Regional spectrophotometric properties of 951 Gaspra Academic research paper on "Earth and related environmental sciences"

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Icarus

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Regional spectrophotometric properties of 951 Gaspra

Deborah L. Domingue^*, Faith Vilasa, Teck Choob, Karen R. Stockstill-Cahilla, Joshua T.S. Cahillb, Amanda R. Hendrixa

a Planetary Science Institute, 1700 E. Fort Lowell, Suite 106, Tucson, AZ 85719-2395, USA b The Johns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD 20723, USA

A R T I C L E I N F 0

A B S T R A C T

Article history: Received 9 February 2016 Revised 21 July 2016 Accepted 22 July 2016 Available online 3 August 2016

Keywords: Asteroid Gaspra Spectrophotometry

Spectrophotometric examination of the Galileo Solid State Imager (SSI) observations from the Galileo spacecraft reveal surface compositional heterogeneities in mineral compositions not related to geologic unit. These include variations in olivine and orthopyroxene content on the order of 15% and 25%, respectively. Opaque mineral phases across the inter-ridge regions vary in quantity, but consistently modeled better with ilmenite. The macroscale fraction of metallic iron varies subtly (0-10%) in quantity and in grain size (60-100 fim). Color properties also vary across the inter-ridge regions, indicating variations in regolith maturity. Comparisons of near-infrared ratio-reflectance suggest changes in regolith maturity that are different from those seen on the lunar surface and asteroid 433 Eros, commensurate with Gaspra's higher olivine content. Visible to near-infrared slopes compared to near-ultraviolet to visible slopes are indicative of a nanophase iron content of 0.01%-0.1%. Spectral mixing modeling studies of the SSI color spectra show results consistent with the presence of both microphase (> 50 nm) and nanophase (< 50 nm) size iron particulates. While the quantity of microphase and nanophase iron appears to be constant within the sample areas studied, the grain size of the microphase component varies. Agglutinates are present in some areas of the inter-ridge regions, but at low abundances (~5%).

© 2016 The Authors. Published by Elsevier Inc.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

The Galileo spacecraft's flyby encounter with 951 Gaspra on October 29, 1991 was the first spacecraft encounter with an asteroid. Among the observations returned were color image sets acquired by the Galileo Solid State Imager (SSI) in six narrow-band filters and one broadband filter. This study focuses on the photometric and spectral information within the six narrow-band color image data sets.

Examining the first set of color images returned of Gaspra, Belton et al. (1992) demonstrated that Gaspra's surface displays only subtle color variations. They identified three spectral classes of materials based on spectral slope between 0.41 and 0.99 /m and the depth of the 1 /m feature. This initial study found that brighter materials with stronger 1 / m features were associated with craters and ridge crests, while darker materials with weaker 1 / m features were associated with inter-ridge areas (Belton et al., 1992; Helfenstein et al., 1994). These studies used Gaspra's shape

* Corresponding author at: 400 Teresa Marie Ct., Bel Air, MD 21015, USA. E-mail address: domingue@psi.edu (D.L. Domingue).

model to derive local incidence and emission angle information. Combining color data from a moderate spatial resolution SSI image color set with a Near Infrared Mapping Spectrometer (NIMS) 17 spectral channel image data set, and using unsupervised spectral classification techniques (classification based on statistics rather than example end-members) for the data between 0.41-4.0 /m, Granahan (2011) demonstrated that Gaspra's surface could be characterized by two spectral units: the 0.99 /m unit (characterized by the 1 / m band centered at 0.99 / m and relatively darker at 2 / m) and the 1.05 /m unit (characterized by the 1 /m band centered at 1.05 / m and relatively brighter at 2 / m). The 0.99 / m unit appears to be associated with ridges and the 1.05 / m unit appears to be correlated to inter-ridge regions. The lower spectral resolution study by Belton et al. (1992) was performed with images at 164 m/pixel spatial resolution, in contrast to the higher spectral resolution study by Granahan (2011) that was performed at the lower 1.3 km spatial resolution.

Helfenstein et al. (1994) performed a more extensive study of the photometric and color properties using the entire Gaspra SSI image data set and ground-based disk-integrated observations to construct Gaspra's disk-integrated phase curve. In addition, they used disk-resolved measurements from the 0.56 / m and

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0019-1035/© 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

broadband clear (0.63 /m) filters (at 163 and 54 m/pixel spatial resolutions, respectively) coupled with the shape model (Thomas et al., 1994) to provide incidence and emission information that accounts for topography to constrain the photometric model. They applied a Hapke model to these data sets to describe the global photometric properties of Gaspra's surface.

Helfenstein et al. (1994) used the global average photometric function derived from the 0.56 /m data, coupled with the clear filter images to construct a photometrically-corrected albedo map of Gaspra's northern hemisphere based on the broadband clear filter images. They found the resulting albedo contrasts to be subdued, on the order of 10% or less (Helfenstein et al. 1994). In addition, they photometrically corrected the color image data sets to examine color properties across Gaspra's surface. It should be noted that the work performed by Belton et al. (1992) used a simple photometric correction, whereas the work by Granahan (2011) did not photometrically normalize the data set. Spectral slopes and absorption band depths within a spectrum change as a function of incidence and emission angle (Gradie et al., 1980; Pieters et al., 1991; Domingue and Vilas, 2007; Sanchez et al., 2012; Reddy et al., 2012), thus affecting quantitative color and spectral interpretations. Thus studies of spectral properties across a surface require photometric normalization to accurately compare different regions.

Helfenstein et al. (1994) demonstrated that most materials on the surface are nearly indistinguishable from the average global color. Examinations of 3 color ratios (0.99/0.41, 0.76/0.41, and 0.67/0.41 / m) with longitude showed that the largest longitudinal variations (~5%) occur in the 0.99/0.41 /m ratio.

Helfenstein et al. (1994) also applied a couple of classification techniques to the color data sets. They used both an unsupervised (statistical) classification technique (principal component analysis, PCA) and a supervised (comparative) classification technique to examine the relation of color with morphology. The PCA analysis correlates well with the Belton et al. (1992) results (Helfenstein et al., 1994). The supervised classification technique examined two color ratios (0.41/0.56 and 0.99/0.56) as a function of four geologic units: dark facets, intermediate materials, ridges, and craters. The results from the supervised classification indicate that dark facets are the least mafic and craters are the most mafic (Helfenstein et al., 1994). Ridges and craters have the stronger 1 / m band, where as dark facets have the weaker 1 / m band (Helfenstein et al., 1994).

The conclusion drawn from the Helfenstein et al. (1994) study is that whatever mechanisms are processing the regolith on Gaspra, they must explain the correlation of bright materials with stronger 1 / m band depths and darker materials with weaker 1 / m band depths. These band depth-albedo trends match well with the group of processes collectively known as "space weathering". The bright materials with stronger 1 / m features correlate with craters and ridges, which are younger surface features (Belton et al., 1992; Helfenstein et al., 1994). Darker materials with the weaker 1 /m feature correlate with older regions that have been exposed to the space environment longer, and are at topographic lows where materials collect over time due to downslope migration (Belton et al., 1992; Helfenstein et al., 1994). The spectrally-average areas are then a mixture of these two endmembers (Belton et al., 1992; Helfenstein et al., 1994). Helfenstein et al. (1994) examined the role of grain size variations and concluded that grain size differences alone could not explain the color and spectral differences. They postulated that the differences might be explained by the addition of impact glasses, rinds on grains, or the formation of agglutinates, all space weathering products.

Space weathering is a set of surface alteration processes that reddens spectral slopes in the visible (VIS) to near-infrared (NIR) and diminishes absorption band depths. Based on laboratory studies and measurements of the lunar soil samples it has been shown that the majority of the optical changes seen in space-weathered

spectra can be attributed to the presence of nanometer-scale particles of metallic iron (Papike et al., 1981; Pieters et al., 200 0; Taylor et al., 200 0). Nanometer-scale metallic iron (npFe0 ) is produced via two dominant mechanisms: (1) micrometeoroid bombardment and (2) solar wind ion implantation and sputtering (solar wind ion irradiation). Micrometeoroid bombardment produces vapor and melt deposits (patinas on regolith grains which contain npFe0 and agglutinates which contain coarser grains of npFe 0 than the patinas). Solar wind irradiation alters the top layers, reducing the top mono-layers and providing an environment for the production of npFe0 . Examination of particles returned from the asteroid Itokawa by the Hayabusa mission contained both nanophase iron and iron sulfide (i.e., trolite; Noguchi et al., 2011, 2014).

In studies of the lunar surface, plots of color ratio vs. reflectance are used to examine regolith compositional and maturity relations and trends (e.g., Lucey et al., 1995, 1998, 2000a, b; Staid and Pieters, 20 0 0). These types of color ratio versus reflectance comparisons are used to separate regolith maturity (degree of processing) from composition (such as iron content). The near infrared (near-ir) ratio-reflectance (0.99/0.76 to 0.76 / m) plots show trends associated with increasing ferrous iron in silicates and reddening and darkening trends associated with soil maturity or space weathering. UV ratio-reflectance (0.41/0.76 to 0.76 /m) separates spectral trends associated with variations in maturity (space weathering) with variations in opaque content (Lucey et al., 1998, 20 0 0a, b).

