Radiative Transfer Modeling of Compositions of Lunar Pyroclastic Deposits

Introduction: While over 100 lunar pyroclastic deposits have been identified remotely [1], their compositions remain poorly constrained. In this work, we attempt to determine the compositions of three lunar pyroclastic deposits for which we have high-quality spectra: the Aristarchus Plateau, Mare Humorum, and Sulpicius Gallus [2]. The spectral behavior of lunar pyroclastic deposits is a combination of five main components: FeO content, TiO2 content, particle size, level of space weathering, and degree of crystallinity. We use radiative transfer theory to model the effects of these components in order to ascertain the compositions of the three remotely observed deposits. Methods: The telescopic spectra (0.6-2.0 μm) were normalized to the reflectance at 0.75 μm of each region, as obtained from Clementine images, and we used the 0.415 μm band from Clementine to extend our study into the UV. We attempted to reproduce these spectra using radiative transfer modeling based on the theory of [3, 4]. This model relies on having optical constants for glasses with any combination of iron and titanium content. We used directly measured optical properties of synthetic glasses of different compositions [5-7] in order to derive relationships between the real and complex indices of refraction and composition. This allowed us to produce reflectance spectra of glasses of arbitrary iron and titanium contents, particle sizes, and degree of space weathering (agglutinate and SMFe abundance). Optical constants are not available for devitrified “black beads” and thus they cannot be directly modeled. Instead, we test the effects of mixing glass with black beads by converting the reflectance of black beads from sample 74001 [8] to single scattering albedo in order to allow mixing with glass in proportion to abundance. We performed a combined grid search/gradient descent model to find the best fit to the telescopic spectra. We modeled each spectrum at a variety of iron contents (0-30 wt%, at increments of 0.25 wt%) and particle sizes (2-60 μm, at increments of 0.5 μm). This allowed us to determine if different combinations of iron content and particle size could provide an equally suitable match to the telescopic spectra. A gradient descent program was applied at each iron content and particle size combination, allowing titanium content, agglutinate abundance, and amount of SMFe to vary until the best possible spectral fit was achieved at that fixed combination of Fe and particle size, and the quality of the fit was recorded. This test was then repeated, this time allowing the abundance of black beads to vary in order to determine if a mixture of black beads and glass would provide a better match. Results: The results of the modeling show that iron content and particle size can mimic each other to some extent. Of the best model fits to each of the telescopic spectra, it is seen that a decrease in iron content can be nearly compensated for with an increase in particle size and vice versa without significantly changing the goodness of the model fit. However, there is a clear minimum where a particular combination of particle size and iron best match the telescopic spectra (Fig. 1). For Aristarchus this is an iron content of 21 wt% FeO and a particle size of 7 μm, for Humorum we find 20 wt% FeO and 6 μm, and for Sulpicius Gallus an iron content of 17 wt% FeO and a particle size of 6 μm fit best (Fig. 2). These iron contents are within the range of sampled pyroclastic glasses [9], but their particle sizes are lower than either the mean value of sampled lunar pyroclastic glasses (40 μm) [10] or the optically dominant size fraction (10-20 μm) [11]. For validation, we modeled the Apollo 15 green glass of sample 15401 [8]. Fitting this sample at its known iron and titanium contents (19.7 wt% FeO and 0.4 wt% TiO2) resulted in a particle size of 18.7 μm. The actual mean particle size of this sample is 33 μm, which implies modeled particle sizes are off by a factor of two. After this offset is accounted for, the particle sizes predicted for the telescopic spectra fall