Spatial Deconvolution Studies of Nearside Lunar Prospector Thorium Abundances

Introduction: Orbital gamma-ray and neutron spectroscopy measurements have greatly contributed to our understanding of the elemental composition of the both the Moon and Mars [1,2,3,4,5]. One drawback , however, to these measurements is that the spatial resolution is quite broad since it is roughly equal to or greater than the spacecraft height above the planetary surface. For example, for the 30-km low altitude Lunar Prospector measurements, the spatial resolution is ∼45 km. For the Mars Odyssey gamma-ray and neutron measurements, the spatial resolution is ∼600 km for an orbital altitude of 400 km. The technique of spatial deconvolution [6] offers a way to improve the spatial resolution of these measurements if the spatial response function of the instrument is sufficiently well known. Previous studies have carried out spatial deconvolution for lunar and Mars neutron data [7,8,9]. A constant difficulty in utilizing these techniques is clearly determining the difference between true signal and noise that is amplified by the deconvolution process. This difficulty is managed in various ways by the different studies. Lunar Prospector data provide a unique opportunity to mitigate this difficulty because large datasets exist for two different altitudes – 100 and 30 km – and hence for two different spatial resolutions. In order to better understand the spatial deconvolution process, we can deconvolve high-altitude data and compare it with the measured low-altitude data, which has a spatial resolution a factor of 3 better than the high-altitude data. A comparison between the deconvolved high-altitude data and measured low-altitude data then provides an indication of the types of errors characteristic of the deconvolution process. With this knowledge, one can then carry out a deconvolution of the low-altitude data. For this set of deconvolution studies, we have used the thorium counting rates measured with the LP gamma-ray spectrometer (LP-GRS). The reason for this is two fold: 1) We have well characterized the LP-GRS spatial response function as a function of altitude [1]; and 2) The thorium counting rates have the highest signal-to-noise of all the LP-GRS data. Deconvolution Algorithm: To carry out the de-convolution, we employ a nonlinear, iterative technique called Jansson's method [6]. For Jansson's method, iterative solutions are obtained using the following: