An analysis of the lunar gamma-ray spectrum as measured by the Lunar Prospector Gamma-Ray Spectrometer has revealed that 8–8.9 MeV gamma rays contain information about the elemental composition of near-surface materials. These high-energy gamma rays are found to be primarily sensitive to the total Fe and Mg content of the surface, although other elements also contribute. This information has been used to identify several regions with unique compositions, including the Hertzsprung and Orientale basins. A method for deriving global Mg abundances from high-energy gamma-ray measurements is presented. The physical mechanism for high-energy gamma-ray production is proposed to be radiation produced during the decay of galactic cosmic ray produced pions within the lunar surface. Laboratory measurements of pion production cross sections are found to be consistent with the empirically derived relationship between the lunar Fe, Mg, and Ti abundances and the measured high-energy gamma-ray count rates.
 Lunar Prospector (LP) was a NASA Discovery-class mission whose primary goal was to obtain a high-resolution, global characterization of the elemental composition of the lunar surface [Binder, 1998]. This was achieved through nuclear spectroscopy techniques with the LP Gamma-Ray and Neutron Spectrometers (GRS and NS, respectively) [Feldman et al., 2004]. The LP orbital measurements, which were made between 17 January 1998 and 31 July 1999, included observation campaigns at altitudes of 100 and 30 km. These altitudes allowed the GRS and NS data to be used to create elemental maps of the lunar surface with full-width half-maximum (FWHM) spatial resolutions of 150 and 45 km, respectively [e.g., Prettyman et al., 2006; Lawrence et al., 2002]. This work presents an analysis of GRS-measured high-energy gamma rays (HEGRs), a previously unexamined portion of the gamma-ray spectrum that contains unique information about the bulk elemental composition of near-surface material.
 Gamma-ray emission from the lunar surface is primarily the result of nuclear interactions initiated by surface-incident galactic cosmic rays (GCRs). This process begins with the production of neutrons within the top few meters of the lunar surface via GCR-induced nuclear spallation. The energy-dependent flux of neutrons that escape the surface contains information about the elemental composition of the medium through which they traversed, including the average atomic mass (<A>) [Gasnault et al., 2001], hydrogen content [e.g., Feldman et al., 1998a] and the bulk abundance of neutron-absorbing elements (e.g., Fe, Ti, Gd) [e.g., Feldman et al., 1998b; Elphic et al., 2000]. These neutrons also excite nuclei into unstable states through inelastic scattering and capture reactions, denoted as (n,n′γ) and (n,γ), respectively. The de-excitation of these excited states results in gamma-ray emission at characteristic energies that were used to quantify the absolute abundances of elements such as O, Mg, Al, Si, Ca, Ti, and Fe [e.g., Lawrence et al., 2002; Prettyman et al., 2006]. Discrete-energy gamma-ray emission also results from the natural decay of radioactive elements such as K and Th [Lawrence et al., 1998; 2000]. Taken together, these processes facilitate a comprehensive characterization of the elemental composition of the lunar surface to depths of tens of centimeters.
 In addition to characterizing discrete-energy gamma-ray peaks, gamma-ray spectrometers also observe a continuum of events over their entire energy sensitivity range. This continuum originates from the downscattering of discrete energy (n,n′γ) and (n,γ) gamma rays as well as from Bremsstrahlung gamma rays produced in the lunar surface and spectrometer-surrounding material [Bielefeld et al., 1976]. A major source of Bremsstrahlung-producing particles (primarily electrons and positrons) in the lunar surface is the decay of neutral (π°) and charged (π+,π−) pions. Pions are produced during intra-nuclear cascades initiated by surface-incident GCRs [e.g., Armstrong, 1972]. The contribution of pion-decay-product Bremsstrahlung to lunar gamma-ray emission was modeled by Moskalenko and Porter , who found that it was the dominant contributor to the ≥ 8 MeV gamma-ray flux for the limited cases they examined.
 The magnitude of proton-induced pion production is a function of the composition of the incident material (see section 4), therefore, the resulting HEGR count rates observed by the LP GRS should contain information about the composition of the lunar surface. This hypothesis is tested by mapping the global HEGR count rates and comparing their magnitude to known surface composition parameters. For this analysis, the HEGR region is defined to be between 8 and 8.9 MeV (see Figure 1). The low-energy threshold (8 MeV) was selected to avoid contamination of the HEGR region by the neighboring Fe (7.631 and 7.646 MeV) and Al (7.742 MeV) (n,γ) gamma rays. The high-energy threshold (8.9 MeV) was selected to avoid overload events in the highest energy channel of the detector (~9.2 MeV).
2 Background Information
2.1 The Lunar Prospector Gamma-Ray Spectrometer
 The LP GRS consisted of a 7.1 cm-diameter by 7.6 cm-long cylinder of Bismuth Germanate (BGO) scintillator surrounded by a BC454 (borated plastic) scintillator that served as an anti-coincidence shield (ACS) [Feldman et al., 2004]. The GRS/BGO sensor was designed to characterize detector-incident gamma rays of energies between 50 keV and 9 MeV with an energy resolution of 12% at 1333 keV. The GRS/ACS measured detector-incident particles in order to eliminate neutron- and charged-particle-induced backgrounds in the GRS/BGO by vetoing BGO-ACS coincident events. The GRS/ACS also had the capability to characterize fast (>700 keV) neutrons from the lunar surface through a double-pulse technique that measured the initial neutron moderating event(s) followed by the 10B neutron capture reaction products. In order to reduce the gamma-ray backgrounds to minimal levels, the amount of material directly surrounding the GRS was minimized, and it was placed at the end of a 2.5 m-long boom. The effectiveness of this arrangement isevident in Figure 1, where the cruise background is observed to be an order of magnitude lower than the signal in orbit for > 5 MeV gamma rays.
2.2 Gamma-Ray Continuum
 The GRS/BGO spectra consist of discrete-energy photopeaks overlying a gamma-ray continuum whose intensity decreases with increasing energy. Figure 1 illustrates summed LP GRS spectra collected over two compositionally distinct regions of the lunar surface corresponding approximately to the KREEP-rich (KREEP stands for Potassium, Rare-Earth-Elements, and Phosphorus) terrain in the center of Oceanus Procellarum and the western lunar highlands. Differences in the intensities of the K (Eγ = 1.460 MeV), Th (Eγ = 2.614 MeV), and Fe (Eγ = 0.847, 7.6 MeV) gamma-ray photopeaks are observed. Additionally, the magnitude of the high-energy (Eγ ≥ 8 MeV) portion of the gamma-ray continuum also differs between these regions, indicating the possibility that it is also sensitive to the regional differences in elemental composition.
