Recent near-infrared spectral data have shown that surficial water (H2O/OH) exists over large expanses of the lunar surface. These results have led to a reexamination of the hydrogen abundance sensitivity limits of orbital neutron data to detect surficial hydrogen on the lunar surface. A wet-over-dry, two-layer stratigraphy is modeled for the first time using neutron transport codes. For thin layers (<30 g/cm2), the epithermal neutron flux increases with increasing hydrogen concentration. This behavior is in contrast to the standard behavior for a single layer or dry-over-wet stratigraphy where the epithermal neutron counting rate decreases with increasing hydrogen concentration. These neutron transport results are applied to a H2O/OH enhancement at Goldschmidt crater. The neutron behavior at Goldschmidt is mostly controlled by spatial variations in neutron absorbing elements. After accounting for variations from neutron absorbing elements, there remain residual neutron enhancements at Goldschmidt crater with marginal statistical significance. If these residual enhancements are due to hydrogen, then their magnitude implies the presence of an upper layer with thickness of ∼3–30 g/cm2 (or 1.7–17 cm for an assumed density of 1.8 g/cm3) having an enhanced hydrogen abundance of 0.1–1 wt % water equivalent hydrogen. However, more work needs to be done to understand systematic variations of neutron counting rates at the 1–3% signal contrast level before a definitive conclusion can be made that the residual neutron enhancement at Goldschmidt crater is due to enhanced hydrogen abundances.
 The possibility that water and/or nontrace amounts of hydrogen might be present on the Moon has been investigated over the past 40 years with both theoretical models [Watson et al., 1961; Arnold, 1979] as well as space-based measurements [Nozette et al., 1996; Feldman et al., 1998, 2000a, 2001; Spudis et al., 2010]. For the most part, these studies have focused on the presence of water and/or hydrogen in permanently shaded regions (PSR) at the lunar poles. PSRs are locations that do not see sunlight and therefore have temperatures cold enough to trap water ice and other volatiles for billions of years. It has been generally assumed that water ice could not be present to any significant extent in lunar sunlit regions due to its high sublimation rate on the relatively hot lunar surface. Thus, recent results that show extensive H2O/OH on the lunar surface detected by near infrared (NIR) spectral data [Pieters et al., 2009; Sunshine et al., 2009; Clark, 2009] must indicate attachment to surface minerals through adsorption rather than as a surficial deposit of water ice. These data show that H2O/OH is spread widely across the lunar surface, may be present to a depth of a few millimeters, and could have an abundance of ∼100–1000 ppm H2O [Clark, 2009]. The exact depth and abundance values, however, are highly uncertain. In addition, data from the Chandraayan-1 M3 instrument show an additional H2O/OH enhancement signature at Goldschmidt crater, which is located in the northern, lunar nearside (73°N, 3.8°W). Coincidently, Goldschmidt crater also shows an enhancement of epithermal neutrons [Lawrence et al., 2006; Pieters et al., 2009], which according to conventional methods of interpreting neutron data, indicate low hydrogen abundances within the top meter of the lunar surface.
 At first glance, the NIR and neutron results at Goldschmidt crater appear contradictory. However, the NIR measurements are consistent with a scenario where there is a relatively wet layer over a dry layer and where the thickness of this wet layer is highly uncertain. Previous studies of planetary neutron transport have investigated two-layer scenarios [e.g., Prettyman et al., 2004; Lawrence et al., 2006; Feldman et al., 2007; Diez et al., 2008], but almost exclusively these studies investigated a scenario with a dry layer over a wet layer. Thus, the scenario suggested by the NIR measurement has not been modeled with neutron transport calculations and the systematic behavior of the neutron flux as a function of a top layer thickness and hydrogen abundance is not known.
 This study has a twofold purpose. First, using neutron transport modeling, we will investigate the layer thickness and hydrogen abundance sensitivity limits of orbital neutron data to detect surficial hydrogen. Second, using these neutron transport models and other compositional data, we will study Lunar Prospector (LP) neutron data at Goldschmidt crater to understand what information, if any, these data reveal about the hydrogen abundances within this region.
