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.