Uncertainty Introduced by Darkening Agents in the Lunar Regolith: An Unmixing Perspective

On the Moon, in the near infrared wavelength range, spectral diagnostic features such as the 1-μm and 2-μm absorption bands can be used to estimate abundances of the constituent minerals. However, there are several factors that can darken the overall spectrum and dampen the absorption bands. Namely, (1) space weathering, (2) grain size, (3) porosity, and (4) mineral darkening agents such as ilmenite have similar effects on the measured spectrum. This makes spectral unmixing on the Moon a particularly challenging task. Here, we try to model the influence of space weathering and mineral darkening agents and infer the uncertainties introduced by these factors using a Markov Chain Monte Carlo method. Laboratory and synthetic mixtures can successfully be characterized by this approach. We find that the abundance of ilmenite, plagioclase, clino-pyroxenes and olivine cannot be inferred accurately without additional knowledge for very mature spectra. The Bayesian approach to spectral unmixing enables us to include prior knowledge in the problem without imposing hard constraints. Other data sources, such as gamma-ray spectroscopy, can contribute valuable information about the elemental abundances. We here find that setting a prior on TiO2 and Al2O3 can mitigate many of the uncertainties, but large uncertainties still remain for dark mature lunar spectra. This illustrates that spectral unmixing on the Moon is an ill posed problem and that probabilistic methods are important tools that provide information about the uncertainties, that, in turn, help to interpret the results and their reliability.