Spectrophotometric modeling of Mercury’s regolith using MESSENGER MDIS data

Mercury can be modeled as an atmosphereless Solar System body. Such objects are covered by a regolith which affects how they scatter light. To deduce physical properties of Mercury’s regolith, we use spectrophotometry from the MDIS (Mercury Dual Imaging System) instrument of NASA’s MESSENGER (MErcury Surface, Space ENvironment, GEochemistry and Ranging) mission. The data comes in eight colors [1] between the wavelengths of 433.2 nm and 996.2 nm, with phase angles from 20 to 130 degrees. There are 37752 data points, of which we use 26610 that are at incidence and emergence angles below 70 degrees. 
A theoretical particulate-medium model is used to interpret the observed reflectance. The model includes a shadowing correction that depends on three geometry parameters of the regolith. The first parameter is the packing density ν, i.e., the ratio of the particles’ volume to the total volume. The other two parameters describe the regolith’s roughness as a fractional Brownian motion (fBm) surface: the Hurst exponent H in the horizontal and the amplitude σ in the vertical direction. 
The numerical implementation of the model includes a set of discrete parameter values [2]. However, using trilinear interpolation, we extend the parameters to have arbitrary values within the range of the discrete values, which are 0.15–0.55 for the packing density, 0.20–0.80 for the Hurst exponent, and 0.00–0.10 for the amplitude (in units of the width of the simulated medium). We optimize the model parameters in least-squares sense using the Nelder–Mead simplex method, followed by Markov chain Monte Carlo (MCMC) sampling that uses proposed parameter values drawn from Gaussian distributions. The model parameters are solved for all wavelengths simultaneously, which means that the result is physically consistent. In the present study, the size of the regolith particles follows a uniform distribution between 0.0006 and 0.003, in units of the medium width. 
Our results indicate that Mercury’s regolith is densely packed (ν = 0.541 ± 0.010) with moderate horizontal variations (H = 0.529 ± 0.009) and large height variations (σ = 0.098 ± 0.002). The MCMC solution allows us to predict the spectrophotometry for differing viewing geometries. Future work includes updating the implementation of the model by increasing the range of the parameter values, especially for the packing density to ν > 0.55. Another improvement is to modify the size distribution of the regolith particles. The results of our study can be utilized in the BepiColombo mission, which will start its science mission in early 2026.  

[1] Domingue et al., Icarus 257, 477 (2015)
[2] Wilkman et al., Planet. Space Sci. 118, 250 (2015)
[3] Nelder and Mead, Comput. J. 7(4), 308 (1965)