Lunar Prospector neutron spectrometer measurements of the epithermal and thermal neutron leakage fluxes are used to provide constraints on TiO2 abundances in lunar surface materials. We use FeO abundance estimates based on both Clementine spectral reflectance techniques and preliminary Lunar Prospector gamma ray spectrometer determinations to first establish a model thermal neutron absorption due to all major elements except titanium. Then we remove the additional absorbing effects due to the rare earth elements gadolinium and samarium by using Lunar Prospector gamma ray spectrometer thorium abundances as a rare earth element proxy. The result can be compared to the ratio of epithermal to thermal neutron fluxes, which point to the presence of the additional thermal neutron absorber, titanium. We can derive abundance estimates of TiO2 and compare to other estimates derived spectroscopically. Our results show a significantly lower abundance of TiO2 than has been derived using Clementine data.
 Lunar mare basalts constitute only ∼17% of the surface area of the Moon and probably less than ∼1% of the volume of the lunar crust. However, lunar basaltic volcanism provides a window into the lunar interior, and important information about the Moon's internal constitution and thermal history from ∼3.9 to perhaps as little as 1 b.y. ago [Hiesinger et al., 2000]. All sampled lunar mare basalts are relatively high MgO and FeO lavas and derive from partial melts at depths of at least 100 km. They are chemically diverse, indicating a complex genesis. Titanium is the major element whose abundance varies most in mare basalts [Taylor et al., 1991]. In addition, the magmas that gave rise to mare basalts assimilated varying amounts of potassium, rare earth element, and phosphorus (KREEP) before eruption [Taylor et al., 1991, and references therein]. Consequently, the lavas preserved clues about chemical and mineralogical compositions of partial melts and information about pressure (hence depths) at which partial melting occurred.
 A recent classification of mare basalt soils by Giguere et al.  is based on spectral reflectance estimates of TiO2 content for soils formed on mare basalts; very low-Ti basalt soils have <1%, low-Ti 1–4.5%, intermediate 4.5–7.5%, high 7.5–10%, and very high-Ti >10%. These values are typically 10–30% lower than the TiO2 values in “pristine” basalt samples. Spectroscopic data suggest that TiO2 abundance varies continuously in mare basalts, not bimodally as suggested by the sample suite [Pieters, 1978].
 Here we further study the distribution of TiO2 in lunar mare basalts. In past work we have used the epithermal and thermal neutron data from Lunar Prospector together with FeO and TiO2 abundance estimates from Clementine spectral reflectance techniques [Lucey et al., 1995, 1996, 1998a, 1998b, 2000; Blewett et al., 1997] to infer the abundance of rare earth elements gadolinium and samarium [Elphic et al., 1998, 2000]. However, in some locations where thorium (hence REE) abundances are low, the TiO2 estimates of Lucey et al. [1998a] and the observed neutron absorption could not be easily reconciled. In this paper we use FeO abundance estimates provided by Clementine spectral reflectance techniques and analysis of Lunar Prospector gamma ray spectrometer data. We then compensate for the effects of the rare earth elements gadolinium and samarium through their good correlation with thorium. By estimating the absorption due to major elements (via FeO) and removing the additional REE absorption effects, we can determine the residual neutron absorption due to titanium alone. This analysis results in a completely independent assessment of TiO2 abundance in the maria.
2. Neutron Leakage Flux and Soil Composition
2.1. Thermal and Epithermal Neutrons
 Galactic cosmic rays with energies of ∼1 GeV shatter the nuclei of regolith atoms into spallation products, including elementary particles, nuclear fragments, including an initial population of neutrons with characteristic energies greater than 1 MeV (“fast” neutrons). The leakage flux of these energetic neutrons depends on the composition of the target materials: iron- and titanium-rich mare basalt soils yield relatively more fast neutrons than iron-poor highlands anorthosites [Gasnault et al., 2000; Maurice et al., 2000]. The energetic neutron population interacts with nuclei and loses energy through inelastic scattering. At “epithermal” energies (<0.5 MeV) the neutron leakage flux varies little with soil composition, because while iron-rich materials produce more fast neutrons, iron is also an effective neutron moderator [Feldman et al., 2000b]. As moderation reduces neutron energy, the cross section for absorption by nuclei increases. The absorption rate for thermal neutrons is highly composition dependent, because the thermal absorption cross section σa of certain major elements such as iron and titanium is large, while for others such as Al and Mg it is small. The thermal neutron leakage flux is thus lower for mare basalts than for highlands terrains.