 A comparison of the HEGR count rate measured in lunar orbit to that observed during the trans-lunar cruise (Figure 1) demonstrates that the HEGR continuum is predominantly lunar in origin. Sources for the continuum include downscattering of (n,n′γ) and (n,γ) gamma rays as well as electron- and positron- (hereafter referred to as leptons) induced Bremsstrahlung, both within the lunar surface and as well as in detector-surrounding material. The latter contribution is minimized by the lack of detector-surrounding material and the placement of the detector on a boom. Monte Carlo N-Particle eXtended (MCNPX; Pelowitz, 2005) simulations of LP GRS spectra resulting from (n,n′γ) and (n,γ) reactions in the lunar surface [Prettyman et al., 2006] revealed that, for energies above 7.8 MeV, downscattered (n,n′γ) and (n,γ) gamma rays contribute ≤ 10% to the total measured flux. This indicates that the HEGR continuum is dominated by Bremsstrahlung gamma rays produced within the lunar surface, a conclusion that is supported by models of the GCR-induced lunar gamma-ray flux [Moskalenko and Porter, 2007]. Additional details on HEGR production in the lunar surface are presented in section 4.
 Past investigations of LP GRS data have utilized spectral analysis to determine photopeak count rates for individual elements as a means to determine their abundances on the lunar surface [e.g., Lawrence et al., 2002; 2004]. Those analyses treated the gamma-ray continuum as a background that must be removed in order to determine the photopeak count rates. The regional differences shown in Figure 1, coupled with the results of the modeling efforts discussed above, provide evidence that the HEGR continuum originates primarily from the lunar surface and that its magnitude should contain information regarding the near-surface elemental composition. This hypothesis is tested by producing a global map of measured HEGR count rates and comparing it to known composition information (e.g., <A>, Fe abundances) as well as to relevant lunar samples (see sections 3.2 and 3.3).
2.3 Data Analysis
 This analysis utilized reduced data products from the LP GRS that were created following the procedure outlined in Lawrence et al. . These data take the form of GRS spectra summed in 0.5° × 0.5° quasi-equal-area pixels over the lunar surface. Prior to spectral summing, the data were corrected for detector gain and deadtime, viewing geometry, variations in the spacecraft altitude, and changes in the magnitude of the surface-incident GCR flux over the course of the mission. The 100 km altitude data set was utilized for this work to enable a comparison to the global elemental abundance maps of Prettyman et al. , which were also derived from the 100 km altitude data set (see section 2.4.2).
 For each 0.5° × 0.5° pixel in the high-altitude data set, the total number of counts in the HEGR energy range is summed and normalized in time to produce the count rate in units of counts min−1. The count rates for each pixel are smoothed over the FWHM of the GRS footprint on the surface (150 km for the 100 km data set) following the procedure outlined in Lawrence et al. . Finally, the smoothed map is binned to 5° × 5° equal-area pixels, a size that was chosen to minimize the statistical errors to ≤ 10% per pixel while preserving the best possible spatial resolution. The resulting map is shown in Figure 2a.
2.4 Other Data Sets
2.4.1 Ground Truth Samples
 Orbital LP measurements are compared to samples from the Apollo and Luna missions in order to test the fidelity of HEGR-derived composition information. The “Soils and Regolith Breccia” (SRB) samples listed in Haskin and Warren  are used for this analysis (Table 1). SRB compositions were chosen because they are thought to be representative of regional composition over large areas and are therefore most analogous to the comparatively poor spatial resolution of the HEGR measurements. However, each 5° × 5° pixel (Figure 2a) covers a much larger area (diameter ~120 km) than the sampled regions represent (< 10 km), and therefore any comparisons are subject to errors originating from unsampled composition types within each pixel. The locations of the SRB sample sites are shown superimposed on the lunar albedo map in Figure 2b.
Table 1. Lunar Sample Sitea Elemental Abundancesb (in wt%) for Comparison to Orbital Measurements
aSample sites are denoted as (A) for Apollo, (L) for Luna, and AFHT for the average ferroan highlands terrain composition inferred from lunar meteorites by Korotev et al. 
bElemental abundances as derived from the “Soils and Regolith Breccia” compositions listed in Haskin and Warren .
cOxygen abundances are set such that the sum of all elemental abundances is 100 wt%. Accordingly, these values differ by ≤ 1.25 wt% from the oxygen abundances calculated directly from the oxides listed in Haskin and Warren .
dThe composition parameter (Cp(2)) is calculated following equation ((3)) and includes contributions from Fe, Mg, and Ti only.
 The SRB compositions include the abundances of all major rock-forming elements within the sample type. Also of interest is the average atomic mass (<A>) for each sample, which was calculated from the SRB elemental compositions as
where wi is the weight fraction and Ai is the atomic mass for element i. On the moon, <A> is dominated by variations in Fe (A = 56) and to a lesser degree Ti (A = 48), the two heaviest of the major rock-forming elements [Maurice et al., 2000; Gasnault et al., 2001]. Calculated <A> values for each SRB sample suite are listed in Table 1, and the global <A> distribution is shown in Figure 2d.
 The SRB compositions do not include a representative sample of the composition of the lunar highlands. For that reason, the average feldspathic highlands terrain (AFHT) composition used by Prettyman et al.  was included in this analysis (Table 1). This composition originates from lunar meteorites that are inferred to have originated from the lunar highlands region [Korotev et al., 2003]. Following the procedure presented in Prettyman et al. , nine sites within the highlands terrain were chosen for comparison to the AFHT composition (see Figure 2b).
2.4.2 Global Elemental Maps
 This work utilizes the LP GRS-derived 5° × 5° maps of FeO, SiO2, MgO, CaO, TiO2, and Al2O3 abundances of Prettyman et al.,  for comparison to the HEGR map. Those results were converted from oxide abundances to elemental abundances in units of wt%. When the individual elemental abundances for each pixel are summed, the global population average and standard deviation were found to be 98 ± 2% suggesting that these maps represent a nearly complete inventory of the composition of the surface with respect to major rock-forming elements. The map of the full range of abundance sum values (92–104 wt%) reveals that it is systematically low (~94%) in western Procellarum and high (~103%) near the Apollo 12 and 14 landing sites. This could be due to 0.5–1 wt% errors for all oxides in these regions, or 3–6 wt% errors for one oxide. These discrepancies are likely due to unknown systematic errors, such as incomplete knowledge of backgrounds as a function of surface composition or problems with the gamma-ray production data [Prettyman et al., 2006]. Despite this issue, the Prettyman et al.  abundances are generally in good agreement with the known elemental compositions at the lunar sample sites (e.g., Figure 3).
