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Keywords:

  • gamma ray;
  • Lunar Prospector;
  • Moon

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Neutron Spectroscopy on Board Lunar Prospector
  5. 3. Initial Processing (Level 0 to Level 1)
  6. 4. Reduction of Systematic Uncertainties (Level 1 to Level 2)
  7. 5. Mapping Neutron Data (Level 2 to Level 3)
  8. 6. Summary
  9. Acknowledgments
  10. References
  11. Supporting Information

[1] From January 1998 to July 1999, Lunar Prospector continuously measured the leakage flux of neutrons from the Moon in four distinct energy ranges from 0 eV to 8 MeV. These measurements were made using two 3He tubes within the Neutron Spectrometer (NS) and the anticoincidence shield of the Gamma-Ray Spectrometer (GRS). This publication details the reduction of raw neutron data (level 0) to develop four maps of neutron counting rates, which can be interpreted in terms of elemental composition of the lunar regolith. Details are given to convert level 0 data into level 1 data, where corrupted and unusable records have been removed because of transmission errors, solar energetic-particle events, or cross-talk with other instruments. At level 2, time series data have been corrected for observational biases and variations of the response function of the instruments. At level 3 the highest-quality neutron data (low-altitude, high time resolution) are mapped onto the Moon. The main characteristics of each map are, for thermal neutrons, energy range 0–0.4 eV, dynamic range 95%, precision 2.7%, and half width at half maximum (HWHM) resolution 23 km, in units of counts/8-s; for epithermal neutrons, energy range 0.4 eV < E < 0.7 MeV, dynamic range 15%, precision 1%, and HWHM resolution 22 km, in units of counts/8-s; for moderated neutrons, energy range 0–0.8 MeV, dynamic range 15%, precision 1.8%, and HWHM resolution <45 km, in units of counts/32-s; and for fast neutrons, energy range 0.8–8 MeV, dynamic range 30%, precision 1.6%, and HWHM resolution 23 km, in units of counts/32-s. All maps are normalized to 30 km altitude, at the equator; and to the flux of cosmic rays in January 1998. They are presented as 720 × 360 arrays equally spaced in latitude and longitude. Results are reproducible from raw data that are available at the Planetary Data System (PDS), together with guidance and numerical values in this publication.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Neutron Spectroscopy on Board Lunar Prospector
  5. 3. Initial Processing (Level 0 to Level 1)
  6. 4. Reduction of Systematic Uncertainties (Level 1 to Level 2)
  7. 5. Mapping Neutron Data (Level 2 to Level 3)
  8. 6. Summary
  9. Acknowledgments
  10. References
  11. Supporting Information

[2] Planetary neutron spectroscopy was first proposed as a technique for remotely measuring the composition of planetary surfaces by Lingenfelter et al. [1961]. In particular, the authors concluded that leakage neutron fluxes from the Moon could provide a sensitive measure of the near-surface hydrogen abundance. Furthermore, they pointed out that determining abundances of other elements (Fe, Ti, Rare Earth Elements) was achievable using orbital neutron spectroscopy, although specific abundances are not unique. The first attempts to perform orbital neutron measurements were planned at Mars; they were unsuccessful because of the failures of Phobos-1 and Mars Observer to orbit Mars [Surkov et al., 1993; Feldman et al., 1993]. The first successful orbital neutron measurements were performed at the Moon using instruments on board the Lunar Prospector (LP) spacecraft. Neutron measurements from LP have been used to determine the surface abundance of hydrogen at both poles of the Moon [Feldman et al., 1998, 2000, 2001], as well as to provide an initial estimate of solar wind implanted hydrogen over the entire lunar surface [Johnson et al., 2002; Genetay et al., 2003]. In addition, LP measurements have been used to map the distribution of Gd + Sm abundances on the lunar surface [Elphic et al., 1998, 2002], to provide a measure of titanium abundances on the lunar surface [Elphic et al., 2002], and to map the distribution of the mean atomic mass of the surface soils on the Moon [Maurice et al., 2000a; Gasnault et al., 2001].

[3] Although numerous interpretations of LP neutron measurements have been published (see above), there has never been a thorough description of the LP neutron data processing procedures. This publication therefore describes the entire data reduction scheme of neutron data. Section 2 first presents the basics of neutron production and moderation in a Moon-like soil. Next, a description is given of the sensors and of the different data collection modes. Sections 3 and 4 define the original data sets, how they are organized with time, and the various corrections that are made to the data. Finally, section 5 describes how the data are mapped onto the surface of the Moon. The final data sets which are presently available for scientific interpretation from the Planetary Data System at Washington University, St Louis are also presented in section 5.

2. Neutron Spectroscopy on Board Lunar Prospector

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Neutron Spectroscopy on Board Lunar Prospector
  5. 3. Initial Processing (Level 0 to Level 1)
  6. 4. Reduction of Systematic Uncertainties (Level 1 to Level 2)
  7. 5. Mapping Neutron Data (Level 2 to Level 3)
  8. 6. Summary
  9. Acknowledgments
  10. References
  11. Supporting Information

[4] Lunar Prospector is a small spin-stabilized spacecraft with a fueled mass of 233 kg [Binder, 1998]. It is a 1.42 m diameter by 1.22 m tall drum made of graphite epoxy with surface mounted solar cells. The science instruments are mounted on three 2.5 m booms to isolate them from the bus. The Neutron Spectrometer (LP-NS) shares its boom with the Alpha Particle Spectrometer (LP-APS) and the Gamma-Ray Spectrometer (LP-GRS) is alone on another boom. The magnetometer and electron-reflectometer occupied the last boom.

2.1. Origin of Planetary Neutrons

[5] Planetary neutrons are created from the interactions of galactic cosmic rays with constituents of near-surface material. Specifically, neutrons are created by either direct nuclear interaction and spallation reactions, or by evaporation from excited nuclei [Bertini, 1969]. These reactions typically occur within the first meter of the surface. Neutron evaporation yields a Maxwellian energy spectrum peaking at ∼8 MeV; spallation and charge-exchange reactions yield a continuum energy spectrum with energies ranging from tens of MeV to several GeV. Subsequent interactions of these “primary” neutrons with the nuclear constituents of near-surface material produce an equilibrium energy distribution both below and above the surface of the Moon. The neutron population at energies greater than approximately 0.5 MeV is called the “fast neutron” population. At lower energies, a different spectrum develops as a result of multiple elastic and nonelastic collisions between the initial cascade-generated neutrons and the nuclear constituents of the surface. The resultant spectrum below ∼500 keV has two distinct energy regimes, epithermal and thermal. In the epithermal range, where losses of energy due to nonelastic nuclear interactions are small, neutrons scatter down at a nearly constant fractional rate. This results in a flux spectrum proportional to E−1 [Fermi, 1950; Drake et al., 1988]. In contrast, the flux distribution at thermal energies is dominated by a two-way energy exchange with nuclei of the moderating material. In this energy range, neutrons gain energy as fast as they loose it and thereby develop a Maxwellian distribution function. The neutron population at thermal energies builds up in amplitude until the rate of injection from higher energies equals the rate of absorption due to thermal capture, plus the rate of loss to space [Fermi, 1950; Feldman et al., 2000b]. Typically the boundary between the “epithermal population” and “thermal population” is approximately at 0.1 eV, an energy below which neutrons are either scattered up by thermal motions or are significantly lost through absorption reactions.

[6] The Moon is a perfect benchmark for neutron spectroscopy. The planet is deprived of atmosphere, so that cosmic rays reach the surface without being absorbed and neutrons can escape the surface without being scattered further or absorbed. In addition, because there is no atmosphere, spacecraft can orbit close to the surface and thus get maximum count rate with a high spatial resolution. Furthermore, the Moon has a characteristic composition pattern (dichotomy between Fe/Ti-rich mare and Al-rich highlands), which is broadly known from Clementine spectral reflectance. Finally, from sample returns, the lunar regolith is recognized to be hydrogen poor at equatorial latitudes (<100 ppm). This a priori information has helped develop our data reduction.

2.2. Sensor Specifications and Collection Principles

[7] Detailed descriptions of the LP neutron and gamma-ray spectrometers (LP-NS, LP-GRS) are given by Feldman et al. [1999, 2004]. However, to maintain self-consistency in this paper, some description of the spectrometers is given here. For more details, the reader is referred to the above referenced manuscripts.

2.2.1. LP Neutron Spectrometer

[8] The LP-NS consists of a pair of 3He gas proportional counters. They have active volumes that are 5.7 cm in diameter and 20 cm length, and are pressurized to 10 atm. Neutrons are detected by being absorbed by 3He through the 3He(n,p)3H reaction. The reaction products have a combined energy of 764 keV that is absorbed and detected by the proportional counters (e.g., Knoll [1989] for details of radiation detection technology). One of the counters is covered by a 0.63 mm thick sheet of Cd. Since Cd very efficiently absorbs neutrons having energies less than 0.4 eV, the Cd covered counter only responds to epithermal neutrons. The other counter is covered by an equivalent layer of Sn, which is transparent to neutrons of all energies. The Sn covered counter therefore responds to both thermal and epithermal neutrons. Every 32-s, the pulse-height spectrum of each 3He counter is measured using a 32-channel analog to digital converter (ADC). In addition to the 32-s pulse height spectra, the total counts within an adjustable window around the spectrum peak are sent to ground at 0.5-s intervals.

2.2.2. LP Gamma-Ray Spectrometer

[9] The LP-GRS contains a 7.1 cm diameter × 7.6 cm long bismuth-germanate (BGO) crystal, which primarily detects gamma rays in the energy range between 500 keV and 9 MeV. The BGO crystal is surrounded by a 12 cm diameter by 20 cm long Anti-Coincidence Shield (ACS). The ACS is a plastic scintillator (Bicron BC454) composed of hydrogen, carbon, and 5% by mass of natural boron. The ACS is used in anticoincidence with the BGO to exclude cosmic-ray events and reduce the effects of escaping radiations from the BGO that would otherwise decrease the gamma-ray signal-to-noise ratio. In addition, the ACS is used to detect the flux of fast neutrons (E = ∼500 keV to a 8 MeV) and moderated neutrons (E < 500 keV).

[10] The process for detecting moderated and fast neutrons is as follows: (1) Upon entering the ACS, neutrons undergo multiple elastic scattering collisions with hydrogen and carbon nuclei of the BC454 plastic. These collisions are rapid and efficiently lower the incident neutron energy to the thermal energy range in a few tens of nanoseconds. If the incident neutron energy is greater than ∼500 keV, the energy loss from this process is detected by the photomultiplier (PMT) on the ACS. (2) Thermal neutrons react with the boron to produce an excited lithium nucleus through the reaction 10B(n,α)7Li* + 2.8 MeV. The energy deposition of this reaction is clearly identified by the electronics. This reaction occurs on average 2.1 μs after the first process; this delay is given only by the amount of boron within the plastic. (3) The lithium de-excites simultaneously by emitting a gamma ray at 478 keV which is detected, which interacts some of the time in the BGO crystal. When the first two charged-particle recoil interactions are positively detected, a fast neutron has been registered. When processes 2 and 3 are detected, but the first one is missing, a moderated neutron has been registered (i.e., it has an energy of that is <800 keV). Two functions are carried out by the GRS front-end electronics to realize the logic above: a time-correlated pair of ACS interactions that occur with an exponentiation time constant of 2.1 μs and a coincident pair of ACS and BGO interactions (details are given by Feldman et al. [2004]).

[11] As with the LP-NS, measurements with the LP-GRS are obtained every 32 seconds s. The sum of all single events within the ACS, coincident with a BGO interaction, yields the measure of the total flux of moderated neutrons. The sum of all double time-correlated events within the ACS yields a measure of the total flux of fast neutrons. In addition, for fast neutrons the pulse height from the multiple proton recoil collisions (first process) yields a 16-channel energy spectrum between ∼0.6 and ∼8 MeV.

2.2.3. Data Reduction

[12] To organize the entire data reduction procedures for neutrons, different levels of processing have been defined (Table 1). Level 0 comprises all science and housekeeping data returned by the spacecraft. For level 1 data, corrupted and unusable records have been removed. Additional information has also been introduced to level 1 data, such as spacecraft position (altitude, latitude, longitude). Simultaneously, the data set is broken into pieces that correspond to different phases of the mission (that are defined by the spacecraft altitude and spin direction). At level 2, data have been corrected for observational biases and the response function of the instrument. In addition, several normalizations have been made to obtain normalized counting rates. Within levels 0-1-2, the data remain organized sequentially with time. Finally, level 3 data contain parameters that have been summed and mapped onto the Moon. The following sections describe how the data are organized and corrected to form maps.

Table 1. Levels of Data Processing for the Reduction of Neutron Data From Lunar Prospector
LevelData Processing
0all data returned by the spacecraft
1time series of “scientifically exploitable” neutron data
2time series of “processed” neutron data
3maps of neutron data ready for scientific interpretation

3. Initial Processing (Level 0 to Level 1)

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Neutron Spectroscopy on Board Lunar Prospector
  5. 3. Initial Processing (Level 0 to Level 1)
  6. 4. Reduction of Systematic Uncertainties (Level 1 to Level 2)
  7. 5. Mapping Neutron Data (Level 2 to Level 3)
  8. 6. Summary
  9. Acknowledgments
  10. References
  11. Supporting Information

[13] Level 0 data consist of a set of time records for different neutron products and housekeeping data. All quantities use the same 32-s resolution time baseline. The transformation to level-1 consists of (1) checking for corrupted level-0 data; (2) removing records that are obviously erroneous; (3) reformatting the data; and (4) integrating auxiliary and support data.

