Determining Water Ice Content of Martian Regolith by Nonlinear

46th Lunar and Planetary Science Conference (2015)
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DETERMINING THE WATER ICE CONTENT OF MARTIAN REGOLITH BY NONLINEAR
SPECTRAL MIXTURE MODELING. S. Gyalay1,2 and E. Z. Noe Dobrea2, 1University of California, Los Angeles, Los Angeles, CA 90024, [email protected], 2NASA Ames Research Center, Moffett Field, CA, 94035
Background: In the search for evidence of life,
Icebreaker[1] will drill in to the Martian ice-rich regolith to collect samples, which will then be analyzed by
an array of instruments designed to identify biomarkers. In addition, drilling into the subsurface will
provide the opportunity to assess the vertical distribution of ice to a depth of 1 meter. The purpose of this
particular project was to understand the uncertainties
involved in the use of the imaging system to constrain
the water ice content in regolith samples.
Mixture Modeling. The key to constraining the water ice content of a mixture is to model said mixture.
Shkuratov et al. modeling[2] was used instead of
Hapke Modeling[3][4] due to the eschewing of viewing
geometry in calculating the albedo (which can be related to the bidirectional reflectance[5]), as well as the
fact that the Shkuratov model is reversible in that the
imaginary index of refraction of a material can be calculated from its albedo.
Subtractive Kramers-Kronig analysis. Knowing the
imaginary index of refraction is of little use without the
real index of refraction as well. By using Subtractive
Kramers-Kronig analysis[6], one can use the real index
of refraction at a specific wavelength to iterate through
and derive the real and imaginary indices of refraction
for the rest of the wavelengths in the range observed[7].
Coming together. The idea then becomes that one
can determine the fraction of water ice in a sample by
taking a spectrum of a regolith sample, wait for the
sample to dessicate, and then taking another spectrum
using the same lighting and viewing geometry. From
the second spectrum, the optical constants for the iceless mixture as a whole can be determined using the
Subtractive Kramers-Kronig analysis. These optical
constants can then be used in conjunction with the optical constants for water[8] to model mixtures of icy
regolith until it matches the spectrum of the observed
icy regolith. Theoretically, this would determine the
water ice abundance of the regolith, which in turn gives
insight to the chemical and geological history of the
region.
A Case Study: Early experiments wherein samples
were observed before and after sublimation of water
ice seemed to support the theory that the water ice content of these samples could be estimated using
Shkuratov modeling and Subtractive Kramers-Kronig
Analysis. An example of this is seen in Figure 1.
Figure 1: Silicate Sand was observed with two concentrations of ice
mixed in. Spectra were taken of these icy samples as well as the
dessicated sample. Above are the modeled mixtures overlaid on the
spectra of the original samples. Grain size of the silicate sand was
assumed to be 100 μm, with a volume fraction filled by particles of
0.85. It was also assumed the silicate sand had a real index of refraction of 1.4 at 550 nm.
For another test of the theory, Phoenix data was
looked at, of samples before and after sublimation on
the Martian surface—in particular of Snow White
Trench between Sol 45 and 50 of Phoenix’s mission[9].
Unlike with the silicate sand observed in Figure 1,
the viewing geometry of the Snow White Trench was
not quite of incidence angle 30°, emission angle 0°;
however, the formula log(R30) = 1.088 * log(A) was
used to approximate the hemispheric albedo used by
Shkuratov et al. modeling from the bidirectional reflectance[5]. This approximation should remain accurate
within a few percent reflectance.
Unlike previous models that attempted to determine
the water ice content of the trench by assuming the
composition of the regolith[10], we derived the optical
constants from the observations of the sublimation lag
using the Subtractive Kramers-Kronig analysis outlined
earlier. Since the true real index of refraction of the
regolith is not known, it is assumed to be between 1.4
and 1.8 at 550 nm. The optical constants of water ice
come from [8]. Various concentrations of water ice and
regolith are then modeled using [2].
The volume fraction filled by particles was assumed to be 0.85. Varying this fraction does not shift
the modeled spectra to a great degree—perhaps by 0.1
albedo when varied from 0 to 99% porosity. The effective grain size of the sublimated regolith was assumed
to be 60 μm[10]. However, it does not matter what
grain size is used to derive the optical constants of the
46th Lunar and Planetary Science Conference (2015)
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regolith so long as this same grain size is used in the
modeling of this regolith.
Results: Various mixture models were generated,
assuming different real indices of refraction for the
regolith, as well as different ice grain sizes. Figures 2-5
show these models alongside the original spectra (both
initial and sublimated).
Figure 5: Modeled mixtures overlaid on actual spectra of the Snow
White Trench before and after sublimation. Assumed n=1.8 at 550
nm, regolith grain size of 60 μm, porosity of 0.15, and ice grain size
of 100 μm. Suggests water ice content lies between 10-30% ice.
Figure 2: Modeled mixtures overlaid on actual spectra of the Snow
White Trench before and after sublimation. Assumed n=1.4 at 550
nm, regolith grain size of 60 μm, porosity of 0.15, and ice grain size
of 10 μm. Suggests water ice content lies between 5-20% ice.
Figure 3: Modeled mixtures overlaid on actual spectra of the Snow
White Trench before and after sublimation. Assumed n=1.4 at 550
nm, regolith grain size of 60 μm, porosity of 0.15, and ice grain size
of 100 μm. Suggests water ice content lies between 5-20% ice.
Figure 4: Modeled mixtures overlaid on actual spectra of the Snow
White Trench before and after sublimation. Assumed n=1.8 at 550
nm, regolith grain size of 60 μm, porosity of 0.15, and ice grain size
of 10 μm. Suggests water ice content lies between 10-30% ice.
The main effect of increasing the assumed real index of refraction of the regolith is to decrease the albedo of the modeled mixtures. Increasing the grain size
of the ice grain meanwhile appears to have little effect
for reasonable size ranges (however far larger increases
would begin to lower the albedo in the near infrared
wavelengths).
The plots show that this water-ice content is likely
between 5 and 30%, but the models are not perfect.
Not knowing the real index of refraction (as well as the
approximation of the hemispheric albedo from the bidirectional reflectance) creates much uncertainty in the
water-ice content of the sample. This can be mitigated
by a closer approximation of the hemispheric albedo
(or more constraining the viewing geometry), and
knowledge of the real index of refraction (which can be
approximated if one knows the constituents of the regolith).
Aknowledgements: We would like to thank Karly
Pitman for her help with Subtractive Kramers-Kronig
analysis, as well as Ted Roush for help with obtaining
the optical constants used throughout the development
and testing of this theory.
References: [1] McKay C. et al. (2013) Astrobio.,
13.4, 334-353. [2] Shkuratov Y. et al. (1999) Icarus,
137.2, 235-246. [3] Hapke B. (1981) JGR, 86, B4
3039-3054. [4] Hapke B. (1993) Theory of Reflectance
and Emittance Spectroscopy. [5] Shkuratov Y. G. and
Grynko Y. S. (2005) Icarus, 173, 16-28. [6] Ahrenkiel
R. K. (1971) Journal of the Opt. Soc. Of America,
61.12, 1651-1655. [7] Dalton J. B. and Pitman K. M.
(2012) JGR, 117, E9. [8] Warren S. G. and Brandt R.
E. (2008) JGR, 113, D14. [9] Smith P. et al. (2009)
Science, 325, 58-61. [10] Cull S. et al. (2010) Geophysical Research Letters, 37, L24203.