 The Lunar Prospector neutron spectrometer consists of two detectors [Feldman et al., 1999]. One 3He gas proportional counter tube covered with Sn detects all neutrons from thermal through epithermal energy range. A separate cadmium-covered 3He tube detects only neutrons with energies above the cadmium thermal neutron capture resonance at ∼0.3 eV; neutrons below this cutoff energy are absorbed in the Cd with high efficiency and are not counted. Otherwise, the two tubes have identical response, so the Sn-tube count rate minus the Cd-tube count rate yields an estimate of the thermal flux (E < 0.3 eV). The Cd-covered tube provides a measure of the epithermal flux. (Fast neutrons were measured by the gamma ray spectrometer instrument but are not used here.)
2.2. Thermal Neutron Absorption and Elemental Composition
 Simulations of neutron transport and absorption reveal a monotonic relationship between the ratio of epithermal neutron leakage flux to thermal neutron leakage flux and a material's ability to absorb thermal neutrons [Feldman et al., 1991, 2000a, 2000b]. This ability is characterized by a material's macroscopic absorption cross section Σa, the weighted sum of all elemental constituents' ability to capture thermal neutrons:
where σai is the thermal neutron absorption cross section (usually expressed in barns, where 1 barn = 10−28 m2), fi is the weight fraction, Ai is the atomic mass of element i, and NA is Avogadro's number. (Σa is the same as Σeff of Elphic et al. [1998, 2000]; we use the former nomenclature here to facilitate comparison with Feldman et al. [2000b]). The cross sections are very well known for elements with isotopes that do not have significant absorption resonances in the thermal energy range. Values of σa at 0.025 eV for all major elements found in lunar mineralogy can be found in the work of Mughabghab et al. . The work of Feldman et al. [1991, 2000a, 2000b] forms the basis for this analysis. Briefly, nuclear Monte Carlo simulation techniques have been applied to the genesis, transport, and leakage of cosmic ray produced neutrons in lunar soils. These simulations use detailed energy-dependent cross section libraries to calculate neutron energy scattering and capture for all major element isotopes as well as gadolinium and samarium [Feldman et al., 1991, 2000b]. The simulations were run on a wide variety of regolith compositions, which results in a relationship between the macroscopic absorption cross section Σa and quantities related to measured epithermal and thermal neutron count rates. Specifically, a linear least squares fit to the simulation results of Table 5 of Feldman et al. [2000b] is
where Fsim is fepi/ftherm and fepi and ftherm are the measured epithermal and thermal neutron fluxes, respectively, obtained in the simulations. The epithermal-to-thermal flux ratio Fsim used by Feldman et al. [1999, 2000b] in these simulations corresponds to the actual responses of the Lunar Prospector neutron spectrometer detectors. Figure 1 shows the relationship between the macroscopic absorption cross section Σa and the flux ratio Fsim from these simulations. Note the flux ratio values for the end-member compositions: Fsim ∼ 0.85 for a ferroan anorthosite with 2 wt% FeO, and Fsim ∼ 2.65 for a high-Ti mare basalt soil from Apollo 17.
Figure 2 shows a map of the flux ratio Fmeas made from measurements taken in the Lunar Prospector 30-km mapping orbit. Lows of ∼0.8–1.0 are found throughout much of the farside highlands and the southernmost nearside highlands, consistent with a predominantly ferroan anorthosite composition there [Feldman et al., 2000b]. One can readily observe the effects of increased thermal neutron absorption (larger values of Fmeas) over the maria, as well as within SPA. Highs can also be found associated with certain impact craters, for example, Aristarchus (23.7°N, 47.4°W) and Aristillus (33.9°N, 1.2°E), due to the presence of enhanced REEs there [Elphic et al., 2000]. Within Oceanus Procellarum and Mare Imbrium a combination of high-Fe, high-Ti mare basalts and REEs contribute to strong absorption and associated highs in Fmeas.