 The Prettyman et al.,  derived abundance maps are utilized for all global comparisons of HEGR data to lunar surface elemental composition (see section 3). A global map of <A> (Figure 2d) derived from fast neutron measurements [Gasnault et al., 2001] is also used for comparison to the HEGR measurements. As will be shown later, the Fe, Mg and Ti abundance maps are of particular interest for this analysis. Unlike the Fe and Ti maps, the Mg map suffers from low precision due to the lack of a strong, energy-resolved Mg gamma ray in the GRS spectra. As a result, the Mg map has larger uncertainties than the Fe and Ti maps, although a comparison of the globally measured Mg versus Fe values follows the trend established by the lunar samples (see Figure 3a), suggesting that the Mg abundances of Prettyman et al.  are accurate.
3 Sensitivity of High-Energy Gamma Rays to Elemental Composition
3.1 Comparison to Other Data Sets
 The 5° × 5° equal-area pixel map of the HEGR count rate is shown in Figure 2a, alongside maps of the lunar albedo (Figure 2b), GRS/BGO-derived Fe abundances (Figure 2c) [Prettyman et al., 2006], and GRS/ACS-derived <A> (Figure 2d) [Gasnault et al., 2001]. The latter two quantities were mapped with the same spatial resolution as the HEGR measurements. A comparison of the HEGR count rates to the lunar albedo illustrates their sensitivity to compositionally distinct regions such as the highlands, mare basalts, and the South Pole-Aitken basin, as these regions are clearly discernible in the HEGR map. This confirms the hypothesis that the magnitude of the HEGR flux contains information about the composition of the lunar surface. The similarity of the HEGR map to the Fe abundance and <A> maps suggests a correlation with these quantities. However, there are notable differences that imply additional parameters are also modifying the HEGR count rate.
3.2 High-Energy Gamma Rays Versus <A> and Fe
 The possibility of a relationship between HEGRs and lunar surface composition had been noted previously by Hareyama et al. , who compared the LP-derived <A> map to the HEGR flux as measured by the SELENE Gamma-Ray Spectrometer. Those authors used gamma rays with energies between 8 and 13 MeV to define HEGRs, a region that differs from the LP energy range (section 2.3). Hareyama et al.  noted a correlation between the SELENE HEGR count rate and the LP-derived <A> map, similar to that observed in Figure 2 for the LP-measured HEGRs. Based on their observation, Hareyama et al.  suggested that HEGRs are a proxy for <A>, and they proposed a HEGR production mechanism similar to that detailed here (section 4) to support that conclusion.
 We test the hypothesis that HEGRs are a proxy for <A> by comparing the LP-measured HEGR count rates acquired over the Apollo and Luna landing sites to the corresponding SRB compositions (Table 1). Despite the difficulty associated with comparing orbital measurements to the SBR samples (see section 2.4.1), the results of this comparison (Figure 4) show a notable correlation (correlation coefficient of R = 0.71) between the HEGR count rate and <A>. The limited number of sample site data points in this comparison prohibits unambiguously identifying the nature of the correlation between these variables (i.e., linear versus non-linear). A similar comparison is carried out for the global HEGR measurements using the <A> map (Figure 2d). This comparison, which is also shown in Figure 4, results in an improved correlation (R = 0.86) and also reveals that the relationship between HEGRs and <A> is non-linear, particularly in low- <A> regions. This non-linearity suggests that the HEGR count rate is related to <A> but it is not a direct proxy for that quantity, contrary to the hypothesis of Hareyama et al. .
 This procedure is repeated to test for a correlation between the HEGR count rate and Fe abundance; both at the lunar sample sites (Table 1) and globally using the Fe abundance map (Figure 2c). Figure 4 details these comparisons, and as was found for the comparison to <A>, strong correlations are observed for both the sample sites (R = 0.74) and global (R = 0.90) measurements. The global measurements also demonstrate a non-linear relationship between the HEGR count rate and Fe abundances, similar to that found for <A>. This non-linearity suggests that the magnitude of the HEGR count rate is predominantly sensitive to Fe, but that an additional dependence exists that is most prominent in low-Fe and low-<A> regions, namely the lunar highlands.
3.3 Elemental Mixing
 Based on the observed correlation between the HEGR count rate and Fe abundances (Figure 4), coupled with the strong correlation between Fe abundances and <A> [Gasnault et al., 2001], we hypothesize that the HEGR count rate is primarily sensitive to the Fe content of the lunar surface. However, the non-linearity of the relationship in low-Fe regions suggests that it is also sensitive additional elemental variability. This section presents a method for determining the sources and magnitude of contributions from elements other than Fe to the measured HEGR count rates. The prime candidate for this variability is Mg, which varies significantly (0.5–6 wt%) in low-Fe (2–5 wt%) regions (Figure 3a). No other major element exhibits such large variability in low-Fe regions (e.g., Ti, Al, Ca; Figures 3b–3d), however, other elements for which we have global abundance data are also considered within the formalism presented here.
 The process of identifying the full elemental dependence of the HEGR count rate begins with the assumption that every element in the lunar surface contributes linearly to HEGR production as a function of its abundance. This dependence is characterized by defining a new composition parameter (Cp), which is derived as
where i represents each element of interest (Fe, Mg, Ti, Al, Ca, Si, and O), wi is the average abundance of element i in each pixel in units of wt%, and Mi is the relative contribution of element i to the HEGR count rate. The normalization constant for Fe (M0), is set to one, therefore, Mi≠0 represents the contribution of element i to Cp relative to the contribution of Fe.
 In order to determine the values of the Mi, the HEGR count rate is plotted on a pixel-by-pixel basis versus the corresponding Cp value calculated from the abundance maps of Prettyman et al.  using equation ((2)). The non-linearity of the correlation between these two quantities is checked, and the Mi values are iterated until the non-linearity of the relationship is minimized (see Figure 5). This is accomplished by minimizing the sum of the absolute values of the deviation of each HEGR value from the expected value for that pixel. The expected value is calculated from a linear fit to the high Cp measurements (e.g., Figure 5). To simplify these calculations, elements were considered one at a time starting with Fe and Mg. The first test was therefore
and M1 was iterated until a minimum non-linearity for the HEGR count rate versus Cp((1)) was found. The resulting value for M1 was 1.14 (see Figure 5). An error of ± 0.15 is assigned to this value to represent the allowed variation in M1, which would maintain the minimum non-linearity value to within 5%.
 Extending this analysis to include Ti, which is known to diverge from Fe at high and low Fe abundances, results in a Cp relationship of
 The minimization process was repeated and an M2 value of 0.17 ± 0.04 was obtained. Calculations of Cp were further extended to include contributions from Al (i = 3), Ca (i = 4), Si (i = 5) and O (i = 6). Like Ti, the remaining elements were found to have small normalization coefficients (M3 = 0.00 ± 0.02, M4 = 0.16 ± 0.04, M5 = 0.26 ± 0.15, M6 = 0.02 ± 0.02). The finding that elements such as Ca and O do not appreciably contribute to linearizing Cp is not surprising given that they do not vary appreciably over the surface (e.g., Figure 3d). The zero value for Al is likely related to the fact that it is strongly anti-correlated with Fe, and, therefore, any impact it has on the HEGR count rate is contained within the HEGR versus Fe correlation (see section 4.2). Relating the Mi values to the proposed HEGR production mechanism is carried out in section 4.
