20XX Vol. X No. XX, 000–000

11institutetext: State Key Laboratory of Lunar and Planetary Sciences, Macau
University of Science and Technology, Taipa 999078, Macau, PR China;
<EMAIL_ADDRESS>
22institutetext: Planetary Science Institute, School of Earth Sciences, China
University of Geosciences, Wuhan 430074, China
33institutetext: CNSA Macau Center for Space Exploration and Science, Taipa
999078, Macau, PR China
44institutetext: State Key Laboratory of Space Weather, National Space Science
Center, Chinese Academy of Sciences, Beijing 100190, China
55institutetext: CAS Center for Excellence in Comparative Planetology, Hefei
230026, China

# Spectral Deconvolution Analysis on Olivine-Orthopyroxene Mixtures with
Simulated Space Weathering Modifications

Hui-Jie Han 11 Xiao-Ping Lu 1 *1 * Te Jiang 22 Chih-Hao Hsia 1133 Ya-Zhou Yang
44 Peng-Fei Zhang 11 Hao Zhang 2255

###### Abstract

Olivine and pyroxene are important mineral end-members for studying the
surface material compositions of mafic bodies. The profiles of visible and
near-infrared spectra of olivine-orthopyroxene mixtures systematically varied
with their composition ratios. In our experiments, we combine the RELAB
spectral database with a new spectral data obtained from some assembled
olivine-orthopyroxene mixtures. We found that the commonly-used band area
ratio (BAR, Cloutis et al. 1986) does not work well on our newly obtained
spectral data. To investigate this issue, an empirical procedure based on
fitted results by modified Gaussian model is proposed to analyze the spectral
curves. Following the new empirical procedure, the end-member abundances can
be estimated with a 15% accuracy with some prior mineral absorption features.
In addition, the mixture samples configured in our experiments are also
irradiated by pulsed lasers to simulate and investigate the space weathering
effects. Spectral deconvolution results confirm that low-content olivine on
celestial bodies are difficult to measure and estimate. Therefore, the olivine
abundance of space weathered materials may be underestimated from remote
sensing data. This study may be used to quantify the spectral relationship of
olivine-orthopyroxene mixtures and further reveal their correlation between
the spectra of ordinary chondrites and silicate asteroids.

###### keywords:

techniques: spectroscopic — instrumentation: spectrographs — methods: data
analysis — minor planets, asteroids: general

##  1 Introductions

The spectral absorption features provided by hyperspectral remote sensing
enable us to investigate the geological and geochemical information over the
imaged area (Cloutis 1996; Clark et al. 2003; Zaini et al. 2014). Therefore it
is widely used to identify the minerals, rocks, water (ices), and organic
materials of the celestial bodies (Adams 1974; Singer 1981; Burbine et al.
2002; Pieters et al. 2009; Basilevsky et al. 2012; Roush et al. 2015; Lauretta
et al. 2019), such as terrestrial planets, moon and asteroids (Cloutis & Bell
III 2000; Ohtake et al. 2009; Lindsay et al. 2015; Zhang et al. 2015; Hu et
al. 2019; Tsuda et al. 2020). Visible and near-infrared (VNIR) reflectance
spectra are susceptible to the mafic minerals (Pieters & Mustard 1988; Lucey
2004; Staid et al. 2011), which contain the characteristics of mineral
composition and crystal structure (Hunt 1977; Mustard et al. 2005). As the
major group of mafic minerals, olivine and pyroxene are important materials in
understanding the geologic evolution, differentiation process and cooling
history of terrestrial bodies (Wells 1977; Ishii et al. 1983; Cloutis & Gaffey
1991; Klima et al. 2011). However, many limited factors should be considered
when using reflectance spectra to analyze remote sensing data from airless
bodies, because most reflectance spectra collected under laboratory are not
consistent with the data by remote sensing (Bishop et al. 1998; Cloutis et al.
2008; Shirley & Glotch 2019). One thing that needs to be focused on is “space
weathering”, which can change the chemical compositions and optical properties
of the surface materials (Pieters et al. 2000; Brunetto et al. 2006; Fu et al.
2012). It can make the spectral curves redden and darken, and difficult to
identify and interpret (Hapke 2001; Chapman 2004; Han et al. 2020). Therefore,
many methods for space weathering spectral deconvolution are extensively
studied in order to acquire the truth data interpretation (Sunshine & Pieters
1993, 1998; Gallie et al. 2008; Han et al. 2020; Potin et al. 2020).

###  1.1 Olivine, Pyroxene and Their Mixture Spectroscopy

Olivine is typically the dominant and foremost mineral crystallizing from
liquid magma in the Earth’s mantle and bears rich information about the magma
ocean (Elthon 1979; Garcia et al. 1995; Danyushevsky et al. 2000; Dyar et al.
2009). Olivines are mafic silicates with the formula (Mg, Fe)2SiO4, solid
solutions ranging from fayalite (Fe2SiO4) to forsterite (Mg2SiO4). The olivine
structure is nearly hexagonally close-packed and there are two octahedral
sites, M1 and M2. Half of the two octahedral interstices occupied by divalent
metal ions, usually either Mg2+ or Fe2+ (Dyar et al. 2009). The color of
olivine is mainly determined by the content of Fe2+ content. It looks green
with lower content of Fe2+ but becomes brown at high iron content. In VNIR
reflectance spectra, olivine is characterized by its Fe2+ electronic
transition absorption bands (Burns 1970; Hunt 1977), and forming a wide and
superimposed absorption near 1.0 $\mu$m region (Figure 1a). As the Fe2+
abundance increases, the 1.0 $\mu$m absorption band center shifts toward
longer wavelength and the band width increses (Sunshine & Pieters 1998; Han et
al. 2020).

Figure 1: Reflectance spectra of olivine with varied Mg-number (Fo#) and the
ones with pyroxene quadrilateral end-members. (a). Spectra of olivine with
varied Fo#. (b). The comparison of the spectra with various pyroxene
quadrilateral end-members: Di (diopside; shown as green), Hd (hedenbergite;
orange), En (Enstatite; red) and Fs (Ferrosillite; blue)

.

Pyroxenes are crystallized from original magma and forming the primary
component of planetary upper mantle and crust, and bear rich magma information
(Elkins-Tanton et al. 2005; Elardo et al. 2011; Head & Wilson 2017). Several
geothermobarometric tools have focused on pyroxene to study the igneous
differentiation in the Earth, asteroids and meteorites (Lindsley 1983; Cloutis
& Gaffey 1991; Sunshine et al. 2004; Klima et al. 2008). Pyroxenes are single-
chain silicates with the general formula XYSi2O6, where X and Y are both
divalent cations (commonly Ca, Fe, Mg, etc.). The stacking of chains gives
rise to two types of cavities, labelled M1 (close to octahedral in shape) and
M2 (more irregular in shape) (Burns 1970). Fe2+ in the two different
crystallographic positions M1 and M2 are responsible for the dominant pyroxene
spectra absorptions in the VNIR region, which produce two prominent absorption
features near 1.0 $\mu$m (Band 1) and 2.0 $\mu$m (Band 2) bands. While
substitutions of other cations such as Ca2+ change the crystal structure and
make the absorption characteristic to move towards longer wavelength (Adams
1974; Klima et al. 2011). Furthermore, it was found that in the spectra of the
pyroxenes (Figure 1b), the wavelengths of the two main absorption bands change
as a function of the concentrations of Fe2+ and Ca2+ (Adams 1974; Klima et al.
2007).

