Shoshana Z Weider

Ian A Crawford

Katherine H Joy

INDIVIDUAL LAVA FLOW THICKNESSES IN OCEANUS PROCELLARUM AND MARE SERENITATIS DETERMINED FROM CLEMENTINE MULTISPECTRAL DATA

Keywords: Cratering, Moon, surface, spectroscopy, volcanism

We use multispectral reflectance data from the lunar Clementine mission to investigate the impact ejecta deposits of simple craters in two separate lunar mare basalt regions, one in Oceanus Procellarum and one in Mare Serenitatis. Over one hundred impact craters are studied, and for a number of these we observe differences between the TiO 2 (and FeO) contents of their ejecta deposits and the lava flow units in which they are located. We demonstrate that, in the majority of cases, these differences cannot plausibly be attributed to uncorrected maturity effects. These observations, coupled with morphometric crater relationships that provide maximum crater excavation depths, allow the investigation of sub-surface lava flow stratigraphy. We provide estimated average thicknesses for a number of lava flow units in the two study regions, ranging from ~80 m to ~600 m. In the case of the Serenitatis study area, our results are consistent with the presence of sub-surface horizons inferred from recent radar sounding measurements from the JAXA Kaguya spacecraft. The average lava flow thicknesses we obtain are used to make estimates

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of the average flux of volcanic material in these regions. These are in broad agreement with previous studies, suggesting that the variation in mare basalt types we observe with depth is similar to the lateral variations identified at the surface.

Introduction

Mapping studies of the nearside lunar mare basalts have demonstrated that they are mosaics of temporally distinct lava flows (e.g. [START_REF] Wilhelms | Geologic map of the nearside of the Moon[END_REF][START_REF] Scott | Geologic map of the west side of the Moon[END_REF][START_REF] Pieters | Mare basalt types on the front side of the Moon: a summary of spectral reflectance data[END_REF]Heather and Dunkin 2002;Hiesinger et al., 2003). These areas therefore potentially contain scientifically valuable localities for future human and/or robotic exploration (e.g. [START_REF] Spudis | The once and future moon[END_REF][START_REF] Crawford | Full moon exploration -valuable (non-polar) lunar science facilitated by a return to the moon[END_REF]Fagents et al., 2010). The analysis of lunar rock samples, collected in-situ from distinct lava flows, would help solve some of the outstanding issues in lunar science, e.g.: (i) the volcanic history and evolution of the lunar mantle would be elucidated in greater detail by the study of samples from numerous, temporally distinct lava flows (e.g. [START_REF] Shearer | Thermal and magmatic evolution of the Moon[END_REF]; (ii) the calibration of the absolute lunar chronology and crater-counting curves would be improved by obtaining absolute radiometric ages for these lava flows (e.g. [START_REF] Stöffler | Cratering history and lunar chronology[END_REF] and; (iii) the study of the ancient Sun, and other early solar system conditions, could be achieved by sampling palaeoregolith material trapped between consecutive lava flows (e.g. [START_REF] Wieler | Secular changes in the xenon and krypton abundances in the solar wind recorded in single lunar grains[END_REF][START_REF] Crawford | Full moon exploration -valuable (non-polar) lunar science facilitated by a return to the moon[END_REF]Fagents et al., 2010). The scientific output from any future exploration within the mare basins would be maximised by choosing a landing site where a diverse array of geological units occurs within an accessible radius. Such sites may include contacts between two or more individual lava flow deposits, or material around impact craters that has been excavated during the impact event, and therefore negates the need for sub-surface drilling. In this paper impact craters within regions of two of the Moon's major nearside maria, Oceanus Procellarum and Mare Serenitatis, are studied with a view to identifying ejecta deposits that have excavated sub-surface lava flows that would otherwise be inaccessible.

Impact craters: windows through lava flows

During the formation of an impact crater, material from different vertical horizons within the original target surface is displaced or excavated. Material closest to the original surface acquires the most energy during the impact; it therefore has the greatest displacement and is deposited in the continuous ejecta blanket that extends for about one crater radius beyond the crater rim [START_REF] Moore | Multiringed basins -illustrated by Orientale and associated features[END_REF][START_REF] Oberbeck | Smooth plains and continuous deposits of craters and basins[END_REF]. Originally deeper material is re-deposited around the rim and interior of the resultant crater. Situations occur in the maria where feldspathic basement material (e.g. the primary lunar crust) is overlain by a stack of temporally and compositionally distinct lava flows (e.g. Hiesinger et al., 2003). Smaller impact craters within this region may have excavated through to underlying lava flows, which, providing the effects of space weathering can be accounted for, may remain identifiable in the ejecta surrounding the craters from orbital remote sensing measurements.

The NASA Clementine mission [START_REF] Nozette | The Clementine mission to the Moon: scientific overview[END_REF] produced a global, high-spatial resolution (100 m/pixel) multispectral dataset suitable for studying local geological and compositional variations of this kind. Indeed, in an earlier study Heather and Dunkin (2002) used Clementine UV-Vis data to investigate impact craters in Oceanus Procellarum, and were able to distinguish anorthositic and basaltic material in a small proportion of the craters studied and from which they derived the total basalt thickness in this area. The aim of this work is to extend this approach to the identification of individual sub-surface lava flow layers with different compositions (as achieved by Rajmon and Spudis 2004, in Mare Tranquillitatis and Mare Fecunditatis).

FeO &TiO 2 abundance algorithms

Mare basalt hand specimens are usually classified primarily by their bulk rock TiO 2 contents [START_REF] Neal | Petrogenesis of mare basalts: a record of lunar volcanism[END_REF]) which can vary from <1 wt. % to ~13 wt. % (e.g. BVSP 1981;[START_REF] Taylor | Lunar rocks[END_REF]. As such, lateral and vertical compositional variations of lava flows in the mare regions can also be classified on this basis from remote sensing data sensitive to TiO 2 concentration. The relationships between lunar surface reflectance spectra and sample FeO and TiO 2 contents have led to the development of several quantitative methods for estimating the composition of the lunar surface (in terms of these oxides) from suitable remote sensing datasets.