Murchie et al. (2002) used the near-lR ratio-reflectance to examine the processing of the regolith on Eros. Murchie et al. (2002) found weathering trends on Eros that differed from those on the lunar surface, indicating that the microphysical results of space weathering on Eros are different than those on the Moon. The color differences observed on lda, while they mimic the maturity trends seen in the lunar surface, the magnitude of the variations are much smaller (Clark et al., 2002). These differences could be due to compositional differences in the regolith of these asteroids compared to the Moon or to differences in the magnitude of the space weathering processes. Micrometeorite and ion bombardment experiments show the effects of these processes vary with composition, where olivine exhibits more pronounced changes than pyroxene (Sasaki et al., 2002; Marchi et al., 2005). Micrometeoroid impacts on asteroids are less energetic and will produce less melt than corresponding impacts on the lunar surface due to the difference in gravity potential (e.g. Cintala, 1992 and references therein). Main-belt asteroids will be exposed to a lower solar wind flux than the lunar surface, and near-Earth asteroids will experience a variable flux depending on its orbital properties. The lower impact energies for micrometeorites on asteroids compared to the lunar surface has led to the hypothesis that solar wind ion bombardment dominates the space weathering of asteroid surfaces (Pieters et al., 20 00). Studies of asteroid families have supported this hypothesis, indicating that ion bombardment operates on shorter time scales than micrometeorite bombardment (Strazzulla et al., 2005; Vernazza et al., 2009). More recent studies of Vesta suggest alternate processes, such as global mixing of the fine-grained component of the regolith, is responsible for altering the spectral properties of asteroid surfaces (Pieters et al., 2012).

The purpose of this study is to examine and characterize the evidence for variations in space weathering across the surface of Gaspra. The goal is to separate out the spectral variations due to photometry, composition, and regolith structure. The approach differs from those of past studies by:

(1) deriving a photometric correction for each color filter within

the SSl data set,

(2) examining the veracity of the photometric correction across the

surface,

(3) mapping NIR to VIS ratio versus reflectance properties across the surface,

(4) mapping UV to VIS ratio versus reflectance properties across the surface,

(5) examining photometrically-corrected, color-image based spectra within broad geologic units,

(6) applying spectral mixing modeling techniques to representative spectra to examine mineral content including nanophase iron and iron sulfide.

This approach differs from past studies in a few distinct ways. The photometric correction used in the Helfenstein et al. (1994) study was based on Hapke model solutions to the green filter (0.56 ¡¡m) observations, assuming that the photometric properties other than albedo do not vary significantly over the SSI filter wavelengths (0.41-0.98 ¡m). Their correction was based on both disk-integrated and disk-resolved measurements, where the shape model (Thomas et al., 1994) was used to provide incidence, emission, and phase angle values for the disk-resolved data set. This study uses disk-resolved measurements and the same shape model to provide incidence, emission, and phase angle values. Disk-resolved measurements are retrieved for each SSI filter and a separate correction is derived for each filter (see Section 4). Like the Helfenstein et al. (1994) study, we assume the shape model is adequate for accurately computing local angles of incidence and emission, though this assumption tends to fail near the limb and terminator and for regions where little control-point information was available. Domingue et al. (2011) demonstrated that photometric corrections derived from measurements that include the geometry to which the data are to be standardized, along with measurements covering the geometries of the data to be corrected, are needed to provide viable photometric correction factors.

Another difference in our approach is in the examination of both color and spectral properties. Helfenstein et al. (1994) examined longitudinal variations in color ratios, but did not include the lunar ratio versus reflectance approach for separating space weathering and composition. This study examines both the NIR to VIS and the UV to VIS ratio versus reflectance properties across Gaspra's surface on a pixel by pixel spatial resolution (see Section 5). Surface maturity in S-class asteroids using UV to VIS spectral slopes in comparison with VIS to NIR spectral slopes (Hendrix and Vilas, 2006; Vilas and Hendrix, 2015) is also examined and placed in context with the color and spectral analyses (see Section 6).

A new aspect of this study is the examination of the spectral properties of representative areas on Gaspra's surface based on the SSI data set. While these spectral data are of much lower spectral resolution than the work of Granahan (2011), they afford a much higher spatial resolution (164 m/pixel in contrast to 1.3 km/pixel). To place these spatial resolutions into global context, Gaspra's dimensions are that of an ellipsoid of 19 x 12 x 11 km (Belton et al., 1992). We apply an intimate mixing model to these spectra to examine mineral and submicroscopic iron component proportions, chemistry, and grain sizes (see Section 6).

2. The data set

The data sets used in this study include images acquired by the Galileo Solid State Imager (SSI) and the shape model derived from these returned images (Thomas et al., 1994). These data were retrieved from the Planetary Data System (PDS) archive. The images from the PDS archive that include the figure of Gaspra (listed in Table 1) were radiometrically calibrated to I/F (reflectance over incident solar flux) using the prescribed software listed in the PDS. The prescribed calibration software is the United States Geological Survey's Integrated Software for Imager and Spectrometers (ISIS) subroutine GLLSSICAL. However, the file format within the PDS

for these images is VICAR. In order to utilize this calibration software (as recommended in the PDS archive), the images were first translated into lSlS format using the lSlS subroutine VlCAR2lSlS. To successfully run the GLLSSlCAL subroutine camera kernels are required, which were not archived in the PDS. Searches for these kernels within the PDS and Navigation and Ancillary lnformation Facility (NAIF) were unsuccessful, thus the camera pointing was assumed to be nadir in order to run the radiometric calibration software. This assumption, if false, would produce only a few percent error in the value of the reflectance (l/F), two orders of magnitude smaller than the measurements errors. The radiometrically calibrated images (listed in Table 1) have been archived in the PDS (Domingue, 2015).

Six color image sets were acquired amongst the Gaspra SSI data set. These are described in Table 2. The plate model for Gaspra's shape (Thomas et al., 1994) was used to derive the incidence, emission, and phase angle values for the pixels of the images within each color set. This was accomplished using a Java-based routine (AsteroidApp-0913) written expressly for this project. AsteroidApp-0913 ingests the plate model and associated labels, Gaspra's rotation model (acquired from the NAlF) that provides the rotation axis and rotation angles, and Gaspra's orbit properties from the Jet Propulsion Laboratory's small bodies file. The AsteroidApp-0913 application provides a 3-dimensional visualization that the user can manipulate to match the illumination and viewing geometries in the SSI image of choice. Once the illumination and viewing geometries have been matched, the application will calculate on a plate-by-plate level the corresponding incidence, emission, and phase values, which can be displayed as requested by the user (Fig. 1 displays a screen capture of the AsteroidApp-0913 user interface). The application then produces a comma separated variable (.csv) table that can be translated into an lSlS image of the surface of Gaspra where the pixel values correspond to the photometric angle values. An example of the full resolution, shape model derived, photometry images are shown in Fig. 2. The spatial resolution of these photometry images far exceeds the spatial resolution of the SSl imagery used in this study. The original shape model provides vertices for the model plates every 2 ° of latitude and longitude. Note that this model was derived using images acquired at higher spatial resolution than those presented in this study.

Using lnteractive Data Language (lDL) the resolution of the photometry images were reduced to the resolution of the SSl images. The individual frames for each color set were obtained at essentially the same viewing geometry (Helfenstein et al., 1994), therefore the SSl images were co-registered to each other assuming a simple translation within the image frames. Once the SSI images within a color set were registered the corresponding photometry images were then registered (at their lowered resolution) to the color image set, thus forming an lSlS image cube. These color and geometry cubes were submitted to the PDS for archive (Domingue, 2016) for all six-color image sets of Gaspra. An example of the geometry backplanes of one of the color and geometry cubes is shown in Fig. 2.

3. Photometric analysis

Photometric modeling examines the variations in reflectance as a function of illumination (incidence angle relative to the surface normal) and viewing (emission angle relative to the surface normal) geometries. The purpose of photometric modeling is two-fold:

(1) provide a means to derive a photometric standardization to a common set of incidence, emission, and phase angle values, and

(2) derive some understanding of the physical properties of the scattering medium, in this case the surface regolith. Spectral properties have been demonstrated to change with incidence, emission, and phase angle (collectively known as photometric angles), thus

Table 1

Radiometrically calibrated image list archived to PDSa.

File name Filter name Scale (m/pxl) File name Filter name Scale (m/pxl)

107310100rcal CLEAR 456 107313765rcal IR-9680 276

107303100rcal RED 801 107313778rcal IR-8890 275

107303145rcal VIOLET 798 107313800rcal GREEN 274

107303200rcal IR-7560 796 107313813rcal RED 274

107303245rcal IR-9680 793 107313826rcal VIOLET 273

107313539rcal GREEN 287 107313839rcal IR-7560 272

107313 552rcal RED 286 107313852rcal IR-9680 272

107313565rcal VIOLET 286 107313865rcal IR-8890 271

107313578rcal IR-7560 285 107314965rcal CLEAR 217

107313600rcal IR-9680 284 107314978rcal CLEAR 216

107313613 rcal IR-8890 284 107315039rcal CLEAR 216

107313626rcal GREEN 283 107316065rcal GREEN 163

107313639rcal RED 282 107316078rcal VIOLET 162

107313652rcal VIOLET 282 107296100rcal CLEAR 162

107313665rcal IR-7560 281 107316113 rcal IR-8890 161

107313678rcal IR-9680 280 107306600rcal CLEAR 628

107313700rcal IR-8890 279 107318313rcal CLEAR 54

107313713rcal GREEN 279 107318326rcal CLEAR 54

107313726rcal RED 278 107278600rcal CLEAR 2006

107313739rcal VIOLET 277 107289100rcal CLEAR 1489

107313752rcal IR-7560 277 107299600rcal CLEAR 973

a See Domingue (2015) for reference to data archive.