2. Neutron Transport Models
 Neutrons are produced on planetary atmospheres or surfaces through spallation reactions of energetic galactic cosmic rays (GCR). In the presence of hydrogen atoms, which have the same mass as neutrons, the neutrons lose their energy very efficiently through elastic scattering collisions because of the large (n,p) scattering cross section. The neutron energies most sensitive to hydrogen are epithermal neutrons, which cover an energy range from ∼0.4 to 500 keV. While not as sensitive, thermal (E < 0.4 eV) and fast neutrons (E > 500 keV) are also sensitive to variations in hydrogen concentrations. All three energy ranges of neutrons are also sensitive to other elemental compositional variations. Thermal neutrons are sensitive to variations of neutron absorbing elements Fe, Ti, Gd, and Sm [Feldman et al., 2000a; Elphic et al., 2000]. Fast neutrons are sensitive to variations in average atomic mass [Gasnault et al., 2001]. Epithermal neutrons are also sensitive to variations of neutron absorbing elements but with a significantly smaller dynamic range than are thermal neutrons [Maurice et al., 2004; Lawrence et al., 2006].
 Various studies of neutron creation and transport on planetary surfaces have been carried out for the Moon [Feldman et al., 1998, 2000a, 2000b, 2001; Lawrence et al., 2006], Mars [Prettyman et al., 2004], and Mercury [Lawrence et al., 2010]. Generally, these studies first determine the GCR-induced neutron flux using particle transport codes such as MCNPX [Pelowitz, 2005]. Modeled counting rates (both relative and absolute) are determined using calculations that account for the neutron transport from the planetary surface to the neutron sensor and account for effects such as flux nonisotropy, planetary gravity effects, finite neutron lifetime, spacecraft motion, and energy angle sensor efficiency. For this study, we use a neutron surface-to-spacecraft transport code that was developed for neutron measurements with the MESSENGER Neutron Spectrometer (NS) and validated with data from the Lunar Prospector neutron spectrometer (LP NS) [Lawrence et al., 2010]. The LP NS response functions were the same as those used in earlier studies with LP NS data [Lawrence et al., 2006]. As was demonstrated by Lawrence et al. , this code, which was coupled to output neutron fluxes from MCNPX, is able to reproduce relative counting rates to an uncertainty of <5% and absolute counting rates to an uncertainty of <20%.
 For this study, we investigate a two-layer scenario (Figure 1) where the top layer thickness t varies from 0.05 to 100 g/cm2 and the hydrogen concentration in the top layer w varies from 0.0009 to 9 wt % water equivalent hydrogen (WEH) (or equivalently 1 to 10,000 ppm H). The limits for the thickness were determined in order to have a thin layer that is below the expected detection sensitivity of orbital neutron measurements and thick enough to approximate a single layer scenario. The limits for the hydrogen concentration were determined to provide a lower limit for detection (1 ppm H) and a reasonable upper limit (9 wt % WEH) for the H2O/OH detection using the NIR data. The composition of the nonhydrous portion of the soil is set to be a ferroan anorthosite (FAN) soil, as has been done with previous lunar polar hydrogen studies [e.g., Feldman et al., 1998; Lawrence et al., 2006].
Figure 2 shows the neutron flux calculated with MCNPX for various permutations of w and t. These fluxes are plotted as flux times energy to better illustrate the flux variability in the epithermal range. These fluxes were calculated with 500,000 histories, where this number of histories was set to keep the uncertainty in the energy-integrated flux less than 0.3%. For small thicknesses (e.g., 0.05 g/cm2 in Figure 2a), no flux variations are seen at any energy for any amount of hydrogen. This result reflects the reality that neutrons are sensitive to the total mass of hydrogen within a layer having thickness comparable to or larger than the mean neutron energy loss length of the material. These lengths range between 0.75 g/cm2 for 100 wt % water and about 100 g/cm2 for 0 wt % water. Therefore, a 0.5 mm thick layer does not contain enough hydrogen to measurably affect the neutron flux. Figure 2b shows the neutron flux from a 3 g/cm2 thick layer. For most neutron energies at this thickness, no effect is seen. However, for thermal energies, there is a clear increased neutron flux for the largest hydrogen concentrations. Figure 2c shows a thickness of 30 g/cm2. Here there are clear effects for all energy ranges. Specifically, thermal neutrons show more pronounced enhancements for increasingly larger hydrogen concentrations. For the largest hydrogen concentrations, flux decreases are seen for epithermal and fast neutrons. Finally, Figure 2d shows the fluxes for a top layer having a thickness of 100 g/cm2. As expected, these fluxes are very similar to a single-layer scenario with various hydrogen concentrations [e.g., Feldman et al., 1998].