The spectral properties of pyroxenes have been intensively studied in the past
(Cloutis & Gaffey 1991; Sunshine & Pieters 1993). The most basic division of
pyroxenes is between orthopyroxenes (OPX) and clinopyroxenes (CPX) which is
based on differences in chemical composition and crystal structure. According
to this scheme, orthopyroxenes essentially contains $<$5 mol% CaSiO3
(wollastonite, Wo) and possess orthorhombic symmetry, while clinopyroxenes can
contain 0 $\sim$ 50 mol% Wo and possess monoclinic symmetry (Adams 1974;
Cloutis & Gaffey 1991). Therefore, they can form a diagram of pyroxenes
quadrilateral, the corners of the quadrilateral are the pyroxene end-members
diopside (Di, CaMgSi2O6), hedenbergite (Hd, CaFeSi2O6), Enstatite (En,
Mg2Si2O6), and Ferrosilite (Fs, Fe2Si2O6). Example spectra are shown in Figure
1b. The olivines and pyroxenes spectral data are all taken from the
Reflectance Experiment Laboratory (RELAB) database support by Brown
University. 111http://www.planetary.brown.edu/relab/.

According to the information described above, retrieving the mafic mineral
features from the obtained reflectance spectra does seem to be a viable task.
It provides an effective method for remote analysis of mafic minerals on the
planet’s surface. However, it is still difficult to directly interpret the
spectra because spectral analysis are hampered by the overlapping absorption
features, especially when dealing with mixture minerals (Clénet et al. 2011).
The spectral properties of mineral mixtures do not linearly vary with the
relative abundances of different end-members (Adams 1974; Singer 1981; Cloutis
& Gaffey 1991).

In this study, we choose the forsterite and low-Fe orthopyroxene as the two
end-members. Low-Fe orthopyroxene spectra show a narrow strong absorption near
0.92 $\mu$m region and a wide absorption near 1.8 to 1.9 $\mu$m region (Klima
et al. 2007). Therefore, center position of these two absorption bands will be
important information for studying the olivine-orthopyroxene mixture spectra.
Figure 2 shows the VNIR reflectance spectra of olivine, orthopyroxene and
their mixture (50% OLV + 50% OPX).

Figure 2: VNIR reflectance spectra of three mineral components with
orthopyroxene (shown as blue), olivine (green), and olivine-orthopyroxene
mixture (red). The RELAB IDs of these spectra are AG-TJM-008 (OLV), AG-TJM-009
(OPX) and AG-TJM-019 (MIX) respectively.

###  1.2 Space Weathering Simulations

The spectra of asteroids and lunar regolith are obviously different from those
of the laboratory minerals. The former are characterized by distinct red
continua slope and weak absorption unlike those of the fresh rocks in the
laboratory. Nanophase iron particles (npFe0) have been widely observed in
lunar soil which is confirmed to be the cause of the difference in these
spectra. It is widely thought that the formation of npFe0 in lunar soil is the
result of space weathering, which include micrometeorite bombardment,
energetic particles, as well as cosmic rays (Dybwad 1971; Hapke 1973; Pieters
et al. 1993). To understand the physical and chemical mechanisms of space
weathering, many simulation experiments were made in the laboratory (e.g.,
Keller & McKay 1993; Yamada et al. 1999; Hapke 2001; Loeffler et al. 2009; Fu
et al. 2012; Jiang et al. 2019). These experiments irradiated pulsed laser
beam onto the different samples to simulate the irradiation of micrometeorite
bombardments; or implanted proton particles (such as H+, He+ and Ar+) onto the
samples to simulate the solar wind implantation; or heated the samples with
microwave furnace at high temperature in a vacuum to simulate the space
environment. Among these methods, pulsed laser irradiation is effective in
generating space weathering effects. Since the pulsed laser can pump energy in
a very short time scale, it can be analogous to a high-speed and low-mass dust
particle micrometeorite impact (Yamada et al. 1999; Yang et al. 2017). In this
study, we utilized the pulsed laser irradiation for space weathering
simulations.

Overview of this study, firstly we collected and assembled some olivine-
orthopyroxene mixture spectra, the assembled samples are also irradiated with
pulsed laser in our experiment. Some calculation methods are utilized to study
these spectra. These spectral data, experiments and research methods will be
presented in Section 2. While, these methods have limitations and do not work
well for some samples. So we developed an empirical procedure to deal with
these spectral data. The results and some discussions are presented in Section
3. The conclusions are summarized in Section 4.

##  2 Samples and Experimental Methods

###  2.1 Samples and Reflectance Spectra Measurements

The spectra of synthetic mixtures presented in this study are taken from the
RELAB database and our experiment. The end-member components of RELAB
synthetic mixture samples are natural olivine (AG-TJM-008) and hypersthene
(AG-TJM-009) with grain sizes smaller than 38 $\mu$m. The mass mixing ratio of
the two minerals are 1/9, 3/7, 5/5, 7/3 and 9/1 respectively. Another part of
synthetic mixture samples from RELAB are natural olivine (PO-CMP-017) and
enstatite (PE-CMO-012) mixtures and the grain size is 45 $\sim$ 75 $\mu$m. The
mass mixing ratio of the two minerals are 1/9, 2.5/7.5, 5/5, 7.5/2.5 and 9/1
respectively. Chemical compositions of these end-member minerals are listed in
Table 1. The reflectance spectra of olivine-hyperthene mixtures are shown in
Figure 3a. In addition, we also utilize some olivine-bronzite mixture samples
whose end-member components are not analyzed. The sample IDs and mixture
compositions of these samples are listed in Table 2. Measurements of these
olivine-orthopyroxene mixtures are conducted using a bidirectional VNIR
spectrometer with an incidence angle of 30° and an emission angle of 0°
ranging from 0.30 (or 0.32) to 2.55 (or 2.60) $\mu$m.