3.4 Lunar Composition From the High-Energy Gamma Rays
 The LP-measured HEGR count rate can now be related to the lunar near-surface composition through the Cp parameter. The global HEGR count rate is plotted versus the corresponding Prettyman et al.  abundance-map-derived Cp values in Figure 6, both for Cp(2) and Cp(6). The resulting fits provide a relationship for converting the measured HEGR count rate to Cp. The lack of an improvement in the correlation for Cp(6) over Cp(2) advocates for the use of Cp(2) as the optimal measure of Cp, particularly given that many elements used to derive Cp(6) have large per-pixel statistical uncertainties.
 Figure 7 shows the HEGR-derived Cp values plotted versus the global abundance-map- derived Cp values. It also shows the HEGR-derived Cp values for the lunar sample sites plotted versus the corresponding SRB-derived Cp values (Table 1). Good correlation coefficients of 0.90 and 0.81–0.82 are found for the global and sample data, respectively, demonstrating that the HEGR-derived Cp measurements are an accurate measure of lunar composition. Maps of global Cp values, derived from both the HEGRs and the elemental abundance maps, are shown in Figure 8. While there is strong agreement for the majority of regions, there are a few locations with notable differences. These include Mare Australe, Hertzsprung basin, Mare Orientale, Mare Nubium, and the region northwest of Oceanus Procellarium (USGS Lunar Quadrangle 3; e.g., Gaddis et al., ). Each of these cases is discussed in detail in section 5.
3.5 Mg Abundances Derived From High-Energy Gamma Rays
 Of the three elements (Fe, Mg, and Ti) that have been identified as contributing the most to HEGR production (equation ((4))), the first two have been mapped globally by LP with low statistical errors and high spatial resolution. Mg has also been mapped, but with lower precision and uncertain effective spatial resolution due to the larger errors associated with deriving abundances for this element. This is primarily a result of the lack of a strong, energy-resolved Mg gamma ray. As a result, HEGR measurements may provide the best LP GRS information available with respect to global abundances of Mg. The relationship between the measured HEGR count rate C(HEGR) and Cp (Figure 6) is
and can be used in conjunction with the definition of Cp(2) (equation ((4))) to produce a HEGR-derived global map of Mg abundances wHEGR(Mg) in wt% as
where C(HEGR) is the HEGR count rate in counts min−1. The resulting Mg abundance map is shown in Figure 9, along with the Mg abundance map of Prettyman et al.  that was created using gamma-ray peak analysis techniques. Note that the Prettyman et al.  Mg map was used to derive the M2 value for Cp (equation ((3))) and the normalization factors to convert C(HEGR) to Cp (equation ((5))), and as a result, the HEGR-derived Mg map (equation ((6))) is not completely independent of that work. Because the calculation of M2 leveraged the global Mg abundance trends to establish the link between the HEGRs to Cp, any problems with the Prettyman et al.  Mg abundance map at the regional level are not expected to bias the HEGR-derived Mg abundances. This is supported by the observation that the global Mg values of Prettyman et al.  agree with the trend established by the sample site compositions (see Figure 3a),
 A comparison of the two Mg maps (Figure 9) shows general agreement, namely higher (> 4 wt%) Mg abundances in mare basalt regions and lower (< 3 wt%) abundances in the highlands. A direct comparison of the two Mg abundance distributions (Figure 10) reveals a mean value of 4.28 wt% and a standard deviation of 2.05 wt% for the HEGR-derived values, compared to 4.28 ± 1.37 wt% for the Prettyman et al.  abundances. These distributions have an identical mean value, but the HEGR-derived values have a larger dynamic range. Additionally, the HEGR-derived Mg abundance distribution suggests the possibility of two distinct distributions, one centered at approximately 2.75 wt% and the other at approximately 5 wt%. There is no evidence in the Prettyman et al.,  Mg abundance distribution for two distinct populations.
 A direct comparison of the HEGR-derived abundances to the corresponding lunar SRB samples provides insight into the validity of these Mg measurements. With the exception of the A11 value, all HEGR-derived Mg abundances are within 2σ of the SRB values (see Table 1). For all sample sites, a correlation coefficient of R = 0.51 is found, however, this value increases to R = 0.70 when excluding the A11 site. This is comparable to the value (R = 0.73) found by comparing the Prettyman et al.  Mg abundances to the sample sites. The discrepancy at the A11 landing site is large, as the HEGR-derived Mg abundance (8.5 ± 1.2 wt%) is significantly higher than the corresponding SRB sample (4.78 ± 0.10 wt%). A similar, although less significant discrepancy is found at for the A12 landing site (8.5 ± 1.2 versus 6.28 ± 0.65 wt%).
 Several possible reasons for the discrepancy between the A11 and A12 Mg abundances and the corresponding HEGR-derived Mg abundances have been identified. Examination of the abundance sum map [Prettyman et al., 2006] highlights regions for which the sum diverges from 100 wt%, suggesting that there are regions for which the total composition is not well known. The A11 and A12 sites both fall within such regions. Furthermore, a comparison of the abundances for Fe, Mg, and Ti at the A11 site from the SRBs (12.75, 4.78, and 4.76 wt%, respectively; see Table 1) to those from LP (9.94, 6.10, and 2.57; derived from the abundance maps of Prettyman et al., ) reveal significant differences. By comparison, the differences are negligible at the A12 site (13.36, 6.28, 1.56 wt% for the SRBs versus 13.18, 6.91, and 2.03 wt% from LP). Because our derivation of the relationship between HEGRs and composition depends on these elemental abundance measurements, it is not surprising that our methodology might break down in regions where the total composition is uncertain. To avoid this problem in future analysis, an independent means of deriving the relationship between HEGRs and Cp is needed (see section 4.3).
 Another possible source for this discrepancy is that our methodology for deriving Cp as a function of the HEGR count rate may be incomplete. It is possible that simply linearizing the relationship between the HEGR count rate and Cp is not sufficient to fully account for the relationship between these variables. Finally, it is possible that the Apollo 11 and 12 SRB compositions are simply not representative of the composition at the larger (> 100 km) scale of the HEGR measurements and therefore a comparison of HEGR measurements to SRB samples for these regions is invalid (see section 2.4.1).
