Journal of Geophysical Research: Planets

Testing polar spots of water-rich permafrost on the Moon: LEND observations onboard LRO

Authors


Abstract

[1] Results are presented for the LEND instrument onboard LRO for the detection of local spots of suppression and excess of epithermal neutron emission at the lunar poles. Twelve local Neutron Suppression Regions (NSRs) and Neutron Excess Regions (NERs) are detected. It is shown using the data from the LOLA and Diviner instruments that six NSRs have the empirical property “less local irradiation and lower temperature – fewer local neutrons.” These NSRs may be identified with spots of water-ice rich permafrost on the Moon. It is shown that detected NSRs are include in both permanently shadowed and illuminated areas, and they are not coincident with Permanently Shadowed Regions (PSRs) at the bottom of polar craters, as has been commonly expected before LEND presented neutron data with high spatial resolution.

1. Introduction

[2] The Moon is known to have a well-aligned polar axis nearly perpendicular to the ecliptic plane: the angle between them is very small, 1.6°. Due to such an accurate alignment of our natural satellite, sunlight rays are practically tangential to the lunar poles. If the Moon were a sphere, the incident solar flux at the poles would be practically zero providing perfect conditions for storage of permanent water ice [Arnold, 1979]. However, for the Moon with real relief, there could be two extreme conditions of solar irradiation: some regions at the tops of polar hills could be almost permanently irradiated and heated by sunlight up to rather high temperatures well above 100 K, and other regions at lowlands of polar craters could be permanently shadowed and extremely cold with a stable temperature well below 100 K. The co-existence of local spots at the lunar poles with these two extremes might result in very interesting physics of lunar volatiles; H2, OH and H2O may be produced from implanted protons of solar wind in chemical reactions at hot spots [Starukhina and Shkuratov, 2000], and they may become permanently trapped at a cold spot nearby [Crider and Vondrak, 2000; Vondrak and Crider, 2003]. Water and other volatiles could also be delivered to the Moon by comets; water molecules could hop from place to place over the surface until resting at some cold trap at the pole, or escape to space [e.g., see Watson et al., 1961; Crider and Vondrak, 2003].

[3] Radar measurements from the Clementine mission [Nozette et al., 1996; Spudis et al., 1998; Simpson and Tyler, 1999] have provided the first evidence that polar regolith at cold spots may contain much higher content of water than at moderated latitudes [see also Fa et al., 2011]. Measurements by the Lunar Prospector Neutron Spectrometer (LPNS) [Feldman et al., 1998; Lawrence et al., 2006] presented observational evidence for the Extended Polar Suppressions of Epithermal Neutrons (EPSEN) at the lunar poles. Based on these data, one could not distinguish between two explanations of the phenomenon of EPSEN: it could be associated with a steady increasing content of hydrogen in the polar regolith toward the poles, or it could be contributed by many local spots of PSRs with high content of H-bearing volatiles, presumably water ice. We will call them spots of water-rich permafrost.

[4] Water on the Moon has also been recently detected by IR imaging spectrometers [Clark, 2009; Sunshine et al., 2009; Pieters et al., 2009]; the IR data have shown that the content of water (or hydroxyl) is gradually increasing toward both poles. Recently, the joint efforts of NASA's Lunar Reconnaissance Orbiter (LRO) and Lunar CRater Observation and Sensing Satellite (LCROSS) missions have provided the most direct evidence to date that regolith of the southern polar crater Cabeus contains significant amounts of water and other volatiles, such as OH, CH4, CO2, H2S, NH3, SO2, C2H4, CH3OH [Colaprete et al., 2010; Gladstone et al., 2010]. In particular, the mass fraction of water in the Cabeus regolith was estimated to be about 0.5–4.0 weight % by the Lunar Exploration Neutron Detector (LEND), onboard LRO [Mitrofanov et al., 2010a, 2010b] and about 5.6 ± 2.9 weight % by instruments onboard the shepherding spacecraft of LCROSS [Colaprete et al., 2010].

[5] Therefore, one may conclude that hydrogen and/or water is experimentally proven to be enhanced in the regolith around the lunar poles in comparison with moderate latitudes, and one local spot with a rather high quantity of water was detected in the crater Cabeus. Several questions arise: Where are another spots of water-rich permafrost at the lunar poles? Are there also spots at the lunar poles with smaller hydrogen content in comparison with the average value at the same latitude? How much do water-rich spots contribute to the bulk quantity of polar water on the Moon?

[6] The neutron telescope, LEND, was selected for NASA's LRO mission to provide answers to these questions. This instrument maps epithermal neutron emission on the lunar surface with high spatial resolution of about 10 km (FWHM) from an orbital altitude of 50 km [Chin et al., 2007; Vondrak et al., 2010; Mitrofanov et al., 2010a, 2010b]. High energy neutrons with energy about 1–20 MeV, which are produced by energetic particles of galactic cosmic rays, are moderated to epithermal energies by multiple collisions within the regolith. The leakage flux of epithermal neutrons depends on the content of hydrogen in the regolith, because more collisions with hydrogen nuclei lead to faster moderation and thermalization of neutrons before they can escape from the subsurface. The observed suppression of epithermal neutron emission at some particular spot in comparison with the surrounding area marks enhanced content of hydrogen or water in the regolith. On the other hand, excess of epithermal neutron emission marks other spots, where regolith has smaller content of hydrogen or different chemical composition in comparison with the reference area.