 The fluxes of Figure 2 are converted into neutron counting rates using the surface-to-sensor transport calculation that is described by Lawrence et al. . These counting rates are represented as relative count rates between a model with a nonzero hydrogen concentration in the top layer and a fully dry case. Counting rates for thermal and epithermal neutrons are taken as the model count rates from the LP NS Sn and Cd covered 3He gas proportional sensors. Epithermal counts are the counts from the Cd-covered sensor and are sensitive to neutrons having energies greater than 0.4 eV [Feldman et al., 2004]. Thermal neutron counts are the counting rate difference between the Sn- and Cd-covered 3He sensors [Feldman et al., 2004].
Figure 3 shows the wet-to-dry count rate ratios as a function of hydrogen concentration for thermal (Figure 3a) and epithermal (Figure 3b) neutrons. For each sensor, the various thicknesses are color coded. The error bars represent the ∼0.3% uncertainties from the MCNPX Monte Carlo neutron flux calculations. On the basis of measured and analyzed LP NS data, a rough detection limit of 1–2% is a practical lower limit for hydrogen detection using existing data, assuming there are no other major compositional variations in the region of interest. Inspection of Figure 3a shows that a 1–2% contrast is seen using thermal neutrons for large (10 wt %) hydrogen concentrations for a thickness of 0.2–0.3 g/cm2. Thus, a practical lower limit thickness for detecting hydrogen with thermal neutrons is >0.5 g/cm2. For epithermal neutrons, the 1–2% signal is seen for a thickness of ∼1 g/cm2, which therefore represents the lower limit thickness for detecting hydrogen using epithermal neutrons.
 For larger thicknesses, the thermal neutrons show a monotonic count rate increase for both increasing thicknesses and hydrogen concentrations. This is similar to the behavior of thermal neutrons for either a single layer or a dry-over-wet two-layer scenario. For hydrogen concentrations larger than 10 wt % (not shown), thermal neutron counts generally plateau and then decrease [Lawrence et al., 2006]. While not modeled here because hydrogen concentrations >10 wt % are unlikely for the lunar regions being studied, we expect similar double valued behavior in this wet-over-dry scenario.
 In contrast to the simple behavior with thermal neutrons, epithermal neutrons show a more complicated behavior. For relatively thin layers where hydrogen is detectable (1–10 g/cm2), Figure 3b shows a counting rate increase for hydrogen concentrations in the range of ∼0.3–10 wt % WEH. This behavior is opposite to the modeled and observed behavior for single layer or dry-over-wet two-layer models that show a monotonic decrease in epithermal neutrons for increasing hydrogen concentrations. The reason for this behavior can be understood by referring to the neutron fluxes in Figure 2. For thin layers, thermal neutrons are seen to be highly sensitive to various amounts of hydrogen concentration while showing little sensitivity in the broad epithermal energy range. However, as the thermal neutron flux increases, the higher energy tail of the thermal peak extends to energies greater than 0.4 eV. These higher-energy thermal neutrons or equivalently lower-energy epithermal neutrons are counted as epithermal neutrons in the Cd covered sensor. Therefore, for thin layers, epithermal neutrons show a count rate increase. For larger thicknesses, the total mass of hydrogen reaches the point to cause a decrease in epithermal neutrons. For the 100 g/cm2 thickness, epithermal neutrons monotonically decrease for all increasing hydrogen concentrations, which is the same behavior as for a single layer scenario.
