Mineral abundance determination: Quantitative deconvolution of thermal emission spectra

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Abstract
A linear retrieval (spectral deconvolution) algorithm is developed and applied to high‐resolution laboratory infrared spectra of particulate mixtures and their end‐members. The purpose is to place constraints on, and test the viability of, linear spectral deconvolution of high‐resolution emission spectra. The effects of addition of noise, data reproducibility, particle size variation, an increasing number of minerals in the mixtures, and blind end‐member input are also examined. Thermal emission spectra of 70 mineral mixtures ranging from 2 to 15 end‐members and having particle diameters of 250–500 μm were obtained. Deconvolution results show that the assumption of linear mixing is valid and enables mineral percentage prediction to within 5% on average with residual errors of less than 0.1% total emissivity. One suite (21 distinct mixtures), varying from <10 μm to 500 μm, was also prepared to test the limits of the model at decreasing particle sizes. Incoherent volume scattering at grain diameters less than several times the wavelength (∼60 μm) produces significant changes in spectral band morphology and hence, an increase in the root‐mean‐squared (RMS) error of the model Because of this, it appears that spectral mixing remains essentially linear to ∼60 μm (using the 250–500 μm size fraction as end‐members). Below this threshold, the linear retrieval algorithm fails. However, with the appropriate particle diameter end‐member spectra for the corresponding mixtures, the errors are reduced significantly and linearity continues through to the 10–20 μm size fraction. Additions of increasing amounts of noise cause a deviation of an additional 2.4%, whereas variability due to spectrometer reproducibility produces an average error of 4.0%. The model is also able to detect accurately minerals in mixtures containing 15 end‐members, well beyond the number of geological significance. Extensive error analysis and model testing confirm the appropriateness of linear deconvolution as a useful and powerful tool to examine complexly mixed emission spectra in the laboratory and the field. The results of this study provide a foundation for remote sensing analyses of thermal infrared data from current airborne and future satellite instruments planned for Earth and Mars.