Table 1: Chemical compositions of these olivine and orthopyroxene samples

Sample ID | AG-TJM-008 | AG-TJM-009 | PO-CMP-017 | PE-CMP-012 | OWN-OLV | OWN-OPX
---|---|---|---|---|---|---
Mineral | Olivine | Hypersthene | Olivine | Enstatite | Olivine | Enstatite
SiO2 | 40.81 | 54.09 | 40.87 | 55.3 | 40.66 | 52.06
TiO2 | 0 | 0.16 | 0 | 0.05 | 0.011 | 0.13
Al2O3 | 0 | 1.23 | 0.01 | 0.12 | 0.34 | 4.1
Cr2O3 | 0 | 0.75 | 0.04 | 0 | 0 | 0
Fe2O3 | 0 | 0 | 0 | 0 | 9.76 | 7.44
FeO | 9.55 | 15.22 | 7.77 | 9.38 | 0 | 0
MnO | 0.14 | 0.49 | 0.14 | 0.15 | 0.11 | 0.13
MgO | 49.42 | 26.79 | 51.58 | 32.8 | 48.00 | 34.85
CaO | 0.05 | 1.52 | 0.03 | 0.45 | 0.056 | 0.98
Na2O | 0 | 0.05 | 0.01 | 0 | 0.008 | 0.13
K2O | 0 | 0.05 | 0 | 0.02 | 0.004 | 0.006
P2O3 | 0 | 0 | 0 | 0.01 | 0.005 | 0.016
H2O | 0 | 0 | 0 | 0 | 0.04 | 0.04
| Fo 90.5 | En 73.6 | Fo 92.2 | En 85.5 | Fo 89.8 | En 87.7
Text | Fa 9.5 | Fs 23.4 | Fa 7.8 | Fs 13.7 | Fa 10.2 | Fs 10.5
|  | Wo 3.0 |  | Wo 0.8 |  | Wo 1.8

0.95The number unit is wt. %.

Table 2: Information summary of the end-member and synthetic mixed samples

Sample ID | OLV : OPX |  | Sample ID | OLV : OPX |  | Sample ID | OLV : OPX (Irradiate)
---|---|---|---|---|---|---|---
AG-TJM-008 | Olivine |  | AG-TJM-017 | 1 : 9 |  | XT-TXH-030-P | 2.5 : 7.5 (No)
AG-TJM-009 | Hypersthene |  | AG-TJM-018 | 3 : 7 |  | XT-TXH-031-P | 5 : 5 (No)
PO-CMP-017 | Olivine |  | AG-TJM-019 | 5 : 5 |  | XT-TXH-032-P | 7.5 : 2.5 (No)
PE-CMP-012 | Enstatite |  | AG-TJM-014 | 7 : 3 |  | XT-TXH-030-P1 | 2.5 : 7.5 (15 mJ)
OWN-OLV | Olivine |  | AG-TJM-020 | 9 : 1 |  | XT-TXH-031-P1 | 5 : 5 (15 mJ)
OWN-OPX | Enstatite |  | XO-CMP-015 | 9 : 1 |  | XT-TXH-032-P1 | 7.5 : 2.5 (15 mJ)
OWN-OL1/EN4 | 2 : 8 |  | XO-CMP-016 | 7.5 : 2.5 |  | XT-TXH-030-P2 | 2.5 : 7.5 (15 mJ * 2)
OWN-OL2/EN3 | 4 : 6 |  | XO-CMP-017 | 5 : 5 |  | XT-TXH-031-P2 | 5 : 5 (15 mJ * 2)
OWN-OL3/EN2 | 6 : 4 |  | XO-CMP-018 | 2.5 : 7.5 |  | XT-TXH-032-P2 | 7.5 : 2.5 (15 mJ * 2)
OWN-OL4/EN1 | 8 : 2 |  | XO-CMP-019 | 1 : 9 |  |  |

0.95Six samples with IDs like OWN-xxxx come from our experiment, with grain
size less than 75 $\mu$m. The others come from RELAB. Seven samples with IDs
like AG-TJM-xxx, with grain size $<$ 38 $\mu$m. The grain size of the other
RELAB samples is 45 $\sim$ 75 $\mu$m. Five samples with IDs like XO-CMP-xxx
are olivine-enstatite mixture samples. Nine samples with IDs like XT-TXH-xxx
are olivine-bronzite mixture samples, and six of these nine samples are
irradiated with pulsed laser to study space weathering effect. The total
amount of each mixture is counted as 10.

Figure 3: VNIR reflectance spectra of mixtures composed of olivine and
orthopyroxene mixed with different proportions. (a). The spectra are obtained
from RELAB database. (b). Spectral profiles are taken from our experiments
(2.14 $\mu$m artificial peaks are removed, narrow $\sim$1.41 and $\sim$2.33
$\mu$m absorption bands presented in some spectra are due to minor
alteration). For the sake of clarity, with the increase of olivine content,
the reflection spectra are superimposed and moved multiple +0.1 on the
ordinate.

The other part of the samples come from our experiment. We collect some
natural pure olivine (OWN-OLV) and enstatite (OWN-OPX) samples as experimental
materials. The samples are ground and sieved into grain size less than 75
$\mu$m. Chemical compositions of these sample powders are analyzed with wet
chemistry method and listed in Table 1. The mass mixing ratios of the two
minerals are 1/4, 2/3, 3/2 and 4/1 respectively (Table 2). A Bruker Vertex 70
Fourier transform spectrometer is utilized to get the VNIR reflectance spectra
of these samples. Each sample is measured four times with the sample holder
rotated 90° every time. The average spectrum is taken as the final spectrum to
reduce the effect of any surface inhomogeneity (Jiang et al. 2019). What needs
our attention here is that the VNIR reflectance spectra of these materials
have an artificial peak near 2.14 $\mu$m when Spectralon panel made of
polytetrafluoroethylene is used as the calibration plate in the near-infrared
(NIR) region (Zhang et al. 2014), two narrow spectral faint wobbles near 1.41
and 2.33 $\mu$m absorption bands presented in some spectra are due to minor
alteration. These two small fluctuations do not affect the results of this
study, because these artificial wobbles are not on the main band absorption
regions (Figure 3b). However, we do need to remove the 2.14 $\mu$m artificial
peak, as it appears in the orthopyroxene absorption features. Here, we utilize
a 4th-order polynomial to fit the data between 1.8 to 2.5 $\mu$m. Then the
data of the artificial peak ($\sim$2.03 to $\sim$2.18 $\mu$m) are replaced for
further study. The modified reflectance spectra are shown in Figure 3b.

###  2.2 Pulsed Laser Irradiation

The detailed experiment process can be found in Jiang et al. (2019). Here is a
brief summary: In order to study the space weathering effects on olivine,
orthopyroxene and their mixture spectra, some natural pure olivine and
orthopyroxene powders (less than 75 $\mu$m) are mixed with a certain
fractions. Each time $\sim$1.0 g of powder samples are uniformly placed in a
2.5 cm $\times$ 2.5 cm square in an aluminum holder. These powder samples are
baked in a dry oven at 120 ℃ for about 12 hours to remove the moisture. The
dried samples covered by a thin glass slide to prevent the powders sputtering
are placed in a vacuum chamber to cool to room temperature and then subjected
to pulsed laser irradiation at a pressure of 10-3 Pa.