[7] The nuclear method was successfully used for the identification of water-rich polar permafrost on Mars [Boynton et al., 2002; Feldman et al., 2002; Mitrofanov et al., 2002]. This paper and two others [Litvak et al., 2012; Sanin et al., 2012] present the first results of testing for lunar water by the LEND instrument with data collected from September 15, 2009 to December 15, 2010. Litvak et al. [2012] addresses global mapping of neutron emission from thermal energies up to the energy of 15 MeV. This paper also presents a comparison of LEND mapping data with the previous mapping data from LPNS, revealing rather good agreement in the case of observations from detectors with omni-directional field of view (FOV). Finally, Litvak et al. [2012] analyzes the background conditions for mapping of epithermal neutrons by the collimated sensors of LEND and provides the current best estimates for local background in these sensors and the count rate from direct neutrons from the Moon. Sanin et al. [2012] focuses on the most intriguing question of the LEND investigation: Do lunar PSRs contain sufficient water to be the primary source of the EPSEN effect? This question has been preliminary studied in [Mitrofanov et al., 2010b], and analysis in Sanin et al. [2012] confirms the results of that paper that emission of epithermal neutrons from PSRs are not essentially different from emission from some spots of sunlit surfaces at the same high latitudes. There are also three currently submitted manuscripts from the LEND team: The first submitted manuscript by William Boynton together with the LEND team (W. Boynton et al., High spatial resolution of epithermal neutron emission from the lunar poles: Constraints on hydrogen mobility, submitted to Journal of Geophysical Research, 2012; referenced hereafter as M/WB) presents results of two methods of data processing for testing the presence of local spots of water-rich permafrost at the poles. Indeed, if PSRs are not any more likely to produce the EPSEN phenomenon, one has to address the possible existence of shadow-independent wet spots on the Moon. This test is much more difficult than the test for PSRs, because in this case one does not have any known information about contours and locations of testing spots. Another submitted manuscript by Maxim Litvak together with the LEND team (M. L. Litvak et al., LEND neutron data processing for the mapping of the Moon, submitted to Journal of Geophysical Research, 2012; referenced hereafter as M/ML) describes the main procedures of LEND data processing, which are used for development of Planetary Data System (PDS) data. There have been criticisms from members of the LPNS investigation [Lawrence et al., 2010, 2011] that LEND could not have such a high counting rate of collimated neutrons, as is inferred from our analysis. Therefore, the third submitted manuscript by R. Sagdeev together with the LEND team (R. Sagdeev et al., Use of Apollo 17 epoch neutron spectrum and Lunar Prospector data on lunar neutron background as a benchmark for the collimated sensors of the Lunar Exploration Neutron Detector, submitted to Journal of Geophysical Research, 2012; referenced hereafter as M/RS) addresses an important subject of the LEND investigation: the total count rate of neutrons in the collimated field of view.

[8] The LEND maps of lunar epithermal neutron emission show the phenomenon of EPSEN at both poles above 70° (Figure 1). The signature of EPSEN is easily seen with Orbital Phase Profiles (OPP) of LEND data for the count rate of epithermal neutrons from the Moon [Mitrofanov et al., 2011; Litvak et al., 2012]. The reference value of epithermal neutron counting rate is found to be 1.7 cps (counts per second) for the reference latitude belt of 60°–70° in agreement with the detailed analysis in M/ML. Here we use the reference value 1.7 cps for epithermal neutron emission from the latitude belt of 60°–70°. According to LEND data, the average EPSEN at the north and south poles is about 5% below the reference value [Litvak et al., 2012]. This measured value of polar suppression of epithermal neutrons is consistent with the amplitude of suppression found by the Lunar Prospector Neutron Spectrometer [Feldman et al., 1998].

Figure 1.

LEND map of epithermal neutrons at the lunar poles above 70° latitude. Raw counting rate maps are smoothed to decrease random fluctuations. Smoothing scale increased outward from the poles to produce similar counting statistics at all latitudes. Black spots and contours of the maps represent the boundaries of PSRs according to LOLA data [Mazarico et al., 2011]. The scale of LEND spatial resolution ∼10 km (FWHM) corresponds to ∼0.3° of latitude. The counting rate is presented in counts per second.

[9] In addition to EPSEN, the polar maps of neutron emission (Figure 1) display spatial variations at the scale of tens of km. The original mapping data were smoothed to make these maps (see below). Spatial variations at smaller scales were intentionally removed from the map by smoothing, because they are dominated by statistical noise. Variations at larger scales, which are visible on the maps, may be produced by real variations of lunar neutron emission or by statistical noise. The goal of this paper is to test these local variations and to determine which are associated with the physical variations of neutron emission.

[10] The observed signature of EPSEN may represent the contribution of two distinct physical effects at the lunar poles; it could be produced by the smooth decrease of epithermal neutron emission toward the poles due to the gradual increase of hydrogen content in the cold regolith (effect I), or it could be explained by a number of locally suppressed areas of epithermal neutron emission representing individual spots of water-rich permafrost (effect II). One does not know a priori, what proportion of effects I and II actually contribute to the observed phenomenon of EPSEN, and one may consider two logical limits that either one or another dominate on the Moon. It is also probable that the true case is somewhere between these two limits. It has already been shown from LEND data [Droege et al., 2011] that the distribution of epithermal neutron count rate at the lunar poles is bimodal. The larger peak of this distribution is thought to be contributed by effect I. A second smaller peak shows larger suppression of neutrons, which is likely associated with effect II and contributed by areas with enhanced hydrogen content. Therefore, we should try to resolve local spots on the surface containing these areas, which are associated with effect II of the epithermal neutron emission at the lunar poles.

[11] There were several earlier attempts to use Lunar Prospector data to study lunar neutron emission with high spatial resolution of several tens of kilometers [e.g., Elphic et al., 2007]. The Pixon method of image processing was used for the analysis of epithermal neutron data from the omni-directional sensors of LPNS. PSRs were tested by this method to estimate the most probable content of hydrogen inside them. However, this method of deconvolution of the Lunar Prospector omni-directional data for higher resolution was based on the assumption that the PSRs are the dominate contributor to the EPSEN, and the obtained results reflect this bias (see more criticism in McClanahan et al. [2010]). Indeed, it is impossible to distinguish between the extended suppression of neutrons over a large area of thousands of kilometers (effect I) and contributions of many smaller spots of suppression (effect II), if the detector does not have the spatial resolution required to resolve each individual spot.

[12] So, to test effect II, one should test both local Neutron Suppression Regions (NSRs) and Neutron Excess Regions (NERs) without any assumptions about their locations. These spots could be directly resolved from LEND data provided they have size >10 km. Two complementary methods of analysis of LEND data are presented in this paper and in M/WB, which describe the different techniques for mapping and smoothing the LEND polar data, calculating and propagating statistical uncertainties from the raw to the mapped data, applying background corrections, and defining the NSRs. We believe it is important to present both alternative methods for testing local spots of neutron variations, because these results are very important for better understanding of the physical conditions at the lunar poles.

