A probabilistic approach to remote compositional analysis of planetary surfaces

Abstract

Reflected light from planetary surfaces provides information, including mineral/ice compositions and grain sizes, by study of albedo and absorption features as a function of wavelength. However, deconvolving the compositional signal in spectra is complicated by the nonuniqueness of the inverse problem. Trade‐offs between mineral abundances and grain sizes in setting reflectance, instrument noise, and systematic errors in the forward model are potential sources of uncertainty, which are often unquantified. Here we adopt a Bayesian implementation of the Hapke model to determine sets of acceptable‐fit mineral assemblages, as opposed to single best fit solutions. We quantify errors and uncertainties in mineral abundances and grain sizes that arise from instrument noise, compositional end members, optical constants, and systematic forward model errors for two suites of ternary mixtures (olivine‐enstatite‐anorthite and olivine‐nontronite‐basaltic glass) in a series of six experiments in the visible‐shortwave infrared (VSWIR) wavelength range. We show that grain sizes are generally poorly constrained from VSWIR spectroscopy. Abundance and grain size trade‐offs lead to typical abundance errors of ≤1 wt % (occasionally up to ~5 wt %), while ~3% noise in the data increases errors by up to ~2 wt %. Systematic errors further increase inaccuracies by a factor of 4. Finally, phases with low spectral contrast or inaccurate optical constants can further increase errors. Overall, typical errors in abundance are <10%, but sometimes significantly increase for specific mixtures, prone to abundance/grain‐size trade‐offs that lead to high unmixing uncertainties. These results highlight the need for probabilistic approaches to remote determination of planetary surface composition.

The Mars Science Laboratory (MSL) Bagnold Dunes Campaign, Phase I: Overview and introduction to the special issue

“…In contrast the coarser sands are darker and bluer, consistent with a greater proportion of mafic minerals such as pyroxene and olivine. The spectra are relatively dust‐free, consistent with orbital data [ Seelos et al ., ; Lapotre et al ., ] and with ongoing aeolian activity that would remove dust in suspension.…”

Hapke-based computational method to enable unmixing of hyperspectral data of common salts

“…The first approach [ 15 , 19 – 21 ] is to find best fitting parameters m i , D i that minimize the root mean square of the difference between the model and data reflectance. The second method is the probabilistic method [ 6 ], that uses a Markov Chain Monte Carlo algorithm and Bayes Theorem to estimate the probability density functions of the model parameters, given the reflectance data and model relationship between parameters. One of the advantages of the probabilistic model is that the detection noise model (which can be non-Gaussian for low count photons per pixel) can be accounted in the calculations.…”

“…Experimental earth material models have been used to better understand their spectral signatures and to answer some related questions. Salt and evaporite minerals are common earth materials that can be investigated for their reflectance parameters [ 1 , 4 – 6 ]. There is much interest in them since they have simple mineralogy yet significant environmental impacts on soils and plants.…”

The Geologic Exploration of the Bagnold Dune Field at Gale Crater by the Curiosity Rover

“…The Curiosity campaign also provided a unique opportunity to rigorously assess the uncertainty associated with orbital methods by comparison with in situ analysis. Mineralogic abundances derived from orbit are within 13 wt % of local measurements, where deviations are likely explained by the poorly constrained abundance/grain size trade‐offs that yield high unmixing uncertainties from the orbit‐based method (Lapotre, Ehlmann, & Minson, ; Lapotre, Ehlmann, Minson, Arvidson, et al, ). Nevertheless, the broader perspective of Bagnold dunes from orbital analysis relative to the spatially limited rover campaign shows that compositional variations are likely due to aeolian fractionation and mixing of multiple sand sources (Lapotre, Ehlmann, Minson, Arvidson, et al, ), as has been proposed for other Martian and terrestrial dune sites (Chojnacki et al, ; Fedo et al, ; Fenton et al, ).…”