 Additional evidence that the HEGR-derived abundance map is inadequate in some mare regions comes from regional measurements of Mg abundances from X-ray spectroscopy measurements, including from the Apollo X-Ray Spectrometer experiments (AXRS) [Adler et al., 1973] and the Chandrayaan-1 X-ray Spectrometer (C1XS) [Weider et al., 2012]. A preliminary examination of AXRS results from the northern portion of Mare Nubium (Mg/Si = 0.20 ± 0.05) and the southern portion of Mare Tranquilitatis (Mg/Si = 0.23 ± 0.05) do not agree with the corresponding values from HEGR-derived Mg/Si abundances values (0.34 ± 0.04 and 0.41 ± 0.04; as calculated from the Mg abundance map of Figure 8a using a lunar average Si abundance value of 21 ± 2 wt%). This disagreement is reinforced by C1XS results from two solar flares with footprints crossing Mare Nubium and Mare Serenitatis, which found Mg/Si abundance ratios (0.18 ± 0.04, 0.18 ± 0.04, 0.25 ± 0.06, 0.20 ± 0.06) that were significantly lower than the corresponding Prettyman et al.  values (0.35 ± 0.04, 0.35 ± 0.03, 0.34 ± 0.09, 0.40 ± 0.04), as noted by Weider et al. .
 Since the HEGR-derived Mg abundances for these regions are generally higher than those of Prettyman et al. , the CIXS results also disagree with the HEGR-derived Mg abundances. Weider et al.  concluded that the LP-derived Mg abundances are incorrect, primarily based on the strong agreement between the C1XS results and the corresponding A14 lunar sample compositions. However, a comparison of the Prettyman et al.  Mg abundances at the SRB sample sites to the respective SRB Mg abundances (see Table 1) also yields a good correlation coefficient (0.73), bringing into question any conclusions based on a single sample site comparison. Weider et al.  note that the LP Mg abundances systematically overestimate Mg by ~5 wt%, and that the SiO2 abundances tend to be lower than the corresponding Apollo soil compositions. They suggest that normalizing the LP Mg abundances instead to a global SiO2 abundance can improve, but not eliminate, the discrepancies between the LP and C1XS Mg abundance ratios. Such an explanation cannot directly explain the difference between the HEGR-derived Mg abundances and the C1XS results, as they do not rely on a Si abundance (equation ((4))), although any problem with the Prettyman et al.  global elemental abundances may propagate to the derivation of the conversion of HEGR measurements to Cp.
4 High-Energy Gamma Ray Production
4.1 Physics of High-Energy Gamma-Ray Production
 In order to interpret the observed variability in the HEGR count rate, it was necessary to identify the nature of its dependence on the composition of the lunar surface. This problem was examined empirically in section 3 by comparing the HEGR count rate to independent measurements of the surface composition (e.g., Fe, <A>), and a new composition parameter (Cp; equation ((2))) was derived to describe the relationship. This section independently examines the relationship between HEGRs and surface composition in the context of the physics of HEGR production.
 As previously indicated (section 2), the LP-measured gamma-ray continuum originates primarily from two sources; downscattering of GCR-induced (n,n′γ) and (n,γ) gamma rays and electron-induced Bremsstrahlung [e.g., Bielefeld et al., 1976] within near-surface material. MCNPX simulations of (n,n′γ) and (n,γ) reactions within lunar-like materials suggests that downscattering of these gamma rays in the lunar surface is not the dominant contributor in the 8–9 MeV region of the continuum [Prettyman et al., 2006]. Moskalenko and Porter  also modeled these processes and found that Bremsstrahlung radiation is the dominant contributor to the lunar gamma-ray continuum in this energy range. At energies relevant to GCR-induced particles, the production of Bremsstrahlung radiation is dominated by the energy loss of electrons and positrons in the lunar surface [Leo, 1994]. The primary source of these leptons, which must have energies ≥ 8 MeV to create 8 MeV Bremsstrahlung photons, is the decay of GCR-induced pions [Thompson et al., 1997; Moskalenko and Porter, 2007]. Understanding GCR-induced pion production and subsequent Bremsstrahlung gamma-ray emission in lunar-like compositions is therefore necessary to derive the relationship between high-energy gamma-ray emission and elemental composition from physics principles.
4.1.1 Pion Production
 Pions are produced in the lunar surface by intra-nuclear cascades initiated by surface-incident GCRs [e.g., Armstrong, 1972]. An introduction to proton-induced pion production can be found in Krane . Thompson et al.,  modeled pion-induced gamma-ray production in the lunar surface at Eγ = 10 MeV and found similar contributions from neutral (π°) and charged (π+, π−) pions. Laboratory measurements of charged pion production from 730 MeV protons (near the mean energy for GCR protons; McKinney et al., ) on H, d, Be, C, Al, Ti, Cu, Ag, Ta, Pb and Th targets exist [Cochran et al., 1972] and can be used to relate pion production to lunar surface composition. Cochran et al.  found that the total production cross sections (σ) for π+ and π− depend on the target composition as
where Z is the proton number and N is the neutron number of the target. The units (mb) are equal to 10−27 cm2. We are unaware of experimental data on π° production under relevant conditions, however, on the basis of isospin considerations (the π+, π°, and π− are the isospin +1, 0, and −1 states of the π, respectively), the π° production cross section can be expressed in terms of the π± cross sections (Lipkin and Reshkin, 1972) as
 Equations ((7)) and ((8)) break down for elements lighter than C (Z, N = 6), where charged pion production decreases significantly. From the perspective of planetary science measurements, this suggests that HEGR production may be highly sensitive to the presence of light elements (Z ≤ 6), particularly H. However, for H to drive the average Z value of bulk surface materials, it will have to be present in much higher abundances than is expected for typical lunar surface materials, with the possible exception being the polar regions. Future studies will investigate the dependence of the high-energy gamma-ray flux versus hydrogen content.
4.1.2 Gamma-Ray Production
 High-energy gamma rays can be produced directly from the π° via its most common decay channel [Nakamura, 2010] as
 The mean lifetime for the π° is 8.4 × 10−17 s, therefore, this decay occurs close to the pion production site, which is within the top few meters of the regolith. The decay gamma rays are subject to downscattering in energy as they traverse the regolith [e.g., Leo, 1994]. As a result, a fraction of the gamma rays that escape into space will have energies within the HEGR range.
 Charged pion decay results in the production of high-energy (> 8 MeV) leptons [Nakamura, 2010] as
The daughter muons (μ) decay to electrons (e−) or positrons (e+) as
with a mean life of 2.197 × 10−6 s [Nakamura, 2010]. This formalism does not distinguish between neutrinos (ν) and their anti-particles (), and which variety is produced during a decay is dictated by conservation of lepton number. There are other less probable π-decay channels that can also lead to lepton production which are not listed as they are not expected to contribute appreciably to the total electron and positron flux in the surface.