 The thermal neutron absorption is due to the combined effect of all absorbers in the regolith, but is dominated by the elements Fe, Ti, Gd, and Sm [Elphic et al., 2000]. We construct a partial value of Σa based on the estimated weight fraction of FeO plus a model for the smaller absorbing effects of other major elements (except Ti). In order to account for the absorption effects due to the REEs Gd and Sm we exploit their strong correlation with thorium (as seen in returned samples) using the new Lunar Prospector gamma ray spectrometer thorium map [Lawrence et al., 2000]. We remove the effects due to the REEs by way of this thorium abundance proxy.
3. Σa (No TiO2) From FeO and Th
3.1. FeO Abundance and a Major Element Model
 Spectral reflectance techniques make use of an infrared ferrous absorption feature largely from pyroxene and olivine to determine iron content [Lucey et al., 2000, and references therein]. From the Clementine UVVIS data it has been possible to infer the quantitative abundance of FeO within ±70° latitude using images of sample stations. Unknown mineralogies may exist at locations very distant from the landing sites, so the inferred FeO and TiO2 values might be less accurate. We use a 0.5° resolution base map of FeO. Estimates of FeO have also been obtained through preliminary analysis of the 8-MeV thermal neutron capture (n-γ) gamma ray line measured by the Lunar Prospector gamma ray spectrometer [Lawrence et al., 1999a, 1999b; D. J. Lawrence, personal communication, 2001]. We also exploit an empirical anticorrelation between FeO and CaO found in low-Fe returned samples, primarily due to variations in the abundance of anorthite plagioclase, which is Ca-rich and Fe-poor [Haskin and Warren, 1991]. At higher FeO contents (>10 wt% FeO) where the correlation flattens, the soil and rock types are typically mare basalts which contain other Ca-bearing minerals, particularly clinopyroxenes.
This model broadly reproduces the variation of CaO with FeO, with a typical accuracy of about ±2 wt% CaO. There are certainly systematic deviations from this model with location. However, Ca is not a strong thermal neutron absorber (thermal neutron capture cross section σaCa = 0.45 barns, while that of iron is 2.58 barns and that of titanium is 6.06 barns), and it is only significant when its net absorptive effect is comparable to that of Fe, i.e., in highlands soils. So systematic abundance errors in CaO are not significant in comparison to the uncertainties in Fe, or those of the REEs Gd and Sm. In any case, we include such uncertainties in our error estimates below.
3.2. Constructing Σa
 The macroscopic absorption cross section Σa is a weighted sum over all elements in a given soil composition. However, we do not yet know the global abundance of all relevant major mineral-forming elements on the Moon. We do, however, have global estimates of the iron abundance based both on spectral reflectance techniques and preliminary analysis of the Lunar Prospector GRS data [Lawrence et al., 1999a; D. J. Lawrence, personal communication, 2001]. We construct a partial macroscopic absorption cross section, ΣaFe, using contributions from only FeO and the model (3) for CaO. That is, ΣaFe lacks the contributions from all other major elements and the effects of the REEs Gd and Sm. We will compare ΣaFe with the more complete cross section Σa* consisting of contributions from all the major element oxides except TiO2 for the same compositions used in the simulation results of Feldman et al. [2000a], but not including REEs. The purpose of this step is to estimate the macroscopic absorption cross section (minus TiO2) based only on measured FeO and modeled CaO abundances. Figure 3 is a plot of the partial macroscopic absorption cross section ΣaFe from FeO and model CaO versus the Σa* from all major element oxides (except TiO2) for the returned sample soil and regolith breccia compositions and the ferroan anorthosite in Table 1 of Elphic et al. . These 10 compositions correspond to the average soil compositions for all the Apollo and Luna sample sites plus ferroan anorthosite, as indicated in the figure. Clearly, for this broad range of known lunar soil compositions we get an excellent estimate of the major element Σa* from our iron-based partial cross section, ΣaFe. A least squares fit provides the relation:
If our estimate of major element Σa* is accurate, then deviations from the ideal relationship expressed by (2) should indicate the additional absorption due to constituents that we have not yet accounted for, namely, the trace REEs Gd and Sm, and TiO2.