An increase in the amount of iron contained within mafic silicate minerals causes a decrease in their albedo and a strengthening of their 1 µm absorption bands (e.g. [START_REF] Pieters | Lunar reflectance spectroscopy[END_REF]. There is also a corresponding decrease in the ratio between the near infra-red and visible wavelengths (NIR/Vis) [START_REF] Burns | Mineralogical applications of crystal field theory[END_REF]). However, these compositional relationships are affected by space weathering effects. Space weathering is the process by which the lunar surface is physically and chemically altered due to its continual bombardment by cosmic rays, solar wind particles and micrometeorites, as well as the subsequent formation of new phases including single-domain nanophase iron, agglutinates (impact-glass welded conglomerates of regolith particles) and amorphous coatings on individual grains (Hapke et al., 1975;[START_REF] Mckay | Grain size and the evolution of lunar soils[END_REF][START_REF] Mckay | The lunar regolith[END_REF][START_REF] Morris | Surface exposure indices of lunar rocks: a comparative FMR study[END_REF][START_REF] Borg | Prolonged KREEP magmatism on the Moon indicated by the youngest dated lunar igneous rock[END_REF]Keller and McKay 1993;Fischer and Pieters 1994;[START_REF] Spudis | The once and future moon[END_REF]. These effects cause a decrease in reflectance and a concomitant increase in the NIR/Vis (950/750 nm) reflectance ratio (e.g. Fischer and Pieters 1994). The opposing effects of space weathering (socalled 'maturity') and iron-silicate abundance on the reflectance spectra must therefore be effectively decoupled in order to make reliable quantitative estimates of surface ferrous iron content. Several such methods have been proposed (e.g. [START_REF] Lucey | Abundance and distribution of iron on the Moon[END_REF]Le Mouélic et al., 2000;[START_REF] Lucey | Lunar iron and titanium abundance algorithms based on final processing of Clementine ultraviolet-visible images[END_REF]Gillis et al., 2004;[START_REF] Wilcox | Mapping iron in the lunar mare: an improved approach[END_REF].

In this work we employ the algorithm of [START_REF] Wilcox | Mapping iron in the lunar mare: an improved approach[END_REF] because it most reliably removes the effects of space weathering from mare reflectance spectra. This method makes use of the relationship between the reflectance in the 750 nm waveband and the 950/750 nm reflectance ratio from Clementine data of different mare materials. [START_REF] Staid | Integrated spectral analysis of mare soils and craters: application to eastern nearside basalts[END_REF] suggested that the trends of samples with different ferrous iron concentrations were parallel on a plot of 750 nm reflectance against the 950/750 nm ratio. It had previously been thought that these trends were more radial in nature and this assumption had been employed in the algorithms of [START_REF] Lucey | Abundance and distribution of iron on the Moon[END_REF]2000) and Gillis et al. (2004). [START_REF] Wilcox | Mapping iron in the lunar mare: an improved approach[END_REF] agree that a parallel model is more accurate and thus use this observation in the formulation of their algorithm. Variations of >0.5 wt. % in the deduced FeO concentration are thought to be due to true iron variations, rather than incomplete suppression of maturity effects [START_REF] Wilcox | Mapping iron in the lunar mare: an improved approach[END_REF]. A complementary means of quantifying the degree of maturity of mare lunar soils is the mOMAT (mare Optical MATurity) parameter of [START_REF] Wilcox | Mapping iron in the lunar mare: an improved approach[END_REF]. This numerical parameter varies between -1.05, for the most mature materials, and -0.65 for the least mature [START_REF] Wilcox | Mapping iron in the lunar mare: an improved approach[END_REF].

The FeO abundance algorithm proposed by Le Mouélic et al. (2000) utilises reflectance values from wavelengths in both the Clementine UV-Vis and NIR datasets (750, 950 and 1500 nm).

These are employed as band ratios only, and so this algorithm is less sensitive to the topographic shading effects that plague the other methods (Lucy et al., 2000;Gillis et al., 2004;[START_REF] Wilcox | Mapping iron in the lunar mare: an improved approach[END_REF]. However, large slopes (e.g. on crater walls) are unlikely to be a problem in this study because only areas that are generally flat are investigated (i.e. mare surfaces and ejecta blankets of small impact craters), and therefore the [START_REF] Wilcox | Mapping iron in the lunar mare: an improved approach[END_REF] FeO algorithm was employed.

Similar methods for estimating the TiO 2 abundance of lunar soils have also been developed (e.g. [START_REF] Lucey | Lunar titanium content from UV-VIS measurements[END_REF]2000;Gillis et al., 2003), based on a correlation between the TiO 2 content and the UV-Vis ratio of mature lunar soils (e.g. [START_REF] Charette | Application of remote spectral reflectance measurements to lunar geology classification and determination of titanium content of lunar soils[END_REF]Johnson et al., 1991;[START_REF] Melendrez | Remote sensing of potential lunar resources 2. High spatial resolution mapping of spectral reflectance ratios and implications for nearside mare TiO 2 content[END_REF]. The [START_REF] Lucey | Lunar iron and titanium abundance algorithms based on final processing of Clementine ultraviolet-visible images[END_REF] algorithm uses the 750 nm waveband and the 415/750 nm ratio of Clementine reflectance values to define this relationship, and is utilised in this study because it is optimised to remove the effects of space weathering. Although it has a quoted estimated 1 error of 1 wt. %, later studies have cast doubts over its ability to accurately determine the true TiO 2 concentration of the lunar surface (Gillis et al., 2003;Gillis-Davis et al., 2006), and so the actual error may be somewhat larger. However, for this particular study, obtaining the absolute abundance of TiO 2 was less critical than ensuring that the differences in maturity of separate regions were properly accounted for and that their relative differences in TiO 2 content are significant.

This study

The large compositional diversity of lava flows in Oceanus Procellarum (Hiesinger et al., 2003) provides a suitable area to test the method of employing impact craters to probe subsurface lava flow stratigraphy. The area chosen for study here contains a significant number of individual lava flows within close proximity. Some regions of Mare Serenitatis are also of interest, as the subsurface structure there has previously been investigated using Kaguya radar data [START_REF] Ono | Lunar radar sounder observations of subsurface layers under the nearside maria of the Moon[END_REF]. The method proposed here may therefore be used to independently check their conclusions.