[14] Before describing the detailed processing, two rules are defined when removing unusable records of the data set: (1) Homogeneity: when one data point is removed because it is corrupted, other data at the same time are also removed to maintain time coherence of the whole data set (e.g., if an epithermal count rate is corrupted, the corresponding fast count rate is also removed from the data set, even if it appears valid). In consequence, there is just one single time baseline for all data products of level-1. This rule greatly eases inter-comparisons amongst all data products. The rest of the data reduction is thereby streamlined because then corrections (like the response function) apply the same way to all the different neutron products. (2) Conservative approach: when in doubt, we do not hesitate to be generous on the size of corrupted data regions, to be sure to include all bad records. Both rules are reasonable because the data set is large and provides very good statistical precision.

3.1. Raw Data (Level 0)

[15] Level 0 data are binary packets, formatted on board the spacecraft and relayed to the Los Alamos National Laboratory through the NASA Ames Research Center. Packets from the spacecraft contain science and housekeeping data for the NS, APS, and GRS subsystems. The first action is to read binary files and check for errors. Bad telemetry data are identified by checking synchronization words at appropriate positions in the data string; data cannot be recovered when there are lost synchronization words. All neutron science (NS and GRS data) and housekeeping products are sorted and tagged with a time from the onboard computer. Transformations between spacecraft clock and UTC time are performed on the ground.

3.2. Time Baseline

[16] All data records are 32 seconds s long. The time tag is at the middle of the acquisition range. The start time is when the instruments were first turned on (7 January 1998 at 03 h 59 mn UTC) and the final instrument turn off happened 19 July 1999 at 0 h, a few days before the spacecraft crashed near the Lunar South pole. Therefore, for the duration of the Lunar Prospector mission, there should be ∼1.5 million data records. We shall refer to “time series” as the time-organized set of these data records.

[17] To further organize the neutron time series data, we will classify the data sets using the following ideas (Table 2): (1) “Data sets” are continuous periods of time delineated by the spacecraft attitude and altitude around the Moon. The cruise phase is defined as the first data set and includes data taken before the LP orbit was circularized at 100 km altitude. Subsequent periods correspond to various spacecraft altitudes above the surface. Some intermediate periods are also of interest when the spacecraft spin axis was not aligned with the lunar rotation axis. See Table 2 for details of each period limits and naming convention. Hereafter we shall refer to LP_high1 as the data set when the spin axis was pointing toward the north ecliptic pole and the altitude was ∼100 km; LP_high2 refers to the data set having an altitude of ∼100 km, but the spacecraft spin axis pointed toward the South ecliptic pole; LP_low refers to the data set having an altitude of 30–40 km with the spin axis pointing southward. These same data sets were also defined for the LP-GRS data as described by Lawrence et al. [2004]. (2) “Map cycles” are defined as continuous periods of time that are half the sidereal rotation month (27.322 days divided by 2). This is the time required for the LP spacecraft to cover the entire lunar surface. Considering that two consecutive orbits are separated by ∼1.07° in longitude, which is smaller than the resolution of the instruments (section 5.3), the entire surface is completely mapped every map cycle. The first map cycle starts on 16 January 1998 at 0 h UTC. The full neutron data set covers 41 map cycles, the last one being incomplete (only 3 days long).

Table 2. Data Sets for the Neutron Studya
NameStart DateStart TimeMap CycleDescription
  • a

    Dates are year/day of year h:mn:s UTC. Variances for the spacecraft altitude are always ±10 km at 10 or 90-percentile levels. In the text, other data sets are LP_high2 = LP_high2a + LP_high2b and LP_low = LP_low1 + LP_low2.

LP_cruise1998-00809:36:00-turn-on; first science data
LP_high11998-01600:00:0001–20S/C at 100 km altitude
LP_flip1998-27816:05:0020flip spin axis from north to south direction
LP_high2a1998-28015:50:0020–23S/C at 100 km altitude
LP_leonid1998-31915:41:0023spin axis reoriented to reduce meteorites hazards
LP_high2b1998-32320:56:0023–25S/C at 100 km altitude
LP_low11998-35318:11:0025–28S/C at 40 km altitude
LP_low21999-02906:55:0028–41S/C at 30 km altitude; turn-off on 1992-200 at 00:00:00

[18] Table 3 summarizes the volume of data for the three primary data sets. The rate of data acquisition is ∼95% of what is theoretically possible, considering the duration of the mission and the constant acquisition rate at 32 s.

Table 3. Number of Data Points for the Primary Data Setsa
Data SetDuration, daysMax Possible Data PointNumber of Level 0 DataNumber of Level 1 Data
  • a

    The maximum number of data points correspond to one measurement every 32 s for the data set duration. The volume of acquired data at level 0 is normalized to the maximum possible number of data points to derive the percentages in parentheses. The volume of workable data at level 1 is normalized to the volume at level 0.

LP_high1262.67709 209684 468 (96.5%)570 843 (83.4%)
LP_high268.88195 974180 133 (96.86%)157 446 (87.4%)
LP_low211.24570 354539 859 (94.65%)439 480 (81.4%)

3.3. Available Data

[19] Level 0 contains all science and housekeeping data. Only housekeeping data that are of interest for data reduction are transferred to level 1. For science data, corrections and modifications need to be made to the primary neutron products before they are considered level 1 data. The epithermal neutron count rate (variable = HeCd) is built from the sum of counts in channels 15 to 30 of the pulse height spectrum. The full pulse height spectrum is also transmitted at level 1 (variable = HeCd_pulse) because of its usefulness for data reduction. The same applies to the thermal+epithermal neutron count rate (variable = HeSn) computed from the pulse height spectrum (variable = HeSn_pulse). The moderated neutron count rate (variable = Cat2epi) is the sum of category 1–2 data of GRS. The fast neutron count rate (variable = fast) is computed from “late time interaction minus early time interaction” of category 3–4 data of GRS (sum of channels 6 to 35) as described by Feldman et al. [1999]. Table 4 contains all variables available at level 1.

Table 4. Summary of Data Available at Level 1a
Variable NameTypeDescription
  • a

    Most variables are inherited from level 0; a few are introduced at level 1. All variables set on the same 32-s time baseline.

  • b

    Variables inherited directly from level 0.

  • c

    Variables built from level 0 data.

  • d

    Variables built on the ground from external sources for 32-s and 8-s resolutions.

Time Baseline
Vcdubscalarspacecraft clock
TimecscalarUTC time
 
Primary Science Data
HeCdcscalarcount rate of epithermal neutrons (>0.4 eV)
HeSncscalarcount rate of thermal + epithermal neutrons (0–0.4 eV)
Cat2epicscalarcount rate of moderated neutrons (0–0.8 MeV)
Fastcscalarcount rate of fast neutrons (0.8–8 MeV)
 
Secondary Science Data
HeCd_pulsebarray (32)pulse height spectrum for HeCd channel
HeSn_pulsebarray (32)pulse spectrum for HeSn channel
HeCd_spinbarray (64)high-resolution (0.5 s) HeCd data
HeSn_spinbarray (64)high-resolution (0.5 s) HeCd data
Fast_spectrumbarray (16)count rate of fast neutron spectrum
Apsscbscalarsum of all APS window count rates
 
Housekeeping Data
Check sumb3 scalarsone check sum for NS + APS, two for GRS
Tempb2 scalarstemperature of the NS and GRS electronic boxes
OverloadbscalarGRS overload
DeadtimebscalarGRS deadtime
Fstatbarray (5)status of the 5 APS windows (on/off)
 
Auxiliary Data
LatitudedscalarS/C latitude
LongitudedscalarS/C longitude (0° to 360° from the Central Meridian)
AltitudedscalarS/C altitude above the sphere of reference (radius = 1738 km)
Spin-angledscalar (64)S/C spin phase
 
Support Data
Topodscalaraltitude of topography at S/C nadir
Albedodscalarsurface albedo (750 nm) at S/C nadir
Local_timedscalarS/C local time (angle Sun-Moon-spacecraft)

[20] In addition to the LP data, information about the spacecraft position is introduced to the level 1 data. In particular, latitude, longitude, and altitude above the ground (sphere of reference having 1738 km diameter), in the Moon frame of reference, were computed by the Flight Dynamics Division of Goddard Space Flight Center and given to the LP team in one-minute increments. These values were then interpolated for the neutron observation time. No attitude data are needed since the spacecraft is spin stabilized, except for the direction of the spin axis (northward or southward of the ecliptic).

[21] Finally, new variables have been added to facilitate the data reduction. First, the spacecraft local time, i.e., the angle (in hours) between the Sun, Lunar Prospector and the Moon, was calculated. The calculation for obtaining local time uses a standard routine which calculates the latitude and longitude of the subsolar point in the Moon reference frame. The local time is necessary to determine whether the spacecraft is traveling on the nightside or dayside of the Moon. In addition, it is straightforward to calculate from local time the angle between the spacecraft orbit plane and a plane that contains the vector to the Sun and the Moon rotation axis (known as the β angle). Second, the topographic altitude at the nadir footprint is determined from the Clementine Lidar data [Smith et al., 1997], although these data are poor poleward of ±70° latitude. The topography information (−13.5 km/+8.5 km around a sphere) must be taken into account because elevation variations are comparable to the spacecraft flight altitude (which was ∼20 km from the sphere of reference at minimum). Later this quantity will be smoothed to match the neutron surface resolution. Third, the surface albedo at 750 nm from Clementine UVVIS instrument is used to help distinguish between mare and highland regions [Lucey et al., 1998].

3.4. Check Sums

[22] Three check-sum numbers were introduced into the GRS/NS/APS data stream to test the integrity of data transmission to Earth. Because of the spacecraft simplicity, there was no possible recovery for the data preceding a check sum (once downloaded to Earth, no copy of the data was saved on board). When a bad check sum occurs, science data are not necessarily corrupt, but according to our caution principle, we removed the whole packet. Data with bad check sums correspond to a nonnegligible 4.9% of the entire mission data set. Events with bad check sums are distributed everywhere over the Moon. Figure 1 shows this mapping, but only when the density in longitude/latitude is above an arbitrary threshold. There is a clear bias of bad check-sum events at the Moon terminator. The explanation is the following: at the terminator the radio beam sent toward Earth was also reflecting off of the nearby lunar surface and arriving at Earth on top of the original beam. This geometric effect introduced noise in the receiver and altered the data.

image

Figure 1. Regions of the Moon where bad check sums have been detected in the data stream for the whole level 0 data set. Only areas where the density of bad check sums is larger than 100 per 10° × 10° pixels have been plotted.

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3.5. Solar Energetic Particle Events

[23] The neutron and gamma sensors on board LP are very sensitive to Solar Energetic Particle (SEP) events. During such events, the counting rates of all neutron products simultaneously rise to saturation (see Figure 9, described later). NS low-energy products (HeCd, HeSn) respond slightly faster than GRS high-energy products (Cat2epi, Fast), but the GRS products return to quiet levels faster than the NS products. We have used proton fluxes measured at geosynchronous orbit by GOES-8 [Onsager et al., 1996] to monitor SEP events. The best match with neutron data is obtained with the 32–83 MeV proton flux channel (Figure 2). Manual inspection for the 18 months of the LP mission shows that every major SEP event observed by the NS and GRS neutron data is confirmed by the GOES-8 proton data. Reciprocally, each time proton fluxes rise above 0.03 proton/s/sr/cm2/MeV (5 hour-averaged data), a sudden increase of the neutron counting rate is observed. We have defined by hand time limits of sixteen SEP events (Table 5). NS and GRS neutron data measured within these limits were removed from the level 1 data set; 10.6% of the initial level 0 data were lost by this edit.

image

Figure 2. Neutron count rates during a period of Solar Energetic Event (SEP). Epithermal and fast data are in counts/32-s (times a scale factor). GOES 8 data are proton fluxes from 32 to 83 MeV. A rapid increase of proton intensity at geosynchronous orbit is simultaneously observed in neutrons around the Moon.

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Table 5. SEP Events That Have Affected Substantially the LP Data Collectiona
EventStartStopMap Cycle
  • a

    Through loss of data. Regarding neutrons in fraction of days since 1 January 1998 (0 hr).

01110.2116.807–08
02121.5131.008–09
03231.8232.516
04236.3243.517
05266.0275.919–20
06291.9292.621
07311.4312.622
08318.1321.623
09326.2326.723
10328.0329.023
11385.8389.228
12479.6481.534–35
13494.5495.036
14512.4513.537
15517.7522.837–38
16526.8527.638

3.6. Off Limits

[24] In addition to SEP events, occasional out-of-range data were observed for reasons that are unclear. Such events are randomly distributed. It is easy to screen them according to some acceptable limits for each neutron product. The limits we have set on neutron data are in counts per 32-s: 300 < HeCd < 900; 600 < HeSn < 1800; 100 < Fast < 800; 60 < Cat2epi < 600. These anomalous counting rates contribute for less than 3 per mil of the data set, in addition to those occurring during SEP events or correlated to bad check sums.

3.7. APS Cross-Talk

[25] Early in the LP mission, it appeared that high currents from the APS were inducing a noise signal on the NS sensors via cross talk between the NS/APS signal wires that were located close to each other. Because this noise in the NS data sometimes reached unacceptable levels, the APS was turned off during portions of the mission to save the quality of the neutron data. Several observational facts, as explained below, suggest that the origin of the high currents on the APS is due to a deterioration of the aluminum light-blocking foils that cover some of the faces of APS.

[26] The APS sensor consists of five pairs of 3 cm by 3 cm square ion-implant silicon detectors, each pair placed on one face of a cube. Each detector is fully depleted to a depth of 55 μm, which is sufficiently thin to reduce the proton background in the prime energy range of Rn-decay alpha-particle lines (between 4.1 MeV and 6.6 MeV) to manageable levels. They are covered by thin, Al-coated polypropylene foils to exclude sunlight, and collimated to a 90° field of view (FOV) at half maximum. The combined FOV of the 5 faces provides about 3.5π sr coverage, the only blind spot is in the direction of the spacecraft bus.