 Electrons and positrons lose energy as they traverse lunar materials via collisions with other electrons as well as via Bremsstrahlung radiation [e.g., Leo, 1994]. For energies greater than 10 MeV, Bremsstrahlung radiation is the dominant source of energy loss, although it contributes at lower energies as well. Bremsstrahlung is the process by which a particle loses energy within an electric field by radiating photons with energies less than or equal to the kinetic energy of the particle. As a result, > 8 MeV particles are needed to create 8 MeV gamma rays through Bremsstrahlung. The efficiency for electrons and positrons to lose energy through Bremsstrahlung is proportional to Z2 [e.g., Leo, 1994], therefore the mean free path of these particles is a function of the surface composition.
4.2 Derivation of the Normalization Coefficients From Laboratory Measurements
 The mechanism for HEGR production presented in section 4.1 provides a template for defining the relationship between the measured HEGR count rate and lunar surface composition. Specifically, if it is assumed that HEGR production is directly proportional to the pion production cross sections (equations ((7))–((9))), then the relative HEGRs count rate (Ci(HEGR)) from any given element i can be calculated from the total pion production cross section for that element (σi) as
 For a given lunar composition (e.g., Table 1), the total cross section (σT) for π production is therefore
where fi is the molar fraction for element i. Molar fractions are necessary because the cross sections rely on the probability that a nucleus of element i is present, which differs from the weight percent (wi) used in the formulation of Cp. The relation between fi and wi is
where i is the element of interest and the sum over j is the sum of all elements in the material. Substituting equation ((12)) into equation ((11)) results in an expression for the total π production cross section to (σT) of a given material in terms of the weight fractions of the elements of interest as
where Pi is a new coefficient that includes the individual pion-production cross sections for each element (equation ((10))) as well as the normalizations for converting wi to fi. The resulting Pi values for the elements of interest are listed in Table 2 for each lunar composition.
Table 2. Calculated Pi Values and for Each Sample Site
 Under the assumption that HEGR production depends on the pion production cross sections only, the composition parameter derived from laboratory measured pion production cross sections () is defined to be equal to σT. is calculated for the lunar samples using all elements (i ≤ 6) and are listed in Table 1. The HEGR measurements at the sample sites are compared to the corresponding values in Figure 11. The good correlation coefficient (R = 0.70) indicates that the framework described here for relating HEGR measurements to pion production cross sections is valid, however, there are a number of uncertainties regarding the proposed HEGR production mechanism that may impact this conclusion (see section 4.4). The good correlation also suggests that comparing to Cp (equation ((2))) can provide insight into the empirically derived Mi normalization values.
4.3 Comparison to Lunar Prospector Measurements
 The assumption that HEGR production is proportional to σT facilitates comparing the empirically derived relationship between the HEGR count rate and composition (equation ((2))) to that predicted from the pion production cross sections as
 Recall that the coefficients Mi were normalized such that M0 (Fe) is set to one and all other coefficients are relative to that value (see section 3.4). A similar procedure was carried out for the mean of the Pi values, which vary for each lunar composition. The results are listed in Table 3, which includes a comparison of the average Pi values to the corresponding Mi values for each element. Good agreement is found for Mg and Ti.
Table 3. Normalized Pi Valuesa and a Comparison to Mi
aThe Pi values for each element were normalized to the value for i = 0 (Fe) for comparison to the empirically derived Mi values, which were also normalized to Fe.
 For those elements where the Pi values differ from the Mi values, all are nearly constant over the surface with the exception of Al (e.g., Figure 3). This suggests that these elements may contribute to HEGR production, but in a constant manner that can be quantified by calculating the relative contribution of these elements to the total normalization as
 This shows that elements i = 0, 1, and 2 (Fe, Mg, and Ti) account for 9% of the total predicted HEGR production, with the rest contributing 91%. The measured HEGR count rates range from 83 to 98 counts min−1, a variability of 8%. This suggests that 92% of the HEGR production is due to elements whose abundance do not vary appreciably over the surface (e.g., Ca, O, and to a lesser degree Si). This value agrees with the prediction of equation ((15)). The contribution of these elements (i > 2) to Cp would not be described properly by simply iterating Mi to achieve a linear relationship between the measured HEGR count rate and Cp (equation ((2))), as that technique leverages compositional variability to derive the magnitude of Mi. As a result, the Mi values derived for elements without significant variability over the lunar surface are not expected to match their respective Pi values. With respect to the discrepancy between Pi and Mi for Al, it is thought that the inverse relationship between Al and Fe abundances may obscure the dependence of the HEGR count rate on Al. This is because varying the Mi coefficient of Al in Cp will mostly serve to change the slope of equation ((4)), but not the correlation between the HEGR count rate and Cp.
4.4 Unknowns in High-Energy Gamma-Ray Production
 Despite identifying possible sources for the differences between the predicted and measured contributions of Al, Ca Si, and O to HEGR production, the fact remains that they disagree. Accordingly, we cannot claim to have a complete understanding of the physics of HEGR production in the lunar surface. Additionally, our assumption that HEGR production is directly proportional to the pion production cross sections can be questioned on the basis that any composition dependency to the conversion process of pion-decay gamma rays and leptons to HEGR gamma rays is omitted. It is expected that these process will be less sensitive to composition than the pion production processes. This is in part because all pion-decay leptons will stop within the surface, regardless of its composition, and therefore composition is expected to drive the depth penetration of the leptons, but not the magnitude of HEGR production. Future efforts to understand the production of HEGRs in a planetary surface should include experimental measurements coupled with simulations to fully understand these processes. Until then, this analysis will utilize the empirically derived relationship between the measured HEGR count rates and Fe, Mg, and Ti presented in section 3.
5 Regional Studies
 The HEGR-derived and Prettyman et al.  abundance-derived Cp maps (Figure 8) show excellent global agreement. This is confirmed by the correlation coefficients of R = 0.90 and 0.81–0.82 for global and sample site comparisons, respectively (Figure 7). Despite this agreement, there are several regions for which there are notable differences at the > 10% level (note that the one-standard-deviation statistical uncertainty of each HEGR-derived Cp pixel is ≤ 10%). This section presents a detailed examination of those regions with the most significant differences. We also incorporate global measurements of the thermal neutron flux as measured by the LP NS [e.g., Feldman et al., 1998b] for these comparisons. Thermal neutrons are highly sensitive to the total abundance of neutron absorbing elements [Feldman et al., 1991], and are therefore an excellent proxy for the total Fe and Ti content, especially for regions with low Fe and Ti abundances [Elphic et al., 2000; 2002]. Since Cp was defined to be a linear combination of Fe, Mg, and Ti abundances (equation ((4))), the thermal neutrons are therefore a proxy for the non-Mg component of Cp.
 For these comparisons, we have started with 5° × 5° equal-area pixel maps of the HEGR- and Prettyman et al.  derived Cp values (section 2.4.2) and a 2° × 2° equal-area pixel map of the thermal neutron count rate. These maps are smoothed over a FWHM of 200 km, which is a slight over-smoothing of the expected 150 km spatial resolution of the 100 km LP GRS data; however, this resulted in slightly improved maps. Additionally, lunar albedo and shaded relief maps are utilized as needed to provide geologic context for each region. Future analysis of high-energy gamma rays, particularly from the low-altitude (30 km) LP data set, will provide improved spatial resolution for examining the distinct compositions of these regions.