Table 2

Gaspra image color sets archived to PDSa.

Radiometrically Full resolution

calibrated image Color set Color and geometry geometry cube

file name Filter name identification cube file name file name

107303100rcal RED A SetA_ColorGeom.cub SetA_Geom.cub

107303145rcal VIOLET A

107303200rcal IR-7560 A

107303245rcal IR-9680 A

107313539rcal GREEN B SetB_ColorGeom.cub SetB_Geom.cub

107313552rcal RED B

107313565rcal VIOLET B

107313578rcal IR-7560 B

107313600rcal IR-9680 B

107313613rcal IR-8890 B

107313626rcal GREEN C SetC_ColorGeom.cub SetC_Geom.cub

107313639rcal RED C

107313652rcal VIOLET C

107313665rcal IR-7560 C

107313678rcal IR-9680 C

107313700rcal IR-8890 C

107313713rcal GREEN D SetD_ColorGeom.cub SetD_Geom.cub

107313726rcal RED D

107313739rcal VIOLET D

107313752rcal IR-7560 D

107313765rcal IR-9680 D

107313778rcal IR-8890 D

107313800rcal GREEN E SetE_ColorGeom.cub SetE_Geom.cub

107313813rcal RED E

107313826rcal VIOLET E

107313839rcal IR-7560 E

107313852rcal IR-9680 E

107313865rcal IR-8890 E

107316065rcal GREEN F SetF_ColorGeom.cub SetF_Geom.cub

107316078rcal VIOLET F

107316113rcal IR-8890 F

a See Domingue (2015, 2016) for reference to data archive.

photometric standardization to a common photometric geometry is needed to reliably compare spectral properties (Gradie et al., 1980; Pieters et al., 1991; Domingue and Vilas, 2007; Domingue et al., 2011). It has also been demonstrated that the measurements used to derive the photometric correction should include the photometric angles to which the data is being standardized to derive a reliable correction (Domingue et al., 2011).

3.1. The model

Currently the most widely-used model is that derived by Hapke (1981, 1984, 1986, 1993, 2002, 2008, 2012), which is based on geometric optics and the equations of radiative transfer. This model incorporates expressions and parameters to account for surface roughness, porosity, grain scattering properties, and both mechanisms ascribed to the formation of the opposition surge

Fig. 1. This is a screenshot of the AsteroidApp-0913 software interface. The upper left corner image displays the asteroid shape and lighting (including the rotation axis) for the date and time given in the lower left corner. The larger image on the right displays the incidence angle values across the surface for the given date. The larger image can also be set to display emission or phase angle values across the surface.

(shadow-hiding, SHOE, and coherent backscatter, CBOE). The form of the Hapke model used in this study is given by

r(I, e, a) =

4ni {[P(a)[1 + Bso Bs (a)]] 4n l^oe + le

+ [H(loe)H(leI - 1 ]}S(i, e, a, 0),

where w is the single scattering albedo, p(a) is the single particle scattering function, Bs0 is the SHOE amplitude and the SHOE term Bs is given by

Bs (a) =

1 + -r-tan hi

where hi is the SHOE width of the opposition peak. S(i,e,a, 0) accounts for the large-scale roughness, and i0e and ie are the modified cosines of the incident and emission angles, respectively, due to roughness. The H functions are the Chandrasehkar H-functions. The mathematical expression of these terms, and their derivation can be found in Hapke (1981, 1984, 1986, 1993, 2002, 20 08, 2012). For this study a Henyey-Greenstein function of the form,

P(a) =

(1 - c)I1 - b2I

(1 - 2bcos(a) + b2 )3i2 (1 + 2bcos(a) + b2)

c 1 - b2

was used for the single particle scattering function, where c is the partition parameter between forward versus backward scattering components, and b is the amplitude of the scattering component.

Since the data set does not include measurements within the opposition surge, the opposition terms related to CBOE were not included. The value of the SHOE opposition terms were taken from the photometric study of Helfenstein et al. (1994) where Bs =1.63 and hi = 0.06.

Helfenstein et al. (1994) applied an early version of this model to a combination of ground-based, disk-integrated observations of Gaspra with disk-resolved observations derived from the highest resolution green (163 m/pixel) and clear (54 m/pixel) filter images. Including the ground-based observations provided Helfenstein et al. (1994) measurements within the opposition surge, thus providing model constraints for the opposition parameters. However, this limited their study in terms of wavelength coverage. We assume here that the opposition surge can be described by the same set of parameters over the SSI wavelength range (0.41-0.99 |m) and thus use the opposition terms derived by Helfenstein et al. (1994).

3.2. Modeling methodology and results

The color and geometry cubes used for this study included the five highest spatial resolution cubes (sets B-F) listed in Table 2. A reflectance, incidence, emission, and phase angle value was extracted for each pixel within the surface region of Gaspra in the color and geometry cube. The resulting data were segregated as a function of SSI camera filter (wavelength). The data from all the cubes were combined to form a disk-resolved photometric data set for each SSI camera filter. The incidence, emission, and phase angle

Fig. 2. Images of the geometry backplanes for image color set B. The left column (a-c) is from the full resolution geometry cube (SetB_Geom.cub). The right column (d-f) is from the last three backplanes of the color and geometry cube (SetB_ColorGeom.cub), where the resolution has been reduced to match the color image data. The top, center, and bottom rows display incidence, emission, and phase angle values across the surface, respectively.

coverage for each filter is shown in Fig. 3. ln this manner, the data to be photometrically corrected provide the measurements for deriving the photometric standardization. ln deriving the photometric correction for the Mercury global color mosaic, it was noted that the Hapke model provided the poorest corrections for those images acquired at high incidence ( > 70°) and high emission (>70°) angles (Domingue et al., 2011, 2014). Measurements characterized with high incidence and emission (Fig. 3) are included in the Gaspra data set as well.

The data from each filter were modeled with the Hapke equations described above using a least squares grid search method, as described in Domingue et al. (2010, 2011), that minimized the value of chi, x, defined by

x = V (rmeasured - rmodelI (4)

where N is the number of measurements, rmeasured is the measured reflectance, and rmodel is the model predicted reflectance. All parameters were varied simultaneously with the smallest grid increment value of 0.01 for all parameters except 9, where the smallest grid value was 1. The resulting parameter values were examined as

о H-1-1-1-1-1-1-1-1-1-1

0 10 20 30 40 50 60 70 80 90 100 Inddenc (deg)

20 H-1-1-1-1-1-1-1-1-1-1

0 10 20 30 40 50 60 70 80 90 100 Incidence (deg)

0 10 20 30 40 50 60 70 80 90 Emission (deg)

Fig. 3. The incidence, emission, and phase angle coverage for the disk-resolved photometric measurements of Gaspra's surface from image color sets B-F.

a function of wavelength where a polynomial was fit to each parameter to determine its value as a function of wavelength. This removes any spectral artifacts due to differences in measurements between filters and round-off errors. Formal errors are based on the grid increment values. The resulting parameter values are provided in Table 3. In contrast, the Helfenstein et al. (1994) models to the different wavelengths assumed that all parameters are constant with the exception of the single scattering albedo. They did not analyze any parameter variations with wavelength in their study.

Table 3

Hapke disk-resolved global parameter values for Gaspra.

Wavelength (^m) w b c 0

0.404 0. 50 0.23 1. 0 19. 9

0.559 0. 63 0.47 1. 0 7. 5

0.671 0. 57 0 . 25 1. 0 1. 8

0.756 0. 58 0. 22 1. 0 0

0.887 0. 63 0 .37 1. 0 0

0.986 0. 54 0. 24 1. 0 0

Error bars: ± 0.01 for w, b. and c; P for 0.

3.3. Evaluation and interpretation

The quality was analyzed in order to evaluate the veracity of the photometric modeling results and the photometric standardization or correction derived from these results. The quality analysis consisted of calculating the model-predicted reflectance at each pixel within the Gaspra images using the shape model derived incidence, emission, and phase angle values. From these calculations, a corresponding "Hapke Image" was created. A ratio of the observed reflectance from the SSI images to the predicted reflectance in the Hapke Images was then calculated, and the resulting "Ratio Images" provide a measure of the accuracy to which the global correction based on the disk-resolved photometric modeling predicts the surface reflectance properties. The results for each filter, within each color image set, are shown in Fig. 4. The images in these figures provide a visual means of correlating the photometric properties and quality of the photometric correction with morphology.