2. Method of Analysis of LEND Data for Testing Local Variations of Neutron Emission From the Lunar Poles

[13] The LEND data allows us to perform the tests described above, because the collimated sensors of epithermal neutrons have a narrow FOV. At an altitude of 50 km, the FOV is about 10 km (FWHM). However, spatial variations of neutron emission which imply real physical differences must be supported by high counting statistics. Indeed, one may only measure the change of neutron emission from a test spot in comparison with the reference surface, provided the counting statistics are high enough to distinguish the physical difference of counts from statistical fluctuations. We propose below the following procedure for resolving and testing individual local spots of suppression or excess on the maps of epithermal neutrons (Figure 1). To get these maps, we have corrected the raw data for variations due to trends of sensor efficiency, variations due to trends of galactic cosmic rays, and we have also estimated the local background of neutrons produced or scattered by LRO (see Mitrofanov et al. [2010a, 2010b], Litvak et al. [2012]; also M/ML and M/RS). A smoothing procedure was also applied to these maps, which is based on a Gaussian filter with a latitude-dependent width. We perform smoothing to exclude small-scale variations of counts, which are dominated by random noise. The smoothing with latitude-dependent scaling maintains about the same relative level of statistical noise for the entire map (Figure 1). Consistent with LEND's spatial resolution, the smoothing radius is 11 km at the pole, and gradually increases to 25 km at 70° latitude.

[14] As the first step of our analysis, we build “reference” maps of lunar epithermal neutron emission, which are made by smoothing raw data with the constant scale of ∼230 km. This value corresponds to ∼7.5° of latitude, and is about 3 times less than the largest scale ∼600 km of spatial variations of the EPSEN phenomenon. In general, all scales of neutron variations may be present in the original maps (Figure 1), starting from about 600 km, as the largest scale of the EPSEN region, down to the resolution scale of several km. One needs to use more sophisticated methods to resolve all components of spatial variations of neutrons over the entire range of measurements. The maps in Figure 2 represent only the largest scales of variations, 230–600 km, and they will be the “reference” maps for the analysis below. One may consider counts from the “reference” map, as representing the gradual variations of epithermal neutrons due to effect I only, provided there are no local variations of neutron emission from the Moon.

Figure 2.

The smoothed “reference” maps of south and north polar regions above 70°, which are produced from the original maps in Figure 1. The counting rate is presented in counts per second.

[15] We have considered producing the reference map from the LEND omnidirectional sensor of epithermal neutrons instead of smoothing the data from the collimated sensors. However, these data cannot be used for the reference map because the uncollimated sensor has different FOV and energy-dependent efficiency than the collimated sensors. The only practical way to get an independent data set would be to divide the raw data set from the four collimated sensors into two independent sub-sets. However, has the unwanted effect of decreasing by two the counting for testing local variations.

[16] To test for the presence of local suppression/excess spots (effect II), one should subtract the average count rate of the reference map (Figure 2) from the count rate on the main map (Figure 1), and then analyze the spatial distribution and amplitudes of the residual map (Figure 3). One may suggest using a null-hypothesis test for local spots of neutron variation. Our “null hypothesis” assumes that the LEND mapping data do not support the presence of any statistically significant local spots of neutron emission on the scale of tens of km. If the result of this test is positive for null hypothesis, one should conclude that effect I dominates, and spatial variations displayed on the main map at small distance scales (Figure 1) are produced by statistical fluctuations. On the other hand, if the test is negative, one should conclude that there are real local spots of neutron excess or suppression on the surface of the Moon.

Figure 3.

Maps of residuals of epithermal neutron counting rate from lunar poles above 70° latitude, as count rates from the initial maps (Figure 1) minus the smoothed reference maps (Figure 2). The linear scale of 10 km is shown, as an illustration of LEND spatial resolution at an altitude of 50 km (FWHM). The counting rate is presented in counts per second.

[17] The map of residuals (Figure 3) displays both positive and negative deviations of neutron flux from the values in the reference map (Figure 2). Real spots of NSRs and NERs are present together with some stochastic variations due to statistical noise. The noise in the LEND mapping data is not uniform around the poles. LRO makes station-keeping orbital corrections at longitudes of about ±90°. LEND does not operate during these maneuvers, and counting statistics are biased in longitudinal segments from −75° to −110° and from 70° to 105° due to rapid changes in sensor efficiency after HV turn on. We exclude these segments from our analysis. We study the north and south polar regions above the latitude of 80°, which is the highest latitude of the boundary of EPSEN (see Figure 2).

[18] For selection of candidate local spots with either negative (NSRs) or positive (NERs) deviations over the testing map (Figure 3) we suggest two thresholds, ±0.0425 cps and ±0.085 cps (cps is counts per second), for residuals with respect to the counting rate of the smoothed reference map at the same location. These thresholds correspond to 2.5% and 5% of the reference count rate of 1.7 cps, respectively, which is attributed to epithermal neutrons from the lunar surface at the latitude of 60°–70°. Negative and positive thresholds determine the contours of potential candidate spots for NSRs and NERs, respectively. The main map (Figure 1) does not allow a simple estimate of the statistical confidence for each selected candidate spot, because smoothing produces artificial correlations of counts within a smoothing scale. To test the statistical confidence of each candidate spot, we sum up all counts of residuals inside the contour of a spot, and compare this value with the total statistical error estimated for raw counts in the same region of the main map (Figure 1). We use a three standard deviation selection criteria for statistical confidence of candidate spots, which are used for further analysis of NSRs and NERs.

[19] We restrict this analysis of local candidate spots of NSRs and NERs to those with area no larger than 2000 km2, which corresponds to a spot's linear size of about 40–50 km. Indeed, the reference map (Figure 2) has a smoothing scale of about 230 km, so it does not contain variations with a moderate linear scale of about 100 km and less. Also, variations on these larger scales could be studied quite well by epithermal sensors with omni-directional field of view and large counting rate, and they are not proper observational targets for collimated sensors of LEND with narrow FOV. So, in this paper we consider only candidate spots for NSRs and NERs, which are selected by thresholds criteria for flux variations ±2.5% and ±5%, have statistical confidence corresponding to 3σ or higher, and have the total area smaller than 2000 km2.

[20] Table 1 contains the list of 12 candidate spots, which correspond to these requirements. The numbers in the first column increase from pole down to the equator (S or N corresponds to South and North poles, respectively). The second and third columns contain latitude and longitude of the center of selected spots. The total area of spots at the level ±2.5% of deviation above or below the reference value is presented in the fourth column. Local effect of suppression or excess is estimated for pixels inside the contour of the spot. Raw counts are used for each pixel for this estimate in the fifth column. The parameter of local suppression or excess is calculated as the ratio of the sum of residual counts of pixels inside the selection contour divided by the reference number of counts, which would be associated with the reference counting rate, 1.7 cps, and total time of exposure of the test spot. Five candidate spots, which were selected by the threshold ±2.5%, are also confirmed by the selection threshold of ±5%. The sixth and seventh columns present the total area inside the contours at the threshold of ±5% and the estimate of local suppression/excess effect inside the contours, respectively. Spots S1, S4, N4 and N5 were included in the list because their area is smaller than 2000 km2 based on the 5% criteria. There are 8 selected NSRs and 4 selected NERs inside the high latitude polar caps >80°.