A nanosecond pulsed laser (1 $\sim$ 50 mJ incident energy per pulse) is
utilized as a micrometeorite bombardment simulation system with pulse
frequency of 15 Hz. The laser spot is focused to a circle with a diameter of
0.5 mm using a lens and its moving speed is 1 mm s-1. Researches show that
after low-energy laser irradiation, the reflectance of olivine has a much
greater change than that of pyroxene. Even after multiple irradiations, the
depth of the pyroxene absorption band does not change much (Yamada et al.
1999; Jiang et al. 2019). In order to better simulate the space weathering, we
choose the maximum energy density (50 mJ) to irradiate the powder samples
twice. The first irradiation is to translate in the vertical direction, and
the second time is to translate in the horizontal direction. Each irradiated
sample is measured immediately after irradiation. Original and irradiated
reflectance spectra with the 2.14 $\mu$m artificial peak removed are shown in
Figure 4.

The irradiation energy density is set to be 3000 mJ mm-2 for each sample in
our experiments. Due to the reflection and absorption of the glass, the energy
transmission rate through the vacuum chamber glass window is about 90%.
Considering energy loss as the presence of the glass lens, glass slide and
aluminum sample holder, as well as the barrier effect caused by the npFe0
vapor deposition and the mineral particles adhered to the inner surface of the
glass slide, we assume that 10% of the energy is absorbed by the samples, so
the energy deposition is about 300 mJ mm-2. Total energy deposition rate by
dust impacts at 1 AU is estimated to be about 10-3 J m-2 yr-1 based on the
calculations of Yamada et al. (1999) and Sasaki et al. (2001). Possibly the
irradiation of samples in our experiments corresponds to about 300 Myr in the
space.

Figure 4: VNIR reflectance spectra of mixtures composed of olivine and
orthopyroxene mixed with different proportions before (solid lines) and after
(dashed lines) 50 mJ*2 laser irradiation. Narrow $\sim$1.41 and $\sim$2.33
$\mu$m absorption bands present in some spectra are due to minor alteration.
The colors of spectral curves are the same as Figure 3b.

###  2.3 The Modified Gaussian Model (MGM)

Originally developed by Sunshine et al. (1990), MGM is a mathematical process
based on the absorption of electronic transitions and is a statistical method
for studying probability distribution. It is a mathematical procedure for
deconvolving the superposed absorption features (Sunshine & Pieters 1993).The
MGM program can be obtained from Brown University
222http://www.planetary.brown.edu/mgm/. So far, some complex minerals and rock
samples have been explored with the MGM approach (e.g., Noble et al. 2006;
Clénet et al. 2011; Pinet et al. 2016). However, we need more efforts to
improve our spectral modeling and interpretation capability when dealing with
the spectra of natural unknown mafic bodies.

To elaborate on this model, four significant characteristics are used for
interpreting and exploiting the MGM, which are: band center, FWHM (full width
at half maximum), band strength, and continuum, as illustrated in Figure 5. In
MGM program, natural logarithm of each spectral curve is modeled in energy
domain (wave number), which means in wavelength domain a natural logarithm
spectrum can be deconvolved into multiple Gaussian distributions with a
continuum. MGM is modeled as:

$\ln\left[R\left(\lambda\right)\right]=C\left(\lambda\right)+\sum_{i=1}^{N}S_{i}\cdot\exp\left[-\frac{\left(\lambda^{-1}-\mu_{i}^{-1}\right)^{2}}{2\sigma_{i}^{2}}\right]$
(1)

where $\lambda$ is the wavelength, _R_ ($\lambda$) is the reflectance at
wavelength $\lambda$, _S_ is the band strength, $\mu$ is the band center,
$\sigma$ is the band width, and _N_ is the number of bands. _C_(_$\lambda$_)
is the function of the continuum in wavelength space.

Here the continua are fitted by using the logarithm of second-order
polynomial. Continua are modeled close to the inflection regions of each
absorption band, and we set an uncertainty within 20% for each parameter:

$C\left(\lambda\right)=\ln\left(c_{0}+c_{1}\lambda+c_{2}\lambda^{2}\right)$
(2)

$\lambda$= wavelength, $c_{0},c_{1},c_{2}$= constants

Figure 5: Four significant characteristic parameters for MGM fitting. For the
sake of clarity, the residuals (pink line) are shifted by +0.1 on the
ordinate.

##  3 Results and Discussions

###  3.1 MGM Parameters of Olivine and Orthopyroxene

In VNIR regions, olivine spectra show a broad and complex absorption feature
near 1.0 $\mu$m. The Gaussian curves presented in the top panels of Figure 6
indicate that olivine spectra are composed of three individual absorption
bands, they are around 0.84 $\mu$m, 1.03 $\mu$m and 1.23 $\mu$m respectively,
which are assigned to the M1–1, M2 and M1–2 sites in olivine crystal (Burns
1970). The width of each Gaussian absorption band in olivine spectra is
related to the iron abundance in olivine crystal and their ratio can be
applied to constrain the parameters in MGM (Sunshine & Pieters 1998).
Preliminary analyses of band strength derived by the MGM from olivine
reflectance spectra show the bandwidths of M1-1 and M2 are similar but the
width of M1-2 is about twice as large as M1-1 and M2. Analogously, the
absorption strength can also be evaluated as a function of composition. Band
strength of M2 and M1-2 are similar and about twice of M1-1.

VNIR reflectance spectra of low-Fe orthopyroxene are dominated by the
absorptions near 0.92 $\mu$m and 1.85 $\mu$m (bottom panels in Figure 6 ).
Each absorption is primarily caused by one electronic transition absorption
band (Sunshine et al. 1990). The strength of $\sim$0.92 $\mu$m band is
stronger than that of $\sim$1.85 $\mu$m band, whereas the band width of
$\sim$1.85 $\mu$m absorption is more than twice as large as $\sim$0.92 $\mu$m
absorption band.

Figure 6: The comparison of MGM fitting results for the spectral curves with
olivine and orthopyroxene obtained from RELAB database (panel (a): RELAB
olivine and panel (c): RELAB orthopyroxene) and our experiments (panel (b):
OWN olivine and panel (d): OWN orthopyroxene).

###  3.2 MGM Parameters of Olivine-Orthopyroxene Mixtures

The initial MGM parameters of the olivine and orthopyroxene in the two end-
member mixture can be used as constraints for further analysis of mixture
spectra. We utilize these parameters to initialize the MGM and an intermediate
ratio mixture in each group for spectral deconvolution. They are sample IDs:
AG-TJM-019 (50% OLV + 50% OPX) in RELAB and OWN-OL3/EN2 (60% OLV + 40% OPX) in
our experiment. The starting and final parameters of these two spectra in MGM
program are listed in Table 3 and the fitting results are shown in Figure 7.

