’’ This componentthus represents materials derived from the 40 pre-Imbriumbasins (including Serenitatis and Nectaris) as well as pre-basin materials from the original lunar crust. Becausebasins other than Imbrium apparently did not form ingeochemically unique regions of the Moon, the identifi-cation of their ejecta in the Apollo 16 regolith is not asstraightforward. The components in the Apollo 16 rego-lith identified by Korotev are summarized in Table 3.These values can be compared, with caution, to our

Table 2. Basin Ejecta Mixing Model Results

RegolithComponent

A B C D

Housen, Mean*Transient Crater, m/2

Pike, Mean*Transient Crater, m/2

Housen, Mean*Transient Crater, m

Pike, Mean*Transient Crater, m

Ancient crustal material 48% 47% 56% 57%Nectarisa 11% 12% 10% 11%Serenitatisa 12% 12% 11% 11%Imbriuma 11% 11% 8% 8%Other basinsa 17% 17% 15% 14%

aForeign regolith component.

Figure 7. Comparison of basin ejecta mixing end-members at the end of the basin forming period, with theexample on the left representing a case where no mixingoccurs between basin ejecta deposits and the example on theright representing the homogeneous mixing case in the formof the modified m/2 mixing scenario. Both cases utilized thePike ejecta scaling equation. In the case with no mixing,ejecta deposits from all 42 basins are preserved. Most ofthese units are too small to be observed at this scale and arecombined, when necessary, into a single color (black).Basins with estimated ejecta contributions greater than 50 mare identified (O, Orientale; I, Imbrium; S, Serenitatis;N, Nectaris; Nu, Nubium; T, Tranquillitatis; W-A, Werner-Airy). In the mixing case, the three mixed zones, whichincorporate material from previous multiple basin events,are identified by letter and the number of previousbasin events. Proportions of material in the small upperzone (O + 41) are summarized by the chart identified by anarrow in Figure 6.

Table 3. Components in Apollo 16 Regolith as Identified by

Korotev [1997]

Material Percent

Pre-basin surface materials 64%Primary Imbrium ejecta(mafic impact-melt breccia)

29%

Mare-derived material 6%Meteoritic material 1%

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model estimates for the amount of primary Imbriummaterial in the Apollo 16 regolith.

7. Discussion and Conclusions

[34] The analysis by Korotev [1997] of Apollo 16 soilsamples presents a geochemical estimate of the abundanceof material derived from the Imbrium basin. This estimate isbased on an apparent relationship between the Imbriumbasin and KREEP-bearing materials [Haskin, 1998], buthow is the abundance of Imbrium material at Apollo 16estimated by Korotev related to the basin ejecta mixingmodeling presented in section 5? A comparison of theKorotev estimates from samples with two BEM modelend-members (no mixing case versus homogeneous mixing,illustrated in Figure 7) may reveal which ejecta emplace-ment model is more likely.[35] The BEM model that assumes homogeneous mixing

of the megaregolith predicts that the regolith at the Apollo16 site contains roughly between 50 and 60% local ancientcrustal material (material from the ancient primary crust andpost-SPA deposits, but prior to the later 42 basins), �10%material from each of the Imbrium, Serenitatis, and Nectarisbasins, and between 10 and 20% from all other basinscombined. The specific contributions from each source arelisted in Table 2. The results of the Haskin model [Haskin etal., 2003a] are similar to the homogeneous BEM modelpresented here despite the differences in the model approachas well as the number of basins investigated. The amount ofprimary Imbrium material estimated by Haskin et al.[2003a] at Apollo 16 is 18%, but the relative proportionof material from Imbrium, Serenitatis, and Nectaris isessentially the same as is estimated in the homogeneousmixing BEM model.[36] In the no mixing BEM case, Imbrium material is

highly concentrated near the surface. If the minor contribu-tion of material from both the Orientale and Schrodingerbasins (Table 1) is ignored, then immediately following theperiod of basin formation, the surface at the Apollo 16 siteconsists entirely of Imbrium-derived material.[37] Regolith gardening and post-basin-formation contri-

butions by lateral transport will reduce the absolute abun-dance of all basin materials, regardless of which basin ejectamixing model is used. For example, if we use the moreconservative estimate of post-basin-formation lateral trans-port discussed in section 3.2 (15%), then the proportion ofImbrium material at the surface of the Apollo 16 site wouldbe �9% in the homogeneous mixing case and 85% in the nomixing case.[38] The application of the BEM model to the Apollo 16

landing site allows us to evaluate whether the Imbrium orNectaris basin (or both) most significantly modified thegeology of the Apollo 16 region. Because the Imbriumbasin was the last major basin to have formed nearApollo 16 (Figures 1 and 2) we expect that it would havesignificantly modified the surface. However, if completelyhomogeneous mixing is assumed, Imbrium ejecta do notdominate the foreign component in the regolith and theproportion of Imbrium, Nectaris, and Serenitatis-derivedmaterial is roughly equal (Table 2). Immediately followingthe formation of the Nectaris basin, Nectaris ejecta isestimated to have been �21% of the Apollo 16 regolith;