For this study we downloaded Clementine UV-Vis multispectral data for the two separate regions (Oceanus Procellarum: 0° -15°N; 300° -315°W, and Mare Serenitatis: 16° -33°N; 20° -26°E) at full resolution (0.1 km/pixel) and in a simple cylindrical projection from the USGS Map-A-Planet website (www.mapaplanet.com) as radiometrically, geometrically and photometrically controlled .raw files (Eliason et al., 1999). These files were extracted and analysed using an in-house IDL (Interactive Data Language) code in order to map the areas in terms of their FeO and TiO 2 contents according to the algorithms of [START_REF] Wilcox | Mapping iron in the lunar mare: an improved approach[END_REF] and [START_REF] Lucey | Lunar iron and titanium abundance algorithms based on final processing of Clementine ultraviolet-visible images[END_REF] respectively. The lava flow boundaries are defined as those mapped by Hiesinger et al. (2003) for the Oceanus Procellarum region and by Hiesinger et al. (2000) for the Mare Serenitatis region.

Albedo images (Clementine 750 nm) of the two regions are shown in Figures 1 and2 (where individual lava flows are identified according to the nomenclature of Hiesinger et al., 2000;2003).

Mean impact crater ejecta compositions are derived from the sampling of multiple (typically 10 -30; see Table 1 and 2 for the precise number) pixels within the continuous ejecta blankets of these craters, which are assumed to extend for one crater radius beyond the rim [START_REF] Moore | Multiringed basins -illustrated by Orientale and associated features[END_REF][START_REF] Oberbeck | Smooth plains and continuous deposits of craters and basins[END_REF], even when an ejecta blanket is not discernable or is observed to extend further. The average composition of the continuous ejecta will be a mixture of all excavated layers, including the surface in which the crater formed. Mean lava flow FeO and TiO 2 values are similarly derived from multiple (>100; see Table 1 and 2 for the exact number) pixels within the inter-crater areas of the deposits.

Results

Study Area 1: Marius Region (0° -15°N; 300° -315°W), Oceanus Procellarum

The TiO 2 concentration map of this area reveals a number of craters within a particular lava flow unit (flow 'P52 ' of Hiesinger et al., 2003, immediately to the east of Marius Hills) that appear to be surrounded by haloes of material with a lower TiO 2 content than the surrounding lava flow, and which approximate the extent of their continuous ejecta blankets. These craters are circled and numbered (1 to 13) in Figure 3, which shows a small subset of the area (a set of 18 craters with no discernable haloes are also shown and labelled 'A' -'S' in Figure 3). We hypothesise that these haloes evidence material with a lower TiO 2 abundance that has been excavated from a lithology beneath the surface flow ('P52'). A candidate for this lithology is the stratigraphically lower lava flow 'P24', which is TiO 2 -poorer (by ~3 wt. %).

Figure 4 is a plot of mean FeO and TiO 2 wt. % abundances for (i) the ejecta of the thirteen craters with TiO 2 -poor haloes identified in lava flow unit 'P52' and (ii) the mean lava flow compositions for 'P52' and 'P24'. It illustrates that the ejecta of the thirteen haloed craters have a distinct composition from that of lava flow 'P52' in which they are located, and that the ejecta compositions are more similar to that of the proposed underlying unit, 'P24'.

The increase in nanophase iron in lunar soils due to space weathering causes a darkening of reflectance spectra, as does increased abundance of ilmenite (the major TiO 2 bearing opaque phase in lunar soils). It is therefore important to confirm that the apparent lower TiO 2 content of these crater ejecta is due to an actual compositional difference compared to the lava flow unit in which they are located, rather than to an unresolved maturity (albedo) issue. We believe that these TiO 2poor haloes are indeed evidence of a true compositional difference for a number of reasons illustrated in Figure 5: (i) On a plot of the 415/750 nm reflectance ratio versus albedo (750 nm), the ejecta of the haloed craters in lava flow 'P52' form a distinct group from the ejecta of a set of craters with no haloes in the same lava flow (Figure 5a); the offset of these two groups follows a trend of increased TiO 2 content rather than one of increased maturity;

(ii) The majority of the craters (both with and without TiO 2 -poor haloes) have a similar, narrow range of mature mOMAT values (Figure 5b), indicating that the sampled craters all have a similar level of maturity; and

(iii) As a function of crater diameter, the two sets of craters display a clear distinction in TiO 2 wt. % values, but not in albedo (Figure 5c,d).

Given that the identified craters with TiO 2 -poor haloes in lava flow 'P52' have indeed excavated material from a deeper, compositionally different lava flow (i.e. 'P24'), their diameters can be used to estimate their maximum depth of excavation and therefore constrain the thickness of the surficial lava flow ('P52'). The maximum excavation depth (D exc ) of simple craters (i.e. those with diameters < 15 km) can be calculated using the following equation [START_REF] Melosh | Impact cratering -a geologic process[END_REF]:

D exc = 0.1 × D t
, where D t is the transient cavity diameter. The transient cavity diameter is defined by [START_REF] Melosh | Impact cratering -a geologic process[END_REF] as: D t = 0.84 × D (where D is the present, rim-rim diameter of the crater).

These values are listed in Table 1.

The maximum excavation depths of the TiO 2 -poor haloed craters are used to provide an upper bound for the thickness of unit 'P52' where it overlies 'P24' in this area, whereas the excavation depths of the non-haloed craters provide a lower limit for this thickness. The maximum excavation depth estimates (in km) for the craters with and without TiO 2 -poor haloes in lava flow 'P52' are shown in Figure 6. The results show that 'P24' is between ~100 m and 300 m below the surface of 'P52' in the area that has been investigated.

The total thickness of the mare basalt deposit within Oceanus Procellarum has previously been estimated using a variety of techniques. Morphometric crater relationships [START_REF] Pike | Depth/diameter relations of fresh lunar craters: revision from spacecraft data[END_REF][START_REF] Pike | Impact and explosion cratering: planetary and terrestrial implications[END_REF] and the heights of exposed rims were used to infer the burial depths of partially buried craters [START_REF] De Hon | Maximum thickness of materials in the western mare basins[END_REF]1979). The isopach map produced by De Hon (1979) gives a total basalt thickness estimate in this study area of 500 to 1000 m. Craters which have excavated basement anorthositic material have been used to estimate the total thickness of the overlying basalt (Heather and Dunkin 2002), and are in broad agreement with the earlier study by De Hon (1979). The new results presented here extend this approach by providing an estimate of the thickness of individual lava flows within a stack of temporally and compositionally distinct deposits. If 'P52' (with an estimated thickness of ~100 to 300 m) constitutes about half of the minimum estimated (i.e. 500 m) total depth of basaltic material in this region, then we predict that 'P24' has a similar thickness and completes the basin fill. However, if there is an additional, un-sampled flow(s) underlying 'P24', its true thickness would be smaller.