Table 1. List of Selected Candidate Spots for NSRs and NERs
Spot IDLatitude (deg)Longitude (deg)Total Area (km2) for 2.5% SelectionLocal Effect of Suppression/Excess for 2.5% SelectionTotal Area (km2) for 5.0% SelectionLocal Effect of Suppression/Excess for 5.0% Selection
South
NSR S188.5 S24.74675−6.3 ± 1.0%643−12.2 ± 2.6%
NER S286.3 S−72.41222+9.6 ± 3.2%268+24.1 ± 7.0%
NSR S386.3 S20.2647−14.4 ± 4.1%--
NSR S485.0 S−52.62287−8.4 ± 2.3%509−14.9 ± 4.8%
NSR S582.7 S30.71099−13.2 ± 4.0%--
NSR S682.4 S65.3786−16.5 ± 5.0%--
NER S781.2 S131.91039+15.1 ± 4.9%--
 
North
NSR N189.5 N44.4243−8.5 ± 2.6%--
NSR N288.5 N119.31215−10.4 ± 2.0%--
NSR N385.5 N−24.61018−10.6 ± 3.4%--
NER N482.8 N−48.42615+8.4 ± 2.7%959+18.6 ±4.5%
NER N582.3 N170.23384+8.7 ± 2.4%1030+12.2 ± 4.1%

[21] One may expect that the majority of the local spots of neutron variation are associated with real variations of the regolith composition. The enhancement of hydrogen is suggested, as the main model of NSRs; additional observational facts are presented below, which support this suggestion. The origin of 4 NERs is not clear. They have a relative amplitude excess of about +(10–20)%, while the total relative amplitude of the large scale suppression EPSEN is about −5%. The excess in the NERs is too large to explain by a local decrease of hydrogen down to values at moderate latitudes. Models which take into account local variations of chemical composition should be also considered in future studies of NERs (and for NSRs as well). It is known that the difference in soil composition of nearside maria and farside highlands significantly influences the spatial distribution of high energy epithermal and fast neutrons. The major cause is a variation of average atomic mass of the lunar soil having more weight fraction of Fe in maria and less in the highlands, where Fe is replaced by a higher weight fraction of Al [see Gasnault et al., 2001]. Also, more analysis is necessary to check the possible contribution of random fluctuations to some of detected spots (see below).

[22] The average area of a single detected spot with local suppression or excess of neutron emission is S ∼ 1700 km2 (see Table 1), and each spot was selected by the 3σ statistical criteria. The probability for >|3σ| deviations due to random fluctuations is known to be rather small 0.0023. However, if the set of independent random variables has a large number of members, N, the probability of finding a case with >|3σ| deviations is about 2.3·10−3·N. N is the number of trials. For N ∼ 500 this probability approaches ∼1. If N ≫ 500, one may expect to find ∼N/500 cases with >|3σ|, which are produced by random fluctuations. For the total area about 5.7·105 km2 of two polar regions above 80° latitude the number of trials N is about 340·(1700 km2/S). Therefore, one may expect to get about 1 false positive due to random fluctuations, while we have detected 12 candidate spots (Table 1). This simple argument supports the idea that the majority of these spots represent real physical variations of neutron emission. However, such a simple estimate is not very accurate because we have applied to observational data several data processing procedures during the detection process, which are not taken into account in this estimate.

[23] For a more accurate validation of our detection results (Table 1) we performed a Monte Carlo test based on simulations of residuals in pixels of tested polar areas, which are produced by fluctuations of counts around the values from the smoothed reference maps (Figure 2). Uncertainty in the counts of each pixel has been obtained from the observed total count statistics for all pixels at the same latitude. The starting value of counts for each pixel has been taken from the smoothed map of actual observations (Figure 2). The Monte Carlo simulation produces maps (see Figures A1 and A2 of Appendix A), which should differ from the smoothed reference map (Figure 2) due to statistical fluctuations only; the dispersion of simulated counts coincides with that of the observed counts (see Figure 3). We then performed the same procedures for detection of NSRs or NERs for the maps of simulated residuals, as we used for the real data from observations. The result of this analysis should represent the test of the “null hypothesis,” which assumes that there are no physical variations of neutron emission in local spots with areas <2000 km2 over the tested polar regions with observable EPSEN (see above). We have produced 24 independent cases of simulated maps, which have been analyzed for the presence of NSRs and NERs by the methods described above.

[24] The average values from these 24 simulations are presented in Table 2. One may see that for both detection thresholds, ±2.5% and ±5.0%, the number of selected spots for real data is about 3 times larger than the number of spots for the simulated data. Similarly, the total area of selected spots is about 3 times larger than for simulated spots. One should conclude that the “null hypothesis” is not supported by the comparison of real and simulated data. Moreover, we may consider the results of Monte Carlo simulation to be an estimate of statistical uncertainty for selected spots; the sample of 12 selected spots might include 4 spots due to statistical fluctuations, and the total selected area of 20230 km2 might include about 6200 km2 associated with these fluctuations.

Table 2. Comparison of Results for Detection of Local Spots With Suppression or Excess of Epithermal Neutrons for Measured and Simulated Residuals of Counts Around the Smoothed Reference Maps
 Analysis of Maps of Measured Residuals (Figure 3 and Table 1)Average Results of Analysis of Maps of Simulated Residuals
Number of selected spots of NSRs and NERs with ±2.5% detection threshold12 spots are detected with total selected area 20230 km24 spots are detected with total selected area about 6200 km2
Number of selected spots of NSRs and NERs with ±5.0% detection threshold5 spots are detected with total selected area 3427 km21.7 spots are detected with total selected area 1060 km2

[25] So, one may conclude that the main fraction of selected spots of NSRs and NERs (Table 1) corresponds to the real physical phenomenon of local variations of emission of epithermal neutrons around the lunar poles.