[27] The APS is an intrinsically low count rate instrument [Feldman et al., 2004]. Sudden counting rate increases by a factor of two or more are not expected under normal circumstances outside of SEP events. However, from the sum of all sensor APS counting rate data available (sum of all faces) we have observed times when APS count rates are very high. Figure 3 shows 48 days of APS data early in the mission. There are clear instances between 25 January and 6 February 1998 when the APS counts were far above nominal values (i.e., greater than 102 cts/32 s). To understand what is happening, we isolate two days of 4–5 February (Figure 4). The histogram of counts has a bell-shape at low values and a long tail (top panel). From this histogram, we estimate that “abnormal” points have values greater than ∼10 counts/32-s. Indeed, on a time series plot (bottom panel) these values are far above a low count background. Such data points are not consecutive in time, but are organized in short bursts equally separated by 2 hours, which is the period of the LP orbit. For the 48 days of Figure 3, we generalize the histogram technique above: a program searches automatically, on a daily baseline, for counting rates that are greater than the high nominal counting rates. Next we order the data, not by time or longitude on the surface, but by local time (Figure 5). This figure shows that all times of high counting rates are well localized in the local-time/latitude space: above 85° North (note that a local time near the pole is not very meaningful) and a narrow window near 16 h and 50° North. This is much more confined than the excursion in the local-time/latitude space for that period of time. Even within these 2 regions, the density of abnormal points is ∼1/4 of the total density of measurements.

image

Figure 3. Measurements by the APS detector early on the mission. Occasionally, several data points go above standard levels around 6 February 1998.

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image

Figure 4. For a 2-day period (out of Figure 3), details of the algorithm that isolates measurements generating cross-talk with NS data. (top) Histogram of APS data. The dashed vertical line indicates the limit of standard counts rates. (bottom) Results of the algorithm; all data points marked by a star have been tagged as “abnormal.”

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image

Figure 5. Within the 48-day period of Figure 3, APS measurements are mapped in spacecraft local time and latitude. Data points tagged “abnormal” are marked by a star. They are mainly located at the north pole and in a narrow window at 16 h local time and 50° latitude North.

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[28] The most probable scenario to interpret these data is that of a “light-leak” through one or more of the Al foils of the APS onto the silicon detectors. It is thought that when the spacecraft separated from the injection stage of the rocket, one of the poleward-facing APS Al foils was punctured. When the LP spacecraft went into orbit around the Moon, light passed through this pinhole under certain orientation conditions. The sunlight induced high counting rates well above the normal state of the instrument. Furthermore, the NS and APS were located on the same boom and had electronics located very close to each other. The high current on APS cables then interfered with the signals on the NS cables inducing a noise signal that resulted in an abnormally high neutron counting rate. The highly localized data in local-time and latitude support the idea of a phenomenon related to the illumination of the Moon and spacecraft. Specifically, it was determined that face 5 of the APS (looking nadir over the north pole during the LP_high1 data set) of APS was the detector causing the noise. Therefore, during the early part of the mission, the preamplifier of face 5 was disconnected from the main APS amplifier in the Electronic Subsystem located on the spacecraft bus. As shown in Figure 6, the abnormal APS count rate was significantly reduced when face-5 was turned off. These high counting rates, however, do not completely disappear. It seems that, even with the preamplifier disconnected, light through the hole in the foil can still bounce around inside of the APS chassis to activate the other sensors in the APS sensor head. For that reason, the APS instrument was completely turned off for two long periods of time toward the end of the mission: 9 February to 22 April 1999 and 25 May to 29 July 1999.

image

Figure 6. APS data during May–June 1998, when “abnormal” points were very frequent. One of the APS faces was turned off to investigate its cross-talk with NS data.

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[29] As the mission continued, the frequency of abnormal counting rates increased. The reasons for this increase could be that the pinhole in the Al foil of sensor 5 was stretching out to let more stray light and/or other Al foils were losing their Al cover. Figure 7 summarizes our search algorithm for the whole mission. Approximately 31 thousand points are found (2.1% of the whole data set outside SEP events) at various latitudes and local times. For 7/8 of the affected data points, the spacecraft was on the lunar dayside (6 h < local time < 18 h), which supports the light leak explanation. However, 1/8 of the data are on the night-side where there should be no light leak. Without reconsidering the light leak interpretation, we blame our search code and raise the possibility of other events that can drive high currents in the instrument (e.g., electron events). To be conservative, even these points (fewer than 35 cumulative hours) are excluded from the data set.

image

Figure 7. Approximately 31,000 data points generating cross-talk with NS data, mapped in local time and latitude. Seven-eighths of the points are on the dayside.

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[30] The effects of APS light-leak events on neutron data are very subtle. They redistribute counts within the pulse height spectrum toward low and high energies. To illustrate this matter, we select a brief period of time, 18–24 December 1998, during which an APS light-leak event occurred (Figure 8), as seen from the APS data (middle panel). On the same timescale we plot the first (channel 0) and last (channel 31) channels of the epithermal pulse height spectra. Both show an enhancement of count rate during the APS event. It is larger for channel 0 than for channel 31 (the former is plotted on a log-scale). Since there are more counts within these two channels, there are fewer in between, particularly from channel 15 to channel 30, which are used to establish the primary quantity HeCd. Indeed, HeCd values are ∼1% lower during APS event. If we bracket the events, not in time but in local time as shown above, the reduction of HeCd is ∼2%. Similar effects can be demonstrated with HeSn data. Since we are looking for very small variations of HeCd to detect H on the Moon [e.g., Feldman et al., 1998, 2000a, 2001], we decided to remove from the data set records that were acquired during APS light-leak events. Although the APS light-leak effect does not apply to the GRS neutron products, we followed our principle of homogeneity and removed data from APS light-leak periods from these quantities as well. At the end, 2.1% of the data were lost because of the APS light-leak effect.

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Figure 8. APS cross-talk effects on NS data for a 6-day period in December 1998. All data are in counts/32-s. (middle) APS data with several “abnormal” values around 21 December 1998. High values of (top) channel 0 and (bottom) channel 31 HeCd pulse height data match APS “abnormal” data points. The correspondence is better for channel 0.

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3.8. Pulse Height Analysis

[31] Pulse height spectra in the NS neutron data were very informative on the health of HeCd and HeSn primary quantities. The tests just described were used to remove most of the out-of-shape pulse height spectra. SEP events for instance, completely distort the shapes of these spectra. For APS events, it is more subtle as shown above: low and high channels are notably affected, but it is barely visible elsewhere. Setting a spectrum filter is a way to check that tests above have removed most of bad records. Figure 9 shows our acceptance filter for pulse spectra. A reference spectrum is derived from all mission data points, except those eliminated by other tests (limits, SEP, check sum, APS). For each channel, we calculate the dispersion around this spectrum, in terms of a standard deviation. Our “acceptance envelope” corresponds to ±5 σ of the reference spectrum. It is plotted between channels 15 and 30, where it is most significant. A few dozen spectra only have a single data point out of these limits. As expected, this is a very low number. If the test would have been run on level 0 raw data, excluding bad check sums, 3% of the data set would have been marked (mostly because of SEPs). As an example, on the same figure we have plotted the mean spectrum during the SEP event of Figure 2 (25–26 September 1998). It is well above our limits.

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Figure 9. Pulse height spectrum from HeCd data. Unit is counts/32-s. The reference spectrum is the mean of all data points at level 1. The shaded area is the acceptance filter that corresponds to ±5 s from the calculation of the reference spectrum. As an example, the spectrum on top corresponds to an SEP event (same unit as for the reference spectrum).

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3.9. Summary of Level 1 Data

[32] The order of the processes applied to our data filter procedure just mentioned is relevant. We start removing records that are obviously unusable (check sum and SEP) and carry out the more complex procedure for APS cross-talk next. Finally the pulse-height acceptance test is used to ensure that no bad records are left over. Table 6 summarizes the effects of each process. At level-1, 16.4% of level-0 data were removed. This is a small amount (equivalent of ∼3.2 Map cycles) considering the conservative approach we have applied. Furthermore, the level 1 data set is ∼80% of what is theoretically possible. See Table 3 for the volume of level 1 data for the primary Lunar Prospector data sets. Figure 10 illustrates the variations of the primary science counting rates with time for the entire level 1 data set. All of LP neutron science data is contained within the vertical deviations of these four time series values.

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Figure 10. Neutron products at level 1 as a function of time: thermal plus epithermal (HeSn), epithermal (HeCd), moderated (Cat2epi), and fast energy range. All units are in counts/32-s. The HeSn and fast data have been offset for convenience.

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Table 6. Number of 32-s Records Available for Reduction of Neutron Dataa
 Number of 32-s RecordsNotes
  • a

    Steps to clean the data set are detailed. This concerns the whole LP mission around the Moon, except for cruise data.

  • b

    Bad check sums and SEP events being already removed.

Maximum possible1,482,300 
Measured data point = Level 01,444,43797.4% of maximum
  Bad check sum71,562 
  SEP event153,625 
  Off limitsb3492 
  APS cross-talkb31,055 
  Pulse height acceptanceb638 
Available data set for science = Level 11,193,73282.6% of Level 0

4. Reduction of Systematic Uncertainties (Level 1 to Level 2)

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Neutron Spectroscopy on Board Lunar Prospector
  5. 3. Initial Processing (Level 0 to Level 1)
  6. 4. Reduction of Systematic Uncertainties (Level 1 to Level 2)
  7. 5. Mapping Neutron Data (Level 2 to Level 3)
  8. 6. Summary
  9. Acknowledgments
  10. References
  11. Supporting Information

[33] The data at level 2 should be, as much as possible, independent of observational biases. They are still neutron count rates (units: counts per 32-s or 8-s) organized by time. The number of records is inherited from level 1. The conversion from level 1 to level 2 is the heart of our data reduction procedure, which is a succession of processes that are either time-dependent or space-dependent. Time-dependent biases result from changing circumstances around sensors that affect measurements. Among these varying parameters are the flux of cosmic rays, the sensor functional parameters (mostly high voltage), the temperature of the electronic box, gains, and the spacecraft altitude. Some of these changes were induced by the operation team to optimize data collection, while most were out of human control. Practically, reduction of time-dependent uncertainties lowers the measured standard deviation. For counting rate instruments, such as neutron and gamma spectrometers, the minimum standard deviation is that of a Poisson distribution [Peebles, 1993, p. 181]. Therefore our data processing aimed at approaching the level of Poisson statistics over given regions of the Moon (see section 5.2 for details in relation to mapping procedures).

[34] Space-dependent biases result from the spacecraft position around the Moon, specifically longitude and latitude. As everything should not depend on longitude because of LP operations mode, space-dependent biases reduce to latitude changes only. This is later referred to as the instrument latitude response function. In contrast to time-dependent biases, latitude biases repeat map cycle after map cycle. While some corrections are common to all primary data sets (i.e., background level, cosmic ray, and altitude variations) other corrections, such as the variation of the latitude dependent response function are specific to each instrument. The level 1 to level 2 processing is performed in priority for LP_high1 and LP_low data sets. The LP_cruise data set is particularly useful to determine the instrument background levels. The LP_high2 data set helps to understand north/south asymmetries of the sensors. Data available at level 2 are summarized in Table 7.

Table 7. Summary of Data Available at Level 2
Variable NameTypeDescription
  • a

    Variables inherited directly from level 0.

  • b

    The fast neutron comes with a 16-element energy array.

Time Baseline
TimeascalarUTC time
 
32-s Science Data
Epithermalscalarcount rate of epithermal neutrons (>0.4 eV)
Thermalscalarcount rate of thermal (0–0.4 eV)
Moderatedscalarcount rate of moderated neutrons (0–0.8 MeV)
Fast_scalarscalarcount rate of fast neutrons (0.8–8 MeV)
Fast_spectrumbarray (16)count rate of fast neutron spectrum (0.8–8 MeV)
 
8-s Science Data
Epithermalscalarhigh-resolution epithermal data (>0.4 eV)
Thermalscalarhigh-resolution thermal data (0–0.4 eV)
 
Auxiliary Data
LatitudeascalarS/C latitude
LongitudeascalarS/C longitude (0° to 360° from the Central Meridian)
AltitudeascalarS/C altitude above the sphere of reference (radius = 1738 km)

4.1. Cosmic Ray Proxy

[35] For decades it has been known that the flux of galactic cosmic rays (GCR), which initiate neutron production, is isotropic. However, the GCR flux is modulated within the Solar System by solar activity. The higher the solar activity, the fewer cosmic rays can reach the inner Solar System, and hence the lunar surface. The flux of cosmic rays, its intensity as well as spectral shape, is therefore modulated with time. The physics of neutron production is linear with GCR flux to a very good approximation, and therefore neutron fluxes must be normalized to the time varying rate of cosmic rays. One challenge for the LP data reduction, especially for thermal and epithermal products, was to find a reliable indicator for the neutron production rate, and hence the cosmic ray flux.

[36] To evaluate the reliability of a cosmic ray indicator, we shall check it against epithermal data. A snapshot data set is constructed from HeCd level 1 data. Data points are smoothed (boxcar average) in time and sorted with latitude. To ensure a large density of points, only values poleward of −80°, near the South Pole, are used as reference for all other points taken under the same geometry. A correction for spacecraft altitude is completed with a solid angle relation normalized to 100 km, as justified in the next section. We do not expect this construction to be a cosmic ray proxy by itself, but to mimic variations of the cosmic ray flux.