Study Area 2: Central Southern Mare Serenitatis (16° -33°N; 20° -26°E)

We have also used Clementine multispectral reflectance data to investigate the lava flow stratigraphy of an area in Mare Serenitatis (Figure 2). It was chosen because it coincides with published Kaguya radar tracks [START_REF] Ono | Lunar radar sounder observations of subsurface layers under the nearside maria of the Moon[END_REF] that were used to infer the depth of a specific lava flow unit beneath the surface. The TiO 2 abundance of the separate lava flow units in this area (whose boundaries and names are taken from Hiesinger et al., 2000) vary significantly, from very low-Ti basalts in the northwest, to high-Ti basalts in the southeast (see Figure 7). A total of 103 (simple) impact craters throughout the region were selected and their continuous ejecta blankets sampled in order to search for evidence of their excavating compositionally distinct material from beneath the surface.

Mean FeO and TiO 2 wt. % content values for the inter-crater areas of the eight lava flow units are shown in Figure 8. Although the difference in the composition of the southern units 'S11' and 'S18' compared to the more northern flows is clear, some of the units identified by Hiesinger et al. (2000) are indistinguishable based on this classification, which is not surprising because the earlier study used morphological features in addition to compositional differences to map the lava flow boundaries. Figure 9 shows a series of FeO vs. TiO 2 plots for each of the lava flow units that contain the craters sampled in this investigation, displaying the mean flow values as well as those for the craters within each particular unit. Details of individual craters studied are given in Table 2 and the estimated absolute ages (Hiesinger et al. 2000) of the lava flows in Table 3.

For the Oceanus Procellarum study (Section 3.1) it was important to determine if the apparently TiO 2 -poor ejecta haloes around selected impact craters was due to true compositional variations or unresolved maturity issues. For the craters in Mare Serenitatis, this issue is less important because most of the craters with compositionally anomalous ejecta appear to have excavated material richer in TiO 2 rather than poorer, and so the trends of maturity and composition are in opposition.

The mOMAT [START_REF] Wilcox | Mapping iron in the lunar mare: an improved approach[END_REF] values of all 103 sampled craters are given in Table 2 and shown in Figure 10; the vast majority fall within a narrow band of mature values, with only three craters (75, 87 and 101) being more immature and fresh. Maximum excavation depths for these latter three craters are therefore ignored in making lava flow thickness estimates.

In the following sections we discuss the results obtained for the various lava flow units (where the lava flow nomenclature is that of Hiesinger et al., 2000).

Lava flow 'S13'

In terms of FeO and TiO 2 content, the ejecta compositions of the seven craters sampled in the small corner of 'S13' (Figure 9a) do not differ significantly from the lava flow itself. The crater diameters and their associated excavation depths therefore provide a lower bound for the thickness of 'S13' in this area; crater 6 is the largest and constrains the thickness of the unit to > 585 m.

Lava flow 'S15'

Two craters in this unit (87 and 101) have higher mOMAT values (see Figure 10) than the vast majority of the 103 craters sampled within Mare Serenitatis (the freshness of crater 101 can explain its apparently low FeO and TiO 2 content; Figure 9b); these two craters were therefore not used in making lava flow thickness interpretations. For the other craters measured in 'S15', the ejecta compositions generally match that of the flow itself (Figure 9b). However, there is a subset that appears to have excavated older, compositionally distinct lithologies. Crater 41 seems to have excavated material from the underlying lava flow 'S13', and can therefore provide a thickness estimate of <120 m for 'S15' in the immediately surrounding area. Craters 42 and 43 are two smaller craters just to the south of crater 41 and they do not appear to have excavated the same material as it. The diameters of all three craters (41, 42, and 43) can therefore be used to constrain the 'S15' thickness estimate to between ~50 and ~120 m. Craters 84, 85 and 91 also appear to have excavated a separate unit underlying 'S15' that possesses a higher content of both FeO and TiO 2 . Although on the basis of Figure 9b it would seem that 'S22' is a candidate for the excavated unit, this cannot be the case if the ages determined by Hiesinger et al. (2000) are correct and 'S22' is indeed younger than 'S15'. It is possible that these four craters have instead excavated a unit with a similar FeO and TiO 2 content to 'S22', but which has no surface expression in this area; or that they have excavated 'S11' and that the average compositions of their ejecta represent a level of mixing between this older flow, which is richer in FeO and TiO 2 , and 'S15' itself. These craters can still be used to constrain the thickness of 'S15' where it overlies such a lava flow to < ~225 m.

In addition, the size of the craters in 'S15' whose ejecta lack any compositional anomalies, indicate that there is considerable variability in the thickness of 'S15' over the study area.

Lava flow 'S16'

Only two craters were sampled from 'S16', however a difference between their ejecta compositions is noted (Figure 9c). The composition of the ejecta from crater 102 resembles that of 'S16', whereas that from crater 103 has a higher content of both FeO and TiO 2 . As for unit 'S15', it is not possible for crater 103 to have excavated material from the younger units 'S18', 'S22', 'S24' or 'S28' and so there is the potential for craters 103 (in 'S16') and 84, 85 and 91 (in 'S15') to have all sampled either an unidentified underlying unit, or 'S11'. In the case of 'S11' having been excavated, the ejecta composition of crater 103 would represent a mixture of 'S16' and the older, more FeO and TiO 2 -rich flow. Using the diameters of the craters 102 and 103, the thickness of this part of lava flow unit 'S16' is estimated to be between ~65 and ~100 m.

Lava flow 'S22'

All of the nine craters sampled within lava flow unit 'S22' have ejecta that match the composition of the unit itself (Figure 9d). As such, they provide only a lower bound for the thickness of 'S22'; it is estimated to be at least ~100 m thick in this region.

Lava flow 'S24'

The ejecta of the five craters sampled in 'S24' (Figure 9e) have slightly elevated TiO 2 contents compared to that of the lava flow itself, suggesting that material from an older lithology such as 'S22', or the unidentified unit potentially sampled by craters in 'S15' and 'S16', has been excavated. Given the position of 'S24' next to units 'S15' and 'S16' and removed from 'S22', the second option is perhaps more likely. It is also possible that the craters in 'S24' have ejecta compositions that are mixtures of the surface lava flow and an older lava flow such as 'S11' or 'S18'. If this set of craters has indeed excavated material from a separate lava flow, the thickness of 'S24' above it can be constrained to < ~125 m.