 The fundamental quantity in Σa*, FeO abundance, is smoothed with the approximate surface footprint of the neutron spectrometer. From the 30-km mapping orbit the thermal neutron footprint has a full-width at half-maximum (FWHM) of ∼110 km; the epithermal footprint is ∼55 km at FWHM. The uncertainties in the CSR FeO abundances are roughly ±1–2 wt% for FeO [Lucey et al., 1998a, 2000], those in the LP GRS estimates of FeO are ±2 wt%. The spread in values of CaO wt% about the model in (3a) and (3b) based on returned samples is roughly ±2 wt%. These uncertainties lead to a conservative overall uncertainty in estimated Σa* of about ±5 × 10−4 cm2/g. The uncertainties in neutron spectrometer data consist of a combination of counting statistics and systematic errors. The resulting calculated standard deviation for values within 2° × 2° pixels is ∼1% for epithermal fluxes and 4% for thermals. Then the measured epithermal to thermal flux ratio Fmeas (fepi/ftherm) has an ∼4.7% typical uncertainty overall.
Figures 4a and 4b show the estimated macroscopic absorption cross section Σa* from (4) versus the measured ratio of epithermal neutron flux to the thermal neutron flux, Fmeas. Σa* in Figure 4a is based on Clementine FeO estimates techniques [Lucey et al., 2000], while Σa* in Figure 4b is from the Lunar Prospector gamma ray spectrometer estimates of Lawrence et al. [1999a]. Also shown is a gray line denoting the linear relationship (2) between Σa and F, the ratio of epithermal to thermal fluxes. If the estimates of FeO, CaO and the other major element abundances in (4) accounted for all the variations in Σa*, then the points would all fall on this line. A subset of the data, corresponding to those points that happen to have estimated CSR TiO2 abundances less than 0.5 wt%, is colored in gray for comparison; median values of this subset are shown as large open squares. Since we have now accounted for neutron absorption by all major elements except titanium, we presume that the scatter below the ideal line is primarily due to additional neutron absorption from both REEs and TiO2. The difference, or ΔΣa illustrated in Figure 4, is then the additional neutron absorption required to account for the observed neutron flux:
3.3. Thorium and Estimated REE Abundances
 We can use the thorium abundance to estimate the concentrations of Gd and Sm in the surface soils and estimate their contribution to (5). Analysis of returned samples has revealed a slightly nonlinear relationship between Th and Sm [Korotev, 2000]. This relationship is shown in Figure 5, a plot of Sm versus Th abundances from Korotev  (from KREEP samples, shown as solid circles) as well as abundances in selected soils and regolith breccias from Haskin and Warren ; also shown is a power law fit to the data:
Assuming an average ratio of [Gd]/[Sm] = 1.17 [Korotev, 2000], this relationship then provides us with an estimate of the contribution of REEs to Σa. For example, a REE contribution to the macroscopic absorption cross section of 30 × 10−4 cm2/g corresponds to a combination of 35.6 μg/g of Gd and 30.5 μg/g of Sm, using values of by Lingenfelter et al. . However, there is currently some debate about the effective macroscopic absorption coefficient as defined by Lingenfelter et al. ; the Sm abundances inferred by Elphic et al.  are larger relative to Th than are found in KREEP samples [Korotev, 2000]. There are no obvious geochemical reasons to explain the high [Sm]/[Th] ratios at high Th abundances in KREEPy terrains. So we will simply find and remove an empirical relationship between the observed absorption and the REE proxy of thorium abundance. We will use the same low-Ti subset of the data (<0.5 wt% TiO2) described earlier, based on the CSR TiO2 maps produced by Blewett et al.  and Lucey et al. [1998a, 2000]. This means that Ti can contribute no more than ∼2.2 × 10−4 cm2/g to the ΔΣa (low-Ti) subset, a very small amount. Figure 6 shows a plot of ΔΣa (low-Ti subset) versus thorium abundance for that subset. The least squares linear relationship is shown by the solid line. The dashed line denotes the expected trend based on the “effective” macroscopic absorption coefficient of Lingenfelter et al.  for Gd and Sm, and the REE-to-Th abundance relationship of Korotev  shown in Figure 5. The top panel comes from ΔΣa of Figure 4a, the bottom panel from Figure 4b. The large open squares denote medians of ΔΣa in bins of 0.5 ppm Th. The result is a very clear trend with Th that provides an empirical fit for the net REE absorption contribution using thorium abundance as a proxy. We can now remove the REE absorption from the entire ΔΣa data set via this proxy and the fit in Figure 6:
ΔΣ′a is thus a measure of the neutron absorption due to the only significant, unaccounted neutron absorber, titanium. For KREEP-rich materials, there is a positive, but complicated, correlation between Th and TiO2. So by removing a trend with Th, we may also be inadvertently removing a small (∼1.5 wt%) amount of TiO2 at high [Th]. With thorium uncertainties of ≤±1 μg/g [Lawrence et al., 2000], the associated uncertainty in ΔΣa′ is roughly ±6 × 10−4 cm2/g from this thorium correction. The uncertainty in ΔΣa is not strictly additive to the thorium-related uncertainty, as they are two independent (orthogonal) sources. The proper uncertainty is the square root of the sum of the squares of the ΔΣa and thorium-correction uncertainties, or ±7.8 × 10−4 cm2/g.
3.4. Neutron-Derived TiO2 Abundance
 The thermal absorption cross section of Ti is 6.06 barns, so we can estimate how much Ti is needed to give the inferred ΔΣa′. A useful rule of thumb is 1 wt% TiO2 = ΣaTi = ∼4.57 × 10−4 cm2/g. Figure 7 is a scatterplot of ΔΣa′ expressed as equivalent wt% TiO2 versus CSR TiO2 abundance estimates. Once again, the top panel derives from CSR FeO and the lower panel from LP GRS FeO. Large open squares denote medians of ΔΣa′ (REEs removed) in 0.5 wt% bins of CSR TiO2. Also plotted are dashed lines denoting a unity slope. Figure 7 reveals clearly what was hinted at by Elphic et al. , namely that TiO2 abundances inferred from neutron absorption are ∼50% of those determined by CSR techniques. There is also scatter about the trend that is consistent with the calculated uncertainty of ±7.8 × 10−4 cm2/g, or ±1.7 wt% TiO2.
Figure 8 shows a stereographic map of the CSR-estimated TiO2 distribution on the lunar nearside. The original data have been smoothed with the approximate footprint of the neutron spectrometers to facilitate comparison. Figure 9 is the same map projection of TiO2 abundance from the foregoing neutron analysis, based on Lunar Prospector GRS FeO (a map based on CSR FeO is very similar and is not shown here). Negative values of the neutron-derived TiO2 abundance have been reset to zero. The color scales of Figures 8 and 9 are different, so as to provide greater sensitivity to inferred TiO2 variations. Note the good correspondence between the two maps overall, with highs in CSR TiO2 abundance in Mare Tranquillitatis and Oceanus Procellarum and a lower local maximum in Mare Imbrium. However, the neutron-derived quantities are generally much lower than the CSR-derived TiO2 values. Locations that show strikingly lower abundances in the neutron-derived TiO2 values can be found in Mare Crisium, most of Mare Fecunditatis, central Mare Serenitatis, and northern Mare Nubium.
 Negative values of the neutron TiO2 estimate (not shown) tend to occur at high northern latitudes. This is probably due to some systematic error in the FeO and possibly the Th abundance estimates. Since the values are within the uncertainties discussed earlier, we do not consider the systematically low or negative values to be meaningful.