[37] First we compare with proton data from the NOAA space environment satellite GOES-8 at geosynchronous orbit [Onsager et al., 1996]. Proton energies are above 850 MeV with a 5-mn resolution for the January–September 1998 period. Although at ∼1/10th of the distance to the Moon, and occasionally within the Earth magnetosphere, variations of proton data at geosynchronous orbit about the Earth match variations of the south pole HeCd snapshots (Figure 11, top panel), particularly early in the mission, but with discrepancies after May 1998. Second we compare with proton data from the NASA Advanced Composition Explorer (ACE) at the Lagrange point L1 (4 times the Earth-Moon distance at closest) over the same period of time. Proton data are hourly averaged from the Cosmic Ray Isotope Spectrometer (CRIS) [Stone et al., 1998]. The match appears better than for GOES data (Figure 11, middle panel), with minor divergences between May and July 1998. Both comparisons justify the need for normalization to the flux of cosmic rays. With practice, we found none of these external data sets to qualify for a cosmic ray proxy over the whole mission. Other attempts have been conducted using Earth-based neutron monitors [Lawrence et al., 2004], with a limited success due to changing conditions within the Earth magnetosphere.

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Figure 11. Correspondence of epithermal count rate at the lunar pole (southward of −80°) with four cosmic ray proxies as a function of time from January to September 1998. Epithermal data (black) are in counts/32-s. Other data have arbitrary units, normalized to epithermal data early on the mission. (top) Comparison to GOES 8 proton data above 850 MeV at geosynchronous orbit. (middle) Comparison with proton data from ACE at L1. (bottom) Comparison with onboard data, the GRS overload channel (red) of the gamma-ray spectrum, and the NS overload channel of the pulse height epithermal data (blue). In all cases, the correspondence is inaccurate.

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[38] On board the spacecraft, there are two sensors that have overload channels for high-energy count rates. The first one is simply called “overload” in the level 1 data set. It originates from the GRS, as the sum of all counts above ∼9 MeV. The second is the highest energy channel of the HeCd pulse height spectrum at level 1. Both quantities agree with each other (Figure 11, bottom panel) but they are different from the HeCd snapshots. They both match variations of the ACE and GOES-8 data above. The four quantities we have described are indeed cosmic ray alternatives, but not the one needed to normalize neutron data. The reason is the following: variations of the intensity of penetrating particles are reproduced, but not that of their spectral shape and hence their neutron production efficiency.

[39] Finally, we decided to build a cosmic ray proxy from the intensity of the oxygen 6.2 MeV line of the GRS spectrum, i.e., a quantity that has been already “filtered” by the Moon. As the content of the lunar soil in oxygen is nearly constant (∼43% within ±3%), its intensity depends only on the rate of cosmic rays. The instrument response function from the GRS data reduction publication [Lawrence et al., 2004] is used to decipher effects of latitude. It is a delicate procedure, because the instrument is highly asymmetric. A simple linear relation accounts for the variation of distance to the surface. Then data are smoothed (boxcar average) over one hour, which is half an orbit. Finally to avoid a debate about a possible bias from composition, we used only data points at high latitude, which we cross every orbit. Figure 12 shows our O-line cosmic ray proxy against HeCd snapshot data. The match appears very good and satisfactory through all the data sets. The cosmic ray proxy is normalized to unity for the mean cosmic ray flux between 16 and 19 January 1998. On two occurrences, we note after the fact the quality of the normalization to the cosmic ray flux: see text associated with Figure 19 and Figure 21.

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Figure 12. Correspondence of epithermal count rate at the lunar pole (southward of −80°) with the “oxygen line” at 6.2 MeV (red), which is derived from the GRS instrument. The correspondence is very good from over the whole duration of the mission. Limits of the different data sets are shown.

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4.2. Background

[40] Neutron flux backgrounds in space are low because free neutrons are unstable, with a mean life to beta decay of ∼900 s. To be detected by LP, neutrons must therefore be produced locally. The three components of the NS were therefore placed at the ends of booms to minimize spacecraft neutron flux backgrounds. This separation and the spacecraft's low mass were sufficient to reduce backgrounds to acceptable levels. To determine background levels, we used data acquired during cruise. The LP_Cruise data set is very limited: it starts when the instruments started to return valuable science data (8 January) and stops when the 100-km circular orbit was achieved (16 January 1998). A few major milestones are noted as shown in Figures 13 and 14: three Lunar Orbit Insertion (LOI) burns for capture and circularization of the orbit and a final adjustment to reach the mapping orbit. The first orbits are within 9000 km of the surface, the following ones within 2000 km, 200 km, and finally around 100 km. On 9 January (4 h 30 mn) the spacecraft spin axis was pointed toward the north ecliptic pole for insertion maneuvers. It was maintained in this configuration (with a few adjustments) until the end of the LP_high1 data set.

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Figure 13. Spacecraft distance to the Moon surface as a function of time, from launch to mapping orbit. Only points when neutron data are available have been represented. Maneuvers for Lunar Orbit Insertion (LOI) are represented. The final orbit is polar at 100 km altitude.

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image

Figure 14. Epithermal count rate as a function of time (LP_cruise data set), from launch to mapping orbit. Individual orbits (see with Figure 13) can be followed from neutron data. This is the first evidence of epithermal neutron production by the Moon. Background is very small.

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[41] During this premapping period, there were no SEP events and the flux of incoming cosmic rays was steady. Neutron data (at least for the four primary science products) are available every 32-s, except around maneuvers. We learned from these data (Figure 14, Figure 15), that local neutron production by the spacecraft, referred to as background, is very low. From averages between 9 and 11 January, we obtain for each 32-s accumulation period: 74.4 counts for HeCd, 71.7 counts for HeSn, 17.3 counts for Cat2epi, and 12.5 counts for Fast quantities. This background results mostly from interactions between GCR protons and material local to the spectrometers. The local production of neutrons by cosmic rays interacting with the spacecraft is negligible. 3He gas proportional counters used here for neutron sensors are known to have a very low intrinsic background (such as electronic noise). Since the HeCd and HeSn backgrounds are very similar, the background for thermal neutrons is nearly zero.

image

Figure 15. Same as Figure 14 for fast count rate. There has been a high voltage adjustment within the BGO that is observable. This is the first evidence of fast neutron production by the Moon. Background is very small.

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[42] When approaching the Moon, the background decreased, because the planet fills almost half of the spacecraft sky in mapping orbit, thereby reducing the flux of cosmic rays onto the instrument. For data reduction, we assume that the background varies as a simple function of the solid-angle subtended by the Moon at the spacecraft altitude: bkg = bkgc (1 − Ω/4π), where bkgc is the cruise background and Ω the solid-angle. At closest approach, the instrument background is almost half of its value during cruise.

4.3. Spacecraft Altitude

[43] Variation of count rates with distance to the source is important, as illustrated by Figure 16 for epithermal neutrons. Imagine a sphere of radius 3738 km around the Moon. This boundary is crossed three times as the spacecraft was on 100 × 9000 km altitude orbits and several times at the apogees of 100 × 2000 km altitude orbits. A careful analysis of Figure 16 shows that, at 2000 km from the surface, the epithermal counts are lower for the short orbits than for the long orbits. The explanation is the following: at the short period apogees, the latitude of the spacecraft nadir point (where most neutrons are coming from) is ∼−30° whereas it is around ±60° for the long period orbits. Different latitudes mean different attitudes of the spacecraft above the lunar surface. As explained in the next section, epithermal count rates are always larger at high latitudes than they are near the equator.

image

Figure 16. For the LP_cruise data set, epithermal count rate as a function of distance to the Moon surface. Regions of overdensity correspond to the apoapsis of transition orbits to mapping configuration.

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[44] To avoid deviations of count rates with spacecraft attitude inherent to data collection by the instruments, we have modeled variations of count rates as a function of distance from the Moon. The neutron production at the surface is computed from the Monte-Carlo code MCNPX, from Los Alamos National Laboratory [Waters, 1999]. See details of this simulation in section 5.3, second paragraph. Runs have been performed for epithermal and thermal neutrons for various distances to the Moon surface (Figure 17). Simulation points have been fitted to a simple algebraic function for later use:

  • equation image

where h is the distance to the surface and r the planet radius. τ and η are scaling factors. With η = 90° and τ = ∞, f is a solid-angle law. This equation is seen to approach the simulated count rates (solid line) for large distances. To improve the fit, we truncate the tail of the solid-angle, hence the parameter η. This parameter accounts for nonisotropic emission from the surface: it is not Lambertian, as shown by the output of the MCNPX code, but cut off near the surface. A value of 80° is enough to obtain a very good fit to simulated data (red line) especially for epithermal data. Finally, for thermal neutrons, we introduce an exponential factor to account for the finite lifetime (900 s) of the neutrons. τ = 4000 is the factor that best fit thermal data. Note that beyond 1000 km, beta decay cannot be ignored as more than 4% of the thermal neutrons never arrive at the spacecraft. The match of the model to simulated data is well within the error bars of the measurements. The LP_cruise data set presents a possibility to test the model against data. Data points from Figure 16 have been extracted for latitudes poleward of ±70° for all orbits before 13 January (Figure 18). This figure shows how the background decreases with altitude, and how well the model matches variations of count rates with altitude.

image

Figure 17. Simulated count rates of thermal and epithermal neutrons at the spacecraft. Runs have been performed for a wide range of distances to the Moon surface. Simulation points are fitted by a solid angle law (black), a function that includes solid angle and limb darkening (red), and finally a function that includes solid angle, limb darkening, and the neutron finite lifetime (blue).

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image

Figure 18. For a fraction of the LP_cruise data set, epithermal counts rate above +70° latitude, as a function of distance to the lunar surface. The solid line corresponds to the predicted variations of the background over the same range of distance. The dashed line corresponds to the simulated model that includes solid angle, limb darkening, and the neutron finite lifetime.

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[45] For the rest of the study, the LP_high data set varies between 74 and 128 km altitude, and for the LP_low data set, the altitude varies between 12 and 58 km. With this range of distances, accounting for the neutron lifetime is not necessary. Parameters η = 80° and τ = ∞ for the model will be used. As the spacecraft comes closer to the surface, the lunar topographic relief becomes important for calculating the distance to the surface. From Lidar data on Clementine [Smith et al., 1997], the Moon's topographic relief ranges from approximately −13.5 to +8.5 km. To include this parameter into our data analysis, the topography map is smoothed at 5° resolution. The smoothed topography ranges from −6.0 to +6.5 km. This topographic altitude is averaged to account for the distance to the Moon. To ensure consistency among all data sets, all neutron products are normalized to an altitude of 30 km above the mean sphere. Observe that if LP_high data are normalized to 30 km, they match the count rates of LP_low data but with a poorer spatial resolution. Figure 19 considers HeCd data for 4 data sets that have been corrected for latitude (see next section) and cosmic rays. Data points are averaged in longitude and latitude, and then binned in altitude. All data points organize themselves very well with the model. Note that if the correction for cosmic rays between the high-altitude and low-altitude data sets was not correct, the data at high and low altitude would not be equal.

image

Figure 19. Epithermal count rate as a function of distance to the Moon. Data are averaged in latitude and longitude and binned in height. All science data sets of the missions are concerned. Prior to this figure, epithermal data have been corrected for cosmic ray, background, and the latitude response function (see text). The different data sets match each other and follow predictions of the simulated model (solid line).

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4.4. Epithermal Data

[46] The epithermal data set is the most straight-forward neutron product to build because the dynamic range of the signal is small and most features in the data reveal information about different observational biases. Initial steps for building the epithermal neutron data product have been previously described: normalization to the cosmic ray flux, correction for altitude variations, and background subtraction. Here we describe an additional correction that is applied for APS cross-talk and corrections for variations in the NS response function.

4.4.1. APS Cross Talk

[47] The APS cross-talk noise was corrected before level 1 by eliminating bad data (section 3.7). A definitive solution was to turn off APS toward the end of the mission. A further correction has been made that is related to the temperature of the APS-NS electronics box. Figure 20 shows the temperature of the APS-NS electronic box for all of 1999. When the APS switches off (shaded regions), we observe a drop of temperature, ΔT = −4.5°C. A subsequent rise of the HeCd counts is observed (not shown), which is difficult to evaluate precisely. With good statistics at the poles each time APS is turned off or back on, we have determined a count rate ratio of 0.97 between the on/off state. The NS data are normalized to the most common “APS-on state,” and all HeCd data points when APS is off are divided by 0.97.

image

Figure 20. Variations of the temperature within the shared APS/NS electronic box. When the APS amplifier was turned off (shaded periods) the temperature dropped by 4.5°C.

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4.4.2. Latitude Response Function

[48] The instrument response function has a complex dependence on latitude because the NS sensors are not isotropic. However, it can be well characterized with HeCd data, since these data, when summed over all longitudes, are relatively featureless so that their variations with latitude are on average equal to the variations of the response function. Several empirical searches have yielded the following functional form:

  • equation image

where λ is the latitude. A series of figures will illustrate each of these terms for the LP_high1 and LP_low data sets. For the following discussion, HeCd data have been averaged in longitude and binned in latitude. The vertical dispersion is always very small and is not discussed here. We also introduce the value HeCd′, which is the same data set as HeCd but the latitudes have been switched to minus latitudes. This helps to decipher between symmetric (given by HeCd + HeCd′) and asymmetric (given by HeCd − HeCd′) counterparts of the latitude response function. Other corrections (cosmic rays, altitude) have been applied to the data already.

[49] The first term, f0, represents the symmetric portion of the response function. It includes the cross section of the instrument changing with latitude, as seen from the lunar surface. This function is independent of the latitude sign, and must be flat (null derivative) at the poles. Figure 21 displays the fit of this function to the data (HeCd plus HeCd′), for the two data sets and all latitudes included. Except for the poles, the fits are excellent. At the poles, the hydrogen deposits [e.g., Feldman et al., 2001] reduce the flux of epithermal neutrons. Note that both curves tie at the equator; which justifies after the fact the exactness of the normalization to the cosmic ray flux, via the GRS oxygen line. Min-to-max variations are ∼11.5% for the LP_high1 model. When the spacecraft is at low altitude, min-to-max variations are ∼6.6%.

image

Figure 21. Symmetric counterpart (f0) of the HeCd latitude response function for two different altitudes, the LP_high1 and LP_low data sets. Data points have been averaged in longitude and binned in latitude. They are fitted by two polynomials of cos2(λ).