Displayed in Fig. 4 are four images for each filter within a color set. From left to right, the columns show the radiometrically-calibrated SSI image, the corresponding Hapke Image, the photometrically-corrected SSI image, and the Ratio Image. The photometrically-corrected image is corrected to the median incidence, emission, and phase angle values of the data set, which are 65.893°, 49.308°, and 34.075°, respectively. The correction factor, C, is derived from the relation:

= CRo.

where Rcorrected is the model predicted reflectance at the desired photometric geometries and Robserved is the model predicted reflectance at the photometric geometry of the observation. Using this definition, the photometrically-corrected image is equivalent to the Ratio Image multiplied by the model predicted reflectance at i = 65.893°, e = 49.308 ° , and a = 34.075°.

The Hapke Image, photometrically-corrected image, and the Ratio Image have all been filtered, such that any pixels outside the photometric angle values of 0° < i < 90°, 0° < e < 90°, and 0° < a < 180°, as extracted from the geometry backplanes, have been set to zero in all image planes. Bright and dark regions within the Ratio Images are indicative of large (>50%) differences between the measured reflectance and the model predicted reflectance (hereafter referred to as "regions of photometric interest"). These differences can be ascribed to multiple sources: (1) departures in the shape model from the actual shape, (2) assumptions within the application of the photometric model, and (3) variations in regolith properties from the global average.

The regions of photometric interest are identified in Fig. 5. These regions tend to be associated with ridge crests or depressions. The shape model was derived using stereogrammetric, limb, and terminator measurements as inputs to the software and techniques described by Simonelli et al. (1993) and Thomas et al. (1994). The model used a 2° by 2° latitude/longitude grid (Thomas et al., 1994). The shape model contains 16 control points to define

Fig. 4. Displayed for each color set are, from left to right, the radiometrically calibrated SSI, the Hapke Image, the photometrically-corrected image, and the Ratio Image. For color sets B-E the rows correspond to (a) the violet filter (0.404 (im), (b) the green filter (0.556 (m), (c) the red filter (0.671 (m), (d) the 756 infrared filter (0.756 (m), (e) the 887 infrared filter (0.887 (m), and (f) the 986 infrared filter (0.986 (m). For color set F the rows correspond to (a) the violet filter, (b) the green filter, and (c) the 887 infrared filter. The Ratio Images contain a scale bar with 4 scale increments. From top to bottom they are 2.0, 1.75, 1.0, and 0.5. Horizontal lines within the SSI images, photometrically-corrected images, and the Ratio images correspond to data noise within the original SSI raw images.

the surface shape in the grey area to the lower right of regions 3 and 7 shown in Fig. 5 (Thomas et al., 1994). The grey shades in this region indicate a good correlation between the measured reflectance and the model predicted reflectance. Region 1 (Fig. 5) was defined by 8 control points within this area and the shape within regions 2 and 3 were not constrained by any control points; they were constrained only with limb and terminator measurements (Thomas et al., 1994). These regions display a poorer correlation between measured and model predicted reflectance. The correlation between regions less well constrained by control points within the shape model, and larger differences between measured and predicted reflectance, indicates that departures in the shape model from the actual shape could be a contributor to the measured versus predicted reflectance differences.

Fig. 4. Continued

A similar test was performed with the Helfenstein et al. (1994) Hapke model parameters (Fig. 6), in an effort to examine the fidelity of the model. The quality of fit is comparable between the two model solutions, though the Helfenstein et al. (1994) fit provides an overall better prediction of the surface scattering. Examination of the incidence and emission values in the photometric regions of interest show that in these regions the values of those angles are high (>70°), especially in incidence (Fig. 7). Domingue et al. (2011, 2014) applied this model to derive a photometric correction for the global color mosaic of Mercury and found that the model tends to poorly predict reflectance values at high incidence and emission angles. Since the quality of fit here for Gaspra is comparable to the Mercury results, the spectroscopic analyses use the same model parameters derived from this study for two reasons: (1) it provides an independent solution for each filter based on measurements within each filter and (2) the parameter values have been trended with wavelength so as not to introduce any additional wavelength dependencies.

Interestingly enough, the regions where there are differences between the measured reflectance and the predicted reflectance from globally average photometric parameters are those regions where regolith differences due to downslope migration and accu-

Fig. 4. Continued

mulation of regolith materials are expected. Ridge crests and slopes could be depleted in regolith due to mass wasting. Material within these areas could be younger as older material has migrated away or been mixed with less weathered material. Conversely, depressions will accumulate material and could be regions of older, more mature regolith. A younger, shallower regolith or an older, deeper regolith will have different photometric properties than the average regolith. The ridges and slopes appear to be brighter than average in the Ratio lmages, whereas the depressions appear to be darker than average (Figs. 4 and 5). Therefore, the quality analysis could indicate regions of varying regolith properties. However, these variations are inseparable from the errors introduced by inaccuracies in the shape model and the robustness of the model at high incidence and emission angles.

4. Color analysis

The near-lR ratio-reflectance has been used to estimate FeO content and soil maturity in studies of the lunar surface (Lucey et al., 1995, 1998; Blewett et al., 1997). Murchie et al. (2002) examined the correlation between the near-lR ratio-reflectance for the surface of Eros, another S-type asteroid. The near-lR ratio-reflectance data trend to a common origin, or 'hypermature'

Fig. 4. Continued

a : Image Color Set F

Fig. 4. Continued

Fig. 5. Displayed are example Ratio Images from the green filter of color sets E (left) and F (right) where areas of large differences between measured and model predicted reflectance values are outlined in red.

Fig. 6. These Ratio Images compare the Hapke model solution from this study for (a) Set B and (c) Set F with that from Helfenstein et al. (1994) for (b) Set B and (d) Set F. Set B and F Ratio lmages are displayed with the same stretches (0-1.5 and 0-2.18, respectively).

endmember, in the lunar case, however Murchie et al. (2002) demonstrated that for the case of Eros the data trends to a different end point than the lunar measurements. They ascribed this to a combination of differences in regolith composition coupled with differences in the affects of space weathering processes on Eros compared with the Moon.

Correlations in the ultraviolet ratio-reflectance have also been demonstrated to be useful in examining maturity in both lunar and asteroid regoliths (Lucey et al., 1995, 1998; Blewett et al., 1997; Gillis-Davis et al., 2006; Hendrix and Vilas, 2006; Vilas and Hen-drix, 2015). The correlations in the ultraviolet ratio-reflectance are used to estimate TiO2 abundance versus maturity on the Moon (Gillis-Davis et al., 2006). Comparisons of UV - VIS spectral slope with VIS - NIR spectral slope in asteroid spectra are used to provide estimates of asteroid regolith maturity (Hendrix and Vilas, 2006; Vilas and Hendrix, 2015, see Section 6).

Color sets B-E contain images in the UV (0.404 /m), VIS (0.756 /m), and NIR (0.986 /m). NIR/VIS and UV/VIS ratio images were constructed from each of these color sets and are displayed

Fig. 7. The top left image is the incidence angle values for E color set, the top right is the corresponding emission angle image. Range of angle values are plotted in Fig. 3. The lower image is the Ratio Image for color set E. The scale bar shows 4 increments from bottom to top of 0.5, 1.0, 1.75, and 2.0, respectively. The photometric regions of interest (Fig. 5) correspond to areas of high incidence and emission.

in Fig. 8. The first column displays color maps constructed from each color image set where the red channel displays the VIS reflectance value, the green channel displays the UV/VIS ratio, and the blue channel displays the NIR/VIS ratio. These maps were constructed using images where the reflectance was not corrected for photometric variations. The second column is a similar set of maps constructed from images that were corrected for photometric variations using the Hapke model solution described above. The third image is the Ratio Image at 0.756 (m for the corresponding color image data set. All images within Fig. 8 are stretched to the same ranges. Color image set C saturates in the UV/VIS ratio due to anomalous behavior in the 0.404 (m filter (see Section 6) and is not considered in the following discussion. All other color sets display similar properties.

The maps in Fig. 8 display differences across the surface attributable mostly to differences in VIS-reflectance. The variations in the photometrically-uncorrected maps can be correlated to differences in illumination and viewing. The variations in the photometrically-corrected maps can be correlated to regions with bright or dark ratio values in the Ratio Image (signifying poor quality of the photometric correction). In order to quantitatively examine the variation in the color ratio properties specific regions across the surface of Gaspra were examined (Figs. 9 and 10).

The specific regions examined are defined in Fig. 9, where the regions are mapped against the color Set D Ratio Image. Regions outlined in red or orange are in areas where the photometric model best predicts the surface reflectance. Areas in blue and yellow are in regions of poor quality for the photometric correction. The plots in Fig. 10 show the VIS versus NIR/VIS behavior of Gaspra's surface derived from these regions. The colors of the points on the plots correspond to the colors of the regions on the Ratio Image. A clear trend is seen in the non-photometrically-corrected data plots. A trend is only discernable in

Fig. 8. Displayed are maps of the NIR/VIS, UV/VIS, and 0.756 mm reflectance for (a) color set B, (b) color set C, (c) color set D, and (d) color set E. The first column shows the color map constructed from non-photometrically-corrected images where the VIS reflectance, UV/VIS ratio, and NIR/VIS ratio are displayed in the red, green, and blue channels, respectively. The second column shows the same color maps constructed from the photometrical- corrected images. The stretch for the red, green, and blue channels are 0-0.095, 0-0.767, and 0-1.114, respectively. The third column is the Ratio Image from the 0.756 (m (VIS) filter.

the photometrically-corrected data plots when the data from those regions of poorest quality in the photometric correction have been removed. A comparison of the incidence and emission angles from the various regions shows a clear correlation with high values of incidence and emission angles with regions of poor quality for the photometric corrections.