Lava flow 'S28'

Crater 75, within lava flow unit 'S28' (Figure 9f) has a higher mOMAT value than the majority of the craters sampled in this study (Figure 10) and therefore is disregarded in estimating the thickness of 'S28'. Craters 9 and 45, in the north of 'S28' appear to have excavated material from the neighbouring unit, 'S15'. Their sizes, along with that of nearby crater 46, are used to constrain the thickness of 'S28' where it overlies 'S15' in this region to between ~120 and ~290 m. About half of the craters in 'S28' have ejecta with a distinct composition to that of the lava flow, and appear to have excavated material from a unit with higher FeO and TiO 2 contents, such as 'S11'. 'S18 or 'S22'. Craters 61, 63 and 64 all have ejecta with compositions different to 'S28', whereas neighbouring craters 60, 62, 90 and 89 do not. The thickness of 'S28' is thus estimated to be between ~40 and ~100 m where it overlies 'S22' (or a similarly FeO and TiO 2 enriched lava flow in this region). Craters 89 and 90 do not have compositionally anomalous haloes, and are larger than the three craters that do, possibly indicating local variations in the surface unit thickness that may be caused by the underlying topography. A large number of craters within the southernmost third of 'S28' have compositionally anomalous ejecta deposits and appear to have excavated material from lava flow 'S22' (or perhaps 'S11' / 'S18'). There are considerable variations in the depth estimates provided by these craters that are probably due to local topographical changes, but for a small area around craters 23 -27, for example, the thickness of 'S28' is estimated at ~80 m. A summary of these findings is illustrated in the map shown in Figure 11. All 103 craters are shown and those that are noteworthy are labelled with their number. Those craters whose ejecta have excavated a sub-surface lithology are represented by circles of the colour corresponding to the lava flow from which it is proposed the material originated; black circles mark craters without compositional anomalies. The three yellow circles represent the craters with immature mOMAT values. Figure 12a shows the estimated maximum excavation depths (in metres) for all the sampled impact craters (other than the three with high mOMAT values); Figure 12b shows approximate thickness estimates (in metres) for the surface flows we have made based on these excavation depth constraints.

Comparisons with other studies

The Lunar Radar Sounder (LRS) on the Japanese Kaguya spacecraft was a high-frequency imaging radar instrument, which allowed the lunar subsurface stratigraphy and tectonic features to be probed, with global coverage [START_REF] Ono | Lunar radar sounder observations of subsurface layers under the nearside maria of the Moon[END_REF][START_REF] Pommerol | Detectability of subsurface interfaces in lunar maria by the LRS/SELENE sounding radar: influence of mineralogical composition[END_REF]. The 5 MHz frequency permitted subsurface data to be obtained to a depth of several kilometres [START_REF] Ono | Lunar radar sounder observations of subsurface layers under the nearside maria of the Moon[END_REF], with an estimated vertical resolution ranging between 25 and 40 m [START_REF] Pommerol | Detectability of subsurface interfaces in lunar maria by the LRS/SELENE sounding radar: influence of mineralogical composition[END_REF]. This technique specifically detects differences in the dielectric constant of the subsurface materials, which is affected on the Moon by factors such as porosity and composition.

On the basis of Kaguya LRS data, [START_REF] Ono | Lunar radar sounder observations of subsurface layers under the nearside maria of the Moon[END_REF] observe a sub-surface reflector at a depth of ~175 m at point A (20°N, 23.3°E) in Figure 12b. They interpret this reflector as a high porosity deposit (buried regolith rather than a pyroclastic deposit or ejecta deposits) on the top of unit 'S11' which they can trace to where it outcrops at the surface. This interpretation is possibly in agreement with our new estimates if 'S22' lies between the surface flow 'S28' and the reflector which marks the top of 'S11'. The craters in 'S28' which appear to have excavated material from 'S22' constrain the thickness of 'S28' at this point to ~ 75 m. 'S22' must therefore be ~ 100 m thick at this point. This fits well with the constraints provided by the craters in 'S22' that do not excavate a deeper lithology. [START_REF] Ono | Lunar radar sounder observations of subsurface layers under the nearside maria of the Moon[END_REF] do not observe a sub-surface boundary corresponding to the top of 'S22', but this may be because such a boundary at a depth of only 75 m is below their resolution. The deeper 'S11' boundary may also be more pronounced than for 'S22' because of its greater TiO 2 content [START_REF] Pommerol | Detectability of subsurface interfaces in lunar maria by the LRS/SELENE sounding radar: influence of mineralogical composition[END_REF]. [START_REF] Ono | Lunar radar sounder observations of subsurface layers under the nearside maria of the Moon[END_REF] also identify the top of 'S11' at a similar depth (~ 175 m) beneath 'S15' at point B (19°N, 25.5°E) in Figure 12b. The craters in this part of 'S15' suggest that an older lava flow does exist at around this depth, but the composition of the ejecta do not obviously indicate that it is 'S11'. These ejecta do have higher TiO 2 (and FeO) contents than that of 'S15', but they do not appear to match any of the lava flow units currently exposed at the surface in Mare Serenitatis. These compositions could therefore represent an additional sub-surface lava flow (the top of which has been imaged by [START_REF] Ono | Lunar radar sounder observations of subsurface layers under the nearside maria of the Moon[END_REF] and misidentified by them as 'S11'), or be due to mixing between the high FeO and TiO 2 contents of 'S11' and the surface lava flow 'S15' in the crater ejecta blankets.

The total thickness of mare fill within the Serenitatis basin has previously been estimated to be ~ 4 km (Williams and Zuber 1998, although larger (~8.5 km;Solomon and Head 1980) and smaller (~3.5 km;[START_REF] De Hon | Thickness of mare material in the Tranquillitatis and Nectaris basins[END_REF]1979;De Hon and Waskom 1976) estimates have also been made. The surface lava flows whose thicknesses have been estimated in this study therefore contribute only a fraction of the total mare fill.

Discussion

It is important to understand the thickness of the mare basalts, and the individual lava flow units of which they consist, so that the total volume of volcanic material at the lunar surface can be determined. This allows the evolution of the lunar interior to be investigated, for example the extent of partial melting of the mantle with time.