4. Comparing Estimates of TiO2
 From the foregoing discussion as well as Figures 7–9 it is clear that regions identified by UVVIS spectral characteristics as having high TiO2 content correspond fairly well to highs in the two neutron-derived estimates of TiO2 abundance (though the latter are generally lower than the CSR TiO2 values). To illustrate the distribution of titanium values in mare basalt soils, Figure 10 shows our inferred TiO2 abundances based on CSR FeO abundance (Figure 10a) and based on LP GRS FeO abundance (Figure 10b) against CSR and GRS FeO abundance. The green points once again denote the low-Ti (based on CSR TiO2 estimates) subset. Also included are solid, colored squares that denote the TiO2 and FeO abundances actually found in soil samples returned from the landing sites and used by Lucey et al.  as calibration points. These include individual Apollo 14, 15, 16, and 17 sample stations, which are resolved in the Clementine data. The returned soil sample data suggest two trends, high-Ti (dominated by Apollo 11 and 17 soil samples) and low-Ti (including Apollo 12 and 15, and Luna 16 and 24 soils), somewhat reflecting a bimodal distribution of TiO2 abundances with FeO as noted in other work [e.g., Taylor et al., 1991]. Figure 10 suggests that the range of FeO-TiO2 values found in soil samples is not inconsistent with the neutron-derived TiO2 abundances, especially those based on LP GRS FeO values (bottom panel). A similar plot of CSR TiO2 versus CSR FeO (not shown here) reveals a global distribution of points that agrees with the sample points except for Luna 24 (Mare Crisium). In that location the CSR TiO2 abundance is much higher than is found in the soil sample.
 A bimodal distribution is not found in the inferred global CSR TiO2 abundances for mare basalt soils, for example as shown by Giguere et al. . They point out that no landing site sampled intermediate-Ti mare basalt soils. Likewise, our neutron-derived TiO2 abundances have a continuous distribution. This can be seen in Figure 11, showing histograms of TiO2 abundance based on CSR estimates (dotted line) and neutron-derived estimates (solid line). These histograms are based on those pixels in Figures 8 and 9b for which FeO is greater than 13 wt%, i.e., mostly the maria. The histograms illustrate the approximately factor of 2 difference between the two global TiO2 estimates. The CSR values have a peak near 3.5 wt%, and a range of up to ∼14 wt% in its smoothed form used here. The neutron-derived TiO2 values peak near 2 wt% and do not go above ∼8 wt%.
Figure 12 is a comparison of CSR- and neutron-derived TiO2 values averaged over 1° × 1° surface elements centered on the Apollo and Luna landing sites, plotted against the TiO2 abundance in presumably representative soil samples from these sites. The dashed line is the unity relationship. Note that the neutron-derived values tend to be lower on average, while CSR-derived values are generally higher. The Luna 20, Luna 24, and Luna 16 values are in better agreement with the neutron-derived values than the CSR-derived values. It should also be remembered that some TiO2 from Apollo 14 may have been removed with the Th correction for the neutron-derived TiO2 values. This discrepancy could amount to as much as 1.5 wt%. The Apollo 11 value for the neutron-derived TiO2 abundance appears anomalously low compared to the CSR-derived value.
 The comparison between TiO2 contents inferred from UVVIS spectra and our neutron-based analysis has yielded an interesting and probably meaningful contrast. We suspect that there is information in the discrepancy, which may have something to do with the complexity and heterogeneity of opaque minerals in the various mare basalt soils. At the same time, we have uncovered some curious features in the neutron data, for example, the odd relationship between our inferred REE abundances and the thorium abundances from the Lunar Prospector gamma ray spectrometer. The neutron data require further analysis and comparison with nuclear Monte Carlo simulations. Nevertheless, if our analysis is correct we must explain why the clear empirical relationship between the UVVIS measure of opaque minerals and sampled TiO2 abundance disagrees with this nuclear analysis of titanium abundance. Two possibilities suggest themselves, first that the UVVIS opaque mineral-TiO2 relationship breaks down at unsampled locations away from the landing sites, hinting that other opaque mineral phases may be significant in the mare basalt soils. For example, spinels may have a higher abundance than we expect on the basis of returned samples. Another possibility is that glasses may play a role in soil optical properties. In any event these results suggest that mare basalt mineralogy may be more complex than has been generally thought. We note that efforts are underway to try to understand this discrepancy through further examination of UVVIS characteristics (J. Gillis, personal communication, 2001).