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[50] The second term, fv, accounts for the position of the NS boom on the spacecraft. Since the boom is located about equation image from the spacecraft bottom, the mean shadow of the spacecraft on the instrument is a function of latitude. As shown Figure 22 (data are HeCd minus HeCd′), this effect is well represented by a straight line, and it is null at the equator. The two observations confirm our interpretation of a spacecraft shadowing: when the spacecraft orientation is flipped from the LP_high1 data set to the LP_low data, this effect has changed sign. Furthermore, the shadowing effect is larger at low altitude, as expected.

image

Figure 22. Asymmetric counterpart (fv) of the HeCd latitude response function for two different altitudes, the LP_high1 and LP_low data sets. Data points have been averaged in longitude and binned in latitude. They are fitted by two linear function of λ.

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[51] The third term, fa, is an aberration effect that depends on the motion of the spacecraft. It is preceded by a scalar ɛ that is +1 when the spacecraft is moving toward the north pole, and −1 when moving toward the South pole. Figure 23 shows a fit to the counting rate data when the spacecraft is moving northward minus the measured rates when it is moving southward. The curve passes through zero at the equator. This function appears to be the same for LP_low and LP_high data sets (see also section 4.8).

image

Figure 23. Motion-dependent counterpart (fa) of the HeCd latitude response function for two different altitudes, the LP_high1 and LP_low data sets. Data points have been averaged in longitude, binned in latitude, and sorted for the direction of the spacecraft. The difference when the spacecraft is moving toward the north pole minus toward the south pole is fitted by a sin(2λ) function.

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[52] One rule of this modeling is to minimize the number of free parameters for the latitude response function, R. We obtain only five (a0, a2, a4, b, c) to account for the different asymmetries and the motion of the spacecraft. All parameters except c depend on spacecraft altitude. Figure 24 is the final fit to the data with the 5 parameters at high altitude (Table 8). As seen, there is a large difference between the response functions for the up and down directions. At the poles, the response functions must reconnect. Figure 25 is the same fit for low-altitude data. When this latitude correction is applied, it is normalized at the equator when the spacecraft is moving toward the north pole for the LP_high1 configuration (spin axis is pointing northward).

image

Figure 24. Modeled latitude response function of HeCd data for the LP_high1 data set and two directions of the spacecraft motion.

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image

Figure 25. Modeled latitude response function of HeCd data for the LP_low data set and two directions of the spacecraft motion.

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Table 8. Numerical Values for the Latitude Response Functionsa
 a0a2a4a6a8bc
HeCd
  LP_high1446.18−250.3589.00--0.26−15.72
  LP_low1375.00−161.0869.83--−0.38
HeSn
  LP_high2787.86−394.00175.79--0.52−95.35
  LP_low2661.51−424.62821.56−779.07288.11−0.77
 a1a2a3a4  c
  • a

    For fast neutrons, it is given for the average of latitude profiles at high and low altitudes. For moderated neutrons, it is given at constant temperature.

Fast
  LP_high431.4140.28−41.68−4.19---
  LP_low428.00−32.88−29.631.51---
Moderated
  LP_low169.466.32−22.92---4.35
4.4.3. Epithermal Data at 32-s and 8-s Resolution

[53] All processes above have been performed using 32-s averaged data. Corrections that have been applied are: background, cosmic rays, altitude, APS cross talk, and latitude. The final product is a flux of epithermal neutrons at level 2. Along with the corrections, it is important to reiterate that the following absolute normalizations have been applied: (1) mean cosmic ray flux between 16 and 19 January 1998, (2) altitude above the surface at 30 km, and (3) latitude effects to the equator. These normalizations have been applied when the instrument is in the following state: the APS is on; the spacecraft is moving toward the north pole; and, the spacecraft spin axis is pointing northward. The ratio of HeCd time series between level 2 and level 1 emphasizes the importance of this data reduction (Figure 26). It varies by ∼45%. Another way of quantifying progress is to compare Poisson statistics and standard deviation (see details in section 5.2). To that end, data have been mapped on the Moon for 4° cylindrical pixels, each containing potentially the same number of measurements since the orbit is polar. Within each pixel (there are 4050 of them), Poisson statistics and standard deviation [Peebles, 1993] (see also section 5.2 for details of this calculation that requires first a mapping of data onto the surface) have been calculated before and after level 1 to level 2 processing (Figure 27). As expected the systematic errors have decreased by as much as a factor 2, to the level of the Poisson statistics. This gives us some confidence in the data reduction performed.

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Figure 26. Summary of all corrections applied to HeCd data as a function of time for the whole duration of the mission. The ratio HeCd at level 2 divided by HeCd at level 2 is shown.

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Figure 27. Summary of all corrections applied to HeCd data from level 1 to level 2 for the low-altitude data set. Data have been mapped onto the Moon within 4° cylindrical pixels. For each pixel (4050 of them) the Poisson statistics and the standard deviation of the mean are calculated. The ratio is plotted before and after processing for all pixels, from the south pole (left) to the north poles (right). On average, the standard deviation cannot go less than the Poisson statistics.

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[54] Finally, we mention NS scalar data that are measured at 0.5-s resolution. This data set has proven to be extremely useful for three purposes: (1) to improve the spatial resolution of the data set, (2) to improve our understanding of the instrument response function, and (3) to infer the shape of the response function. The first objective is the most helpful for science issues, while other purposes are more technical and will prove to be extremely useful to process thermal data (see next section). In principle, the spatial resolution can be lowered to the theoretical limit of the instrument footprint on the surface. However, another practical limit arises earlier: the time summation should not be smaller than the duration of the spin. Thus 8-s is found to be adequate, just above the rotation period of the spacecraft (12 rpm) and an integer division of the initial 32-s resolution. As mentioned in Table 4, 0.5-s data are part of the level 1 data set. The process to build level 2 HeCd data at 8-s resolution is straight forward. After sums are performed, all multiplicative adjustments are that of the 32-s processing: the correction function (Figure 26) is applied to level 1 data. The result is the epithermal data set at 8-s resolution.

4.5. Thermal Data

[55] Thermal count rates are determined by measuring the difference of Sn-covered and Cd-covered 3He tubes. The reduction of HeSn data follows the steps of HeCd for altitude, cosmic ray and background. The main difficulty for the HeSn reduction is to understand the latitude dependent response function. The amplitudes of HeSn variations due to surface composition (∼100%) preclude a method that assumes a minimal dispersion of the data, as was done with epithermal data. The course to a response function for HeSn requires a careful analysis of 0.5-s data for both HeCd and HeSn products. Note that the HeSn data are affected by APS cross-talk in the same way as the HeCd data. The correction for this effect is therefore the same.

4.5.1. Latitude Response Function (First Step)

[56] Geometrical factors of Sn-covered and Cd-covered 3He tubes are identical. On the basis of what has been found for epithermal neutrons (equation (2)), we adopt the same functional form for the HeSn response function:

  • equation image

New numerical values must be evaluated for the different counterparts of R. Generally speaking, the overall intensity of the HeSn signal is larger than that of HeCd. We find that on average RHeSn = 2 RHeCd. This is expected from our understanding of the energy efficiency of 3He gas proportional counters when the number of neutrons per energy decade is constant, as is approximately the case for neutrons coming from the Moon. The first step is to calculate a new function fa that varies with neutron energy. To that end, the difference when the spacecraft is moving upward minus downward is plotted as a function of latitude (Figure 28). Data are binned in latitude and averaged in longitude, before the satellite was flipped (LP_high1) and after (LP_low). The curves do not match very well because of north-to-south asymmetries, which will be corrected later, but the average of the two data sets (dotted line) is a perfect sin(2λ) function with c = −95.35. When normalized to the response function at the equator, it is 3 times larger than for HeCd count rates. This difference is explained in section 4.8. To visualize the importance of this correction, HeSn data are mapped on the Moon with 4° cylindrical pixels (Figure 29). The standard deviation per pixel is shown without (black) and with (red) the sin(2λ) correction. After correction, measured errors are independent of latitude. The parameter c is common to all thermal data sets.

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Figure 28. Motion-dependent counterpart (fa) of the HeSn latitude response function for two different altitudes, the LP_high1 and LP_low data sets. The average of the two curves is also plotted (dotted line). Data points have been averaged in longitude, binned in latitude, and sorted for the direction of the spacecraft. The difference when the spacecraft is moving toward the north pole minus toward the south pole, for the average of the two data sets, is fitted by a sin(2λ) function.

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Figure 29. Effects of the motion-dependent correction onto the HeSn latitude response function. Data have been mapped onto the Moon within 4° cylindrical pixels. For each pixel the standard deviation of the mean is calculated. It is plotted before and after processing of this correction.

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4.5.2. Spin Phase Data

[57] High-resolution 0.5 s data are useful to visualize interactions of neutrons with the spacecraft and other apparatus blocking the sensors field of view. For one single Map cycle, Figure 30 displays HeCd and HeSn data for different spin phases and different latitudes of the spacecraft (summed over all longitudes). Spin phase data have been computed from an algorithm supplied by the MAG/ER team at University of California, Berkley, Ca (Principal investigator: R. P. Lin). The origin of the spin phase corresponds to an attitude when the NS boom is included within a lunar meridian and oriented toward the planet; the spin phase increases in the direction of the rotation. The data correspond to 0.5-s resolution (times 64), divided by the nearest 32-s data. Therefore this quantity is independent of cosmic ray flux, of spacecraft altitude, and even of composition. It explores only the distribution of counts within a single rotation of the spacecraft. An attached sketch (Figure 31) shows four instrument orientations with respect to the Moon. Remember that the spacecraft spins with its axis nearly parallel to the lunar rotation axis. Consider the HeCd data first (top panel). At the poles (red and green overlays), the counts are independent of spin phase since the sensor is looking at the Moon without any obstruction. At the equator (blue overlay), the maximum counts are toward the planet, but not exactly at 0°. At 90° the sensor has a small cross-sectional area facing the Moon, and the counts are correspondingly low. As the rotation continues, the count rate rises again as the cross-sectional area facing the Moon becomes larger. At 180°, the count rate is locally maximum, but not as large as at 0° because the spacecraft shields part of the detector. Further on, the count rate drops, as expected since the areal cross section switches again to the long axis of the tube. But now, near 270°, the small area of the sensor toward the Moon is itself obstructed by the Sn-covered tube and an electronics box. These shadows and effects of cross section sum to ∼30% of the signal, at the equator. This proportion decreases regularly as the spacecraft moves toward the poles. For HeSn data (bottom panel), the same behavior is observed offset by 180°. Note that for the HeSn data at the poles, the count rates do vary slightly with spin phase.

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Figure 30. (top) HeCd and (bottom) HeSn data as a function of spin phase for map cycle 7 (as an example). Data are originally in counts/0.5-s, but they have been multiplied by 64 and normalized to the nearest 32-s data. Along the spin phase angle, data have been smoothed (boxcar average ±4 points) for a better clarity. Data have been binned in latitude: red and green profiles correspond to the north and south poles, and the blue profile corresponds to the equator. Variations are due to various shadows and geometrical effects on the 3He tubes.

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Figure 31. Schematic of four positions of the NS boom with regard to the Moon. At the equator (for simplicity): at 0° phase angle the NS boom is looking directly at the Moon; at 180° the spacecraft is between the Moon and the sensors. The two Cd- and Sn-covered tubes are shown to illustrate results of Figure 30.

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[58] In order to use spin phase data to obtain useful information for the 3He tube response functions with latitude, we assume that spin phase modulations contain most information about f0. This can be tested from HeCd data, for which f0 is very well defined. The spin data are integrated along the phase angle within different latitude bands. As above, spin data at 0.5-s resolution are normalized to nearest 32-s data, so that they become independent of altitude, composition, and cosmic rays. To be safe, the calculation is done twice, when the spacecraft is moving northward and southward, and then averaged. The results given in Figure 32 are very encouraging: for both high and low data sets, integrated values vary with latitude and follow the model of f0 (solid line) normalized at the equator, within the 1-σ error bars of the data. A similar exercise is conducted from HeSn data (Figure 33), this time in order to derive a f0 function characteristic of HeSn data. Variations with latitude are fit by a cos2(λ) polynomial. At high altitude, three coefficients are sufficient, as with the HeCd data at both high and low altitude. For the low-altitude data set, the shape requires two extra powers of cos2(λ) (for which coefficients are called a6 and a8). In both cases, the latitude variations are softer for HeSn data than for HeCd data because low-energy neutrons are on ballistic orbits that come from many more directions than high-energy (escape) orbits. At low altitude, the response function is independent of latitude between ±45°.

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Figure 32. Comparison of the symmetric counterpart (f0) of the HeCd latitude response function with spin data for the high- and low-altitude data sets. Spin data have been integrated over the spin phase and compared to the f0 model derived directly from 32-s data. The match in both cases is within the ±1 σ error bars.

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Figure 33. Construction of the symmetric counterpart (f0) of the HeSn latitude response function from spin data for the high- and low-altitude data sets. Spin data have been integrated and binned in latitude. For each data set a polynomial of cos2(λ) is adjusted to the data. Three coefficients are sufficient for LP_high1, and five are needed for LP_low.

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4.5.3. Latitude Response Function (Step 2)

[59] At this point, new parameters have been derived for fa and f0 functions. The last term fv corrects a north-to-South asymmetry in the data. The best way to determine b is to compare latitude profiles, using data already corrected for fa and f0, both before and after the spacecraft was flipped, and for different values of b (Figure 34). We find that b for HeSn must be equal to 2 times the values of b for HeCd, to match latitude profiles. The agreement is extremely good between ±60°, but does not match at the poles. The reason for this is not understood. The simple straight line to define this effect could be reviewed. However, in absence of solid constraints, it appears safer to keep the linear profile, which scales with the increase of count rate from HeCd to HeSn.