 Understanding which elements can contribute to the Cp maps (Figure 8) is important when interpreting the meaning of differences examined in the regions of interest (Figures (12-16)). The Prettyman et al.  derived Cp values are calculated from the global trends (equation ((4))) and utilize the Fe, Ti, and Mg abundance maps only. As a result, any observed variability in the abundance-map-derived Cp values can only be attributed to those elements. This is not true for the HEGR-derived Cp map, which although scaled from the Fe, Mg, and Ti abundance trends (equation ((5))), includes contributions from any element that influences HEGR production.
5.1 Mare Australe
 Mare Australe is an 880 km diameter, pre-Nectarian age mare located along the southeastern boundary between the lunar near and far sides (Figure 12a). The thermal neutron count rates (Figure 12b), Prettyman et al.  derived Cp values (Figure 12c), and HEGR-derived Cp values (Figure 12d) for this region all show a notable feature that is caused by the enhanced Fe concentrations of the dark basaltic material within the mare. However, the HEGR-derived Cp map shows higher values and a larger spatial extent for the enhancement than is observed in the abundance-map derived Cp map. The spatial distribution of the HEGR-derived Cp values more closely matches the distribution of the mare basalts than the abundance-map derived Cp values. However, a pixel-by-pixel comparison of the Cp values to the corresponding thermal neutron count rates found that the abundance-derived values have a slightly better correlation coefficient (−0.84) than the HEGR-derived Cp values (−0.78) do.
 The differences between the abundance-map- and HEGR-derived Cp maps suggest the possibility of elemental variability in this region that is not expressed in the Prettyman et al.,  elemental maps. Variability in Mg is considered to be the most likely source, based on both the strong dependence of Cp on Mg coupled with the fact that Mare Australe is not cleanly resolved in the Prettyman et al.  Mg abundance map (Figure 9b). The mare is spatially resolved in the HEGR-derived Mg abundance map (Figure 9a). Due to the uncertainties associated with extrapolating Mg abundances from HEGR measurements of mare basalts (see section 3.5), contributions from other elements such as Ca or Al cannot be ruled out. However, Ca and Al would have to increase within in the mare relative to the surrounding highlands to appear as a local high in Cp value, a scenario that is considered unlikely.
5.2 Hertzsprung Basin
 Hertzsprung is a well-preserved, 570 km diameter Nectarian-age basin located within the western portion of the lunar highlands (Figure 13a). It is located near some of the highest elevation regions on the Moon, likely resulting from its location adjacent to the rim of the South Pole-Aitken basin. Basins of this size are expected to excavate to depths of at most 40 km, with the majority of the ejecta originating from depths of ≥ 25 km [Spudis, 1993]. The crustal thickness in the region is expected to be about 70–90 km [Zuber et al., 1994], which suggests that Hertzsprung basin may have sampled the upper half of the lunar crust.
 Examination of the composition of Hertzsprung basin deposits using Clementine spectral reflectance data has shown that the ejecta have a low mafic-silicate abundance, with the western portion having Clementine-derived Fe abundances ranging from < 1 to 2 wt% [Stockstill and Spudis, 1998]. Analysis of the southeastern portion is complicated as a result of contamination by ejecta from Orientale basin. The lowest Fe abundances correspond to the inner basin ring and are suggestive of outcrops of nearly pure anorthosite. Analysis of data from the SELENE Spectral Profiler has also identified regions of nearly pure anorthosite on the inner and outer basin rings [Yamamoto et al., 2012], consistent with the Clementine observations.
 The finding of low Fe in the western half of Hertzsprung is supported by LP-measured thermal neutron fluxes (Figure 13b), which show a local high in that region corresponding to unusually low abundances of neutron absorbing elements. That the source of the thermal neutron enhancement does not appear in the Prettyman et al.  derived Cp value (Figure 13c) is surprising, given that the unusually low thermal neutron count rates in this area suggest a decrease in Fe abundance of ~3 wt% should be observed. A portion of the thermal neutron enhancement region does appear to be distinct in its HEGR-derived Cp values (Figure 13d), particularly along the outer basin rim. It is noted that the thermal neutron and Cp signatures have different spatial distributions, suggesting that there is a contribution to Cp from a non-neutron absorbing element. As a result, the enhanced HEGR-derived Cp values must be the result of either enhanced Mg abundances that are not represented in the Prettyman et al.  abundance map or some other compositional dependence for the HEGR signal. Clementine and SELENE observations of nearly pure anorthosite in this region suggest the possibility of enhanced Ca or Al, which could also be responsible for the increase in Cp (see section 4). Additional studies to understand the mineralogical content of this unusual region should be carried out with high spectral resolution reflectance data, similar to that of Mustard et al. , as well as with the 30 km altitude LP data set.
5.3 Mare Nubium
 Nubium is a 715 km-diameter, pre-Nectarian age mare located on the lunar near side to the southeast of Oceanus Procellarium (Figure 14a). The thermal neutron count rate in this region is low (Figure 14b), indicating an enhancement of Fe and/or Ti, similar to other mare regions. While both the Prettyman et al.  and HEGR-derived Cp maps show a regional high associated with the mare (Figures 14c and 14d), the HEGR-derived values are notably higher and more closely match the boundaries of the mare than the abundance-map-derived Cp values. While the differences here may be due to compositional effects not observed in the Prettyman et al.  results (e.g., enhanced Mg), it is also possible that they result from uncertainties in the conversion of HEGRs to surface composition parameters for high-Fe regions, as noted previously (section 3.5).
 Several lines of evidence support the hypothesis that some of the observed differences in this region are the result of uncertainties in the LP gamma-ray measurements. The first is the observation that the sum of the LP-derived elemental abundances in the region is around 103% [Prettyman et al., 2006]. This suggests that the LP measurements are overestimating the abundances on one or more elements within Mare Nubium. Because these abundances are used as input to derive the Cp values, this discrepancy may be the source of the difference between the abundance-map- and HEGR-derived Cp values. This may be related to the observed discrepancies between the HEGR-derived Mg abundances and X-ray and sample data in some mare basalt regions (see section 3.5), which could be inferred to extend into Mare Nubium. However, as noted in section 3.5, a comparison of the Prettyman et al.  Mg abundances at the SRB sample sites to the respective SRB Mg abundances (see Table 1) yielded a correlation coefficient of 0.73. These comparisons are predominately of mare-basalt-filled regions and suggest that there is not a significant discrepancy within the mare regions. Future studies of HEGR production physics will provide insight into this issue.