Table 3: MGM modelling parameters of mixture samples spectra

Sample ID | AG-TJM-019 |  | OWN-OL3/EN2
---|---|---|---
Abundance | 50% OLV + 50% OPX |  | 60% OLV + 40% OPX
Gaussian Fitting Parameters | Starting | Final |  | Starting | Final
Parameters | Parameters |  | Parameters | Parameters
| Parameter 1 | 6.00E-01 | 6.17E-01 |  | 6.60E-01 | 6.57E-01
Continua | Parameter 2 | 8.50E-05 | 8.49E-05 |  | 1.10E-05 | 1.10E-05
| Parameter 3 | -2.30E-08 | -2.50E-08 |  | -1.50E-08 | -1.68E-08
| Center | 840 | 836.8 |  | 840 | 859.1
M1-1 | FWHM | 150 | 102.9 |  | 150 | 141.7
| Strength | -0.08 | -0.802 |  | -0.07 | -0.069
| Center | 1035 | 1056.1 |  | 1030 | 1050.0
M2 | FWHM | 150 | 183.6 |  | 170 | 168.6
| Strength | -0.15 | -0.152 |  | -0.13 | -0.141
| Center | 1245 | 1221.6 |  | 1220 | 1211.4
M1-2 | FWHM | 300 | 258.3 |  | 320 | 353.2
| Strength | -0.16 | -0.117 |  | -0.15 | -0.145
| Center | 920 | 919.6 |  | 920 | 919.1
Band 1 | FWHM | 200 | 176.8 |  | 200 | 179.5
| Strength | -0.65 | -0.686 |  | -0.20 | -0.203
| Center | 1885 | 1888.5 |  | 1800 | 1800.1
Band 2 | FWHM | 500 | 541.2 |  | 450 | 439.5
| Strength | -0.40 | -0.422 |  | -0.12 | -0.114
Root Mean Square Error | 2.523E-03 |  | 3.588E-03

0.97Band center and FWHM are in the unit of nanometers. The final parameters
are rounded off to proper precision. Band 1 is for absorption near 1.0 $\mu$m
in OPX, while Band 2 is for absorption near 2.0 $\mu$m in OPX.

The results show that when olivine and orthopyroxene are mixed in equal
amount, orthopyroxene dominates the spectral absorption features of the
mixture. As shown in Figure 6 and Figure 7, the center positions of the
orthopyroxene’s absorption bands are relatively stable, the strength is close
to half of the pure orthopyroxene and the ratio of FWHM parameters remains the
same. While, parameters of the three Gaussian absorption bands in olivine
spectra change a lot, the strength of each absorption band is about 1/3 of the
pure olivine mineral, and the strongest absorption M1-2 band decrease sharply.
When the content of olivine is more than orthopyroxene, the spectral curve of
the mixture near 1.0 $\mu$m region show a broad asymmetric complex absorption
feature, and the absorption features of olivine dominate the spectra curve
between 1.0 to 1.5 $\mu$m regions.

Figure 7: MGM fitting results for the samples composed of olivine and
orthopyroxene mixed with different proportions. The fitting curves with the
OPX absorption features are plotted as the blue curve. The red curve
represents the olivine absorption bands fitting by using the Gaussian
function.

###  3.3 Modified BAR of Olivine-Orthoyroxene Mixtures

We also utilize the band area ratio (BAR) method (Cloutis et al. 1986) to
analyze these spectra. BAR method does not need MGM processing and it is
generally considered as a very useful indicator for interpreting the
olivine–orthopyroxene mixture spectra, which is nearly independent of mineral
composition and mineral grain size (Cloutis et al. 1986). However, we found
that the BAR values of each mixture sample group show a well linear trend, but
not all of them follow the trend line given by Cloutis et al. (1986). In the
calculation results of some samples, especially for the BAR values of our
newly acquired spectral curves, the deviation between the estimated mineral
abundance value and its true value maybe more than 30% (Figure 8).

The deviations are mainly caused by using different spectrometers as stated in
Hapke (2012), band depths and band shapes depend on illumination and viewing
geometry. It can cause differences in band shapes between spectra of the same
material measured bidirectionally and using an integrating sphere to measure
the directional–hemispherical reflectance. Therefore, we should use this trend
line with caution, especially when the spectrometers and/or the viewing
geometry used for measurement are different and the abundances and/or end-
member chemistries are unknown. Fortunately, the well linear trend shown by
each BAR parameter group provides a direction for solving this problem. As
shown in Figure 6 and Figure 7, M1-2 band ($\sim$1.23 $\mu$m) in olivine
absorption features is able to be distinguished from the absorption band of
orthopyroxene. The absorption strength of olivine M1-2 band and overall
absorption feature near 1.0 $\mu$m contain the information about the relative
content of olivine and orthopyroxene. It indicates that we can use the MGM
fitting results to estimate the mineral abundance.

Figure 8: BAR values derived from the spectra with olivine–orthopyroxene
mixtures utilized in this study. The solid line represents the trend line
given by Cloutis et al. (1986). Black dots and triangles denote the results
estimated from RELAB and our original experiment samples respectively.

Firstly, we utilize MGM to obtain the absorption features of olivine and
orthopyroxene in the mixtures. Secondly, a modified band area ratio (MBAR)
indicator is obtained by using MGM fitting result parameters. The MBAR is
modeled as:

$MBAR=Area\\_2\mu m/Area\\_1\mu m$ (3)

where, _Area_ is calculated with an approximation and it is defined as:

$Area=\sum_{i=1}^{N}1.065*FWHM_{i}*STR_{i}$ (4)

where, 1.065 is the factor to get the integral of Gaussian curve by using
_FWHM_. _STR_ is the absolute value of absorption strength. There are 4
absorption bands in Area_1$\mu$m, which are the three diagnostic absorption
features of olivine and one absorption of orthopyroxene (that is Band 1).
There is only one orthopyroxene absorption band (Band 2) in Area_2$\mu$m. The
illustration in Figure 9 explains these definitions in detail.

Figure 9: The spectral diagnostic feature of modified band area ratio (MBAR)
derived from MGM fittings. For the obvious absorption feature close to 1.0
$\mu$m, the area of this band composed of four Gaussian curves (shown as blue)
is defined as Area_1$\mu$m. For the band at around 2.0 $\mu$m, this feature is
made by single Gaussian curve with orthopyroxene (orange line) and then
defined as Area_2$\mu$m.

Finally, MBAR can be regarded as the absorption intensity coefficient of the
two main absorption bands in the olivine–orthopyroxene mixture spectra. As is
mentioned above, M1-2 band in olivine spectra are easy to extract from the
mixture spectral curves. Dividing MBAR by the olivine M1-2 band absorption
strength value (abbreviated as: MBAR/OLV_STRM1-2) can get the end-member
composition information. The result values show a good pattern on the
estimation results, as the orthopyroxene abundance increases, the MBAR value
increases, the OLV_STRM1-2 value decreases and the ratio data of the two
values show an exponential growth trend. In order to show their changing
patterns clearly, we use an exponential ordinate to display them. Figure 10
shows the calculation results and the regression equation. The overall error
in predicting the mixture composition based on MGM fitting results is less
than 15%.

