Mineral abundance determination: Quantitative deconvolution of thermal emission spectra

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.