In the plots depicting near-IR ratio-reflectance surface properties (Fig. 10), where the regions of poorest quality in the photometric correction have been removed, two trend lines are depicted. The first (solid black) is the trend seen in the Eros data set from Murchie et al. (2002). The second (dashed black) is the trend in the Gaspra data. The two trends are similar in the non-photometrically-corrected data. In the photometrically-corrected data the two trends are divergent. The Eros trend is derived from data photometrically-corrected to i = 30°, e = 0°, a = 30°, whereas the Gaspra data have been photometrically-corrected to i = 65.893°, e = 49.308°, a = 34.075 ° (the median angles within the data set).

It might be expected that asteroids with a similar composition would demonstrate trends to a common end point, as is seen on the Moon. While both Gaspra and Eros have been classified as S-type asteroids, their compositions have been demonstrated to be very different. Elemental and mineral compositions are commensurate with an ordinary chondrite composition for Eros (McCoy et al., 2001; Nittler et al., 2001; Lim and Nittler 2009),

Fig. 9. This image identifies specific regions and their locations on the Ratio Image for color Set D. Regions outlined in red and orange are in areas where the photometric model predicts the surface reflectance well, regions outlined in blue or yellow are in areas where the photometric model predicts the surface reflectance poorly. The color codes also correspond to the VlS-lR ratio-reflectance graphs shown in Fig. 10.

with an orthopyroxene/(orthopyroxene + olivine) ratio of 0.42 (McCoy et al., 2001). While the elemental and mineral compositions for Eros are not consistent with a single meteorite class (evidence ranges from L to LL chondrites), the consensus is that Eros is an ordinary chondrite whose regolith has been depleted in sulfur due to space weathering processes (McCoy et al., 2001; Nittler et al., 2001; Lim and Nittler, 2009; Peplowski et al., 2015). In contrast, Gaspra's composition is more similar to pallasites or pyroxene-poor achondrites (Granahan, 2011), with an orthopyroxene/(orthopyroxene + olivine) ratio of 0.10 (Granahan, 2011). The difference in orthopyroxene/(orthopyroxene + olivine) ratios between these two objects implies that Gaspra is more olivine rich than Eros. The spectral analysis by Granahan (2011) demonstrates that Gaspra is not an ordinary chondrite, but is more consistent with an olivine-bearing meteorite. The divergence in the trend lines in the near-lR ratio-reflectance plots in the photometrically-corrected data sets is consistent with this difference in composition.

The spectral slope properties in the UV wavelength range are suggested to be a more sensitive indicator of the onset of space weathering in the S-class asteroids (Hendrix and Vilas, 2006; Vilas and Hendrix, 2015). Although the mafic mineral olivine ((Mg,Fe)2 SiO4 ) is not opaque, an unweathered olivine-rich surface will show a UV absorption - a significant decrease in reflectance at wavelengths just short of 400 nm - related to the transition from volume scattering in the VlS to NlR to surface scattering (controlled by Fresnel reflection) in the UV (Wagner et al., 1987). In addition, olivine has an Fe2+ -O charge transfer absorption band centered around 270 nm (Cloutis et al., 2008). In contrast, elemental iron is opaque, dominated by surface scattering, and is spectrally flat from the UV to the NlR. With a very small amount of npFe0 on the Fe-bearing olivine component of a planetary surface, space weathering effects become apparent when the UV spectrum undergoes bluing (increased reflectance with decreasing wavelength) due to olivine's UV absorption being masked by the increased npFe0 (Hendrix and Vilas, 2006; Vilas and Hendrix, 2015). Eventually, as npFe ° coatings expand in area, the VIS to NIR reddening

and diminution of absorption features becomes apparent. Fig. 11 plots the slopes of reflectance spectra fit across the near-UV to VlS (320-400 nm) range versus across the VIS to NIR (550-1650 nm) spectral range for S-class asteroids, ordinary chondrites, and the two asteroids 433 Eros and 951 Gaspra. The Gaspra data point is based on the spectral properties of a reference area spectrum discussed in the next section. As expected for Eros, the surface spectral properties in the near-UV to VIS confirm the weathered surface observed by NEAR Shoemaker. Gaspra shows a less-weathered surface consistent with previous studies of this asteroid. Applying the relationship defined by Vilas and Hendrix (2015), Gaspra shows 0.01-0.1% npFe0 in the surface material compared to the greater than 0.1% indicated for Eros. This is commensurate with Gaspra's surface being less space weathered than Eros.

5. Spectrophotometric analysis

One advantage of the SSl data set is the higher spatial resolution compared with the NIMS observations (Fig. 12). The SSI data have been corrected to standard values of i = 65.893°, e = 49.308°, and a = 34.075° across the entire spectral range of the imaging data set, accounting for reflectance variations due to illumination and viewing conditions based on the asteroid's shape model. Four sets of images through all six SSl filters (four color-image sets) were acquired on approach of the spacecraft. ln these images, twenty-three areas, defined by 3 x 3-pixel boxes, were sampled across Gaspra's surface (Fig. 13). The reflectance values of the pixels within each box were averaged for each filter in each color-image set; therefore, each defined area is represented by four SSl spectra. For each of the 23 areas, the four spectra were median-filtered to produce one representative spectrum. While these spectra lack the spectral resolution of the NIMS observations, some constraints on mineralogical variations across the asteroid's surface and their possible correlation with surface geology can be made due to the higher spatial resolution of the SSl data.

51. Evaluation of spectral properties

The median spectrum for each of the 23 areas was first compared with the Eight Color Asteroid Survey (ECAS) observations acquired of Gaspra (Zellner et al., 1985). The ECAS data measures of Gaspra's disk-integrated reflectance was used here as a representation of Gaspra's average spectrophotometric properties. Based on this comparison, a "reference area" that displays similar spectral properties as the ECAS spectrum was selected (Fig. 14). The spectra of the remaining areas were compared to the reference area in a search for spectral variations across Gaspra's surface. Among the possible spectral differences identified, we concentrate here on slight variations in the signals in the 0.887 and 0.986 jam filters. These filters sample the 1.0 jam Fe2+ mafic silicate absorption feature. The properties of this feature are attributable to the presence and state of Fe in olivines and pyroxenes, two major minerals that have been identified on the surface of Gaspra based on the higher spectral resolution NlMS data (e.g. Granahan, 2011).

We base our search on the concept that areas where the subtle reflectance differences between Gaspra's average spectrophoto-metric properties (the reference area spectrum) and an individual spectrum of another area, as shown in these two filters, suggest differences in Fe-bearing pyroxene and olivine in the underlying material. The presence of pyroxenes will cause increased absorption at the shorter wavelength due to orthopyroxene's narrower absorption feature centered near 0.9 jam and clinopyroxene's slightly longer absorption. Olivine has a much broader, less well-defined absorption feature centered near 1.2 jam. We suggest that areas containing relatively less pyroxene will display a spectrum with less apparent absorption at 0.887 jam; this implies a higher

Uncorrected

Uncorrected

Fig. 10. These diagrams explore the surface maturity trends on the surface of Gaspra as extracted from the color image set D. The color codes in the Gaspra near-IR ratio-reflectance graphs correspond to the region color codes in Fig. 9, where red and orange symbols correspond to red and orange areas on the image, respectively, and the blue and black symbols correspond to blue and yellow areas, on the image, respectively. (a) and (b) show the relationship based on the photometrically-uncorrected data and (c) and (d) display the relationship based on the photometrically-corrected data. The graphs on the left (a & c) chart all the data, the graphs on the right (b & d) show the trends where the data from the areas with the brightest and darkest regions on the Ratio Image have been removed (the poorest correspondence between model and measured reflectance). The near-IR ratio-reflectance diagram for the Moon and Eros (e), taken from Murchie et al. (2002), is shown for comparison. The trend in the Eros data have been charted on graphs (b) and (d), depicted by the solid black arrow, for comparison with the trend in the Gaspra data, depicted by the dashed black arrow. Note that the Eros data have been corrected to i=30° e=0, a=30, whereas the Gaspra data in graph (b) have not been corrected and the Gaspra data in graph (d) have been corrected to i=65.893,, e=49.308,, a=34.075° (see Section 4). The distribution in incidence and emission angles (f) is shown within each region, emphasizing the correlation between high angle values and poor quality of photometric correction.

percentage of olivine compared to the pyroxene. We determine this by ratioing the reflectance at 0.887 jam in the normalized spectra of an area compared to the reference area. Those areas where the spectral ratio has values greater than unity were considered to indicate regions of relatively less pyroxene content than the reference area. Those areas where the spectral ratio has values less than unity were considered to indicate regions of relatively more pyroxene content than the reference area. We defined percentages of difference to show the level of spectral variation in these two wavelengths (0.887 and 0.986 jam). We divide the levels into three categories: 1-3 %, 3-5%, and > 5%. These are subtle differences, however the whole-disk color only indicates albedo variations on the order of 10% (Helfenstein et al., 1994). The areas in Fig. 13 are color-coded to identify those regions with relatively more pyroxene

(shades of red) versus those with relatively more olivine content (shades of green). Fig. 13 compares the reference area spectrum to spectra of two representative areas, one displaying a mafic silicate feature extending more strongly to shorter wavelengths ("M") indicating more orthopyroxene than the reference area, and another showing a mafic silicate feature less apparent at the shorter wavelengths ("L") indicating less orthopyroxene than the reference area.