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Figure 34. Effects of the asymmetric counterpart (fv) of the HeSn latitude response function. Data are averaged in longitude and binned in latitude. LP_high1 and LP_low data sets are compared. (top) The correction is ignored and latitude profiles do not match. (bottom) The correction is introduced and latitude profiles match.

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[60] The full response function for HeSn data can be reconstructed (Figure 35). The important assumption is that the form of R is inherited from HeCd. It uses seven parameters (a0, a2, a4, b, c, a6, a8) to account for the different asymmetries and the motion of the spacecraft. Six of these parameters depend on spacecraft altitude (Table 8). When this latitude correction is applied, it is normalized at the equator when the spacecraft is moving toward the north pole for the LP_high1 configuration (spin axis is pointing southward), to match HeCd normalization.

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Figure 35. Modeled latitude response function of HeSn data for the LP_high1 and LP_low data sets and two directions of the spacecraft motion.

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4.5.4. Thermal Data at 32-s and 8-s Resolution

[61] All processes above have been performed using 32-s averaged data. Corrections that have been applied are: background, cosmic rays, altitude, APS cross talk, and latitude. The absolute normalizations are the same as the HeCd normalizations. The ratio of HeSn time series between level 2 and level 1 is shown in Figure 36. It varies by ∼50%. For the statistical uncertainties, the systematic errors have decreased by as much as a factor 4 to the level of the Poisson statistics (Figure 37), as was also seen with the HeCd data. The uncertainties, however, are not well defined above the equator where the signal varies drastically because of central mare. HeSn data exist also at 8-s resolution from the original 0.5-s data. All multiplicative adjustments of the 32-s processing (Figure 36) are applied to HeSn data to obtain 8-s resolution at level 2. At both resolutions, the final product is a flux of thermal neutrons at level 2, derived from the difference between HeSn and HeCd.

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Figure 36. Summary of all corrections applied to HeSn data as a function of time for the whole duration of the mission. The ratio HeSn at level 2 divided by HeSn at level 2 is shown.

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Figure 37. Summary of all corrections applied to HeSn data from level 1 to level 2 for the low-altitude data set. Data have been mapped onto the Moon within 4° cylindrical pixels. For each pixel (4050 of them) the Poisson statistics and the standard deviation of the mean are calculated. The ratio is plotted before and after processing for all pixels, from the south pole (left) to the north poles (right). On average, the standard deviation cannot go less than the Poisson statistics.

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4.6. Fast Neutron Data

[62] At level 1, there are three fast neutron products: the sum of all double time-correlated events within the ACS (coincident with a BGO interaction), a scalar named “Fast” in Table 4 and a 16-channel spectrum named “Fast_spectrum.” The data reduction below was developed from the scalar count rate. The multiplicative correction function obtained from the scalar was ultimately applied to each individual channel of the spectrum.

4.6.1. Varying Detection Parameters

[63] As with NS data, level 1 to level 2 processing for fast neutrons starts with background and altitude. As shown hereafter, it is not necessary to apply the cosmic ray correction, since all data are normalized to the pole. The response function variations with latitude is an issue, as the anticoincidence shield of the gamma-ray spectrometer is cup-shaped to encase the BGO crystal such that its cross section, as seen from the lunar surface, varies with latitude. Contrary to other neutron products, this function is independent of the spacecraft motion. But it meets another challenge: parameters that control the coincidence measurement between ACS and BGO vary with time. On the one hand, the BGO gain changed progressively [Lawrence et al., 2004]. Such drifts were monitored and the high voltage supply was raised periodically to maintain an optimum gain. On the other hand, the gain and zero offset of the ACS drifted slowly with time. There was no adjustment of this variation, nor any possible monitoring. Aging of the photo-multiplier tubes explain the long term variations. Short term variations appear related to the sensor temperature. Figure 38 displays temperature values within the electronic box of GRS, which is explained by the orientation of the spacecraft orbit relative to the Sun (also called the β angle). When the spacecraft is orbiting the Moon along the dawn-to-dusk meridian (β = 90°), temperature variations are less than 2°. Variations are maximum, up to 18°, for noon-to-midnight orbits (β = 0°). As shown on the same figure, hot temperatures are reached at the poles, since the spacecraft gains monotonically heat along its path over the dayside. The inertia is large enough that the minimum temperature is reached close to the other pole.

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Figure 38. Temperature within GRS for the whole duration of the mission. Temperatures at the north and south poles have been specially highlighted.

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[64] Figure 39 shows the variations of fast neutron count rates poleward of +87°, after corrections for background, altitude and cosmic rays (for Figure 39 only, the cosmic ray correction is applied) have been performed. Where there should be a steady behavior, we observe changes by ∼40%. There is no method to recover from such a drift of the ACS and BGO gains, other than a severe normalization. The data poleward of +87° are therefore smoothed for 20 adjacent records and extrapolated along the spacecraft orbit. Fast neutron data are then divided by northern polar data early on the mission. After the spacecraft is flipped, southern polar data (<−87°) are reduced the same way and used for normalization. Such a construction implies that we are ignoring possible composition inhomogeneities (in longitude) above the poles. Furthermore, this normalization independently accounts for variations of the cosmic ray flux.

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Figure 39. Variations of fast neutron count rate (counts/32-s) at the north pole. Data have been corrected for cosmic rays and altitude. The spacecraft turnover is marked because the geometry of the instrument as seen from the Moon changes. Data are smoothed for 20 adjacent records.

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4.6.2. Latitude Response Function

[65] A simple response function with latitude can only be derived for periods of time when the temperature is steady along an orbit. From Figure 38, we isolate four periods when β ∼ 90°. For each period, data are averaged in longitude and binned in latitude. Another selection is required to restrict the data to nonmare units, because the fast signal is shown to be extremely variable in mare units due to composition variations on the lunar surface [Maurice et al., 2000a]. This selection is done using an albedo map (750 nm basemap at 2° resolution extracted from the Clementine UVVIS database [Lucey et al., 1998]) that scales between 113 and 255 (arb. Units). The cut for nonmare units is at 180, which removes 31% of the Moon surface. While this selection could be different, it yields empirically the best results. On Figure 40, the four time periods are shown. After the spacecraft is flipped, the profiles are reversed in latitude. All profiles are tied together, meaning that the response function is steady in time, since the four periods span the entire mission. Furthermore, the response is low when the BGO is facing the surface and high when the BC454 plastic is looking directly at the surface (see Lawrence et al. [2004] for a discussion of the LP-GRS orientation). The technique to remove mare units, mostly at northern midlatitudes, appears appropriate, otherwise latitude profiles before and after the flip would not match. A single functional form,

  • equation image

is suitable for the latitude response function. The four periods of interest account for about 3 months of data, enough to build a map of fast neutrons for the steady response function. The amplitude of this response function is about 80 counts, about ∼20% of the data set dynamic range.

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Figure 40. Fast neutron count rate for four periods of time when the GRS temperature is nearly constant (times in day of year since 1 January 1998). Data are selected for nonmare units and fitted by a polynomial of sin(λ). After the spacecraft is flipped, latitude profiles have been reversed to match the early part of the mission.

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[66] The response function above is then applied to all data. Residuals of variations with latitude have been tentatively sorted with temperature for β ≠ 90°. When the temperature cools down, the gain (BGO + ACS) increases. At night, gain and temperature vary linearly. On the dayside, the picture is different and difficult to model. Failing to correct fast neutron data for temperature variations, our solution is to recalculate a response function periodically, the same way it was done for a steady temperature. For LP_high1 data set, eight different functions have been derived, two for LP_high2 and seven for LP_low. They are shown on Figure 41, except for LP_high2. Coefficients of equation (4) are given in Table 8, for the mean of high-latitude and low-altitude profiles respectively. The low count rate part shows wide variations, when the BGO is partly shadowing the ACS. The response function for steady temperature (dashed line) is also shown for comparison. Each time a map is built for a different data set, we average data in longitude and compare the latitude profile to that one of the steady temperature map. No differences above ±0.5% have been observed. That gives us confidence in the set of variable response functions changing with time.

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Figure 41. Fast neutron latitude profiles at nonconstant temperature for the high- and low-altitude data sets. Data are selected for nonmare units. For LP_high1, eight different functions have been derived, and seven have been derived for LP_low. The latitude profile at constant temperature (see Figure 40) is shown for comparison (dashed line).

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4.6.3. Fast Scalar and Spectrum Data at 32-s

[67] All processes above have been performed using scalar data. Corrections that have been applied are: background, cosmic rays (implicitly), altitude, latitude. The final product is a flux of fast neutrons at level 2. The absolute normalizations that have been applied are (1) altitude above the surface at 30 km and (2) latitude effects to +90° North, and all efficiency/gain parameters normalized to the north pole in early January 1998, to the south pole after the spacecraft was flipped.

[68] The ratio of Fast time series between level 2 and level 1 illustrates the work accomplished (Figure 42). It varies by ∼100%. This correction factor every 32-s is applied to each energy channel of the fast spectrum data. As with the previous products, we make a ratio of the standard deviation to Poisson statistics (4° square pixels) before and after processing (Figure 43 for LP_low data set). Systematic errors have decreased by as much as a factor 2.5 to the level of the Poisson statistics. Errors at the south pole are higher because for the low-altitude data set, data points are forced to match at the north pole.

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Figure 42. Summary of all corrections applied to fast data as a function of time for the whole duration of the mission. The ratio Fast at level 2 divided by Fast at level 2 is shown.

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Figure 43. Summary of all corrections applied to Fast data from level 1 to level 2 for the low-altitude data set. Data have been mapped onto the Moon within 4° cylindrical pixels. For each pixel (4050 of them) the Poisson statistics and the standard deviation of the mean are calculated. The ratio is plotted before and after processing for all pixels, from the south pole (left) to the north poles (right). On average, the standard deviation cannot go less than the Poisson statistics.

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4.7. Moderated Neutron Data

[69] The case of moderated neutrons (<500 keV) is the most complex of all neutron products. However, there is nothing new that we have not dealt with before: this data reduction combines the difficulties of the fast neutrons (drift of ACS and BGO gains, temperature effects, asymmetry of the detector shape) as well as of epithermal neutrons (spacecraft motion). Because of this complexity, we restrict the following presentation to the low-altitude data set. Very limited new information is contained in the high-altitude portion of the mission. The difficulty again is to estimate the shape of the response function with latitude.

4.7.1. Varying Detection Parameters

[70] As with fast neutrons, variations of the BGO and ACS gains modulate the detection of moderated neutrons. No control or monitoring of the ACS gain was possible, but for the BGO several adjustments were applied to the high voltage [Lawrence et al., 2004] to maintain count rates for moderated neutrons above ∼150 counts/32-s. Figure 44 displays raw counts of moderated neutrons (corrected for altitude, cosmic ray and background) at low altitude. The high voltage adjustments are clearly seen. These adjustments have helped to ensure an acceptable signal-to-background ratio, but their discreteness complicates data reduction. To stay away from this problem, the discrete variations are removed from the data set. The ratio of counting rates averaged over two days before, to that over two days after each adjustment, is used to normalize data. To obtain the best possible result, data have been previously corrected for latitude variations (see next paragraph) through an iterative procedure, as well as variations in the altitude, cosmic ray and background counting rates. As a result of this process, the counting rates decrease continuously with time. For the north pole above +87° latitude (Figure 45) the drop is a factor ∼2. The idea is to use north pole data to normalize data at all latitudes, accounting this way for all gain variations and simultaneously for cosmic ray variations. The north pole was selected because the instrument temperature over this region was almost constant over the entire LP_low data set (see Figure 38). To minimize bias because of inhomogeneities at the north pole, polar data have been smoothed.

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Figure 44. Count rate of moderated neutrons as a function of time for the low-altitude data set. Data are for all latitudes, but corrected for altitude, cosmic ray, and background. High-voltage adjustments applied to the BGO are marked by a vertical dashed line. They correspond to discrete jumps of the fast neutron count rate.

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Figure 45. Variations of moderated neutron count rate (counts/32-s) at the north pole. Data have been corrected for cosmic rays, altitude, and background. Discrete jumps because of high-voltage adjustments have been removed.

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4.7.2. Latitude Response Function

[71] A well-defined response function with latitude can be derived for the beginning (day <25 January 1999) and for the end (day >11 June 1999) of the LP_low data sets, when the temperature is the same at both poles. Its functional form is that of epithermal neutrons, but we ignore the term that accounts for the position of the boom on the spacecraft:

  • equation image

ɛ = ±1 accounts for the motion of the spacecraft. fa has been described for epithermal and thermal neutrons. It fits the data (Figure 46) but not perfectly. This effect is known to be independent of composition at the surface. Therefore the reason for departure from a simple sin(2λ) form must be the special shape of the detector. Since the discrepancy is small (less than 2 counts) a new functional form will not be derived. It is more important to maintain the symmetry of this effect. The asymmetry is all included in the second term f0, as is shown in Figure 47. This term accounts for most variations of count rates with latitude. The data are averaged for the northward and southward motions. The two periods of time under consideration match very well. The functional form was chosen to be flat at the poles, for reasons of geometry, with a minimum number of parameters. The asymmetry is 30 counts, about 20% of the data set dynamic range. It is similar to the shape of fast neutrons, but with a higher peak near the equator. When both terms are added, we obtain the response function with latitude for the two directions of the spacecraft (Figure 48) at constant temperature. Coefficients are given in Table 8. It is important to verify that models connect at the poles with zero slope. Although not shown here, very similar shapes were found for LP_high1 data, but reversed (because of the spin axis flip). This proves that this fit to the data is on average independent of composition, since compositional features are different between the two lunar hemispheres.

