Figure 17.  To delineate the region with the deepest ~2.2 µm absorption within the Sands of Forvie ROI the highest valued areas with this endmember were retrieved using values >0.75 areal abundance/pixel. Both the means of the overall ROI and the highest concentration areas are plotted, with the highest concentration areas (fifty-six 12 m wide pixels) mapped as green on the HiRISE color image.
The MDI endmember spectrum shows the dominance of the spectral pattern with an increasing value at longer wavelengths that is slightly brighter than the mean spectrum. On the other hand, the SoF spectral comparison shows that the spectral endmember is darker and has an even deeper ~2.2 µm absorption as compared to the mean value. In summary, the margins of the sand deposits do exhibit local bedrock contributions and the interior deposit endmembers do represent the extreme values that produce the spectral patterns evident in the mean spectra for the ROIs for the two deposits.
7 Hapke-based Retrieval of Mineral Abundances and Grain Sizes
Overview: The Hapke (2012) radiative transfer model was developed for particulate materials whose grain size is larger than the radiation wavelength and has a non-zero porosity. The MDI and SoF sand deposits are ideal candidates for use of this model, and it has been used previously with CRISM data for the Bagnold dunes complex to retrieve abundances and estimates of grain sizes for selected mineral phases (Kreisch et al., 2017; Lapotre et al., 2017a, 2017b; Rampe et al., 2018). As noted in Section 2, we employ an MCMC method developed by Lapotre (2017b) to retrieve relevant chemical and mineralogical information, after first retrieving optical constants from laboratory-based spectral reflectance data using methods based on Lucey (1998). These optical constants, along with grain size information, are needed by the MCMC unmixing algorithm to synthesize SSA spectra on the fly as it iterates over ranges of grain sizes that are input into the system. Based on grain size analyses of active aeolian sands in Weitz et al. (2018, 2022, and references therein), we allow a grain size range of 50‑800 µm for each of our selected endmembers. We focus on modeling the endmember spectra for MDI and SoF deposits (Section 6) to ensure lack of contamination by local bedrock sources and to use spectra that have better diagnostic absorptions relative to the more mixed signals from the mean spectra. We also follow Occam’s razor and use the minimum number of endmember spectra that explain the CRISM-based spectra for the MDI and SoF endmember spectra.
Selection of Endmember Spectra: As noted in Section 3, CheMin data for MDI sand samples show the presence, in order of decreasing amount, of an amorphous phase, plagioclase feldspar, olivine, pigeonite, and augite. We started computations with these phases, with an intent of using additional information to narrow down the range of compositions associated with these phases. We assume that, because of the lack of metal-OH combination bands and extensive H2O combination bands in the spectral region of interest, the ubiquitous and relatively abundant XRD‑amorphous phase within the sand deposits as found by CheMin (Rampe et al., 2018, 2020) is an igneous glass component, as opposed to amorphous products of, for example, aqueous alteration of primary material.
We proceeded initially by establishing a database of optical constants from reflectance data for candidate glasses and crystalline minerals typically found in sands dominated by basaltic compositions. Following the methods of Lucey (1998), we use the Hapke (2012) function along with assumed values of the real index of refraction and grain size diameters to invert and solve for the imaginary indices of refraction for each endmember. We use values for the real indices of refraction as given by Lapotre et al. (2017a), assuming that it remains constant over the wavelength range of 0.9 to 2.5 µm (Hiroi & Pieters, 1994). The average grain diameter represents the average of the sieved grain size ranges for each sample. We then proceeded to run many different combinations of models, retrieving mineral abundances and grain sizes for the MDI and SoF sand deposits. Consideration of the root mean square errors (RMSE) and correlation coefficients (R2) between data and models allowed us to narrow down the range of likely components. As noted later in this section, a range of plausible results, rather than a single model, was a consequence of the nature of input spectral data and modeling methodology.
Amorphous Phase: Glasses with basaltic or near-basaltic compositions exhibit variable spectral reflectance patterns that are largely governed by the presence of iron. The broad spectral features centered near 1.05 µm and 1.9 µm in basaltic glasses are attributed to Fe2+ in octahedral and tetrahedral sites, respectively. (e.g., Bell et al., 1976; Cannon et al., 2017; Horgan et al., 2014). Additionally, coupling CheMin XRD mineralogy and APXS bulk chemistry gave different chemical compositions for amorphous components of Gobabeb and Ogunquit Beach sand samples (Rampe et al., 2020). To cover a range of possible Mars-like glass spectra resulting from different chemical compositions, we included a variety of endmember spectra from synthetic glass samples generated using APXS-based compositional measurements (e.g., McSween et al., 2008, normalized to SO3 = Cl = 0.0 wt.%) acquired by the Spirit rover for representative rocks and basaltic soils (rocks Wishstone, Irvine, Clovis, Grahamland, Gusev Mean Soil, Panda, Doubloon, and Independence; Table S1). The Spirit-based measurements are relevant because numerous measurements were made by this rover, thereby providing a range of samples and associated reflectance spectra and chemical compositions. Refer to Supporting Information for chemical compositions and synthesis procedures. For completeness, we also included a terrestrial glass sample from Hawaii (C1BE100_Gl) whose spectrum was employed in previous spectral-modeling studies as the amorphous component (Lapotre et al., 2017a; Rampe et al., 2018).