5.2. Spectral mixing modeling

Theoretical foundation. The radiative transfer model of Hapke (1981, 1993, 2001, 2012) can be used to predict the bidirectional reflectance spectra in a forward modeling approach

E c o in 10

¡Q. 0.0003

o ___„„

0.001 0.002 0.003 0.004 0.005 0.006 0.007

NUV slope (320-400 nm)

Fig. 11. This graph shows spectral slopes (in units of reflectance/nm) of S-class asteroids, ordinary chondrites, and near-Earth asteroids Eros and Gaspra. The mean 1-ff error for the UV slopes of the S-class reflectance spectra included for comparison is plotted on the S(I) asteroid open square. The mean 1-cr errors for the UV slopes of laboratory measurements of ordinary chondrite meteorites is contained within the symbols for the meteorite slopes. The ovals mark regions where different percentages of npFe° correlate with the UV to VIS slopes that are observed. 433 Eros plots among weathered S-class asteroids; data for 951 Gaspra show it is a less weathered surface having 0.01-0.1% npFe0 on the asteroid's surface. Figure adapted from Vilas and Hendrix (2015).

(Lucey, 1998; Wilcox et al., 2006). The single-scattering albedo (w) is the probability that a photon incident on a regolith particle will be scattered rather than absorbed. This property is independent of illumination or viewing geometry and is a function of a grain's scattering behavior and absorption coefficient. The absorption coefficient is in turn governed by the material's complex index of refraction, which is a function of the optical constants. The optical constants (n, k) are wavelength-dependent quantities that are unique to each particle type in a regolith and represent the inherent physical and chemical properties of each material (Palik, 1991). The single-scattering albedo is extremely useful because the single-scattering albedo of an intimate mixture is a linear function of the single scattering albedos of the pure end members. Therefore, for simplicity, all mixing in the VIS-NIR is performed in the single-scattering albedo domain.

In Hapke's model, the reflectance spectrum of a regolith or powder is approximated from the single-scattering albedos of the mineral end-members using the Hapke's (2001, 2012) isotropic multiple-scattering approximation:

r(i- e- a) = T

rn ffo

4 fio + f

[|1 + BSoBs (a)}p(a) + H (fo)H (f) - 1]

where reflectance (r) is a function of the incidence angle (0 ), the emergence angle (e), and the phase angle (a). This form is the same as that given in Eq (1), where surface roughness has been omitted ( 0 = 0°).

For the phase function, a two term Legendre polynomial of the form:

p(a) = 1 + b cos (a) + c°1. 5 x cos2a - 0 . 5° (7)

is used instead of the Henyey-Greenstein function. Here b defines the amount light scattered in the scattering plane and c defines the amount of light scattered outside of the scattering plane. Essentially, this equation is a probability function for how much light is scattered by an average particle in the direction of the detector.

The opposition function is the same as given in Eq. 2. Essentially, this equation describes the degree to which the reflected light is enhanced is the direction of opposition. As the phase angle increases, the value of B°(a) drops off rapidly so that this term becomes fairly negligible at large phase angles (a > 30°).

Finally, the model uses Hapke's (2012) approximation of Chan-drasekhar's function that defines isotropic scattering of light within a medium:

j«x |r,

H(x) = [rnx| r0 +

1 -*!* ln |

(x = f or ffo) (8)

where r0 is diffusive reflectance. Essentially, this calculates the contribution of light that is scattered isotropically by the medium in the direction of the detector and is function of the angles of incidence and emergence.

Modeling space-weathering products or particleSi Hapke (2001) applied Maxwell-Garnett equivalent theory to combine optical properties of iron metal with those of host lunar materials to successfully produce the observed reddening and darkening seen in space weathered spectra. Space weathering is the chemical and physical alteration of regolith grains through mi-crometeoritic impact and solar wind ion bombardment. Both

Fig. 12. Comparison of the spatial resolution between the SSI color images (left) and the NIMS spectral images (right). NIMS image from Granahan (2011).

0.6 0.7 0.8 wavelength (tun)

Fig. 13. The top 0.887 (m SSI image identifies the 23 surface areas sampled. The blue-mottled box (labeled "R") represents the area selected as the color reference based on comparison with ECAS photometry (Fig. 14). The green boxes represent areas with potentially less pyroxene and the red boxes represent areas with potentially more pyroxene in the regolith compared to the reference area. Blue boxes represent areas with similar spectral characteristics as the reference area at 0.887(m and 0.986 (m (less than 1% variation). Purple boxes represent areas with less than 1% variation at either wavelength, and thus are considered "indeterminate". Light shades indicate spectral variations at 0.887 (m that are between 1-3% of the reference area reflectance at 0.887(m. Moderate shades indicate variations within 3-7%, and bright red regions represent variations greater than 7% at this wavelength. The bottom graph compares two example spectra with the spectrum of the reference area, one labeled "L" in the image representing an area of potentially less pyroxene and another labeled "M" representing an area of potentially more pyroxene content than the reference area. All spectra are scaled to unity at 0.559 (m and the size of the symbol represents the extent of the normalized reflectance error bars. The algorithm for determining relative olivine/pyroxene content is described in the text (See Section 5.1).

processes produce amorphous materials within the regolith. Condensation of vaporized or sputtered materials under reducing conditions produces submicroscopic particles (predominately iron (SMFe) metal in Fe-bearing silicates) on the grain surfaces and in glassy rinds, which causes reduction of their overall spectral albedo (Hapke, 2001). These amorphous coatings and submi-croscopic particles change the observed single-scattering albedo and reflectance of the material. Hapke (2001) modeled the space weathering effects as:

rn = Se +

(1 - se) (1 - Si)e-(ah+ag+acID 1 _ S,e —(ah +ag+ac) D

where SE is the external surface reflectance, S, is the internal surface reflectance, D is the host particle diameter, and ah, ag, and

0.6 0.7 0.8 wavelength (|im)

Fig. 14. Comparison of the ECAS spectrum (grey circles) (Zellner et al. 1985) with the reference area identified in Fig. 13 (open diamonds). Both spectra are scaled to unity at 0.550 jam.

ac are the absorption coefficients of the host material, the sub-microscopic particles within the host material, and submicroscopic particles in the coating of grains, respectively. In this treatment, absorption coefficients are calculated as:

4n nh kh

36n Mg ph

36n zMi ph

(10a-c)

where Mg and Mc are the mass fraction of iron in the grain and coating relative to the host, ph and pFe are the density of the host and iron, and z is the effective optical constant. Note that this treatment does not consider the size of the SMFe particles. Hapke (2001) further calculated the effective optical constant, z, from Maxwell-Garnett theory as:

nF e kF e nh3

(n2e — k2e + 2 n2h I + ( 2nFe IkFe )2

where nh, kh, nFe, kFe are the real and imaginary indices of refraction (aka optical constants) of the host mineral or glass and iron. Optical constants are inherent properties of a material, independent of particle size, illumination or viewing geometries, but do vary with wavelength and are used to calculate the single-scattering albedo. Using the above equations (Eqs. 6-11), reflectance can thus be derived from the single scattering albedo. Therefore we can derive the reflectance of a given rock using the indices of refraction of the minerals present within that rock.

Using the spectral properties of silica gels infused with nanophase iron particles from Noble et al. (2007), Lucey and Noble (2008) showed that this model does hold true when the particles are extremely small; however, when the particle sizes are larger (n d/X > 1), the models match the slopes and albedos only at the longer wavelengths but fail to reproduce the spectrum at shorter wavelengths (Lucey and Noble, 2008). These intermediate-sized particles have been named microphase or Britt-Pieters (BP) particles (Lucey and Noble, 2008). To address this, Lucey and Riner (2011) used Mie theory to produce a size-dependent model for the fine-grained Fe particles within the host material, which calculates ag as:

ag = aMie =

3qa Mf e Ph

dF e PFe

where dFe is the iron particle diameter in centimeters. This formulation provided a much better fit to the Noble et al. (2007) data (Lucey and Riner, 2011). Their work demonstrated that for the NIR,

particles < 300 nm will darken and redden whereas particles up to ~10 00 nm will only darken, but not redden.

Model description. To interpret reflectance spectra for airless bodies accurately, the effects of opaque phases (e.g., ilmenite, troilite, graphite) and metals (e.g., Fe, Ni) must be considered properly. Opaque metals are generally present as native igneous minerals in meteorites and on planetary surfaces in the form of grains significantly larger than the wavelength of the incident light. However, submicroscopic metal grains, a key by-product of space weathering (Hapke, 2001; Keller and McKay, 1997; Pieters et al., 200 0; Noble et al., 2007), are also present and introduce confounding effects on UV, VIS, and NIR spectra.