3. Studies of NSRs and NERs With Data From LOLA and Diviner

[26] Data from the LRO Lunar Orbiter Laser Altimeter (LOLA) [Smith et al., 2010a, 2010b; Mazarico et al., 2011] and Diviner Lunar Radiometer Experiment [Paige et al., 2010a, 2010b] allow us to study the physical conditions of solar irradiation and average temperature for 12 selected spots of local suppression or local excess of epithermal neutrons (Table 3). The first column contains the names of these spots, the second to fifth and sixth to ninth columns present the average values of parameters of these spots for selection thresholds of ±2.5% and ±5.0%, respectively. The third and seventh columns present the average incident flux according to LOLA data. This dimensionless parameter is estimated in Mazarico et al. [2011] as solar illumination modulated by the cosine of the incident angle. It is compared with the reference value of the incident flux for the area at the same latitude, which excludes the test spot (shown in brackets). The fourth and eighth columns present the parameter of illumination, which is also deduced from the LOLA data. This dimensionless parameter is estimated in Mazarico et al. [2011] and is averaged over the lunar nodal precession period to give the percentage area of the visible Sun. These columns also present the average value for illumination at the same latitude, when the area of the test spot is excluded. In the fifth and ninth columns we present the average temperature of the surface derived from the Diviner data. The average value for the temperature is also presented, which is measured at the same latitudes with the area of test spot excluded.

Table 3. List of Individual NSRs and NERs With Measured Parameters of Irradiation and Surface Temperature
Spot ID and Crater NameSelection Thresholds ±2.5%Selection Thresholds ±5.0%
Local Effect of Suppression or ExcessIncident Flux in 10−4 (With Latitude Average)Illumination in Percent (With Latitude Average)Average Temperature in K (With Latitude Average)Local Effect of Suppression or ExcessIncident Flux in 10−4 (With Latitude Average)Illumination (With Latitude Average)Average Temperature in K (With Latitude Average)
South
NSR S1 Shoemaker−6.3 ± 1.0%145 ± 3 (238 ± 1)11.1 ± 0.2 (18.5 ± 0.1)72.7 ± 0.4 (93.9 ± 0.2)−12.2 ± 2.6%0 ± 1 (179 ± 2)0.0 ± 0.1 (14.4 ± 0.1)42.7 ± 0.1 (83.7 ± 0.3)
NER S2+9.6 ± 3.2%215 ± 8 (243 ± 2)22.7 ± 0.4 (20.7 ± 0.1)97.8 ± 0.8 (96.7 ± 0.3)+24.1 ± 7.0%134 ± 13 (254 ± 3)15.1 ± 0.9 (22.6 ± 0.2)82.2 ± 1.7 (99.4 ± 0.4)
NSR S3 Malapert−14.4 ± 4.1%86 ± 8 (299 ± 2)6.0 ± 0.4 (24.8 ± 0.1)60.3 ± 1.4 (106.9 ± 0.3)----
NSR S4 Cabeus−8.4 ± 2.3%99 ± 5 (351 ± 2)6.9 ± 0.3 (25.4 ± 0.1)69.7 ± 0.8 (112.1 ± 0.2)−14.9 ± 4.8%20 ± 3 (325 ± 3)1.6 ± 0.2 (24.2 ± 0.1)51.8 ± 0.6 (109.1 ± 0.3)
NSR S5−13.2 ± 4.0%364 ± 16 (477 ± 3)24.5 ± 0.5 (32.0 ± 0.1)119.4 ± 1.2 (128.0 ± 0.2)----
NSR S6 Amundsen−16.5 ± 5.0%309 ± 19 (469 ± 3)23.3 ± 1.1 (31.2 ± 0.1)108.2 ± 2.2 (126.9 ± 0.2)----
NER S7+15.1 ± 4.9%445 ± 18 (465 ± 3)29.1 ± 0.7 (31.2 ± 0.1)125.4 ± 1.5 (127.8 ± 0.2)----
 
North
NSR N1 Peary−8.5 ± 2.6%75 ± 3 (206 ± 4)13.0 ± 0.3 (17.1 ± 0.2)74.6 ± 0.4 (87.7 ± 0.5)----
NSR N2 Whipple−10.4 ± 2.0%177 ± 5 (125 ± 1)18.9 ± 0.4 (13.8 ± 0.1)89.2 ± 0.7 (76.2 ± 0.2)----
NSR N3−10.6 ± 3.4%318 ± 11 (296 ± 2)29.0 ± 0.6 (26.5 ± 0.1)114.1 ± 1.1 (108.3 ± 0.3)----
NER N4+8.4 ± 2.7%402 ± 8 (405 ± 2)34.1 ± 0.5 (30.9 ± 0.1)125.5 ± 0.7 (120.9 ± 0.2)+18.6 ± 4.5%432 ± 17 (397 ± 3)32.6 ± 0.8 (30.0 ± 0.1)124.7 ± 1.5 (119.1 ± 0.3)
NER N5+8.7 ± 2.4%552 ± 11 (432 ± 2)33.5 ± 0.3 (32.1 ± 0.1)133.1 ± 0.8 (124.3 ± 0.2)+12.2 ± 4.1%600 ± 16 (414 ± 3)36.4 ± 0.2 (30.6 ± 0.1)141.0 ± 0.8 (121.0 ± 0.3)

[27] The data in Table 3 for individual spots highlights the generic tendency that NSRs are usually much colder than the local vicinity at the same latitudes (see Figure 4). This is the case for NSRs S1, S3–S6 and N1. For all six NSRs S1, S3–S6 and N1, which are to the left of the dashed line of zero temperature difference one may suggest the simple phenomenological property “less local irradiation and lower temperature – fewer local neutrons,” though there is no direct linear correlation between the decrease of temperature and neutron suppression for these spots. For each spot the incident flux and solar illumination parameters are smaller than for the average values for the area at the same latitude (see Table 3). For NSRs S1 and S4 one may also compare irradiation and average temperatures for surfaces inside the spots for selection threshold −2.5% and −5.0%. It is evident that the estimated total suppression is much larger in the inner contours for −5.0% selection criteria, and correspondingly irradiation parameters and temperatures are much lower. For NSR S1 in Shoemaker the average irradiation was found to be zero, which means that this part of the surface is in the permanent shadow (see below).

Figure 4.

Detected spots of NSRs and NERs are shown with local effect of suppression/excess (vertical axes) and absolute difference of the temperature between a spot with the latitude-average value outside it (horizontal axis). The values used for these spots correspond to the detection level of ±2.5% (see Table 3). The red points represent six spots, which have the property “less local irradiation and lower temperature – fewer local neutrons.”