Plagioclase: CheMin data for the Ogunquit Beach MDI dune sample showed a composition of An48±5 (i.e., labradorite) for the feldspar component (Rampe et al., 2018). Earlier CheMin sand analyses have calculated additional plagioclase compositions of An49±4 and An63±5 (Rampe et al., 2020). The labradorite sample selected for our modeling provides a representative spectrum of plagioclase, with a shallow and broad ~1.2 µm feature due to iron in the crystal structure (Burns, 1970; Crown et al., 1987). This feature tends to be ubiquitous in basaltic assemblages (Adams et al., 1978; Crown et al., 1987), and the labradorite spectrum was considered by us to be a suitable endmember spectrum for our calculations.
Olivine: In olivine, Fe2+ and Mg2+ partition between the smaller M1 and larger M2 sites based on multiple factors including ion size configuration of the crystallographic site (Burns, 1970; Dyar et al., 2009). Olivine exhibits three absorption bands due to spin allowed Fe2+transitions in Fe2+ residing in both the M1 and M2 cation sites (Burns, 1970, 1993; Sunshine et al., 1998; Trang et al., 2013). The two M1 site absorptions are centered at ~0.85 and 1.25 µm, whereas the single M2 band is centered at ~1.03-1.05 µm. These features overlap to form a broad absorption envelope centered near 1 µm (Burns, 1970).
The olivine composition determined by CheMin for the sand deposits (Rocknest, Gobabeb, and Ogunquit Beach) have a mean composition of Fo55±5 (Achilles et al., 2017). We utilized a spectrum for our modeling that was acquired for a Fo51 sample (Table 2). This sample was chosen because the composition is within the range found in-situ by CheMin, has a well-defined broad 1 µm Fe2+ olivine spectral feature, minimal extraneous spectral features (i.e., from chromium or titanium), and a well-documented chemistry (Kokaly et al., 2017).
Pyroxenes: Clinopyroxenes, primarily pigeonite and augite, have been detected as a significant component of sand deposits in Gale crater (Achilles et al., 2017; Ehlmann et al., 2017; Rampe et al., 2018). CheMin-based pyroxene analyses do not readily distinguish among pyroxene minerals, because instrumental limitations result in strong overlap of the pyroxene diffraction peaks (Achilles et al., 2017; Rampe et al., 2018). Thus, pyroxene spectra were chosen based on compositions of Martian meteorites Elephant Moraine EET 79001 for pigeonite (Wo10-11En61-45Fs29-44; McFadden et al., 2005) and Lafayette for augite (Wo37-40En35-41Fs20-28; Boctor et al., 1976). However, reflectance spectra for bulk meteorite samples represent a mixture of minerals (felspar as diaplectic glass) rather than pure pyroxene signatures. Thus, we chose spectra for pure, synthetic pyroxene samples that have comparable compositions to the pyroxenes in Martian meteorites as stated above (Tables 1, 2).
Relationship to previous studies: Our spectral endmember set is similar to that utilized by Lapotre et al. (2017a) and Rampe et al. (2018) in their SSA-based analyses of sands from the Bagnold dunes. Both sets used plagioclase (labradorite), Fo51 olivine, pigeonite, and augite, with basaltic glass as the amorphous component. The significant difference is in the chemical composition of the glass component. We use a variety of potential basaltic glass endmembers having a range of Mars-like chemical compositions derived from chemical compositions of Martian basalts at Gusev crater. The above authors used a basaltic glass from Hawaii (C1BE100) and additionally incorporated a magnetite endmember. As discussed next, the glass is a significant spectral component, so that chemical compositions derived by inverting spectral data depend on the chemical composition of the glass whose spectral properties complement the best fit the model. More simply, two glasses with equivalent spectral properties but different chemical compositions necessarily result in two valid sets of derived chemical compositions.
Model Results: For each glass endmember, we ran 2000 unmixing models using MCMC while always including plagioclase, olivine, and pyroxene as part of the assemblage (Table S2). As noted by Lapotre et al. (2017a) spectral unmixing is nonunique, where tradeoffs between grain sizes and abundances can produce similar spectral features. The advantage of MCMC is that it solves for the probability density functions of each endmember’s abundance and grain size (i.e., it provides a range of possible solutions). To that end, we used violin plots to show the probability density functions superimposed on box-and-whisker plots to provide a visual representation of the distribution of the data, along with basic measures of central tendency (Hintze & Nelson, 1998). Some glass endmembers produced only a small number (~a dozen) good fits and were eliminated from consideration. The GMS_Gl (Gusev Mean Soil), Grahamland_Gl, and C1BE100_Gl endmembers produced the largest number (≥ 30) of best fit models (RMSE ≤ 0.005 and R2 ≥ 0.96) for both sand deposits. These runs also produced similar trends in mineral abundances and grain sizes.
As an illustrative example of model runs, we show in Figure 18 the SSA endmember spectra and model results that had the lowest RMSE and highest R2 between the data and retrieved models using GMS_Gl for the glass endmember.