Before discussing the SNASA technique as applied to a collimated neutron detector, we address here the use of existing Lunar Prospector Neutron Spectrometer (LP-NS) data to validate the SNASA technique. To carry out such a validation, a data set where surface compositional abundances are independently known is required. Such independent knowledge does not exist for LP epithermal neutron measurements of lunar hydrogen abundances. However, LP thermal neutron data can serve as a validation proxy for epithermal neutrons. The reasons for this are four-fold. First, as mentioned in Section 1
, thermal neutrons are sensitive to the presence of neutron-absorbing elements gadolinium, samarium, iron, and titanium. Gadolinium and samarium are incompatible rare earth elements that closely track thorium abundances in lunar soils (Haskin and Warren, 1991
). Iron and titanium have been mapped with high spatial resolution with the use of Clementine spectral reflectance (CSR) data (Lucey et al., 2000
). The CSR data sets can thus serve as a “ground truth” for iron and titanium abundances. Second, the spatial response of the LP-measured thermal neutrons is sufficiently similar to that of epithermal neutrons (Maurice et al., 2004
) so that thermal neutrons can adequately represent epithermal neutrons for the purpose of a validation. Third, because the thermal neutron counting rate decreases with increasing iron and titanium abundances (Feldman et al., 2000b
), measured thermal neutrons can be used to mimic the effect of hydrogen on epithermal neutrons. Finally, there exist multiple locations on the Moon where thermal neutron reductions are smaller than the FWFM spatial response of the NS, which is the Moon's horizon at 30
km altitude, or ~600
km. Further, such locations are relatively isolated in regions of higher thermal neutron counts. These regions thus serve as good test cases for a validation.
To carry out the validation, a ground truth relationship must be established between surface thermal neutron counts predicted from CSR-measured iron and titanium abundances and those measured from orbit using the LP-NS. shows a plot of global CSR-derived [Fe]
2.36[Ti] abundances versus thermal neutron counting rates. The CSR-derived abundances are combined to equalize the effect of neutron absorption, where the thermal (E
eV) absorption cross section of iron and titanium is 2.58 and 6.11 barns, respectively. The factor of 2.36 is the ratio of the two cross sections. The iron and titanium data sets were smoothed with the thermal neutron spatial response to enable a proper comparison between the CSR and thermal neutron data sets.
To reduce thermal neutron variations from gadolinium and samarium and keep only variations from iron and titanium, data in were restricted to regions with thorium abundances less than 1.5
ppm (Lawrence et al., 2003
). At high iron and titanium values, shows a reasonable correlation with thermal neutrons. For this analysis, we assume this correlation holds for all iron and titanium values, although at low iron/titanium abundances the thermal neutron counts respond primarily to the composition of other elements in the regolith that have variable (and, for this analysis, unknown) relative abundances.
Next, seven locations on the Moon were identified that satisfy the criteria of being isolated counting-rate reductions with sizes smaller than the LP-NS FWFM spatial response. These seven regions are listed in along with their sizes, locations, and associated values for fepi
(see Section 4.1.4
for how fepi
is calculated). For the case of LP-NS, fback
0 since there is no collimator, and neutrons out to the horizon are detected in the omni-directional FOV.
Locations Used for SNASA Validation
To carry out the validation of the SNASA technique, the counting-rate ratio R
) is used to compare “ground truth” to the SNASA prediction. gives an example of how the comparison is carried out. is a CSR iron map (0.5°
0.5° pixels) of the Moscoviense region, and are unsmoothed and smoothed thermal neutron maps of the same region, respectively (Maurice et al., 2004
). The unsmoothed thermal neutron map shows the data set used for calculating total thermal neutron counts; the smoothed thermal neutron map shows a higher signal-to-noise version of the thermal neutrons, but with a broader (smoothed) spatial response that allows the thermal neutron features to be clearly delineated. The mean [Fe]
2.36[Ti] value within Moscoviense (indicated by the center circle) is 18.9
wt % (titanium map is not shown). Using the correlation in , these abundances translate to a “ground truth” thermal neutron counting rate of 549 counts per 32 seconds. Based on the total number of collected measurements in this region (86), the total “ground truth” counts are 47,218. To mute compositional variations when using background counts, four equivalent-sized regions were selected, which are shown by the outer circles in as background regions. The total counts in each region are determined by calculating the total counts in each circle and scaling the number of measurements to be equivalent to the number of measurements in the center circle (the SNASA model as given in Eqs. 13
assumes that the signal and background regions have the same counting time). The total counts in each background region are: 62,254, 66,854, 63,011, and 59,824. By combining measurements from the four background regions, a “ground truth” mean value of RGT
0.761 and a standard deviation σRGT
0.039 (see ) are obtained. Here, the standard deviation represents variances in RGT
mostly due to residual compositional differences in the background regions.
The “prediction” of RGT
*, (Eq. 14
) is determined via the total measured counts in the central region [C
49,851] and the total counts in the background regions [C
62,254, 66,854, 63,011, and 59,824]. Since uncertainties in the thermal neutron counts have been shown to be mostly Poisson (Maurice et al., 2004
), here the uncertainties in each region are assumed to be the square root of the total number of counts. A signal-to-noise, Sn
, is calculated by ΔC
; and, as with RGT
, mean and standard deviation values are determined: R
(see ). The procedure described above was carried out for the seven lunar locations, and results for all locations are shown in . In all cases, the relative differences between RGT
* (last column in ) are less than 15%. shows a plot of RGT
*. The correlation coefficient is 0.74, which is a moderate correlation. In summary, this validation analysis has shown that the SNASA model can reproduce measured LP thermal neutron data to within a relative difference of 15%, which provides better confidence in the SNASA technique.
R* versus RGT for the seven selected regions of thermal neutron reductions due to high iron and titanium abundances. The error bars represent variability due to different total counts in the background regions.