Table 4 shows estimated (and approximate) values for various parameters relating to the lava flow units studied in both Oceanus Procellarum and Mare Serenitatis. Using the estimated average thickness of the flows, for which this has been determined, and their surface area (Hiesinger et al., 2000;2003), an approximate minimum volume for the units can be determined. A maximum time interval within which the individual flows were emplaced can be constrained from the difference in absolute ages of the flow in question and the unit immediately older than it in the stratigraphy (Hiesinger et al., 2000;2003). This enables an average 'flux' of magma eruption to be calculated.

Of course, the actual length of time over which these flows erupted would have been essentially instantaneous on these timescales, so the flux derived here is purely a measure of the amount of material that reached the surface within each several hundred million year interval. Even for these gross averages there are several caveats: (i) the apparent (absolute) age dating of the lava flow units by crater counting inherently involves large errors; (ii) extrapolation of the thickness of a whole lava flow from only a few spot estimates may be problematic; (iii) the area of the surface flows, and especially the older flows, as given by (Hiesinger et al., 2000;2003) are likely to be underestimated due to coverage by subsequent flows and; (iv) the TiO 2 abundances upon which our thickness estimates are based, are estimated from an algorithm [START_REF] Lucey | Lunar iron and titanium abundance algorithms based on final processing of Clementine ultraviolet-visible images[END_REF] which has a 1 error of at least 1 wt. %. Although this algorithm may over or underestimate the true TiO 2 wt. % content of the regolith by up to ~5 wt. % in some areas (Gillis et al., 2003), it is the relative difference between the values from different deposits that is important in this study, as well as the suppression of any maturity effects.

Knowledge of the flux of lunar volcanism can help refine the understanding of mare basalt petrogenesis and the relationship between the basalts and the Moon's magmatic and thermal evolution (e.g. Head and Wilson 1992;[START_REF] Zhong | Early lunar evolution and the origin of asymmetric distribution of mare basalts[END_REF][START_REF] Parmentier | On the relationship between chemical differentiation and the origin of lunar asymmetries[END_REF][START_REF] Wieczorek | The "Procellarum KREEP Terrane": implications for mare volcanism and lunar evolution[END_REF][START_REF] Wilson | Ascent and eruption of mare basalts on the Moon[END_REF][START_REF] Shearer | Thermal and magmatic evolution of the Moon[END_REF]. The precise shape of the lunar mare basalt flux curve is still uncertain; different shapes are derived from various methods (see discussion in Head and Wilson 1992). The determination of individual lava flow thicknesses and fluxes in different lunar maria would improve the overall accuracy to which this curve is known (Hiesinger et al., 2003).

Figure 13a illustrates the estimated flux for the lava flow units in this study (from Oceanus Procellarum and Mare Serenitatis) as a function of their crater-count age. Although the number of points in our dataset is quite small (Table 4), the overall shape of the curve produced is similar to the generalised mare basalt flux of Head & Wilson (1992), which is based on a combination of approaches (e.g. data from returned samples and remote sensing) and superimposed for comparison in Figure 13a. Giguere et al. (2000) investigated the apparent dichotomy between the bimodal distribution of lunar basalts in terms of TiO 2 content according to sample data, and the more unimodal distribution suggested by remote sensing data. They concluded that of the mare basalts, the low-Ti basalts are the most spatially abundant. If the flux of the lava flow units presented here is used as a proxy for their total abundance, then the trend observed in Figure 13b can be compared to the work of Giguere et al. (2000), with which it appears to agree. Figure 13b shows that the flux of the low-Ti basalt units tends to be greater than that of the high-Ti units, i.e. the vertical variation in the abundance of different basalt types shown here is similar to the lateral (surface) variation previously identified.

Conclusions

Clementine UV-Vis reflectance data have been used to estimate the FeO and TiO 2 contents of impact crater ejecta in two study areas (in Oceanus Procellarum and Mare Serenitatis). This information has led to the identification of crater populations which have excavated material from deeper, compositionally distinct lava flows. The depth-diameter relationship of simple craters allows some constraints to be placed on the thickness of the surface units. Being able to constrain the depth of lava flows in this way allows the volcanic history of the area to be better understood, and by extrapolation allows lava flow volumes and fluxes to be estimated. This information in turn allows a more detailed view of spatial and temporal variations in the thermal history of the Moon.

The results presented are in broad agreement with previous work on lava flow thicknesses, and with recent radar sounding results. It would therefore be of value to extend this method to wider areas of the maria, and to employ newer, higher quality datasets. Data from the Spectral Profiler (SP) onboard Kaguya (500 m spatial footprint; 296 spectral channels covering wavelengths between 0.5 and 2.6 µm; [START_REF] Matsunaga | Discoveries on the lithology of lunar crater central peaks by SELENE Spectral Profiler[END_REF], and the Moon Mineralogy Mapper (M 3 ) onboard Chandrayaan-1 (80 m spatial footprint; up to 260 spectral channels covering wavelengths between 0.42 and 3.0 µm; [START_REF] Pieters | The Moon Mineralogy Mapper (M 3 ) on Chandrayaan-1[END_REF], will be especially valuable in this respect. (2000). Dashed lines show two tracks of LRS on Kaguga [START_REF] Ono | Lunar radar sounder observations of subsurface layers under the nearside maria of the Moon[END_REF], results from which are discussed in section 3.2. Figure 3. Surface TiO 2 wt. % composition (Lucey et al., 2000 algorithm) map for part of the Oceanus Procellarum study area (Figure 1) around lava flow unit 'P52'. Indicated are (i) the thirteen impact craters with TiO 2 -poor haloes (labelled 1 to 13) and (ii) additional impact craters in the same unit with no observable halo (labelled 'A' to 'S' and circled with dashed lines). (a) 415/750 nm reflectance ratio vs. 750 nm reflectance (albedo) values for the craters in 'P52'; the trend of the two groups is one for increased TiO 2 content rather than increased maturity. (b) mOMAT (according to algorithm of [START_REF] Wilcox | Mapping iron in the lunar mare: an improved approach[END_REF] values for both sets of craters; all the craters fall within a narrow range of mature values, there is considerable overlap between the two groups suggesting similar maturity levels. (c) Mean TiO 2 (according to the algorithm of [START_REF] Lucey | Lunar iron and titanium abundance algorithms based on final processing of Clementine ultraviolet-visible images[END_REF] wt. % values for the continuous ejecta of the haloed and non-haloed craters as a function of their diameter; there is a clear distinction in terms of TiO 2 abundance between the two groups, with the haloed craters tending to be larger. (d) Albedo of both populations of craters, as a function of their diameter; the range of values for both groups is equal. Figure 6. Maximum excavation depths (in km) for (i) the thirteen impact craters with TiO 2 -poor haloes (grey) and (ii) the eighteen craters lacking compositional haloes (black) in lava flow unit 'P52'. There is only limited overlap between the values of the two groups (see Figure 5c); this overlap is probably due to underlying topography variations (e.g. buried craters) which cause local variations in the thickness of 'P52'.