To address this issue, our model includes optical constants for opaque mineral and metal phases (Stockstill-Cahill et al., 2015). Metals are present in planetary regolith in three possible physical forms categorized by grain size: macroscopic, microphase, and nanophase (Hapke, 2001; Britt and Pieters, 1994; Pieters et al., 20 0 0; Noble and Pieters, 2003; Noble et al., 2006; Lucey and Noble, 2008; Lucey and Riner, 2011). Macroscopic metal particles are large relative to the wavelength of light and grains of this size are often found as native igneous species in meteorites and lunar samples (Lawrence and Lucey, 2007). Microphase particles have diameters from ~50 nm to ~300 0 nm and produce an overall decrease in reflectance with few effects on the continuum slope of a spectrum (Noble et al., 2007; Lucey and Noble, 2008; Lucey and Riner, 2011). These are also referred to as Britt-Pieters or BP particles (Lucey and Noble, 2008). Finer-grained metal, < 50 nm in diameter, is referred to as "nanophase metal" (e.g., npFe0 ) and decreases the overall reflectance and introduces a strong positive spectral slope across the VIS to NIR (i.e., spectral "reddening") (Pieters et al., 20 00; Noble et al., 2007).

The model used for this study was adapted from the work of Cahill et al. (2012, 2015, 2016), which uses optical constants for metals (Fe, Ni) to introduce the darkening and reddening effects on reflectance spectra caused by nanophase metal particles. The updated version now includes the Mie-modifications of Lucey and Riner (2011) that introduces the darkening-only effects of microphase (BP) metals. In addition, the updated model allows the user to include additional macrophase opaques (e.g., ilmenite, graphite, troilite). Finally, optical constants for a wider assortment of metals and opaques have been added for inclusion as nanophase and microphase metals. In addition to Fe and Ni, the model can include troilite, MgS, CaS, graphite, as well a thermally-shocked versions of the sulfides (Stockstill-Cahill et al., 2015). These additional materials are based on space weathering studies of the Itokawa samples (Noguchi et al., 2011, 2014) and Mercury (Domingue et al., 2014).

Required inputs are 1) the abundance and composition of (macrophase) host silicate particles, including plagioclase, olivine, orthopyroxene, clinopyroxene, glass, and agglutinates; 2) opaques (including macroscopic oxide, sulfide, or carbon phases); 3) macrometal; 4) the abundance of microphase (BP) and nanophase and metal; and 5) the grain sizes of the (macrophase) host particles and the micrometal (i.e., BP particles). The model varied the amounts of macroscopic host (e.g., olivine, pyroxene), opaque (e.g., illmenite, FeS), macrometal (e.g., Fe) phases, and the microphase (BP) particle size (50-30 0 0 nm) to produce an array of spectra that can then be compared to a spectrum of interest (SOI), in this case spectra of Gaspra. The macrophase phase abundances are varied from 0-100% at a selected step size (e.g., 5%) producing thousands of mineral combinations that total 100%. Spectra for these mineral combinations are then generated and compared to the SOI. The user can iteratively try various mineral phases (e.g., ilmenite vs. graphite for the opaque phase) and compositions (e.g., varying the Mg# of the mafic silicates) to improve the fits to the measured spectrum.

To identify which modeled spectrum provides the best fit to the SOI, we use two metrics to assess the quality of fit. First, we calculate a sum of the square of the residuals (SSR) for each model spectrum using the equation:

SSR — y (rmeasured rmodeled I

where n represents the number of channels and r represents the reflectance for a given channel. The SSR is essentially a measure of how well the measured albedo is matched in the modeled spectrum: a low SSR indicates a good match to the albedo.

Second, we calculate a sum of the square of the slope differences (SSSD) for each model spectrum using the equation:

SSSD = J2

/ (rn+1 - rn I \ V ( Xn+1 - Xn I '

measured

( (rn+1 - rn I

V (Xn+1 — Xn I

where n represents the number of wavelengths, r represents the reflectance for a given wavelength, and X represents the value of the wavelength. The SSSD is essentially a measure of how well the shape of the spectrum is matched by the modeled spectrum; a low SSSD indicates a good match to the shape of the measured spectrum. Finally, we calculate a goodness of fit (GoF) parameter from the product of these two quantities (GoF=SSR*SSSD) and the lowest values are identified as the "best fits" to the observed spectrum.

Application to Gaspra, Analysis of Gaspra NIMS spectra suggests there are at least two spectral units, both containing relatively high proportions of olivine (Granahan, 2011). This asteroid has undergone igneous differentiation and displays a 2.7 (m spectral feature that is attributable to the presence of structural OH (Granahan, 2011). Band area ratios between the 1 (m and 2 (m bands (assumed to be due to the presence of olivine and orthopyroxene) indicates that the ratio of orthopyroxene to (orthopyroxene + olivine) is ~0.10 (Granahan, 2011). Gaspra spectra are consistent with the spectra of meteorites composed of monomineralic olivine, such as pallasites, pyroxene-poor ureilites, and pyroxene-poor brachinites (Gaffey et al., 1993). Most main group pallasites contain olivine and orthopyroxene with Mg# values of ~88% (e.g., Mittlefehldt et al., 1998; Boesenberg et al., 2012). This informs our inputs to the mixing model for application to Gaspra.

In addition, laboratory experiments by Loeffler et al. (2009) demonstrate that the space weathering effects observed in S-class asteroids are due to heavy ion irradiation on both particulates and fragments of Fe-bearing olivines. Kohout et al. (2014) show that a logarithmic trend is observed between the amount of npFe° created as the result of laboratory irradiation of samples and darkening of the spectrum of olivine-bearing silicates, reduction of the 1-(m olivine absorption band, spectral reddening, and changes in the 1-(m bandwidth. These laboratory results, coupled with the high olivine content indicated by the NIMS spectral analysis, indicate the mixing model will need to account for at least some space-weathering components.

For the macrophases, the spectral mixing models for analysis of Gaspra SSI data were allowed to include olivine, orthopyrox-ene, a user-selected opaque phase, and user-selected macrometal. The abundance of these phases were varied 0-100% for olivine, orthopyroxene, and macrometal and 0-15% for the opaque phase (ilmenite or FeS) with 5% step sizes, resulting in 1551 different mineral combinations. Initially, we set the Mg# of olivine and or-thopyroxene to 88, to reflect that found for pallasites (Mittlefehldt et al., 1998; Boesenberg et al., 2012). Iterative processing showed that decreasing the Mg# from 65-75 lead to better fits. Note here, that Mg# is derived from the mole percent of MgO and

Table 4

Best-fit mixing model compositions.

Macrophase components Reference area Area "L" Area "M"

Olivine 0% 15% 80%

Orthopyroxene 70% 45% 0%

Mg# (Ol & Opx) 75 70 75

Opaque (Ilmenite) 20% 40% 10%

Opaque (FeS) - - -

Macrometal 10% (Fe) 0% (Fe) 10% (Fe)

Macrophase grain size 75 fim - 100 pirn

Space-weathering components

Agglutinates 0% 0% 5%

Microphase (BP) metal 0.1% (Fe) 0.002% (Fe) 0.1% (Fe)

BP grain size: 30 0 0 nm 300 nm 20 0 0 nm

Nanophase metal 0.1% (Fe) 0. 1 « (Fe) 0.01% (Fe)

Goodness of fit parameter 1.77388e-07 8.59843e-07 3.39730e-07

FeO, where Mg# = 100*[Mg0/(Mg0+Fe0)]. Furthermore, iterative processing indicated that agglutinates provided a minor contribution to the spectrum, so their abundances were limited between 0-10%. The microphase (BP) and nanophase metals were varied in composition between Fe and FeS. Nanophase abundances were constrained to values of 0.001, 0.002, 0.01, 0.1, 1%, and 2% based upon UV/VIS slope analyses (see Section 5). Finally, the microphase metal grain size was set to 50, 100, 200, 600, 1000, 2000, and 300 0 nm. The models with the lowest values for the GoF parameter were identified and their model spectra were compared to the observed spectrum. From these, a best fit was selected based on which model provided the best match to the overall albedo and spectral shape of the observed spectrum.

Recall that the mixing modeling is initially performed in terms of single scattering albedo, not reflectance. Single scattering albedos for each of the components are calculated from the optical constants of each potential constituent. The real (n) and imaginary (k) indices of refraction for olivine and pyroxene are derived from the formulas based on the works of Lucey (1998) and Trang et al. (2013). In the case of plagioclase, the optical constants are calculated using the methods of Lawrence and Lucey (2007), which are based on the analysis of a standard anorthite reflectance spectrum (Anorthite HS201) from the United States Geologic Survey Denver Library. The agglutinate optical constants were obtained from measurements of a lunar highlands sample from the NASA Reflectance Experiment Laboratory (RELAB) library. The optical constants for the graphite used in this study are an average from four sets of values provided in Querry (1985). The triolite (FeS) optical constants are those provided in Pollack et al. (1994) and the Fe and Ni metal optical constants are from Cahill et al. (2012, 2015, 2016). The optical constants for ilmenite were calculated from a reflectance spectrum (Clark et al. 1993) using the methods of Lucey (1998). Using these optical constants, a single scattering albedo for each constituent is calculated, which in turn are used to calculate the single scattering albedo of a potential mixture. Once the single scattering albedo is derived for a given mixture, it is converted to reflectance and then compared with the Gaspra spectrum under analysis.

