We specifically used log ratio values of compositions in a
correspondence analysis (Aitchison, 1994) to reduce the dimensionality
of the compositional data sets to explore the extent of regolith
contributions to the sand measurements. The final data set consisted of
laboratory-based spectra used in the Hapke (2012) modeling of mineral
assemblages to retrieve phase abundances and grain sizes (Tables 1 and
2).
SSA spectra were retrieved from both the S and L CRISM data (Murchie et
al., 2007). The processing included explicit modeling of atmospheric
gases and aerosols using the DISORT radiative code (Stamnes et al.,
1988; Wolff et al., 2009) adapted for Mars conditions and the Hapke
photometric function (Hapke, 2012) as a surface boundary condition
(Arvidson et al., 2006). SSA spectral cubes were regularized, and the
best estimate of surface spectral properties were retrieved in the
presence of Poisson noise using a log maximum likelihood approach (MLM)
and projected at 12 m/pixel (Kreisch et al., 2017; He et al., 2019).
Comparison of the sensor space view shown in Figure 2 with the map
projected view shown in Figure 3 demonstrates the effectiveness of this
processing pipeline for our two sand deposit study sites (MDI and SoF).
Both the S and L 12 m/pixel processed data cubes for FRT00021C92 were
registered to the 25 cm/pixel HiRISE mosaic. The separate S and L data
cubes were also joined to retrieve full VNIR spectra from 0.50 to 2.60
µm.
CRISM SSA spectra are a representation of a mixture of minerals and
amorphous phases at varying abundances and grain sizes. Two techniques
were used to infer sand mineralogy, spectrally speaking. First, the
Sequential Maximum Angle Convex Cone (SMACC) endmember model (Gruninger
et al., 2004) was used to delineate endmember spectra for regions of
interest (ROIs) for both sand deposits. The procedure was used to choose
endmember spectra from the scene and then model each pixel within the
sand deposit as a linear combination of endmembers. This approach helped
to evaluate the spectral heterogeneity of the sands. Second, we
retrieved mineral phase abundances and grain sizes using the Hapke
(2012) model and laboratory spectra (Table 2). We employed a Bayesian
implementation of the Hapke model using a Markov chain Monte Carlo
(MCMC) algorithm as developed by Lapotre et al. (2017b). The MCMC
algorithm produced a variety of best fit spectra over ranges of
abundances and grain sizes, and thus we employed violin plots (Hintze &
Nelson, 1998) to show the statistical distribution of fits for numerous
runs. The runs were conducted on two representative CRISM spectral
endmembers identified by the SMACC method, chosen to avoid bedrock
regolith contributions to the ferrous silicates within the sand deposits
and thereby making model retrievals more robust.
Table 2. Reference information for model endmembers.