[28] Two other suppressions, NSRs N2 and N3, have different thermal property (see Table 3 and Figure 4) than the six previously mentioned NSRs; these spots have local neutron suppression similar to NSRs S1, S3–S6 and N1, but their surface is hotter than the average surface at the same latitude. The currently available data do not allow us to speculate on the physical origin of these suppressions, but it is clear that they should be physically different from the six NSRs S1, S3–S6 and N1.

[29] There are also four selected spots with an excess of epithermal neutron emission NERs S2, S7, N4 and N5 (Tables 1 and 3). Two southern spots S2 and S7 do not show a clear relationship between the excess of neutrons and heating conditions. Their areas inside the +2.5% detection threshold do not have any significant difference in irradiation and temperature (Table 3). The area of S2 for the +5.0% threshold has the contradictory property – it has a large excess of epithermal neutrons together with a decrease of solar irradiation and average temperature in comparison with latitudinal average values (Table 3). We cannot explain the local neutron excess of these two spots by some particular irradiation conditions. They could result from some local chemical variation of regolith, which could change the flux of epithermal neutrons. Also, one cannot exclude that these two paradoxical spots, S2 and S7 of local excess, as well as two spots N2 and N3 of local suppressions, are produced by random noise of counts – the Monte Carlo simulation has shown that there could be ∼4 cases of such spots in the detected sample of 12 spots (see Section 2).

[30] Two other local spots with an excess of neutrons, NERs N4 and N5, have the property of greater irradiation and temperature for the areas selected by both thresholds, +2.5% and +5.0%. One may suggest that the same physical mechanism, which produces suppression of epithermal neutrons at spots NSRs S1, S3–S6 and N1 with smaller heating, is also responsible for the excess of these neutrons at these spots with larger heating. This mechanism could be related to the presence of less or more hydrogen bearing volatiles in the regolith. When heating is small, the regolith contains a higher content of volatiles. Conversely, larger heating leads to less hydrogen in the subsurface. However, the local measured effect of neutron excess in NERs N4 and N5 is rather large +(8–18) % (Table 3) in comparison with the average suppression of −5% due to the EPSEN around them. So, even if all the hydrogen were eliminated from the regolith at these spots, they should still radiate more epithermal neutrons than the hydrogen-poor regions at moderate latitudes. This problem may be solved in the future using more models for analysis and larger statistics of data for interpretation.

[31] So, there are six local suppressions NSRs S1, S3–S6 and N1 with the total area about 104 km2 above 80 degrees of latitude, which have the property “less local irradiation and lower temperature – fewer local neutrons”. They all have good significance of detection (Table 1): NSR S1 in Shoemaker has the confidence of 6.3 σ and the NSR in Cabeus has the confidence of 3.7 σ. They all have additional confirmation from independent measurements for illumination from LOLA and average temperature from Diviner: they all have a much colder surface and much smaller irradiation, compared to other areas at the same latitude (Table 3 and Figure 4). Regolith with such low temperature may contain free water ice below the uppermost layer of several centimeters [Paige et al., 2010b]. In Section 4 we will focus our attention on these six NSRs, as possible spots of water-rich permafrost on the Moon.

4. Properties of Individual NSRs as Possible Spots of Lunar Permafrost

[32] Five south polar spots of local suppression of epithermal neutron flux are shown in Figure 5. The NSR S1 in Shoemaker crater (Figure 5) is the best illustration for the law “less local irradiation and lower temperature - fewer local neutrons.” The contour of suppression at −5% is found to practically coincide with the boundary of the PSR in this crater. Data in Table 3 show no irradiation of the surface inside this inner contour. This finding is important for experimental confirmation of the imaging capabilities of LEND. Indeed, the spot with zero solar illumination was found by neutron data only, and has independently been identified by data from LOLA. The area of the inner segment of S1 is 643 km2 (Table 1), which corresponds to the equivalent radius of 14 km. The complementary papers [Sanin et al., 2012] and M/WB show the perfect consistency between cross-section of relief at Shoemaker and cross-section of measured neutron suppression. This observation confirms that LEND has spatial resolution of about 10 km (FWHM) [Mitrofanov et al., 2008, 2010a, 2010b], as was required of this instrument by the LRO mission statement [Chin et al., 2007; Vondrak et al., 2010]. These data clearly demonstrate that the instrument is capable of high spatial resolution, refuting claims to the contrary [Lawrence et al., 2010, 2011].

Figure 5.

(left) Map of the south pole is presented above the latitude of 80°. (right) The map of detected local spots of NSRs is also shown, which could be associated with water-rich lunar permafrost, shown in blue. Bright blue and dark blue regions correspond to detection thresholds of −2.5% and −5.0%, respectively. Black spots and contours of the maps represent the boundaries of PSRs according to LOLA data [Mazarico et al., 2011].

[33] Average suppression values inside the inner and outer contours are −12.2 ± 2.6% and −6.1 ± 1.0%, respectively. The local suppression effect is estimated in accordance with the neutron flux outside the local vicinity of this spot. Total suppression inside the inner contour could be estimated, as the sum of local suppression of NSR compared to the average suppression of about 5% of EPSEN at this latitude. So, the total suppression is about −17% and −10% for inner and outer contours, respectively. The PSR of Shoemaker has already been compared with the sunlit area around it in a preliminary analysis of LEND data by Mitrofanov et al. [2010b]. The local effect of suppression in this PSR was found to be −6.2 ± 1.2% in comparison with this sunlit vicinity. It is consistent with the difference between the values of neutron suppression for the area inside the inner contour of the NSR, which is close to the permanent shadow, and the area inside the outer contour, which includes a large sunlit area around the PSR. The outer contour of NSR S1 also includes a part of Haworth crater, another large southern PSR, but does not include the third large southern PSR of Faustini crater. It is unclear, why three similar large craters Shoemaker, Haworth and Faustini with similar PSRs inside them are different in emission of epithermal neutrons and, consequently, in the estimated content of water ice deposits.