 In summary, these model results show that in the absence of significant nonhydrous compositional variability, which could mask these small signals, hydrogen within the two-layer scenario of Figure 1, can be detected with both thermal and epithermal neutrons. However, in the presence of moderate variations of Fe, Ti, Gd, and Sm that are typically seen on the Moon, hydrogen variations can be easily masked and not seen with thermal neutrons [Lawrence et al., 2006]. For thin layers (<10 g/cm2), the hydrogen signature is a relative increase in both thermal and epithermal neutrons. A relative decrease in epithermal and relative increase in thermal neutrons is a signature of a thicker layer (>30 g/cm2). As was reported for a dry-over-wet model [Lawrence et al., 2006], a relative epithermal neutron decrease and a nondetection with thermal neutrons is consistent with a top layer having a thickness of ∼10–30 g/cm2 and enhanced hydrogen in the lower layer.
 Finally, these results show that thermal and epithermal neutrons together are sensitive to layer thicknesses of a few g/cm2 or greater. Thus, even if there is no detected and/or verified signal at specified locations with LP NS data, these models can be used to provide an upper limit of the thickness of any hydrogen-enriched top layer.
3. Lunar Prospector Neutron and Elemental Composition Data at Goldschmidt Crater
 A straightforward application of the modeling results described in section 2 can be made for the Goldschmidt crater, which is a 113 km diameter crater located at 73°N, 3.8°W. The primary reason Goldschmidt crater provides a good test of the models in section 2 is that the NIR data from the Chandraayan-1 M3 instrument identifies Goldschmidt crater as an isolated location that is especially enhanced in H2O/OH and is easily distinguishable from other regions that already show an H2O/OH enhancement. Thus, if any of the surficial water seen with the NIR data can be detected with neutron data, Goldschmidt crater would be a likely location. Other than being enhanced in H2O/OH compared to the surrounding regions, it is not reported what the thickness or H2O/OH content might be of the hydrogen-enriched region at Goldschmidt crater. Therefore, in regard to the model results of section 2, here we will try to determine if the enhanced H2O/OH seen with M3 data can also be detected with neutron data.
Figure 4 shows maps of thermal and epithermal neutrons of the region around Goldschmidt crater (the location and size of Goldschmidt crater is indicated by a cross and the center circle). As given by Maurice et al. [2004, Table 9], these maps were made by smoothing the raw thermal and epithermal neutron data using a two-dimensional Gaussian function with a half-width, half-maximum of 30 and 32 km, respectively. These maps show relative counting rate increases for both neutron energy ranges at Goldschmidt crater. The enhancement of epithermal neutrons was already identified by Pieters et al.  as a location of low hydrogen at depth, using the implicit assumption that the epithermal neutrons are inversely related to hydrogen abundances. On the basis of the results of Figure 3 and the combined data of Figure 4, an initial and alternative conclusion could be that Goldschmidt crater may have a top layer ∼1–10 g/cm2 thick of enhanced hydrogen concentrations. However, prior to reaching this conclusion, other data should be investigated to see if compositional variations from other elements might be related to the observed thermal and epithermal variations.
Figure 5 shows maps of Fe and Th abundances in the Goldschmidt crater region measured with the Lunar Prospector gamma ray spectrometer (LP GRS) [Lawrence et al., 2002, 2003]. These maps represent neutron-absorbing elements known to cause nonhydrous variability in thermal and epithermal neutrons. In particular, the spatial variation of Th on the Moon is very similar to that of the strong neutron absorbers Gd and Sm [Elphic et al., 2000] and therefore serves here as a proxy for Gd and Sm concentrations. In this region, the spatial variations of Fe and Th have a large dynamic range and are similar with relatively large abundances (11 wt % Fe and 6 ppm Th) in the southern portion of the region and low abundances (<5 wt % Fe and <2 ppm Th) in and around Goldschmidt crater. In particular, both Fe and Th have relative abundance decreases in the same location as the thermal and epithermal neutron enhancements.
