Exponential Gaussian approach for spectral modeling: The EGO algorithmI. Band saturation

Curve fitting techniques are a widespread approach to spectral modeling in the VNIR range [Burns, R.G., 1970. Am. Mineral. 55, 1608–1632; Singer, R.B., 1981. J. Geophys. Res. 86, 7967–7982; Roush, T.L., Singer, R.B., 1986. J. Geophys. Res. 91, 10301–10308; Sunshine, J.M., Pieters, C.M., Pratt, S.F., 1990. J. Geophys. Res. 95, 6955–6966]. They have been successfully used to model reflectance spectra of powdered minerals and mixtures, natural rock samples and meteorites, and unknown remote spectra of the Moon, Mars and asteroids. Here, we test a new decomposition algorithm to model VNIR reflectance spectra and call it Exponential Gaussian Optimization (EGO). The EGO algorithm is derived from and complementary to the MGM of Sunshine et al. [Sunshine, J.M., Pieters, C.M., Pratt, S.F., 1990. J. Geophys. Res. 95, 6955–6966]. The general EGO equation has been especially designed to account for absorption bands affected by saturation and asymmetry. Here we present a special case of EGO and address it to model saturated electronic transition bands. Our main goals are: (1) to recognize and model band saturation in reflectance spectra; (2) to develop a basic approach for decomposition of rock spectra, where effects due to saturation are most prevalent; (3) to reduce the uncertainty related to quantitative estimation when band saturation is occurring. In order to accomplish these objectives, we simulate flat bands starting from pure Gaussians and test the EGO algorithm on those simulated spectra first. Then we test the EGO algorithm on a number of measurements acquired on powdered pyroxenes having different compositions and average grain size and binary mixtures of orthopyroxenes with barium sulfate. The main results arising from this study are: (1) EGO model is able to numerically account for the occurrence of saturation effects on reflectance spectra of powdered minerals and mixtures; (2) the systematic dilution of a strong absorber using a bright neutral material is not responsible for band deformation. Further work is still required in order to analyze the behavior of the EGO algorithm with respect to the saturation phenomena using more complex band shapes than pyroxene bands