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Figure 46. Motion-dependent counterpart (fa) of the moderated neutron latitude response function for the low-altitude data set at two periods of time when the GRS temperature is constant. The difference when the spacecraft is moving toward the north pole minus toward the south pole is fitted by a sin(2λ) function.

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Figure 47. Main counterpart (f0) of the moderated neutron latitude response function for two periods of time at low latitude, when GRS temperature is constant. Data points have been averaged in longitude and binned in latitude. They are fitted by a polynomial of sin(λ).

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Figure 48. At constant temperature, modeled latitude response function of moderated neutron data for the LP_low data set and two directions of the spacecraft motion (solid line). Data points have been averaged in longitude and binned in latitude.

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[72] Outside the two periods of constant temperature, the response function had to be recalculated for both f0 and fa terms every map cycle (10 times). The residual between the data and the response function determined at constant temperature was fitted with simple polynomials of latitude (degree 3 or less). This second-order correction exhibits an hysteresis shape between the northward and southward motions, because of the thermal inertia of the instrument (Figure 49). It corrects the response function at constant temperature by −15% to +7%. When the latitude correction is applied to all data, it is normalized to the north pole, when the spin axis is pointing northward (the BC454 plastic is looking at the planet).

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Figure 49. Correction to the constant temperature (Figure 48) latitude function for moderated neutrons. A new model is derived every map cycle (10 times) during the low-altitude part of the mission.

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4.7.3. Moderated Neutron Data at 32-s

[73] The time resolution of moderated neutrons is 32-s. Corrections that have been applied are: altitude, background, cosmic ray (implicitly), latitude. The final product is a flux of moderated neutrons at level 2. The absolute normalizations that have been applied are (1) altitude above the surface at 30 km (2) and latitude effects to +90° North, and all efficiency/gain parameters normalized to the north pole counting rate in early January 1999.

[74] As with the other data products, the ratio of moderated neutron time series at level 1 to that at level 2 illustrate the data corrections (Figure 50). This ratio varies by more than 100% and was translated in terms of standard and Poisson statistics over 2° cylindrical pixels in Figure 51. The ratio is well over 3 before data processing and close to 1 after. This last result, however, is probably too optimistic because the counting statistics are not as significant as they appear because counting rates have been artificially lowered when the high voltage adjustments have been removed. It is enough to validate the accuracy of our data processing.

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Figure 50. Summary of all corrections applied to moderated neutron data as a function of time for the low-altitude part of the mission. The ratio Cat2epi at level 2 divided by Cat2epi at level 2 is shown.

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Figure 51. Summary of all corrections applied to moderated neutron data from level 1 to level 2 for the low-altitude data set. Data have been mapped onto the Moon within 4° cylindrical pixels. For each pixel (4050 of them) the Poisson statistics and the standard deviation of the mean are calculated. The ratio is plotted before and after processing for all pixels, from the south pole (left) to the north poles (right). On average, the standard deviation cannot go less than the Poisson statistics.

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4.8. Doppler Effect

[75] Previously in sections 4.4 and 4.5, it was shown that variations with latitude of the neutron response function depend on the spacecraft direction, upward or downward. Accounting for the Doppler effect is important, especially for low-energy neutrons because LP orbits the Moon at a speed (1.64 km/s) that is comparable to the speed of a thermal neutron (2.2 km/s at a temperature of 293 K). This effect has been reported previously [Feldman and Drake, 1986; Drake et al., 1988; Feldman et al., 1993]. Here, it can be modeled qualitatively from simple geometrical considerations. Figure 52 summarizes the observations, when the spacecraft is going upward and downward. HeSn and HeCd coefficients are used to obtain thermal data. All inputs are normalized for the mean of upward and downward motions, to account for the intrinsic dynamics of each detector. From the data reduction discussed previously, the facts that need to be reproduced are (1) the shape with latitude is sin(2λ); (2) the amplitude relative to the mean is energy dependent, being larger for smaller energies; (3) there is no effect for fast neutrons (not shown); (4) the effect does not depend on the spacecraft orientation (spin axis up or down); and (5) the effect reverses for moderated neutrons.

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Figure 52. Modeled aberration effect (function fa) at different energies. The profile for thermal neutrons is obtained from the difference HeSn minus HeCd. The amplitude is normalized to the mean number of counts at each energy; it is shown as a percentage.

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[76] A simple geometrical model for both NS and GRS is given in Figure 53. When averaged for spin phase, both sensors are seen from the Moon as a torus, with a mean radius R and a cross section α by μ (α = μ = 5 cm for NS; α = 20 cm and μ = 12 cm for GRS). The length of the instrument in the spin plane, radially away from the spacecraft does not matter. When above the equator, the instrument effective surface seen from the Moon is 4Rα and is 2πRμ at the poles. At other latitudes, it is

  • equation image

Because of the spacecraft velocity vector, at a latitude λ, neutrons arrive in the spacecraft frame of reference θ degrees ahead of λ, where θ is a function of neutron energy Therefore neutron fluxes at the spacecraft are given by equation (7), when the satellite is moving upward and downward, respectively:

  • equation image

The difference yields

  • equation image

which contains the sin(2λ) shape. For both HeCd and HeSn tubes, πμ > 2α, while it is the opposite for the ACS, therefore the change of sign. This difference is indeed independent of the direction of the spin axis (pointing northward or southward). With the same geometrical factor, the amplitude would be much larger for moderated neutrons. The aberration angle relative to the local nadir, θ, is given by

  • equation image

with E0 = 0.014 eV, the energy of a neutron traveling at the speed of the spacecraft. When the neutron energy E gets larger, θ gets smaller and the amplitude of the Doppler effect is smaller. Note that for fast neutrons, θ ∼ 0. While this model ignores various effects such as shadow effects on the sensors and energy shift in the spacecraft frame of reference, it is adequate to explain the observations qualitatively.

image

Figure 53. Schematic to explain aberration effects for both NS (thermal, epithermal) and GRS (moderated) neutrons. Because of the fast spin rate, all sensors are seen from the Moon as a tore, with a mean radius R and a section α by β. Dimensions are not to scale.

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5. Mapping Neutron Data (Level 2 to Level 3)

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Neutron Spectroscopy on Board Lunar Prospector
  5. 3. Initial Processing (Level 0 to Level 1)
  6. 4. Reduction of Systematic Uncertainties (Level 1 to Level 2)
  7. 5. Mapping Neutron Data (Level 2 to Level 3)
  8. 6. Summary
  9. Acknowledgments
  10. References
  11. Supporting Information

[77] Time series data are mapped onto the lunar surface to create level 3 neutron data using only the low-altitude data to obtain the best dynamic range and spatial resolution. Figure 54 illustrates the enhanced dynamic range of the low-altitude sets by comparing histograms of epithermal neutron data for the high- and low-altitude data set. In addition thermal and epithermal neutron maps used 8-s data to enhance spatial resolution.

image

Figure 54. Histograms of epithermal data from 2° equal-area maps at high and low altitude. The low-altitude histogram is wider than the high-altitude one. Occurrences are in percentage of the total number of pixels (10,538).

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5.1. Mapping Technique

[78] A comprehensive set of routines has been developed by the Lunar Prospector team to map neutron and gamma-ray data onto a planet [Gasnault et al., 2003]. This toolkit is particularly suited to spatial resolutions larger than 20 km for the Moon. A 0.5° cylindrical grid, i.e., 720 longitudes by 360 latitudes, is the basemap for all geographical projections. As a result, all projection routines (global or local, cylindrical, Mercator, or stereographic for instance) are coded onto that single basemap. Thus level 3 products are 720 × 360 raster files, with a label for the color coding of the physical values. Since 0.5° pixels oversample the spatial resolution, two ways of mapping data onto the surface have been developed:

[79] 1. Straight mapping: Initially, time series data fill 0.5° tiles at the spacecraft nadir. Then, 0.5° tiles are averaged together to form larger pixels. Two choices are possible: (1) Pixels have equal angular dimensions in latitude and longitude. This is the “cylindrical mapping,” with approximately equal statistics within each pixel (e.g., Figures 27 and 43). However, pixels have smaller areas toward the poles. (2) Pixels have the same angular dimension for the latitude, but the longitude extent is adjusted so that pixels have close to the same area. This is the “equal-area mapping,” adapted to analyze the distribution of neutron fluxes over the planet, with no emphasis on the poles (see figures next paragraph). For instance, at two-degree equal-angle resolution, a cylindrical map encompasses 16,200 pixels, whereas the equal-area map encompasses 10,538 pixels. In the first case, the pixel area varies from 0.07 at the poles to 4.00 square-degrees at the equator with a standard deviation of 1.23; in the second case, the pixel area varies from 3.14 to 4.41 with a standard deviation of only 0.23. The latter case has still small variations of the pixel area because pixel borders must match borders of the 0.5° basemap tiles.

[80] 2. Smooth mapping: At the spacecraft nadir, within the basemap tile, the value corresponds to the weighted average of nearby 0.5° pixels. The weight function is a Gaussian of the distance to the spacecraft nadir. It is given by its half-width-half-maximum (HWHM) value. As a result of this process, the signal-to-noise ratio increases and maps do not have a grainy aspect.

5.2. Two Degree Equal-Area Maps

[81] Although each neutron product has its own spatial resolution (see next section), two degrees (=60 km at the equator) is a reliable approximation for all, which allows comparisons. Thus we can calculate dynamic ranges and precisions of level 3 maps under the same conditions. The equal-area technique is chosen. Therefore each map consists of 10,538 data points with associated latitude and longitude limits for each pixel. At this resolution there are no missing pixels. The maps are shown (Figure 55) with a color scale that ranges from the minimum to the maximum of each data set.

image

Figure 55. Two degree equal-area maps of thermal, epithermal, moderated, and fast neutrons. The color scale ranges from minimum to maximum for each data set.

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5.2.1. Dynamic Range

[82] Figure 56 presents histograms of each 2° map, which are centered on the data mean values for comparison. Epithermal and moderated neutrons have equal dynamic range (defined as “max–min)/mean,” 15%. Their histogram shape is a Gaussian, justifying after the fact that their spatial distribution is featureless on average. The dynamic range of fast neutrons is 30%. Low values of fast neutron counting rates distribute as a Gaussian. The dynamic range of thermal neutrons is 95%.

image

Figure 56. Histograms of level 3 products from 2° equal-area maps. Occurrences are in percentage of the total number of pixels (10,538). Along the x axis, data are normalized to their mean for comparison.

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5.2.2. Precision

[83] Precision refers to the dispersion within each pixel, since the same quantity has been measured several times. When mapped onto the planet, we are interested in the mean count rate equation image for n measurements xi taken at different times within a given pixel. Two quantities are meaningful, (1) the measured standard deviation,

  • equation image

and (2) the standard deviation of a Poisson distribution of the same mean,

  • equation image

to characterize the dispersion of the signal. As reduction of time-dependent biases in the data set progresses (cross-talk, SEP events, cosmic ray fluxes, altitude, background, gain, and temperature), the measured standard deviation decreases toward that of a Poisson statistic. Comparisons between the measured standard deviations and statistics have already been presented (Figures 27, 43, and 51). For thermal neutrons, it is close to the results of Figure 37.

[84] Here the absolute measured standard deviation tells us how reliable our estimate of the mean is per pixel. For each level 3 map, the standard deviation is calculated and normalized to the mean value per pixel (Figures 57 and 58). The x axis corresponds to 10,538 2°-pixels, which are ordered from the south pole to the north pole. The mean, median, 1-percentile and 99-percentile levels of the standard deviation are calculated. We use the 99-percentile level to define the precision of each neutron product. Data reduction of thermal neutrons is good to 2.73%. Periodic maxima correspond to pixels over the mare (low count rate). Data reduction of epithermal neutrons is good to 0.96% and for moderated neutrons to 1.87% and fast neutrons to 1.60%. At the poles it is always smaller than 0.5%. The most straight-forward data to reduce has been the epithermal population, hence the high precision. Conversely, reduction of moderated neutrons was complex. The case of thermal neutrons was difficult too, because of the amplitude of the dynamic range.

image

Figure 57. Standard deviations of thermal and epithermal neutron count rates from 2° equal-area maps. Each time, mean, and median is indicated, as well as 1-percentile and 99-percentile limits. Pixel indices range from 0 (south pole, left) to 10,537 (north pole, right). Standard deviations are in percentage of the mean within each pixel.

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image

Figure 58. Same as Figure 57 for moderated and fast neutron count rates.

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5.3. Intrinsic Spatial Resolution

[85] Surface resolution is an important characteristic of neutron maps at level 3. In principle, a direct estimate of that parameter can be derived from the shape and size of a signal due to an isolated point source on the surface. However, in contrast to the thorium distribution measured with the GRS [Lawrence et al., 2003], no neutron feature that is consistent with emission from a point source can be identified within any of the neutron maps. Therefore our estimate of the surface resolution relies on numerical modeling of the response function for each sensor. Surface resolution is given in terms of half-width at half-maximum (HWHM) and for 90% of the signal (HW90), both at 30 km altitude.

[86] A detailed model of the NS response function was developed by one of us (R.E.) for the spacecraft above the equator. The surface composition is assumed to be ferroan-anorthosite with a mean temperature of 293 K. The nominal cosmic ray flux is 2 proton/cm2/s. The Monte-Carlo transport code developed at Los Alamos National Laboratory MCNPX [Waters, 1999], with a special planetary patch to account for the gravitational binding of thermal neutrons, was used to calculate the residual neutron flux below and above the surface. The leakage flux was described in terms of phase space density to be mapped from the surface to orbit, according to Liouville's theorem. In parallel of this calculation, a model of the helium tube area-efficiency product was set up for all possible directions of arrival of the neutrons [Lawrence et al., 2002]. The neutron flux at the spacecraft could therefore be translated to counting rates. Because the spacecraft travels at an equivalent neutron energy of 0.025 eV (2.2 km/s), its motion was taken into account in the simulation. Distances traveled by neutrons are large, therefore the neutron half-life (∼15 min) was also included. At 30 km above the equator, counting rates have been estimated for different orientations of the helium tubes, averaged over all spin phases within 32-s.