 To summarize how the neutron data vary in comparison to neutron absorbers, quantitative neutron absorption from Fe, Gd, and Sm can be calculated. For Fe, the macroscopic neutron absorption is Σa,Fe = σFeNAw/AFe, where σFe = 2.59 barns, NA is Avogadro's number, AFe = 56 atomic mass units, and w = weight fraction Fe. The macroscopic neutron absorption from Gd and Sm is determined using the empirical relation developed by Elphic et al.  that relates measured Th abundances to Gd + Sm neutron absorption: Σa,Gd+Sm = 1.85 + 4[Th], where [Th] is Th concentration in ppm, and Σa,Gd+Sm is in units of 10−4 cm2/g. Figure 6 shows Σa,Fe+Gd+Sm plotted versus counts in each neutron energy range. The black data points in Figure 6 show global values, and the red data points show values within the Goldschmidt crater region given in Figures 4 and 5. As seen, on a global scale, both thermal and epithermal neutrons show a strong correlation with neutron absorbers, which is a known behavior from previous studies [Feldman et al., 2000a; Elphic et al., 2000; Maurice et al., 2004; Lawrence et al., 2006]. In the region around Goldschmidt crater, there is an even tighter, monotonic correlation between counts in both neutron energy ranges and neutron absorbers, such that surface variations of neutron absorbers appear to be a dominant controlling factor in the measured neutron counting rates. For comparison, Figure 6b shows epithermal neutron data from the lunar poles (orange data points) where there is no correlation with neutron absorbers. This is consistent with previous studies indicating the presence of enhanced hydrogen at both lunar poles [Feldman et al., 1998, 2000a, 2001; Lawrence et al., 2006]. Such enhancements do not have correlations with any other known elemental abundance distributions [Feldman et al., 2001; Lawrence et al., 2006].
 While it appears that neutron absorbers control the observed neutron counting rates in the Goldschmidt region, the observed correlations of Figure 6 by themselves do not rule out the presence of enhanced hydrogen at Goldschmidt crater. To check for possible variations due to hydrogen (or other systematic effects), the regional Goldschmidt neutron data (i.e., the entire region of Figure 4) should be detrended based on the empirically observed global and/or regional trends of thermal and epithermal neutron counting rates versus neutron absorbers. If the detrended data show no statistically significant enhancement at Goldschmidt crater, then such a result would provide strong confidence that the variations in neutron absorbers solely control the measured thermal and epithermal neutron data. However, it is possible that there might be a measurable hydrogen signal at Goldschmidt crater that is also spatially correlated with neutron absorbers and other related compositional control of H2O/OH activation energies of near surface minerals. In this case, an expected result would be a regional correlation trend that is different from that derived using global data. If a measurable hydrogen signal at Goldschmidt is spatially uncorrelated with variations in neutron absorbers, then a detrended map using a correlation derived from either regional or global data should show a statistically significantly enhancement at Goldschmidt crater. Finally, even if a detrended map shows a statistically significant enhancement at Goldschmidt crater, attributing such an enhancement to variations in hydrogen can only be done if it is known that all other systematic uncertainties are understood and accounted for, and have a magnitude less than any observed enhancement.
 We investigate these possibilities by developing two detrended data sets where the correlation trends are derived from either global or Goldschmidt-regional data. For the epithermal neutrons, we found that their correlation with neutron absorbers is best represented as a linear function for Σa,Fe+Gd+Sm > 30 × 10−4 cm2/g. For thermal neutrons, the observed correlation in the range of interest is best represented as a second order polynomial function. Global and regional fits of Σa,Fe+Gd+Sm to thermal and epithermal neutrons are shown in Figure 6. The global fit is shown by a solid red line, and the regional fit is shown by a dashed red line. The fit coefficients are given in Table 1. Inspection shows that the global and regional fit parameters do not match, which gives some indication that the empirical, global trends do not fully account for the regional trends at Goldschmidt.
Table 1. List of Parameters for the Neutron-to-Neutron Absorption Correlation Fitsa
All correlations are fit to the function f(ai) = a1 + a2p + a3p2, where p = Σa,Gd,Sm,Fe. For epithermal neutrons, a linear function is used so that a3 = 0. Uncertainties in the fit parameters are based on the assumption that the uncertainties in the neutron data are Poisson [Maurice et al., 2004] and include a propagation of errors for the smoothed mapped data [see also Hagerty et al., 2006].