Figure 7. Maps of the Mare Serenitatis study area in terms of (a) FeO (according to the algorithm of [START_REF] Wilcox | Mapping iron in the lunar mare: an improved approach[END_REF] and (b) TiO 2 (according to the algorithm of [START_REF] Lucey | Lunar iron and titanium abundance algorithms based on final processing of Clementine ultraviolet-visible images[END_REF]. The lava flow boundaries and names according to Hiesinger et al. (2000) are shown and the 103 impact craters sampled in this investigation are circled. Figure 8. FeO (according to the algorithm of [START_REF] Wilcox | Mapping iron in the lunar mare: an improved approach[END_REF] vs. TiO 2 (according to the algorithm of [START_REF] Lucey | Lunar iron and titanium abundance algorithms based on final processing of Clementine ultraviolet-visible images[END_REF] wt. % content values for the mean inter-crater areas of the eight lava flow units in the Mare Serenitatis study area. Although the pixels used for sampling the lava flows were chosen at random, an effort was made to avoid any obvious contamination by ejecta rays from distant craters. Error bars represent one standard deviation of the individual pixel values used to determine the mean. Figure 9. FeO wt. % (according to the algorithm of [START_REF] Wilcox | Mapping iron in the lunar mare: an improved approach[END_REF] vs. TiO 2 wt. % (according to the algorithm of [START_REF] Lucey | Lunar iron and titanium abundance algorithms based on final processing of Clementine ultraviolet-visible images[END_REF] compositions for the mean inter-crater areas of the eight lava flow units in the Mare Serenitatis study area (Figure 8). Overlain on these lava flow compositions are: (a) the seven craters in lava flow unit 'S13' that all have a similar composition to the actual unit; (b) twenty-four craters in unit 'S15'. Some of these craters cluster around the composition for the actual unit, however a number of craters plot away from it. Crater 101 is much fresher than the rest of the craters; crater 41 has a composition similar to that of 'S13' and; several craters have more FeO and TiO 2 -rich compositions than the flow itself; (c) two craters in unit 'S16'. Crater 102 plots close to the composition of 'S16' whereas crater 103 is more similar to the flow 'S22' with a higher FeO and TiO 2 content; (d) nine craters in unit 'S22'. All the craters cluster around the composition of the unit itself; (e) five craters in unit 'S24'. All these craters cluster close to the composition of the unit itself, however a deeper unit with higher TiO 2 content, such as 'S22' may have been excavated and; (f) fifty-six craters in unit 'S28'. Many of the craters cluster close to unit itself, however two deeper units (distributed laterally rather than vertically), one with a lower and one with a higher TiO 2 content seem to have been excavated by two sets of the craters. Figure 10. mOMAT (according to the algorithm of [START_REF] Wilcox | Mapping iron in the lunar mare: an improved approach[END_REF] values for the 103 sampled craters in the Mare Serenitatis study area. All the craters fall within a narrow band of mature values except of the three craters that are labelled; these are fresher, immature craters and are not used in making estimations of lava flow thicknesses.

Figure 11. Map of the Serenitatis study area with the separate lava flow units and each of the 103 impact craters investigated. Circles indicate the sampled impact craters; those which are black have no discernable compositional difference between their ejecta and the lava flow in which they lie; those which appear to have excavated material from a different lithology have been filled with a colour that matches the proposed source. Those in brown have either excavated material from an unidentified deeper lava flow unit with a similar FeO and TiO 2 content to that of 'S22', or whose ejecta are a mixture of the surface lava flow and either 'S11' or 'S18'. The three yellow craters are those which have been identified as fresher than the rest of the population on the basis of their mOMAT values (see Figure 10). The size of the circles is proportional to the diameter (present day rim to rim) of the craters. Serenitatis. Grey numbers are for those craters whose ejecta have originated from a deeper lava flow unit and therefore provide upper bounds for the thickness of the surface lithology (i.e. the surface lava flow must be thinner than the crater's excavation depth). Black numbers are for craters whose ejecta compositions match the lava flow in which they are found and therefore provide lower bounds for the thickness of the surface unit (i.e. the surface lava flow must be thicker than the crater's excavation depth). (b) Surface lava flow unit thickness estimates (in metres) for various points around the study area. These estimates are based on the crater excavation depths shown in (a) and are formulated using crude averages and mid-points. Points A and B are locations cited in [START_REF] Ono | Lunar radar sounder observations of subsurface layers under the nearside maria of the Moon[END_REF] where they state that lava flow unit 'S11' lies at a depth of ~175 m below the surface (at both locations).

Figure 13. The estimated flux of each of the lava flow units listed in Table 4, as a function of (a) their crater counting age and (b) their mean TiO 2 wt. % content (according to the algorithm of [START_REF] Lucey | Lunar iron and titanium abundance algorithms based on final processing of Clementine ultraviolet-visible images[END_REF]. Arrows from the data points indicate that the flux values given are likely to be lower limits due to coverage by older lava flows. The shape of the curve in (a) which indicates the change of flux with time (dashed line) compares well with the generalised mare basalt flux model of Head & Wilson (1992) (grey line), especially considering that the actual flux of many of the data points may be considerably higher. The curve shown in (b) illustrates that the flux of the low-Ti basalts is generally higher than that of the high-Ti basalts and therefore the vertical heterogeneity of the mare basalts is similar to that observed purely on the surface. High and low-Ti basalt classification is taken from [START_REF] Neal | Petrogenesis of mare basalts: a record of lunar volcanism[END_REF].

Table 1. List of craters and inter-crater areas for which measurements were obtained in the Oceanus Procellarum study area. Errors listed are 1 .

Table 2. List of craters and inter-crater areas for which measurements were obtained in the Mare Serenitatis study area. Errors listed are 1 . Table 3. Estimated absolute ages for the lava flow units in the Mare Serenitatis study area. Data are taken from Table 9 of Hiesinger et al. (2000). Table 4. Estimated volumes and fluxes for the lava flow units in Oceanus Procellarum (P) and Mare Serenitatis (S) for which thickness estimates have been made. The flow areas and time intervals over which the flows were emplaced are taken from Hiesinger et al. (2000;2003). The estimated flow thicknesses are established from the spot values shown in Figure 12b.