Figure 10: A plot of MBAR/OLV_STRM1-2 ratio versus orthopyroxene abundance.
The solid line represents a linear least-square fit for all data with the
orthopyroxene abundance between 10% and 90%. The notations of data points are
the same as Figure 8.

Here, to test the deconvolution analysis and the trend lines described above,
we choose two olivine-orthopyroxene mixture samples with the same end-member
minerals as examples (RELAB ID: XT-LXM-057 and XT-LXM-060, whose grain sizes
are 32 $\sim$ 63 $\mu$m, with 50% olivine + 50% orthopyroxene). These two
reflectance spectra are measured by placing identical samples in different
sample dishes. XT-LXM-057 is placed in an aluminum dish coated with black
Teflon and XT-LXM-060 is placed in a Nicolet dish. Two different spectral
curves are obtained by changing the sample holding dishes. Their reflectance
spectra are shown in Figure 11a. The deconvolution fitting results are
obtained by using the MGM and the mineral abundance estimation results are
shown in Figure 11b. MBAR of the two mixture samples are 0.850 and 0.861,
olivine M1-2 band absorption intensity values are $\sim$0.078 and $\sim$0.094.
MBAR/OLV_STRM1-2 values are 10.9 and 9.2 respectively. The orthopyroxene
abundance estimation results are 61.9% and 58.1%. Compared to the true value
(50%), these two results are all within the accuracy range of 15% given above.

Figure 11: Spectral reflectance of two RELAB olivine–orthopyroxene mixture
samples and mineral abundance estimation results obtained by MGM. Dot
represents the true value and square represents the estimated value.

###  3.4 Fitting Results of Irradiated Samples

Some RELAB samples irradiated with the pulsed laser to simulate the space
weathering effect are mentioned in Table 2, but it seems no significant
spectral alteration with their spectral curves. However, for our samples, the
fresh spectra and irradiation spectra by high energy laser show obviously
difference (Figure 12), which are suitable for further study. After
irradiation, the spectral features turn weaker and shallower. Absorption
intensity and albedo of the visible region decrease faster than the NIR
region, whose behaviors redden and darken the irradiated VNIR spectra. In a
high-intensity or long-term space weathering environment, the spectra of
pyroxene appear more reddening, and olivine spectra appear more darkening.
This is consistent with the results presented in Yamada et al. (1999) and
Jiang et al. (2019).

Figure 12: Comparison of the spectral curves composed of olivine-orthopyroxene
admixtures mixed with different proportions and their irradiated results.

A widely utilized continuum remove method is employed to compare the spectral
absorption features and the band depth of these samples before and after
pulsed laser radiation (Clark & Roush 1984). Band center positions of the
continuum-removed spectra before and after laser irradiation are compared in
Table 4, it is generally believed that continuum-removed band positions are
less affected (shift a few nanometers) by space weathering (Pieters et al.
2000; Fu et al. 2012). Figure 13 shows the parameter comparison of these
original and irradiated spectral curves. The absorption features near 1.0
$\mu$m is the superposition of olivine and orthopyroxene. Obviously, the
higher the proportion of olivine is, the more band depth decreases after laser
irradiation. While the absorption features near 2.0 $\mu$m is only due to the
spectral absorption of orthopyroxene, the spectral curves in this region
change uniformly. A sub-figure shows the albedo value of these samples and
here it uses the average of the spectral reflectance from 0.5 to 0.8 $\mu$m
(close to visible region). This figure shows that orthopyroxene has stronger
resistance to space weathering than olivine. On the whole, the higher content
of olivine is in mixture, the weaker absorption features are in its irradiated
spectra, which may make these spectra more difficult to identify and
interpret.

Table 4: Comparisons of the absorption band centers before and after
irradiations

Sample ID |  | Original |  | Irradiated
---|---|---|---|---
|  (1$\mu$m) |  (2$\mu$m) |  |  (1$\mu$m) |  (2$\mu$m)
OWN-OPX |  | 912.16 | 1795.26 |  | 913.45 | 1803.38
OWN-OL1/EN4 |  | 911.52 | 1801.50 |  | 912.16 | 1805.26
OWN-OL2/EN3 |  | 915.38 | 1804.01 |  | 915.38 | 1809.04
OWN-OL3/EN2 |  | 931.16 | 1824.32 |  | 922.55 | 1808.41
OWN-OL4/EN1 |  | 1037.15 | 1824.32 |  | 1041.11 | 1824.32
OWN-OLV |  | 1056.17 | \- - |  | 1057.03 | \- -

0.7Band centers are in nm, values listed in this table are approximations.

Figure 13: Variations of band-depths and albedos (average of the spectral
reflectance ranging from 0.5 to 0.8 $\mu$m) of olivine-orthopyroxene mixtures
before and after pulsed-laser irradiation. Figure 14: Deconvolution results of
the olivine-orthopyroxene mixtures derived from MGM fittings. (a). The
evolution of MBAR ratios (Band M1-2 absorption strengths) of olivine-
orthopyroxene mixtures with different proportions before and after pulsed-
laser irradiation. (b). Correlation of truthful and estimation abundances of
the mixtures with pulsed-laser irradiation, the blue circles and orange
squares represent the truthful and estimation abundances of these mixtures
respectively.

Also, we deconvolve these space weathered spectra based on the prior mineral
knowledge and the constraints mentioned above. After pulsed laser irradiation,
the MBAR of these samples all increase (Figure 14a). It can be inferred that
the spectra of the short wavelength are more susceptible to space weathering
than the longer wavelength in the VNIR region. What is more, as olivine is
more susceptible to space weathering, the spectral absorption strength of
olivine will reduce significantly. The more olivine content is in the
mixtures, the greater ratio decrease of Band M1-2 absorption strength (Figure
14a), which will further increase the deviation in the mixture composition
prediction results. MGM deconvolution results of these irradiated mixtures are
shown in Figure 14b. The distance between two points in the horizontal
direction represents the deviation value of the prediction result. With the
increase of olivine (decrease of orthopyroxene) content, the deviation of
estimate results also increases.

In addition, an extended calculation shows that it will get a slightly larger
MBAR/OLV_STRM1-2 value than the original spectrum when using MGM to deconvolve
the continuum-removed spectrum, that means it will slightly underestimate the
olivine abundance. This finding will be used later. All these results remind
us that we cannot be too cautious when identifying and interpreting the
spectra of space weathered celestial bodies. If the effect of space weathering
is not taken into account, MGM deconvolution results will usually
underestimate the proportion of olivine in the mixtures.

###  3.5 Estimating the Composition of Olivine-Orthopyroxene Asteroids

The research results obtained above are very promising and they can be used to
study the space weathered celestial bodies, such as asteroids or lunar rocks.
Asteroids are considered to be smaller and rotating faster than solid planets,
with minimal gravity, these asteroids have thinner regolith (Chapman 2004).
Q-type and S-type asteroids are characterized by spectra with moderate
silicate absorption features near 1.0 and 2.0 $\mu$m (Chapman 2004; DeMeo et
al. 2015). Vernazza et al. (2008) and Thomas et al. (2014) analyzed the VNIR
spectra of many Q-type and S-type asteroids and reported that most of them
have spectral properties similar to LL chondrites, whose main minerals are
hypersthene and olivine. Here we choose some asteroids dominated by olivine-
orthopyroxene for further study to estimate their mineral compositions.