Thermal neutrons, global fit
963.2 ± 0.3
−16.71 ± 0.02
0.104 ± 0.0002
Epithermal neutrons, global fit
636.7 ± 0.2
−0.541 ± 0.003
Thermal neutrons, regional fit
1109.3 ± 1.88
−25.3 ± 0.12
0.244 ± 0.002
Epithermal neutrons, regional fit
658.0 ± 0.4
−0.998 ± 0.01
 Detrended data are defined as Cdetrend = C − f(ai) + Cmean, where C is the original neutron counting rate, Cdetrend is the detrended neutron counting rate, Cmean is the global mean counting rate, and f(ai) is the fitted linear or polynomial function with coefficients ai shown in Table 1. Scatterplots of the globally detrended data are shown in blue in Figure 6. For purposes of clarity, the regional detrended data are not shown in Figure 6, as they have substantial overlap with the globally detrended data.
 Maps of globally detrended data are shown in Figure 7. These thermal and epithermal neutron maps show residual enhancements around Goldschmidt crater that, while not completely spatially colocated, appear to be significant. To quantitatively determine the statistical significance of the signal at Goldschmidt crater compared to its surrounding region, we have selected three regions shown as circles in Figures 5–7. These circles outline Goldschmidt crater (center circle) and two equivalently sized regions 20° in longitude to the east and west of Goldschmidt crater.
Table 2 lists mean counting rates that are taken from raw, unsmoothed data, and defined by the circular regions in Figures 5 and 7. Unsmoothed data are used here to simplify the determination of counting rate uncertainties. Counting rates have been determined for original and detrended thermal and epithermal neutron data using a global correlation and a regional correlation. For each case, the mean counting rates are given for the center region (i.e., at Goldschmidt crater) as well as the west and east background regions. A counting rate ratio R (Table 2) gives the magnitude of the Goldschmidt enhancement. Table 2 also gives the three-sigma uncertainty in the measured ratio 3 × σR, where the uncertainty for each region was summed in quadrature. The uncertainty for each region was determined by assuming the uncertainties are purely Poisson [Maurice et al., 2004] such that σ = , where Ctotal is the total measured counts in the region. Overall uncertainties due to uncertainties in the fit parameters and detrending were found to be small due to the large number of data points used in deriving the fit parameters. Finally, a signal-to-noise parameter Sn is determined using Sn = (R − 1)/σR.
Table 2. List of Neutron Counting Rates for Original Data, Detrended Data With the Global Correlation Trends, and Detrended Data With the Regional Correlation Trendsa
Goldschmidt (counts per 32 s)
Background Region (counts per 32 s)
Uncertainty, 3 × σR
The counting rate ratio is the ratio between the counting rate at Goldschmidt crater and the given background region. The uncertainty is the propagated 3σ uncertainty in the calculated ratio. The signal-to-noise parameter is defined as Sn = (1 − R)/σR.
Detrended Data With Global Correlation Trend
Regional Correlation Trend
 The signal-to-noise results show that, for uncorrected thermal and epithermal neutrons at Goldschmidt crater, there are clear, statistically significant enhancements of >30σ and ∼4–5σ, respectively. On the basis of the trends shown in Figure 6, this is an expected result. For the globally detrended thermal neutron data, the results in Table 2 show there is still a statistically significant enhancement at Goldschmidt crater of >7σ. The locally detrended thermal neutron data show marginally significant enhancements of 4σ and 2.7σ. The globally detrended epithermal neutrons show a marginally significant enhancement of 3.4–3.7σ. Finally, the regionally detrended epithermal neutrons have a less statistically significant enhancement of 2.0–2.9σ. From these results, there is the suggestion that whatever is causing the variations in thermal and epithermal neutrons, it has a trending relationship with Σa,Fe+Gd+Sm that is not the same as the overall global relationship. In summary, these results show that, after the global detrending with neutron absorber variations, there is still a nonnegligible neutron enhancement at Goldschmidt crater.
 Given the strong, monotonic correlation of neutrons with neutron absorbers, it is somewhat surprising that even after the global detrending of the neutron data, there remains an enhancement that cannot be immediately dismissed as being statistically insignificant. For completeness sake, we will first determine the implications if this remaining signal is only due to hydrogen. Afterward, we will discuss qualifications to this hydrogen-only conclusion.
