Interpreting spectral unmixing coefficients: From spectral weights to mass fractions

1Arne Grumpe, 1Natascha Mengewein, 1Daniela Rommel, 2Urs Mall, 1Christian Wöhler
Icarus (in Press) Link to Article [https://doi.org/10.1016/j.icarus.2017.07.008]
1Image Analysis Group, TU Dortmund University, Otto-Hahn-Str. 4, Dortmund D–44227, Germany
2Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, Göttingen D–37077, Germany
Copyright Elsevier

It is well known that many common planetary minerals exhibit prominent absorption features. Consequently, the analysis of spectral reflectance measurements has become a major tool of remote sensing. Quantifying the mineral abundances, however, is not a trivial task. The interaction between the incident light rays and particulate surfaces, e.g., the lunar regolith, leads to a non-linear relationship between the reflectance spectra of the pure minerals, the so-called “endmembers”, and the surface’s reflectance spectrum. It is, however, possible to transform the non-linear reflectance mixture into a linear mixture of single-scattering albedos of the Hapke model.

The abundances obtained by inverting the linear single-scattering albedo mixture may be interpreted as volume fractions which are weighted by the endmember’s extinction coefficient. Commonly, identical extinction coefficients are assumed throughout all endmembers and the obtained volume fractions are converted to mass fractions using either measured or assumed densities. In theory, the proposed method may cover different grain sizes if each grain size range of a mineral is treated as a distinct endmember.

Here, we present a method to transform the mixing coefficients to mass fractions for arbitrary combinations of extinction coefficients and densities. The required parameters are computed from reflectance measurements of well defined endmember mixtures. Consequently, additional measurements, e.g., the endmember density, are no longer required. We evaluate the method based on laboratory measurements and various results presented in the literature, respectively. It is shown that the procedure transforms the mixing coefficients to mass fractions yielding an accuracy comparable to carefully calibrated laboratory measurements without additional knowledge. For our laboratory measurements, the square root of the mean squared error is less than 4.82  wt%. In addition, the method corrects for systematic effects originating from mixtures of endmembers showing a highly varying albedo, e.g., plagioclase and pyroxene.

Zinc and Germanium in the Sedimentary Rocks of Gale Crater on Mars Indicate Hydrothermal Enrichment Followed by Diagenetic Fractionation

1Jeff A. Berger et al. (>10)
Journal of Geophysical Research, Planets (in Press) Link to Article [DOI: 10.1002/2017JE005290]
Department of Earth Sciences, University of Western Ontario, London, ON, Canada
Published by arrangement with John Wiley & Sons

Zinc and germanium enrichments have been discovered in sedimentary rocks in Gale Crater, Mars, by the Alpha Particle X-ray Spectrometer (APXS) on the rover Curiosity. Concentrations of Zn (910 ± 840 ppm) and Ge (65 ± 58 ppm) are 10s-100s of times greater than in Martian meteorites and estimates for average silicate Mars. Enrichments occur in diverse rocks including minimally to extensively altered basaltic and alkalic sediment. The magnitude of the enrichments indicates hydrothermal fluids, but Curiosity has not discovered unambiguous hydrothermal mineral assemblages. We propose that Zn- and Ge-rich hydrothermal deposits in the source region were dispersed in siliciclastic sediments during transport into the crater. Subsequent diagenetic mobilization and fractionation of Zn and Ge is evident in a Zn-rich sandstone (Windjana; Zn ~4000 ppm, Ge ~85 ppm) and associated Cl-rich vein (Stephen; Zn ~8000 ppm, Ge ~60 ppm), in Ge-rich veins (Garden City; Zn ~1300 ppm, Ge ~650 ppm), and in silica-rich alteration haloes leached of Zn (30-200 ppm). In moderately to highly altered silica-rich rocks, Ge remained immobile relative to leached elements (Fe, Mn, Mg, Ca), consistent with fluid interaction at pH << 7. In contrast, cross-cutting Ge-rich veins at Garden City suggest aqueous mobilization as Ge-F complexes at pH < 2.5. Multiple jarosite detections by the CheMin XRD and variable Zn concentrations indicate diagenesis of lower Mt. Sharp bedrock under acidic conditions. The enrichment and fractionation of Zn and Ge constrains fluid events affecting Gale sediments and can aid in unraveling fluid histories as Curiosity’s traverse continues.

Hf isotope evidence for effective impact melt homogenisation at the Sudbury impact crater, Ontario, Canada

1Gavin G. Kenny, 2,3Joseph A. Petrus, 4Martin J. Whitehouse, 5J. Stephen Daly, 1Balz S. Kamber
Geochmica et Cosmochimica Acta (in Press) Link to Article [https://doi.org/10.1016/j.gca.2017.08.009]
1Department of Geology, School of Natural Sciences, Trinity College, Dublin, Ireland
2School of Earth Sciences, University of Melbourne, Parkville, Australia
3Department of Earth Sciences, Laurentian University, Sudbury, Ontario, Canada
4Department of Geosciences, Swedish Museum of Natural History, 104 05 Stockholm, Sweden
5UCD School of Earth Sciences, University College Dublin, Belfield, Dublin 4, Ireland
Copyright Elsevier

We report on the first zircon hafnium-oxygen isotope and trace element study of a transect through one of the largest terrestrial impact melt sheets. The differentiated melt sheet at the 1.85 Ga, originally ca. 200 km in diameter Sudbury impact crater, Ontario, Canada, yields a tight range of uniform zircon Hf isotope compositions (εHf(1850) of ca. -9 to -12). This is consistent with its well-established crustal origin and indicates differentiation from a single melt that was initially efficiently homogenised. We propose that the heterogeneity in other isotopic systems, such as Pb, in early-emplaced impact melt at Sudbury is associated with volatility-related depletion during the impact cratering process. This depletion leaves the isotopic systems of more volatile elements more susceptible to contamination during post-impact assimilation of country rock, whereas the systems of more refractory elements preserve initial homogeneities. Zircon oxygen isotope compositions in the melt sheet are also restricted in range relative to those in the impacted target rocks. However, they display a marked offset approximately one-third up the melt sheet stratigraphy that is interpreted to be a result of post-impact assimilation of 18O-enirched rocks into the base of the cooling impact melt.

Given that impact cratering was a more dominant process in the early history of the inner Solar System than it is today, and the possibility that impact melt sheets were sources of ex situ Hadean zircon grains, these findings may have significance for the interpretation of the early zircon Hf record. We speculate that apparent εHf-time arrays observed in the oldest terrestrial and lunar zircon datasets may be related to impact melting homogenising previously more diverse crust.

We also show that spatially restricted partial melting of rocks buried beneath the superheated impact melt at Sudbury provided a zircon crystallising environment distinct to the impact melt sheet itself.