####  3.5.1 Spectral Deconvolution on Olivine-Orthopyroxene Asteroids

The center positions of 2.0 $\mu$m absorption band are useful for determining
the compositions of pyroxene. Low-Fe orthopyroxene spectra show that the
absorption band center near 2.0 $\mu$m is ranging from 1.80 to 1.95 $\mu$m
(Klima et al. 2007). These informations can help us to search the suitable
asteroid spectra for studying their mineralogical characterization. Six
asteroids with high quality spectra are selected, they are: (4) Vesta, (15)
Eunomia, (158) Koronis, (631) Philippina, (2335) James and (4954) Eric. The
VNIR spectra of these asteroids are obtained from the Small Main-Belt Asteroid
Spectroscopic Survey (SMASS), which are presented on the MIT planetary
spectroscopy website 333http://smass.mit.edu/home.html.

Absolute spectral albedos are difficult to obtain with accuracy in many remote
sensing situations, so all spectra from MIT are normalized to unity at 0.55
$\mu$m. This work smoothed and shifted these asteroids spectra reflectance
curves to acclimatize to the MGM. First, the spectra are smoothed using the
Savitzky-Golay (SG) filter procedure (order = 3 and framelen = 25) (Savitzky &
Golay 1964). Then, the spectral curves should be shifted to the suitable
positions: if the maximum value of the asteroid albedo is less than 1.4, the
whole spectral curve will be shifted downward by 0.6, while if it is greater
than 1.4, it will be shifted downward by 0.7 (Figure 15). The purpose of this
shifted operation is to ensure that the spectral curves of these silicate-rich
asteroids can be compared with the experiment spectra. Subject to slight space
weathering, the slope of the mafic mineral spectra will increase slightly. The
steep visible band region and overall inclined spectral curves reveal that
these asteroids have suffered space weathering.

Figure 15: VNIR spectra of six asteroids (4) Vesta, (15) Eunomia, (158)
Koronis, (631) Philippina, (2335) James and (4954) Eric. These spectra are
normalized at 0.55 $\mu$m and shifted downward to suitable positions.

It is feasible to use the MGM deconvolution approach to estimate the mineral
abundances. MGM with the logarithm of a second-order polynomial continuum
removal method is employed to deconvolve these spectra. The deconvolution and
estimated results are shown in Figure 16 and Table 5. As shown in Figure 14
and described above, MGM will usually underestimate the proportion of olivine
in the mixtures when deconvolution is applied to space weathered spectra, so
the olivine content on these asteroids is only conservatively estimated in
this paper. It means that the fresh rocks or subsurface materials of these
asteroids may contain more olivine.

Figure 16: Decomposition of the components of 1.0 and 2.0 $\mu$m features for
six asteroids (4) Vesta, (15) Eunomia, (158) Koronis, (631) Philippina, (2335)
James and (4954) Eric. The OPX absorption bands fitted by MGM method are
plotted as blue curves and red lines represent the absorption features with
olivine. The black curves are the sum of all band profiles plus the continuum.

Table 5: MGM results and mineral abundance estimation results of the asteroids

Asteroids |  Area_1$\mu$m |  Area_2$\mu$m |  OLV_STRM1-2 | Calculation | OLV : OPX
---|---|---|---|---|---
(4) Vesta | 264.48 | 341.82 | 0.0939 | 13.76 | 33% : 67%
(15) Eunomia | 127.96 | 41.89 | 0.1752 | 1.87 | 77% : 23%
(158) Koronis | 123.33 | 55.31 | 0.0821 | 5.46 | 53% : 47%
(631) Philippina | 144.59 | 63.87 | 0.1103 | 4.00 | 60% : 40%
(2335) James | 142.63 | 83.67 | 0.0915 | 6.41 | 50% : 50%
(4954) Eric | 152.56 | 88.34 | 0.0832 | 6.96 | 48% : 52%

0.85Calculation represents the value of MBAR/OLV_STRM1-2

####  3.5.2 More Olivine on Asteroid (4) Vesta

Asteroid (4) Vesta is the second most massive and probably the second largest
asteroid (Thomas et al. 2005). It has been considered that olivine and
hypersthene are likely to be ubiquitous over the whole surface of Vesta (e.g.,
Hanna & Sprague 2009; Ammannito et al. 2013; Zambon et al. 2014; Le Corre et
al. 2015; Poulet et al. 2015). Ammannito et al. (2013) inferred the presence
of olivine using two primary methods, which are: Continuum removed spectral
curve matching method and Band centers with the BAR parameters. The average
spectra of (4) Vesta and olivine-rich site from a bright crater are given in
that paper. The spectrum of the bright crater reveals clear olivine
signatures, with the band near 1.0 $\mu$m centered at slightly longer
wavelength than the average (4) Vesta spectrum, and the area of the 2.0 $\mu$m
band is smaller than the average spectrum. The data are shown in Figure 17d.

Figure 17:  Decomposition of the components of absorption features for main-
belt asteroid (4) Vesta. (a). Modeled spectral fitting of the crater area with
olivine-rich. (b). Modeled spectral fitting of average Vesta spectrum. (c).
The estimations of mineral abundances derived from the SMASS and Dawn spectral
data. (d). Comparison of the continuum-removed spectra obtained from various
areas of (4) Vesta (Data from Ammannito et al. (2013) and olivine-
orthopyroxene systematic mixtures with different proportions.

These data can infer that the surface of the asteroid (4) Vesta contains a
high content of olivine. The olivine modeled abundance is about 20%, and the
spectra of some fresh rocks from the impact crater are interpreted as having
an olivine content of more than 50%, maybe even up to 70% $\sim$ 80%
(Ammannito et al. 2013; Clénet et al. 2014; Poulet et al. 2015). In order to
deconvolve these two continuum removed spectral data, we adjusted the MGM
parameters to the study in this work. The deconvolution results (shown in
Figure 17) of the spectral data obtained by SMASS and Dawn are very
consistent. Remote sensing and orbital average spectral data of the asteroid
(4) Vesta show that there are about 30% olivine + 70% orthopyroxene in its
surface mafic materials. While the deconvolution results of the bright crater
spectrum reveals that there is approximately 70% olivine. Considering that the
spectraum of the bright impact crater is continuum removed (as described at
the end of Section 3.4) and it has also been slightly weathered in space, we
infer that the olivine composition of partial craters on asteroid (4) Vesta
are greater than 70%. This result is consistent with the findings of Ammannito
et al. (2013) and Poulet et al. (2015). Based on these findings, we can infer
that the other asteroids mentioned above also have a high olivine content.
However, space weathering prevents the correct deconvolution and
interpretation of these spectra.