Figure 1 .

 1 Figure 1. Clementine 750 nm (albedo) image of the Oceanus Procellarum study area, indicating the major geological features of the region. Reiner and Marius craters are marked, as is the Reiner Gamma magnetic anomaly. The white lines are the lava flow boundaries, as mapped by Hiesingeret al. (2003). Two of the lava flows focused on in this work, 'P24' and 'P52', are labelled.

Figure 2 .

 2 Figure 2. Clementine 750 nm (albedo) image of the Mare Serenitatis study area, indicating the lava flow boundaries and nomenclature of Hiesinger et al. (2000). Dashed lines show two tracks

Figure 4 .

 4 Figure 4. The mean FeO (according to the algorithm of Wilcox et al., 2005) and TiO 2 (according to the algorithm of Lucey et al., 2000) wt. % contents for the ejecta of the thirteen haloed craters in lava flow unit 'P52', and mean inter-crater values for lava flow 'P52' and 'P24'. Error bars indicate one standard deviation of the individual pixel values used to produce the mean values.

Figure 5 .

 5 Figure 5. Graphs illustrating that the TiO 2 -poor haloes of craters in lava flow unit 'P52' are caused by TiO 2 wt. % content variations rather than surface maturity issues. Data from craters with TiO 2 -poor haloes are compared with neighbouring craters without such haloes.

Figure 12 .

 12 Figure 12. (a) Estimated maximum excavation depths (in metres) of the sampled craters in Mare

Table 2 Lava flow unit Model age (Ga) Error (Ga

 2

	)

Table 3

 3

Acknowledgments

We would like to thank Miriam Riner and David Rajmon for helpful reviews. S.Z.W. thanks the UK Science and Technology Facilities Council (STFC) for the award of a post-graduate studentship. I.A.C. and K.H.J. thank the Leverhulme Trust for financial support. This is LPI contribution number 1557.

De Hon, R.A., 1979. Thickness of the western mare basalts, Proceedings of 10 th Lunar and Planetary Science Conference, 2935-2955. De Hon, R.A. & Waskom, J.D., 1976. Geologic structure of the eastern mare basins. Proceedings of 7 th Lunar Science Conference, 2729-2746. Eliason, E., Isbell, C., Lee, E., Becker, T., Gaddis, L., McEwen, A. & Robinson, M., 1999. The Clementine UVVIS global lunar mosaic. NASA Planetary Data System CD-ROM Archive, CL-4001-4078. Fagents, S.A., Rumpf, M.E., Crawford, I.A. & Joy, K.H., 2010. Preservation potential of implanted solar wind volatiles in lunar palaeoregolith deposits buried by lava flows. Icarus, 207, 595-604.

Fischer, E.M. & Pieters, C.M., 1994. Remote determination of exposure degree and iron concentration of lunar soils using VIS-NIR spectroscopic methods. Icarus, 111, 475-488. Fischer, E.M. & Pieters, C.M., 1996. Composition and exposure age of the Apollo 16 Cayley and Descartes regions from Clementine data: normalizing the optical effects of space weathering. Journal of Geophysical Research, 101, 2225-2234. Giguere, T.A., Taylor, G.J., Hawke, B.R. & Lucey, P.G., 2000. The titanium contents of lunar mare basalts. Meteoritics and Planetary Science, 35, 193-200. Gillis, J.J., Jolliff, B.L. & Elphic, R.C., 2003. A revised algorithm for calculating TiO 2 from Clementine UVVIS data: a synthesis of rock, soil, and remotely sensed TiO 2 concentrations. Journal of Geophysical Research, 108 (E2), doi: 10.1029/2001JE001515. Gillis, J.J., Jolliff, B.L. & Korotev, R. L., 2004. Lunar surface geochemistry: global concentrations of Th, K, and FeO as derived from lunar prospector and Clementine data. Geochimica et Cosmochimica Acta, 68 (18), 3791-3805. ACCEPTED MANUSCRIPT Gillis-Davis, J.J., Lucey, P.G. & Hawke, B.R., 2006. Testing the relation between UV-vis color and TiO 2 content of the lunar maria. Geochimica et Cosmochimica Acta, 70, 6079-6102. Hapke, B., Cassidy, W. & Wells, E., 1975. Effects of vapor-phase deposition processes on the optical, chemical, and magnetic properties of the lunar regolith. The Moon, 13, 339-353. Head, J.W., III & Wilson, L., 1992. Lunar mare volcanism: stratigraphy, eruption conditions, and the evolution of secondary crusts. Geochimica et Cosmochimica Acta, 56, 2155-2175. Heather, D.J. & Dunkin, S.K., 2002. A stratigraphic study of southern Oceanus Procellarum using Clementine multispectral data. Planetary and Space Science, 50, 1299-1309. Hiesinger, H., Jaumann, R., Neukum, G. & Head, J.W., III, 2000. Ages of mare basalts on the lunar nearside. Journal of Geophysical Research, 105 (E12), 29-239-29,275. Hiesinger, H., Head, J.W., III, Wolf, U., Jaumann, R. & Neukum, G., 2003. Ages and stratigraphy of mare basalts in Oceanus Procellarum, Mare Nubium, Mare Cognitum, and Mare Insularum. Journal of Geophysical Research, 108 (E7), doi: 10.1029/2002JE001985. Hood, L.L. & Williams, C.R., 1989. The lunar swirls: distribution and possible origins. Proceedings of 19 th Lunar and Planetary Science Conference, 99-113. Johnson, J.R., Larson, S.M. & Singer, R.B., 1991. Remote sensing of potential lunar resources 1. Near-side compositional properties. Journal of Geophysical Research, 96 (E3), 18,861-18,882. Keller, L.P. & McKay, D.S., 1993. Discovery of vapour deposits in the lunar regolith. Science, 261, 1305-1307. Le Mouélic, S., Langevin, Y., Erard, S., Pinet, P., Chevrel., S. & Daydou, Y., 2000. Discrimination between maturity and composition of lunar soils from integrated Clementine UVvisible/near-infrared data: application to the Aristarchus Plateau. Journal of Geophysical Research, 105 (E4), 9445-9455.