[34] The NSR S3 is another interesting spot with the total area of 647 km2 (Figure 5). It is located at the southeast part of Malapert crater, and includes a large fraction of the PSR in the poleward facing part of the surface as well as part of the highland with equator facing slope. In the area of the PSR, this NSR should have no solar irradiation. On the other hand, the slope of the highland feature should be illuminated by the Sun daily, and its surface should get large irradiation and large average fluence of protons from the solar wind. During sunlit conditions, chemical reactions could take place in the regolith of the irradiated slope, which transform solar protons to hydroxyl and water molecules [Starukhina and Shkuratov, 2000; Crider and Vondrak, 2000]. The top layer of a slope on the rim of Malapert could be a unique spot on the Moon, where this chemistry takes place either just centimeters above a very cold subsurface, or just few kilometers away from a surface in permanent or temporary shadow. The average temperature of this spot is rather low, about 60 K (Table 3). During a lunar day, water molecules produced in this way might migrate downward to the subsurface to become trapped in a cold layer below, or evaporate from the heated surface, migrate and become trapped in a nearby shadowed region. This mechanism could produce the water-rich permafrost of NSR S3, and we believe it could also be source of water for other detected NSRs at the lunar poles. We suggest calling this mechanism the Solar Water Chemical Reactor (SWCR below). NSR S1 of Shoemaker is located in the same polar area as NSR S3, and SWCR of S3 may also work for S1. S1 and S3 could possibly merge into one suppression region between craters Malapert and Shoemaker, provided the selection threshold would be smaller than −2.5% (Figure 5). There are many questions about the model of SWCR. For example, why does the SWCR of S3 not produce water for other PSRs, which are in the closet vicinity of S1 and S3 (Figure 5)? There could be other physical conditions to be taken into account, such as local relief, local electrostatics, or other properties of the surface. However, the main concept of SWCR could work for many spots in the polar regions of the Moon, where a hot irradiated top layer of regolith lies above the cold permafrost, and NSR S3 may be the best example of that. Further analysis may explain why there are strong suppressions at S1 and S3, but no detectable suppressions in Shackleton and other large PSRs at the Malapert-Shoemaker province of the South pole.

[35] NSR S4 is another frequently analyzed spot at the South pole due to the recent successful LCROSS mission [Colaprete et al., 2010]. NSR S4 is identified within the southern polar crater Cabeus, which is to the west of Malapert (Figure 5). This NSR has also been selected by two suppression thresholds at −2.5% and −5.0% with confident local suppressions of −8.4 ± 2.3% and −14.9 ± 4.8% inside the outer and inner contours, respectively. This spot has the strongest measured effect of local suppression (Table 1). The inner contour of NSR S4 includes two large PSRs with sunlit surface between them. The northern PSR was suggested by the LEND team for LCROSS impact using preliminary data from the initial stage of orbital mapping [Mitrofanov et al., 2010b]. Current data from LEND observations give an estimate of local suppression for this PSR of −14.4 ± 4.7% [Sanin et al., 2012], which is comparable with the average value for the area inside the inner contour of NSR S4.

[36] The area inside the inner contour of −5% of NSR S4 (∼510 km2) contains a large fraction of illuminated surface, and estimated values of suppression are similar inside and outside the shadow in this area (Figure 5). Therefore, one may conclude that the shadow and sunlit surfaces of S4 might have the same hydrogen content. The estimated total suppression of epithermal neutrons in S4 is about −20% which corresponds to about 0.5 wt% of water ice in the regolith, provided it is homogeneously distributed throughout the surface and subsurface [Mitrofanov et al., 2010b]. However, the average temperature of the sunlit part of NSR S4 is about 50 K (Table 3) and could only be constantly at such low temperature if covered by several centimeters of regolith [Salvail and Fanale, 1994; Vasavada et al., 1999]. The top layer is heated up to much higher temperatures, and the SWCR mechanism should work here. Therefore, one should use a two-layer model for interpretation of the observed neutron suppression at NSR S4. It is known from numerical simulations that for the same suppression of epithermal neutrons, the content of water ice in the subsurface layer would increase with increasing thickness of the top dry layer with small water content. The estimate of water content in the PSR of Cabeus for a two-layer subsurface gives about 4 wt% of water ice [Mitrofanov et al., 2010a] in good agreement with direct measurements from LCROSS [Colaprete et al., 2010]. We take this estimate for the entire inner part of the surface of NSR S4 (Figure 5).

[37] Two other southern spots, NSRs S5 and S6 (Figure 5), are different from poleward NSRs S1, S2 and S4, because they have 2–3 times larger solar irradiation (Table 3). However, the property “less local irradiation and lower temperature – fewer local neutrons” is also seen for these spots (Table 3). While poleward NSRs include some large PSRs, these two spots have entirely sunlit surfaces, with no large PSRs inside them. One would expect that regolith with water ice should be covered by a dry top layer for these spots, S5 and S6. The average surface temperature at S5 and S6 110–120 K is still low enough to trap the water ice in the shallow subsurface, and the SWCR mechanism might work at these sites with the major transport of water molecules down to the cold subsurface. The shape of S5 seems to be consistent with the features of local relief: there is a pole-facing slope of the mountain to the northwest side and lowlands at the southeast side (Figure 5). The contour of another spot, S6, also includes the local lowland surrounded by craters with PSRs, which are not included in the S6 area (Figure 5). This spot also includes the pole-facing slope of un-named crater near the craters Amundsen and Nobile. We may suggest that counting statistics are still not sufficient for accurate determination of the boundary of S6, and this spot could actually include PSRs from the nearest vicinity (Figure 5). More data are necessary to resolve the contour of this spot and to test the possible link of suppression with the local features of lunar landscape.

[38] The northern NSR N1 (Figure 6) has also very good consistency with the property “less local irradiation and lower temperature – fewer local neutrons” (Table 3). Irradiation of N1 with high northern latitude at the bottom of crater Peary is rather small, much smaller than for the local vicinity at the same latitude (Table 3). The poleward part of the contour of N1 accurately follows the bottom line of the floor of the crater Peary just below the equator-facing slope above it (Figure 6). This spot does not include PSRs, while there are several large PSRs around it. This slope may provide SWCR for NSR N1, because the rather low average temperature of 75 K in the regolith may preserve trapped water in the shallow subsurface.

Figure 6.

The map of local spot NSR N1 is shown in the vicinity of the north pole. The contour of detection threshold of −2.5% is shown by blue. Black spots and contours of the map represent boundaries of PSRs according to LOLA data [Mazarico et al., 2011].