[87] Figure 59 shows the result of this simulation for the Cd-covered tube. Zero km corresponds to the spacecraft nadir point. The response function expands along the spacecraft motion (x axis) and in the perpendicular direction (y axis). When integrated over the entire footprint, the calculated absolute counting rate is ∼686 counts/32-s, which agrees very well with the range of measurements at 30 km altitude (see Figure 10). The shape of the response function for the Sn-covered tube is not shown, since it is very similar to that of the Cd-covered tube. The calculated absolute counting rate is ∼1360 counts/32-s, in agreement with measurements. In both cases, the response function appears Gaussian near the peak, with power law tails away from the nadir. Along the x axis, it is well represented by a κ distribution [Kivelson, 1995],

  • equation image

where A is the amplitude, x0 an offset in the ram direction, σ a characteristic width of the distribution. κ quantifies the importance of the counting rates within the tails. We obtain κ = 1.08 and κ = 0.79 for the Cd- and Sn-covered tube respectively (Figure 60, solid line). For comparison the Gaussian shape is plotted as a dash line. The width of the distribution can be derived from σ: HWHM = 23.3 and 21.7 respectively. The Sn-covered tube has a better resolution at half maximum, but also has more counts distributed in the tails. These effects seem to compensate since both distributions register 90% of their signal (HW90) within ±70 km of the nadir point. The parameter x0 gives the relative magnitude of the aberration effect due to the motion of the spacecraft. The offset is 2.6 and 4.2 km for the Cd- and Sn-covered tube respectively. As expected, the aberration is larger for thermal neutrons, which have speeds close to, or smaller than the speed of the spacecraft. In both cases, the offset is small enough that it could be ignored in the data reduction procedures. The precision on HWHM is of the order of ±3 km, because of approximations in the model.

image

Figure 59. Model of the response function of the Cd-covered 3He tube. A 3-D view is shown as an inset. It is then projected in a plane that contains the motion vector of the spacecraft. Solid lines are for the response functions that have not been changed by the projection.

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image

Figure 60. Fit of the (left) Cd-covered and (right) Sn-covered response functions by κ distributions.

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[88] Fast neutrons travel along straight paths from surface to orbit and their decay is negligible. Therefore they can be modeled as photons. Consequently, we shall assume that the response function for fast neutrons is that of gamma rays detected by the GRS. A minor difference arises, not at the spacecraft but at the surface, where the emission of gamma rays is more focused toward the zenith than the emission lobe of fast neutrons. Lawrence et al. [2003] have simulated the spatial response function of the GRS to study small thorium features on the Moon. The authors also modeled the GRS response function by a κ distribution (equation (10)). At 30 km, they obtain σ = 22.5, x0 = 0, and κ = 0.62. Because fast neutron energies are orders of magnitude above 0.014 eV, there is no offset. However, contributions from the tails are large. The characteristic dimensions are HWHM = 23.2 km and 90% is within ±95 km. From the model, the precision on the HWHM is of the order of ±5 km. Because fast neutrons are less focused at the surface than gamma rays, the characteristic dimensions of the tails may be larger than above, but still their HWHM dimensions should be equal to that for gamma rays within error bars.

[89] No model of response function is available for moderated neutrons. From the next section, we shall see that 45 km is an upper limit of HWHM for moderated neutrons. Moderated maps (Figure 64) are indeed coarser than maps of other neutron products.

5.4. Noise Reduction

[90] Data points can be distributed around the spacecraft nadir according to a Gaussian distribution. As explained in section 5.1, such a technique produces smoother maps. Therefore it increases the signal-to-noise ratio while reducing the spatial resolution only slightly. We use the standard deviation over the entire planet, computed from the 0.5° basemap, as an indicator of the general variations of each map. “Variations” is used here as a broad term that includes all structures, signal and noise. The standard deviation (of all 10,538 pixels) is calculated for different HWHMs of the Gaussian (Figure 61). For each neutron product, the standard deviation decreases rapidly for small values of HWHM, until it follows a straight line for high values of HWHM. The initial decrease is due to the removal of very small structures associated with the noise. When the plateau is reached, large structures start to be eroded. The limit in between is the optimum parameter to obtain better neutron maps. This cutoff should be less than the intrinsic spatial resolutions of the maps.

image

Figure 61. Standard deviations of neutron count rates over the entire planet for different smooth parameters. The smooth is performed with a Gaussian given by its HWHM. The best parameter is determined when the curve meets the linear fit to high values of HWHM.

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[91] We obtain for the thermal, epithermal, moderated, and fast neutrons, HWHM equal 30, 37, 45 and 27 km, respectively. The thermal neutron data have a very good statistics. Hence the necessity to remove noise is reduced (with infinite statistics, a smoothing should not be necessary). Statistical fluctuations are small within the range of the data intrinsic resolution. Figures 6265 display smooth maps with the optimum HWHM parameter. While science interpretation of these maps is not the purpose of this publication, a summary will be given (section 6). By comparison with results of section 5.3, we verify that cutoff values for thermal, epithermal and fast neutrons are indeed above the intrinsic spatial resolution of the maps. They are very close for thermal and fast neutrons, as are their spatial resolutions. The cutoff of epithermal neutrons is also larger, as expected from its resolution.

image

Figure 62. Map of thermal neutron data, with an optimum smooth at HWHM = 30 km (unit is counts/8-s). The projection is cylindrical, with a shaded relief map from USGS to emphasize the main lunar structures.

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image

Figure 63. Map of epithermal neutron data, with an optimum smooth at HWHM = 37 km (unit is counts/8-s).

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image

Figure 64. Map of moderated neutron data, with an optimum smooth at HWHM = 45 km (unit is counts/32-s).

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image

Figure 65. Map of fast neutron data, with an optimum smooth at HWHM = 27 km (unit is counts/32-s).

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6. Summary

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Neutron Spectroscopy on Board Lunar Prospector
  5. 3. Initial Processing (Level 0 to Level 1)
  6. 4. Reduction of Systematic Uncertainties (Level 1 to Level 2)
  7. 5. Mapping Neutron Data (Level 2 to Level 3)
  8. 6. Summary
  9. Acknowledgments
  10. References
  11. Supporting Information

[92] This publication is an archive of the way Lunar Prospector neutron data have been reduced. All steps have been justified and documented and results are reproducible from raw data that are available from the Planetary Data System (PDS). Characteristics of final maps available at level 3 are detailed in Table 9.

Table 9. Summary of Data Available at Level 3
Neutron DataCharacteristicsValue/Explanation
  • a

    HWHM and 90% of the signal.

  • b

    Min-to-Max from 2° equal area maps.

  • c

    The 99-percentile level.

  • d

    Other normalizations are 30 km altitude and mean cosmic ray flux between 16 and 19 January 1998.

  • e

    Parameter (HWHM of Gaussian) for reduction of noise.

Thermal neutronsintrinsic resolutiona23.3 km, 70 km
dynamicsb95%
precisionc2.73%
latitude normalizationdequator
smoothe30 km
unitscounts/8-s
Epithermal neutronsintrinsic resolutiona21.7 km, 70 km
dynamicsb15%
precisionc0.96%
latitude normalizationdequator
smoothe32 km
unitscounts/8-s
Moderated neutronsintrinsic resolutiona<90 km
dynamicsb15%
precisionc1.87%
latitude normalizationdnorth pole
smoothe45 km
unitscounts/32-s
Fast neutronsintrinsic resolutiona23.2 km, 95 km
dynamicsb30%
precisionc1.60%
latitude normalizationdnorth pole
smoothe27 km
unitscounts/32-s

[93] This publication is a major milestone for planetary neutron spectroscopy in general, but specifically for the neutron experiments on board Lunar Prospector. Sources of errors have been minimized. Using repeated mappings of the Moon, for a surface signal that is time-independent, most instrument biases have been eliminated. Remaining instrument biases are contained within the error bars given in Table 9. The only parameter that is not constrained by the repetition of measurements is the latitude profile. Its inaccuracy would imply systematic errors within the final products (no effects on the precision). Latitude profiles are constrained by arguments of symmetry (between northern and southern hemispheres) and geometry (over the poles). To quantify their accuracy, latitude profiles before and after the spacecraft was flipped have been compared. Differences yield an absolute latitude accuracy better than 1% for epithermal and fast neutrons, better than 3% for thermal neutrons. It is not possible to derive such a number for moderated neutrons, because data before the spacecraft was flipped have not been reduced. There should be no other systematic errors.

[94] Further improvements on data reduction should be confined to details, especially at level 1 and level 2 where the number of free parameters and assumptions introduced are limited. Improvements subsequent to level 3 can be achieved by signal processing in the form of a full spatial deconvolution of the signal with an accurate model of the instrument spatial response function at the surface. A follow-up on this study will also be to turn level 3 products, which are in counts per unit of time at 30 km altitude, into absolute neutron flux at the surface. This work is in progress to match in situ measurements by the Apollo missions and to determine the absolute neutron number density in order to reduce the LP-GRS gamma-ray data.

[95] Turning level 3 neutron data into elemental concentrations on the Moon is not the purpose of this publication. The reader is referred to the following publications:

[96] 1. Fast neutrons are produced at the top of the energy cascade most efficiently for heavy and abundant nuclei, predominantly Fe and Ti [Maurice et al., 2000a; Gasnault et al., 2000]. More precisely, fluxes of fast neutrons can be tied to the mean atomic mass of the regolith [Gasnault et al., 2001].

[97] 2. Epithermal neutrons hold no memory of their history in the fast energy range. Hydrogen is detectable using epithermal neutrons, as polar water deposits [Feldman et al., 1998, 2001] or implanted by the solar wind at all latitudes [Maurice et al., 2001]. Rare earth elements, Sm and Gd are clearly seen, even at concentrations of a few tens of ppm [Maurice et al., 2000b] because they have very large absorption resonances above 0.1 eV.

[98] 3. Thermal neutrons are not completely separated from epithermal neutrons, in terms of compositional information, since REE are clearly detectable with thermal neutrons [Elphic et al., 2002]. The effects of hydrogen are completely muted for the concentrations observed on the Moon. Major elements are relatively more important in the order of their macroscopic absorption cross sections for neutrons, i.e., Ti, Fe, Na, Ca, Al, and Si [Elphic et al., 1998, 2002].

[99] 4. Moderated neutrons span such a large energy range that all effects above merge, and no more information is available [Genetay et al., 2003]. For LP data, this energy range can be used as a validation check for the other energy products.

[100] Neutron spectroscopy provides a measure of elemental composition, but, with the exception of hydrogen, not of a single element, since often, several elements share the same nuclear properties within the wide energy ranges under consideration for neutron spectroscopy. A maximum science return is obtained when this technique is exploited in conjunction with results from gamma-ray spectroscopy, X-ray spectroscopy, or spectral reflectance.

[101] Since Lunar Prospector, neutron spectroscopy is being applied to several planetary missions. It is currently active on Mars Odyssey, where it has mapped the Martian hydrogen reservoirs [Feldman et al., 2002], as well as CO2 using the thermal energy channels. In contrast to the Moon, variations of major elements appear small on Mars. REE are also at very low concentrations and are not detectable. Hydrogen and carbon therefore become the primary targets of this technique on Mars. Further applications of neutron spectroscopy will be for Mercury with Messenger and asteroids with Dawn.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Neutron Spectroscopy on Board Lunar Prospector
  5. 3. Initial Processing (Level 0 to Level 1)
  6. 4. Reduction of Systematic Uncertainties (Level 1 to Level 2)
  7. 5. Mapping Neutron Data (Level 2 to Level 3)
  8. 6. Summary
  9. Acknowledgments
  10. References
  11. Supporting Information

[102] This research was carried out in Toulouse with support from CNES and the “Pôle National de Planétologie.” In Los Alamos, it was carried out under the auspices of the Department of Energy, with support from NASA through the Lunar Data Analysis Program.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Neutron Spectroscopy on Board Lunar Prospector
  5. 3. Initial Processing (Level 0 to Level 1)
  6. 4. Reduction of Systematic Uncertainties (Level 1 to Level 2)
  7. 5. Mapping Neutron Data (Level 2 to Level 3)
  8. 6. Summary
  9. Acknowledgments
  10. References
  11. Supporting Information
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Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Neutron Spectroscopy on Board Lunar Prospector
  5. 3. Initial Processing (Level 0 to Level 1)
  6. 4. Reduction of Systematic Uncertainties (Level 1 to Level 2)
  7. 5. Mapping Neutron Data (Level 2 to Level 3)
  8. 6. Summary
  9. Acknowledgments
  10. References
  11. Supporting Information
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jgre1821-sup-0001-tab01.txtplain text document0KTab-delimited Table 1.
jgre1821-sup-0002-tab02.txtplain text document1KTab-delimited Table 2.
jgre1821-sup-0003-tab03.txtplain text document1KTab-delimited Table 3.
jgre1821-sup-0004-tab04.txtplain text document2KTab-delimited Table 4.
jgre1821-sup-0005-tab05.txtplain text document1KTab-delimited Table 5.
jgre1821-sup-0006-tab06.txtplain text document1KTab-delimited Table 6.
jgre1821-sup-0007-tab07.txtplain text document1KTab-delimited Table 7.
jgre1821-sup-0008-tab08.txtplain text document1KTab-delimited Table 8.
jgre1821-sup-0009-tab09.txtplain text document1KTab-delimited Table 9.

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