###  3.6 Different Orthopyroxenes

The orthopyroxene measured in RELAB and our experiment are both low-Fe
orthopyroxenes. To understand whether the mixture of olivine and high-Fe
orthopyroxene is also suitable for the method presented here, we carried out
the following study. As is shown in Figure 1b, the spectral curve of
Ferrosillite, a kind of high-Fe orthopyroxene, shows an obvious absorption
characteristic near 1.2 $\mu$m. This spin-allowed crystal field absorption
band is attributed to the presence of Fe2+ in the crystal M1 site, which is on
the shoulder of the 1.0 $\mu$m band (Klima et al. 2007). This position is very
close to olivine’s M1-2 band and thus care must be taken when interpreting the
data. In addition, the two main absorption bands centered around 1.0 and 2.0
$\mu$m shift towards longer wavelength as the iron content increasing. Here we
choose the asteroid (1862) Apollo (Figure 18a) for further study, as its
spectral curves show an olivine reflectance peak near 1.6 $\mu$m with two
high-Fe orthopyroxene absorption bands (Gaffey et al. 1989; Buratti et al.
2004).

Figure 18: VIR Spectral curve of asteroid (1862) Apollo and decomposition of
the components of 1.0 and 2.0 $\mu$m features. (a). The observed and smoothed
spectra are normalized at 0.55 $\mu$m and shifted downward to the suitable
positions. (b). Comparison of the continuum-removed spectral curves and
olivine-orthopyroxene mixtures with different proportions. (c). Decomposition
of the components of absorption features without considering $\sim$1.2 $\mu$m
sub-band composed of high-Fe orthopyroxene. (d). The curve is fitted by using
same method as (c) panel, but considering $\sim$1.2 $\mu$m absorption band
(marked as green line).

Spectral curve matching method is used for this spectrum, and three absorption
features near 1.0 $\mu$m, 1.2 $\mu$m and 2.0 $\mu$m are compared with
systematic mixtures (Figure 18b). It derived olivine abundance is about 80% in
the olivine-orthopyroxene mixtures. Two MGM deconvolution procedures are
utilized here, one considering the $\sim$1.2 $\mu$m absorption of the high-Fe
orthopyroxene and the other does not considering this band. The deconvolution
results are shown in Figure 18c and 18d.

If we ignore the absorption of the $\sim$1.2 $\mu$m band, the deconvolution
result of MGM will get a larger absorption intensity in the olivine M1-2 band
than the one who adds the $\sim$1.2 $\mu$m absorption band. The actual
$\sim$1.2 $\mu$m absorption band will increase the area of 1.0 $\mu$m band,
which will lead to the MBAR value decreasing. The combination of these two
factors will be misinterpreted as the content of olivine in the material is
higher than the actual abundance. Figure 18c shows that the surface material
of asteroid (1862) Apollo is composed of 96% olivine and 4% orthopyroxene,
which does not meet our perception. However, Figure 18d shows it contains
about 88% olivine and 12% orthopyroxene (here we have deducted the area of the
$\sim$1.2 $\mu$m absorption band). Although the results of these two estimated
values are close, we have proved that the deconvolution result considering the
$\sim$1.2 $\mu$m absorption band is relatively reliable.

##  4 Conclusions

In this article, a new empirical procedure based on MGM with some prior
mineral absorption bands is presented to estimate the end-members abundance
from olivine-orthopyroxene mixture spectra. The accuracy of the end-member
abundance can be estimated within 15% by using this new procedure.

Integrated with RELAB database, a new spectral set obtained from olivine-
orthopyroxene mixtures assembled at 20% mineral abundance intervals in our
experiments is exploited. The VNIR absorption spectra of olivine-orthopyroxene
mixtures systematically varied with their various abundances. However, we
found the commonly-used BAR does not work well for some mixtures and the BAR
of different mixture sets show large deviations. As a powerful tool, MGM is
utilized to reveal the composition of mafic mineral assemblages. A modified
BAR (namely MBAR) is introduced to describe new-defined band area ratio based
on the fitted parameters by MGM. Two parameters of MBAR and olivine M1-2 band
absorption strength (as defined in the MGM) are used to estimate the mineral
abundances of olivine-orthopyroxene mixtures. The systematic procedure is
quite efficient for deconvolution of olivine-orthopyroxene mixture spectra and
estimation of the mineral abundances for mafic materials from the VNIR
reflectance spectra.

Additionally, space weathering effect on olivine-orthopyroxene mixtures and
silicate asteroids is investigated based on the new proposed procedure. Some
samples are irradiated by high-energy laser in our experiments and the
spectral profiles of these samples vary with irradiation fluxes significantly.
After irradiation, we find that mineral diagnostic spectral features
($\sim$1.0 and $\sim$2.0 $\mu$m bands) become weaker and shallower. The
intensities of absorption bands and albedos of these spectra in the visible
region decrease faster than that in the NIR region. The MGM deconvolution
results of these irradiated mixtures indicate that orthopyroxene has stronger
resistance to space weathering than olivine. Among the results, MBAR
increases, while olivine M1-2 band absorption strength decreases, which makes
these irradiated spectra more difficult to identify and interpret. This
usually leads to an underestimate of olivine abundance. The VNIR spectra of
main-belt asteroid (4) Vesta from SMASS catalog and Dawn mission are
investigated by applying the new procedure and the results are consistent with
the others’ studies.

Besides, the influence of absorption band strength of high-Fe orthopyroxene at
$\sim$1.2 $\mu$m is also discussed in this study and we claim that this band
should not be ignored in the analysis of olivine and high-Fe orthopyroxene
mixtures. In the future, more experiments for spectral deconvolution of
different mafic mixtures and studies for various space weathering effects will
be implemented to extend the applications of the new proposed procedure and
MGM.

###### Acknowledgements.

We thank the anonymous reviewer for useful comments to improve our manuscript.
This work is supported by the Foundation of the State Key Laboratory of Lunar
and Planetary Sciences, Macau University of Science and Technology, Macau,
China. X. Lu is also funded by The Science and Technology Development Fund,
Macau SAR (No. 0073/2019/A2). C. H. Hsia acknowledges the support from The
Science and Technology Development Fund, Macau SAR (No. 0007/2019/A). Y. Yang
is supported by Beijing Municipal Science and Technology Commission (No.
Z181100002918003). T. Jiang and H. Zhang are supported by Natural Science
Foundation of China (Nos. 11773023, 11941001, 12073024 and U1631124). We are
very grateful to Xiao-Yi Hu and Pei Ma for their assistances in the
experiments, whose comments and suggestions also improved the manuscript. Part
of the spectral data utilized in this study are obtained and make available by
the RELAB Spectral Database at Brown University and Planetary Spectroscopy
data at MIT. The MGM program is developed and provided by Brown University. We
acknowledge the support of Brown University and MIT.

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