5. Conclusions

[39] Analysis of the LEND maps of epithermal neutron emission at the lunar poles (Figure 1) demonstrates that together with effect I of Extended Polar Suppression of Epithermal Neutrons (EPSEN), which is thought to be related to the gradual increasing content of hydrogen in the regolith in the poleward direction, there is also effect II from local spots of variations of neutron emission, Neutron Suppression Regions (NSRs) and Neutron Excess Regions (NERs). Twelve spots of NSRs and NERs were detected at the lunar poles (Table 1). They were selected with high statistical confidence above 3σ, and in two cases the confidence of selection was larger than 5σ (see Table 1). All selected spots have been studied using independent data for solar irradiation from LOLA and for average surface temperature from Diviner. It was found that six local spots S1, S3–S6 and N1 have significantly different parameters of solar irradiation and surface temperature compared with the surrounding surface at the same latitude (Table 2). They have the empirical property “less local irradiation and lower temperature – fewer local neutrons.” We assume that the hydrogen content is the driving factor for this law: There are six NSRs, which might have more hydrogen in the regolith than the area around them, because they are colder. We consider them to be possible spots of water-rich lunar permafrost (Figures 5 and 6).

[40] Comparison of selected NSRs and large PSRs leads to the conclusion that NSRs are not linked directly with PSRs, as has been commonly accepted before LEND investigation. In several cases large PSRs have been found inside NSRs. Thus, the inner contour of NSR S1 in Shoemaker is practically coincident with the boundary of its PSR (Figure 3). Interestingly, in this case the contour of the PSR was experimentally determined by LEND neutron data only, which demonstrates the good capabilities of this instrument to resolve spatial variations of epithermal neutrons with high spatial resolution. The distance between the inner contour of neutron suppression and the contour of optical shadow is about 10 km or less, which agrees with the distance scale of LEND spatial resolution [see also Sanin et al., 2012]. However, in general, analysis of all selected NSRs (Figures 5 and 6) shows that there are some NSRs with large PSRs inside them, as well as many large PSRs outside detectable NSRs, and finally, there are some NSRs, which are not associated with large PSRs. One may conclude that favorable physical conditions for formation of NSRs at the lunar poles are not directly related with permanent shadow, rather the spot of permanent shadow could have larger suppression within the area of NSRs. Moreover, we may only study neutron suppression effects in large PSRs, greater than the linear resolution of LEND, about 10 km. There could be many small and very small PSRs, whose physical relationships with NSRs cannot be tested by LEND data. We suspect that some NSRs, like northern NSRs N2 and N3, could be associated with areas with large numbers of such small PSRs. However, another conclusion can also be drawn from this analysis – NSRs may exist within a sunlit surface, which is regularly irradiated and heated by the Sun.

[41] The property of six NSRs “less local irradiation and lower temperature – fewer local neutrons” leads to the hypothesis that irradiation and implantation of hydrogen from solar wind may work together, like chemical reactor that produces water molecules during a sunlit time. We call this mechanism, Solar Water Chemical Reactor (SWCR). These NSRs have rather cold average temperature in the subsurface (Table 3), and a water molecule, produced in a heated top layer from solar protons, might either diffuse down to the cold subsurface for permanent trapping, or migrate from the hot sunlit surface to be trapped in a cold shadowed region. The efficiency of SWCR depends on the local landscape and on properties of the surface: implantation of protons, solar irradiation, efficiency of reactions for producing OH and H2O, migration of molecules vertically down to subsurface and horizontally over the surface; all these conditions together could produce more or less favorable conditions for the origin of a NSR with water-rich permafrost. In many cases, the contours of selected NSRs look very similar to particular features of the surface landforms. Local conditions may explain why some NSRs appear at one place, while there are no NSRs at another. For example, the existence of NSR S1 in Shoemaker, S3 in Malapert and S4 in Cabeus should be considered in comparison with the absence of NSRs at nearby craters Shackleton, Haworth and Faustini.

[42] Physical distinctions found between selected NSRs and large PSRs leads to another interesting question of the lunar polar region: what is the source of lunar water? There are two potential origins of lunar water, cometary water delivered by comets and solar water produced by chemical reactions in regolith from solar wind protons. In the first case, water vapor from a comet would condense similarly in all cold traps of PSRs around the impact site. In this case, one would expect that similar large PSRs should have similar deposits of water, and that there should be no water deposits in sunlit surfaces outside permanent shadow. Data presented here shows that it is not the case. These data are more favorable for the second option, solar water produced in situ from solar wind. In this case the difference between water-rich and water-poor PSRs could be explained by more or less favorable surface morphology for production of water at some local spots with SWCRs and for storage of water ice permafrost in the cold subsurface.

[43] We may try to answer questions presented in the Introduction:

[44] Are there spots of water-rich permafrost at the lunar poles? – Yes, we detected six NSRs, which are good candidates for water-rich permafrost, NSR S1, S3–S6 and N1 (see Tables 1, 3, Figure 5 and 6).

[45] Are there also spots at lunar poles with smaller hydrogen content in comparison with the average value at the same latitude? – Yes, there are two NERs, N5 and N6, which may be hot spots with decreased content of hydrogen in their soil, but this result does not have the same confidence level as the pervious one for NSRs.

[46] How much do the wet spots contribute to the bulk quantity of polar water on the Moon? – The estimated total area of all detected spots of water-rich permafrost is about 104 km2 (Table 1) and assuming the weight fraction, ζ, of at least 1 wt% of water ice at these spots, this represents about 108·(ζ / 1%) tons of water ice within a 1 m shallow layer of subsurface.

[47] There are still many questions remaining about the physical nature of NSRs, and it is necessary to study more data to understand the physical model of water-rich permafrost on the lunar surface, which is described by the law “less local irradiation and lower temperature – fewer local neutrons.” Also, we need to better understand several selected spots of NSRs and NERs, which are not consistent with this law. However, these first results of LEND observations point out that local spots of water-ice permafrost should exist at the lunar poles, and the physics of this phenomenon is more complex than the simple trapping of water in the permanent cold of PSRs.

Appendix A

[48] The results of Monte Carlo simulations of neutron emission are shown in Figures A1 and A2. They are based on the smoothed reference maps for EPSEN at North and South pole with random noise of counts at individual surface elements.

Figure A1.

Simulated maps of neutrons emission for the north pole made by adding random noise to the smoothed reference map (Figure 2).

Figure A2.

Simulated maps of neutrons emission for the south pole made by adding random noise to the smoothed reference map (Figure 2).

Acknowledgments

[49] This investigation was performed due to valuable support of all people of the LRO project, and authors are very much thankful to them for this excellent opportunity to study the Moon. The work for this paper was partially supported by grant for the research project “Nuclear Planetology” from the International Space Science Institute. The authors are also very much thankful to anonymous reviewers of this paper and to the Editor of the Journal of Geophysical Research—Planets for helpful comments and questions, which improved the paper.