Three sample spectra were modeled: the reference area spectrum, a spectrum representing a suspected, relatively-lower or-thopyroxene content area ("L" in Fig. 13), and a spectrum representing a suspected, relatively-higher orthopyroxene content area ("M" in Fig. 13). Table 4 shows the compositional results from the mixing model for these three representative areas. Fig. 15 shows a series of results for the reference spectrum where the only compositional components to be varied are the space-weathering microphase (BP) and nanophase metal components. All other components are included as listed in Table 4. This figure demonstrates that a space-weathering component is necessary in order to fit the

measured spectrum. However, it also demonstrates that the range of grain sizes and quantity of the space weathering components (microphase, BP, grains and nanophase metal) can vary greatly within the measurement error bars. This was the case for all the Gaspra spectra modeled, whose best fits are shown in Fig. 16.

Analysis of the spectral data predict that the relative amounts of pyroxene between the reference area and regions "L" and "M" differ. The mixing modeling suggests that both regions "L" and "M" contain less pyroxene than the reference area (45% and 0%, respectively). What is interesting to note, however, is that region "L" contains a small amount more olivine (~15%) but region "M" contains a significantly greater percentage of olivine (80%) than the reference region. There is also some indication that the Mg# of the olivines and pyroxenes could change across the surface. The best fit models for the reference and "M" areas are found with an Mg# of 75, where as the "L" area is better fit with models that include olivines and pyroxenes with an Mg# of 70.

The mixing modeling results also indicate variations in the abundance of the opaque ilmenite between the three areas. The reference area is best fit with 20% ilmenite, whereas the other two regions required 40% for area "L" and 10% for area "M" to model the measured spectra.

In terms of macrometal phases, the reference area and area "M" measured spectra were best matched by a model containing 10% macrophase Fe, whereas area "L" was best modeled without the presence of macrophase metal. We also note that the reference area was modeled best with a slightly coarser grain size (75 /m) for the macrophase components relative to area "M" (100 /m).

In terms of the space weathering components, there appears to be a relatively low abundance of agglutinates (0-5%) for all three regions. The nanophase space-weathering component shows Fe proportions present at the 0.01-0.1% level, consistent with the abundances predicted from the technique of Vilas and Hendrix (2015). The microphase (BP) Fe metal in the reference and "M" area spectra show a modeling content of 0.1% while the "L" area spectrum shows a lower model derived content of 0.002%. The size of the BP particles ranges from 300 nm in the "L" area to 20 00 nm and 30 00 nm in the "M" and reference areas, respectively.

6. Discussion

The goal of this study was to examine and characterize the evidence for variations in space weathering across the surface of Gaspra by separating the spectral variations due to photometry, composition, and regolith structure. Previous studies have noted spectral differences between ridges, craters, and inter-ridge (facet) regions, however we have found that the photometric behavior along ridges and depressions is very difficult to characterize and to standardize for comparisons with the inter-ridge regions. The difficulty in characterizing the photometric behavior along ridges and depressions could be due to shape model inaccuracies, photometric model limitations, or differences in the regolith within these regions from the global average.

The work of Helfenstein et al. (1994) indicated that the inter-ridge or facet regions were less mafic (lower abundances of olivine and pyroxene) than craters on the surface, also displaying weaker 1 /m bands. Granahan (2011) found that these regions also had their 1 /m band center shifted to slightly longer wavelengths (1.05 /m) compared to ridges (0.99 /m band centers). The correlation between bright materials with stronger 1 / m bands and darker materials with weaker 1 /m bands, where the differences could not be ascribed solely to grain size variations made Helfenstein et al. (1994) postulate that Gaspra's surface is space weathered. This is also commensurate with their observation that craters, which have excavated and exposed younger regolith, show stronger 1 / m bands.

n 0.18

g U13 c

jj 0.08 1 nm

tj 0.05

| 0.05

£ 0.03

Best Unweathered Fit GoF = 0.000333531

Best Fit with 50nm BP GoF = 1.09777e-06

Best Fit with lOOnm BP GoF = 6.88083e-07

£ 0.03

& 0.03

-1-1—

0.3 0.5 0.7 0.9 1.1

Wavelength (Mm)

0.3 0.5 0.7 0.9 1.1

Wavelength (^m)

0.3 0.5 0.7 0.9 1.1

Wavelength (|im)

Fig. 15. These graphs illustrate the best spectral fits achieved by varying the microphase grain size. The top left model included no space weathering (i.e., no microphase or nanophase metal) and provided a very poor fit to the measured SSI data. The remaining models, with a microphase grain size ranging from 50 (m (top middle) to 30 00 (m (bottom right), provide much better matches to the measured spectrum. By comparing the goodness of fit (GoF) values and examining the quality of the match, a best fit spectrum can be selected. In this case, the microphase metal grain size of 30 00 (m (bottom, right) provided the best match to the measured spectrum. In these remaining cases the npFe content was allowed to range from 0.001%-2%.

The analysis of the near-IR ratio-reflectance (a diagnostic of maturity on the lunar surface) from our analyses shows evidence of varying maturity across the inter-ridge regions. The trend in maturity is different from that displayed by both the lunar surface and that of Eros. This is consistent with the differences in surface composition between these three objects, where Gaspra is a more olivine-rich surface. Examination of the VIS-NIR versus NUV-VIS spectral slopes indicate that Gaspra has a less weathered surface than Eros, and contains a space-weathering component of npFe in the 0.01 - 0.1% range. In comparison, Eros' surface is estimated to contain greater than 0.1% npFe, using this same technique.

The spectral and mixing modeling analyses indicate that the variations in Gaspra's surface composition, including space-weathering products, could vary within the inter-ridge regions. The spectral analysis shows subtle variations in the edge of the 1 (m region indicative of variations in amounts of both olivine and pyroxene. Three representative regions were selected for compositional analysis using mixing modeling techniques based on initial spectral classifications defined by spectral differences in the 1 (m band as compared to a reference area. These three regions were the reference area (which matched the spectral signature of the ECAS telescopic observations of Gaspra), a spectrum with a lower reflectance at edge of the 1 (m band (labled "M" in Fig. 13), and a spectrum with a higher reflectance at the 1 (m band edge (labled "L" in Fig. 13). The reference area's spectrum was best matched with a predominately orthopyroxene (70%) composition with comparable amounts of opaque (ilmenite, 20%) and macro-size metal iron (10% with a 150 (m grain size). Spectrum "M", with the relatively deeper 1 (m band edge, was best matched with significantly more olivine (80%) and no orthopyroxene, and with a 10% opaque component (ilmenite), lower in abundance than that indicated for the reference area. The macro-size metal quantity for area "M" was

equivalent (10%) but of larger grain size (100 (m) than the reference area for this spectrum. Spectrum "L", with the relatively shallower 1 (m band edge, was best matched with more olivine (15%) and less orthopyroxene (45%) than the reference area, and with a significantly larger opaque component (40%) as either the reference or area "M" spectra. The macro-sized metal component is absent from the area "L" spectrum model results. These results indicate that the olivine and pyroxene abundance across the surface of Gaspra could vary up to 80% and that opaques are a non-negligible component (15% or more). The macro-sized iron metal component is also a potential contributor (~10%) and most likely varies in grain size across the surface. The mixing modeling also indicates potential variations in the space weathering components of the regolith across the surface, however the errors in the Gaspra measurements do not adequately constrain the properties of these components.

The mixing modeling results showed that microphase (BP) particles were a necessary component in order to match Gaspra's spectral properties. While the modeling indicates that the quantity of this component might not vary significantly, the grain size could vary (300-30 00 nm) over the inter-ridge regions. The modeling results also show that the nanophase component is present at the 0.01-0.1%, as predicted by the VIS-NIR and NUV-VIS slope analyses, and might not vary significantly over the inter-ridge regions. The best matches to these representative spectra all indicated that both the microphase and nanophase components are most probably iron and not iron sulfide (unlike what is seen in the Itokawa samples). The presence of agglutinates is intermittent across the surface, perhaps at the 5% level. The results of this project indicate that the space-weathering components within Gaspra's regolith may vary across the surface, which is commensurate with a surface that has not reached complete maturation.

Reference Spectrum

=■0.09

= 0.09

c 0.05

=■0.09 a*

0.3 0.5 0.7 0.9

Wavelegnth (mm)

L Spectrum

0.3 0.5 0.7 0.9

Wavelegnth (mm)

M Spectrum

0.3 0.5 0.7 0.9

Wavelegnth (mm)

Fig. 16. These graphs compare the measured spectrum of the reference area (black) extracted from the SSI color data with the best mixing model spectrum (red). The corresponding mixtures are given in Table 4, for the reference area (top), region "L" (center), and region "M" (bottom).

Acknowledgment

This work was supported by NASA's Planetary Mission Data Analysis Program's grant NNX10AP77G.

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