Statistical Analysis of the Links among Lunar Mare Soil Mineralogy, Chemistry, and Reflectance Spectra

A principal goal of the Lunar Soil Characterization Consortium (LSCC) is to evaluate tools that might be successfully used in remote compositional analysis of the lunar surface. Mathematical methods are extremely valuable to assess whether variations exist in a statistically significant manner, independent of their interpretation. The bounds of widely used correlation of visible to near-infrared spectral parameters with composition are first defined and evaluated. We then evaluate direct (or indirect) links between the combined spectral properties of lunar mare soils and their compositional properties (elemental abundance and mineralogy) through a statistical analysis of the variance across each measurement using principal component analysis (PCA). We first separately analyze LSCC elemental abundance, mineralogy, and spectroscopy data (0.35 to 2.5 μm) using PCA to capture the variance of each system with a relatively small number of independent variables. With this compact set of independent variables for each type of data, we derive functions to link composition and spectroscopy. For these mare soils, one of the best empirical predictive capability is that for FeO. This is not surprising since the effect of ferrous iron on optical properties is well documented. Although Al2O3 has no direct effect on optical properties, its strong anticorrelation with FeO also produces a relatively high predictive capability from spectra. Similarly, a high accuracy in predicting the abundance of pyroxene is observed and should be expected since iron-bearing pyroxene is one of the most optically active components of lunar soil. The accuracy for predicting either TiO2 or ilmenite, on the other hand, is disappointing. High- and low-Ti soils are readily distinguished, but these statistics suggest that making subclass distinctions based on spectral predictions of TiO2 would be risky.