however, the following 14 basins and subsequent cateringreduced its proportion of the regolith by roughly half(Tables 1 and 2). In terms of total amount of material, theSerenitatis basin is estimated to have contributed morematerial to the Apollo 16 site than Imbrium and Nectaris(Table 1 and Figure 7, left). Because of its age andsubsequent events the proportion of material remaining inthe upper regolith has been reduced. The results of thehomogeneous mixing case in the BEM model indicate thatthe Imbrium, Nectaris, and Serenitatis basins contributedsignificantly to the development of the megaregolith, but allthree are predicted to be in roughly equal proportions of theregolith today.[39] Korotev’s estimate of the amount of Imbrium mate-

rial at Apollo 16 falls between the two end-member mixingcases but is closer to the homogeneous mixing case. At leastthree options can account for the difference between thesample estimates and the BEM models, all of which couldhelp bring the models and sample data into agreement. One,a smaller mixing ratio with homogeneous mixing wouldpredict a higher amount of Imbrium material at Apollo 16.Two, a gradient in the mixing that occurs during ejectaemplacement would concentrate Imbrium material near thesurface. Three, the estimate from samples is overly highbecause it incorporates material compositionally similar toImbrium ejecta that was introduced to the Apollo 16 site byother, subsequent craters. These options are discussedbelow.[40] The use of a smaller mixing ratio in the BEM model

reduces the depth to which foreign material mixes duringejecta emplacement and concentrates the foreign materialcloser to the surface. This would have the effect of increas-ing the proportion of all basin-derived material in theregolith therefore reducing the amount of ancient crustalmaterial. If a mixing ratio 1/3 the m value of Oberbeck(equation (1)) were employed in the BEM homogeneousmixing model, the amount of Imbrium-derived material inthe Apollo 16 regolith would be �25%, in agreement withthe Korotev estimate. However, recall that m values up to5.00 appear to be consistent with remote measurements[Pieters et al., 1985; Head et al., 1993; Blewett et al., 1995].While reducing m values by 1/2–1/3 may satisfy thegeochemical estimate for Imbrium derived material atApollo 16, such a reduction may not be appropriate for allapplications.[41] A gradient of ejecta mixing could also concentrate

foreign material in the near surface. This might be accom-plished if there is a significant difference in velocity ofarriving material. The early arrival material would mixdeeper and later arrival material would mix to shallowerdepths. The scale of such a gradient is largely uncon-strained and would require a number of additional assump-tions and parameters if it were to be incorporated into aBEM model.[42] The Korotev estimate of Imbrium-derived material in

the Apollo 16 regolith is a measure of material withcompositional properties associated with the Imbrium basin,but not necessarily material introduced to the Apollo 16 siteby the Imbrium event. In addition to the Imbrium ejectacomponent contributing KREEP-bearing mafic impact-meltbreccias to the Apollo 16 site, lateral transport of materialfrom the PKT by neighboring basins and/or subsequent

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impacts have likely contributed compositionally similarimpact materials to the site, potentially resulting in anoverestimate of Imbrium ejecta using the criteria of Korotev.[43] Actual basin ejecta mixing is likely to be some

combination of the above three options. At locations otherthan Apollo 16, with no ground truth data, a combination ofa smaller mixing ratio with a gradient of mixing can beexpected to characterize megaregolith evolution. It is clearthat, in light of the sample data available, mixing betweenbasin ejecta and local material must occur to a significantdegree. The BEM model with homogeneous mixing is veryuseful when assessing the relative proportion of materialderived from specific basins in the regolith. In this case, thedegree of mixing can be approximated by a factor of 2–3smaller mixing ratio than modeled by Oberbeck or by agradient of mixing with depth (or by a combination of both).However, determining the absolute proportion of materialderived from one or more basins may not be completelyconstrained by the BEM model. Additionally, the BEMmodel without mixing can be used when assessing theoverall spatial distribution of total basin-derived materialacross the lunar surface. The combined analysis presentedhere does not address whether assessment of regolithevolution should incorporate the ejecta model of Pike[1974] or of Housen et al. [1983]. Although the absoluteamount of material redistributed across the Moon and theresulting depth of mixing differs substantially between thetwo ejecta models, the relative proportion of basin-derivedmaterial in the regolith is approximately the same for both ifhomogeneous mixing is assumed.[44] In summary, the BEM model is used to assess the

effects of large-scale crustal evolution and predict theprovenance of components in the Apollo 16 regolith. Sucha model allows for the relative proportions of basin-derivedmaterial present in the regolith to be estimated by quanti-fying the relative effects of basin formation and post-basin-formation lateral transport. Use of the BEM model inconnection with lunar sample data has constrained uncer-tainties in the degree of mixing that occurs during ejectaemplacement. For global-scale issues it appears appropriateto use a mixing ratio less than the Oberbeck defined m. Wesuggest m/2 is reasonable for assessing global regolithissues. With these constraints the BEM model can be usedto examine the character of diverse locations across theentire lunar surface.

[45] Acknowledgments. The authors would like to thank BarbaraCohen and Randy Korotev for their thorough and insightful reviews thatgreatly improved the quality of this manuscript. Editorial comments byVicky Hamilton are appreciated. NASA support (NNG04GG11G) for thisresearch is much appreciated.

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�����������������������N. E. Petro and C. M. Pieters, Department of Geological Sciences, Brown

University, Providence, RI, 02912, USA. (noah_petro@brown.edu)

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