Figure 8 shows the model results of Figure 3 recast as a contour plot, where the contours show relative signal strength (epithermal neutrons in black, thermal neutrons in red) versus both WEH abundance and top layer thickness. Since these small signals (<1.03) are close to the uncertainty limits of both model and data, we are therefore interested in general trends and will not attempt to determine precise values.
 If the globally detrended enhancements at Goldschmidt crater are due only to hydrogen, then from the global correlation in Table 2, the relative enhancements are 3.3–3.4% for thermal neutrons and 1.6% for epithermal neutrons, which imply counting rate ratios of 1.035 and 1.016, respectively. For these two measurements, the region in Figure 8 of the strongest overlap is between the 1.01 and 1.02 epithermal neutron contour and between the 1.03 and 1.05 thermal neutron contour. In general terms, this overlap occurs for a thickness range of ∼3–30 g/cm2 and 0.1–1 wt % WEH (111–1111 ppm H), with the larger thickness having the lowest hydrogen concentration. While these are broad constraints, these results indicate at least the possibility that the H2O/OH detected with NIR data might also exist at a depth of up to tens of centimeters. In addition, the abundance range is broadly consistent with the 10–1000 ppm H2O given by the analysis of NIR data [Clark, 2009].
 However, as stated earlier, the conclusion that these results imply enhanced hydrogen at depth at Goldschmidt crater cannot be made without knowing the magnitude and character of other systematic variations and uncertainties in the thermal and epithermal neutron data and the models used to interpret the data. For each neutron energy range, this is a counting rate regime both in magnitude (high counting rates) and precision (1–3%) that is largely unstudied and not well understood. Therefore, in principle there are multiple possible causes for the neutron enhancement at Goldschmidt crater that may not be related to hydrogen.
 In regard to general variations of epithermal neutrons with surface composition, there is much that is understood. For example, based on modeling and data from the Moon and Mars, the behavior of epithermal neutrons with bulk hydrogen content as well as a dry-over-wet layering is relatively well understood. In particular, the interpretation that decreases of epithermal neutrons at the lunar poles indicates the presence of enhanced hydrogen abundances has been preliminarily confirmed with measurements from the LCROSS mission [Colaprete et al., 2010] and possibly Lunar Reconnaissance Orbiter [Spudis et al., 2010]. Further, both bulk and layered hydrogen measurements at Mars [Feldman et al., 2002, 2007; Diez et al., 2008] have been broadly confirmed with in situ data from the Phoenix lander [Arvidson et al., 2009; Mellon et al., 2009] and thermal inertia data [Titus and Prettyman, 2007]. For nonhydrous regions, there is also a good, qualitative understanding based on both models and data of how epithermal neutrons behave in the presence of large amounts of neutron absorbers [Maurice et al., 2004; Lawrence et al., 2006]. Finally, there has been a general observation that epithermal neutron enhancements on the Moon are related to immature regions (i.e., fresh craters) that likely have low hydrogen (e.g., Tycho crater). However, a detailed study of epithermal neutron enhancements [Johnson et al., 2002] showed a poor correlation with observed optical maturity [Lucey et al., 2000], indicating a more complex behavior than a simple correlation with surface maturity.
 The global trends for epithermal neutrons show complexity as indicated by Figure 6. For regions with large concentrations of neutron absorbers, there is the relatively simple, approximate linear correlation with neutron absorbers. However, for regions with low concentrations of neutron absorbers, there is an apparent trend with a different slope and smaller dynamic range. Soils with these ranges of elemental abundances have not been systematically modeled and so the corresponding behavior of epithermal neutrons is not understood at the 1–2% level found in Goldschmidt crater. Finally, there remains a lack of quantitative agreement between data and models in regard to the neutron absorption from the rare Earth elements Gd and Sm [Lawrence et al., 2006].