5.4 Orientale Basin
 Orientale is a 930 km-diameter impact basin formed during the Upper Imbrian period, and is located southeast of Oceanus Procellarum (Figure 15a). Mare Orientale was produced by low-Ti basalt infill of the Orientale basin [Bussey and Spudis, 1997], consistent with the low thermal neutron count rate in the center of the basin (Figure 15b). There are additional mare deposits, Lacus Veris and Lacus Autumni, located within the outer rings of the northeastern portion of the basin (Figure 15a) which also appear to influence the thermal neutron count rates. These two small mare are associated with fresh outcrops of basalt that have been identified in the northeastern portion of the inner and outer basin rings using Clementine spectral reflectance data [Bussey and Spudis, 1997]. Specifically, both lacus contain enhanced Fe and Ti as well as distinctive spectral properties that are consistent with the presence of the mafic minerals pyroxene and olivine [Bussey and Spudis, 2000].
 The area immediately surrounding Mare Orientale, and in particular Lacus Autumni, is collocated with higher HEGR-derived Cp values (Figure 15d) that are not observed in Prettyman et al.  abundance-map-derived Cp values. This suggests that these mare have distinct compositions for which the HEGR measurements are particularly sensitive, for example enhanced Mg abundances. The presence of Mg-rich pyroxenes and olivine in these mare such as those noted by Bussey and Spudis  could account this local Cp enhancement. Additionally, Mg-abundances within this region, as inferred from Clementine spectral reflectance data benchmarked by LP GRS measurements, also indicate that these lacus contain material with enhanced Mg abundances [Shkuratov et al., 2005; Wöhler et al., 2011]. This is consistent with the HEGR-derived Mg abundances in this region (Figure 9a), but not those of Prettyman et al.,  (Figure 9b). Finally, the observation of small regions of nearly pure anorthosite in the inner and outer basin rings by the SELENE Spectral Profiler [Yamamoto et al., 2012] suggests the possibility that Al or Ca enhancements could account for the Cp signal. Maps of the HEGR-derived Cp parameter using the 30 km altitude LP data set may provide sufficient spatial resolution to more closely correlate the Cp enhancements with the Clementine and SELENE measurements.
5.5 Highlands North-West of Oceanus Procellarum
 Finally, we note that the lunar highlands northwest of Oceanus Procellarum (designated as USGS Lunar Quadrant 3, e.g., Gaddis et al., ; Figure 16a) has a distinct composition as observed by the HEGR-derived Cp parameter (Figure 16d). This region is not distinct in thermal neutrons (Figure 16b) or the abundance map derived Cp values (Figure 16c). The Prettyman et al.  abundance maps do not sum to 100 wt% in this region, suggesting that there may be compositional effects that influence gamma-ray production in this area that are poorly understood. Any compositional effects must enhance HEGR production, suggesting that there is an increase in some element(s) in this region for which HEGR production is most sensitive that is not represented by the existing LP composition measurement. Figure 16b indicates that such variability is not driven by Fe or Ti, which would appear in the thermal neutron measurements.
 This leaves the possibility of higher Mg, Al, or Ca abundances in the region as compared to the LP-derived abundances, with Al and Ca being the most plausible given that this region in located within the plagioclase-rich highlands. Mg-abundances within this region, as inferred from Clementine spectral reflectance data benchmarked by LP GRS measurements, indicate a moderate Mg enhancement with abundances between those of typical mare basalts and highlands materials [Shkuratov et al., 2005; Wöhler et al., 2011], consistent with the HEGR-derived Mg abundances in this region (Figure 9a) but not those of Prettyman et al.,  (Figure 9b). If it is assumed that the entire deficit of the LP summed oxide abundances for this region (~2%) is assigned to Mg, than the abundance-map-derived Cp values for this area would increase by approximately 20%. This increase would result in a much closer agreement between the two Cp maps, and supports the hypothesis that this region has a Mg content that is intermediate between the nominal highlands value and that of the mare basalts.
 This work represents the first use of high-energy gamma rays (HEGRs) to study the elemental composition of a planetary surface. A global map of the Lunar Prospector measured HEGR count rate revealed that it is sensitive to the elemental composition of the lunar surface, as it clearly delineates compositionally distinct regions such as the mare, highlands, and South-Pole Aitken basin. The definition of a new composition parameter (Cp) was required to explain the relationship between the HEGRs and the lunar surface composition. The nature of Cp can largely be understood in terms of galactic-cosmic-ray-induced pion production within the lunar surface, a process that results in gamma ray production via pion-decay lepton Bremsstrahlung within the top tens of centimeters of the lunar surface. The dependence of proton-induced pion production as a function of target composition has been measured in the laboratory and agrees with the empirically derived composition parameter with respect to Fe, Mg, and Ti abundances.
 When combined with LP GRS-derived Fe and Ti abundance maps, the HEGR data was used to produce a map of variable Mg abundances over the lunar surface. This abundance map suggests that a wider range of Mg abundances can be found across the lunar surface than previous LP results had suggested, although there are some outstanding uncertainties associated with this map, particularly in some mare basalt regions. Since the derivation of the relationship between HEGRs and elemental abundance was derived using LP measurements, including that of Mg, the HEGR-derived Mg abundance map is not entirely independent of previous analysis. The discrepancy between the HEGR-derived Mg abundances at the Apollo 11 and 12 landing site and those of the returned samples suggests that further effort may be required to verify the validity of HEGR-derived Mg abundance maps, particularly in mare basalt regions. Because knowledge of lunar Mg abundances is crucial to understanding the evolution of the lunar crust and magmatic outflows on the surface within the lunar mare, it is hoped that HEGR-derived Mg abundance maps will one day provide sufficient improvement to our understanding of the global Mg abundances to address these issues.
 The technique presented here is applicable to any orbital gamma-ray data set, for example the MESSENGER GRS measurements of Mercury or the Dawn Gamma-Ray and Neutron Detector measurements at 4 Vesta [Prettyman et al., 2011]. Considerations will need to be made for differences in surface compositions of these bodies, as these planetary surfaces may result in very different elemental dependencies for the new composition parameter. For example, Fe has low concentrations on the surface of Mercury [e.g., Nittler et al., 2011; Evans et al., 2012], therefore it is likely not a driving factor in HEGR production as is the case on the moon. Similarly, the anti-correlation between Fe and Al on the moon that may be responsible for the lack of contributions from Al to the lunar HEGR count rate is likely not repeated on other planetary surfaces. A comprehensive, planet-independent understanding of HEGR production will be the focus of future work in order to extend the effectiveness of this technique to other data sets.
 This project was carried out under the auspices of the Johns Hopkins University Applied Physics Laboratory node of the NASA Lunar Science Institute and partial support for this work was provided by the NASA Lunar Advanced Science and Exploration Research Program. We thank Thomas Prettyman and Shoshana Weider for providing thoughtful reviews that resulted in a greatly improved manuscript.