 Substantial work has been done to understand thermal neutron variations in the context of neutron absorbers on nonhydrous planets. In particular, on the Moon and Mercury, thermal neutrons in conjunction with other measurables have been used to quantitatively obtain the abundances of various elements (e.g., Fe, Ti, Gd, and Sm) [Elphic et al., 2000, 2002; Feldman et al., 2000b; Lawrence et al., 2010]. Thermal neutrons are well studied and quantitatively understood in regard to measurements of Mars' atmosphere, CO2 polar caps, and hydrogen abundances [e.g., Prettyman et al., 2004]. However, almost no work has been done to quantitatively understand thermal neutrons at the Moon in regions having low concentrations of neutron absorbers, which exist over most of the lunar highlands. There are clear systematic trends in these regions, but almost nothing is understood about how these trends relate to surface composition. Goldschmidt crater is one such region, and prior to the M3 results, there was no indication that this location was any different than other numerous lunar highlands neutron enhancements.
 To make progress in understanding Goldschmidt crater and other possibly similar regions, much work needs to be done that is beyond the scope of this study. Nevertheless, some directions regarding how to proceed are given below.
 An initial task is to search for other regions that have similar enhancements and compositional character as Goldschmidt crater. Such a search should be done with both the neutron and NIR data. As an example, Figure 7 shows an epitermal neutron enhancement south of Goldschmidt crater (66°N, 2.8°E) that has a similar detrended magnitude (∼2%) and significance (>4σ) as the Goldschmidt enhancement. Is this enhancement also due to hydrogen, or is it the result of other systematic effects? Is there a similar H2O/OH signal seen here in the NIR data? What makes these two regions similar or dissimilar? These are the types of questions that need to be addressed in a systematic way to gain understanding regarding what information neutrons provide about hydrogen in these nonpolar regions.
 Second, there should be a systematic study using both modeling and data to better understand neutron variability in regions with low concentrations of neutron absorbers. In particular, such studies would expand the compositional and stratigraphy studies given here and in Lawrence et al.  to have a wider range of compositions and higher statistical precision. Such a study should also include a systematic survey of neutron data to understand the spatial variations of thermal and epithermal neutron data in lunar highlands regions. While the 30 km altitude LP data set is ideal for this type of study because of its combination of good spatial resolution and high counting rate, it can be complemented by the 100 km altitude LP data set as well as data from the Lunar Exploration Neutron Detector on board the Lunar Reconnaissance Orbiter [Mitrofanov et al., 2008]. In particular, by combining these data sets, it should be possible to obtain better confidence of the statistical significance of various lunar highlands neutron enhancements. Finally, the neutron models and data should be combined with other compositional data sets (e.g., maturity, NIR, mineralogical) to search for, identify, and characterize various regions of interest.
 We have completed the first planetary neutron transport models for a wet-over-dry stratigraphy for a nonhydrous planet. With these models, we found that epithermal neutrons show an increased signal for thin (<30 g/cm2) upper layers that have enhanced hydrogen, which is contrary to previous studies and expectations for the behavior of epithermal neutrons in the presence of hydrogen.
 On the basis of these neutron transport studies, we have investigated Lunar Prospector thermal and epithermal neutron data in the Goldschmidt region and have found that there are neutron enhancements in both neutron energy ranges. To first order, these neutron enhancements correlate and are likely related to variations in the concentrations of neutron absorbing elements. In particular, the relative neutron enhancements are due to a relative depletion of neutron absorbing elements Fe, Gd, and Sm. However, after empirically accounting for the global variations in neutron absorbing elements, Goldschmidt crater shows a residual enhancement that is consistent with an upper layer that has enhanced hydrogen abundances. If this signal is due to hydrogen, then it would have a thickness of ∼3–30 g/cm2 and an abundances of 0.1–1 wt % WEH. However, systematic variations and uncertainties of both thermal and epithermal neutrons at the 1–3% level are not sufficiently known to enable a strong conclusion to be made if the residual variation is due to hydrogen or some other compositional variation. Thus, ideas have been presented for future studies to investigate the systematic behavior of thermal and epithermal neutrons in relation to compositional variability in order to better constrain our knowledge of hydrogen abundances at Goldschmidt and other possible similar regions.
 D. Lawrence (SDG), D. Hurley, and R. Miller conducted this work with the support of NASA Lunar Science Institute.