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Deconvolution of Reflectance Spectra Using Nonlinear Least Squares Curve Fitting: Application to Martian Meteorites

Introduction: We present a spectral deconvolution technique and model based on the description of electronic transition absorption bands in continuumremoved spectra. The model differs from the standard gaussian modeling in the way the continuum is removed. An improved nonlinear curve fitting algorithm is used to fit the model to the data. The approach represents also an alternative to the MGM model [1] and results in suitable deconvolution of the highly overlapping bands in martian meteorites. Samples: Two meteorites have been selected for study here: Allan Hills 84001 and Elephant Moraine 79001. Allan Hills 84001 (ALH84001), is primarily orthopyroxene [e.g 2]. Minor olivine is also present [3]. Reflectance spectra of this meteorite clearly show the presence of orthopyroxene [4]. Elephant Moraine 79001 (EETA 79001) is a unique shergottite containing two different igneous lithologies (labeled A and B). Lithology B contains both low-Ca pyroxene (pigeonite) and high-Ca pyroxene (augite) with some maskelynite [5]. Lithology A is made up of a basaltic host similar to lithology B containing crystals of olivine and orthopyroxene [e.g. 6]. Development of the Algorithm: Spectral deconvolution is a particular type of nonlinear curve fitting problem in which we try to fit a nonlinear model to the data. gaussian [e.g. 7, 8] or modified gaussian [1] models have been used for spectral deconvolution. We chose to model the electronic transition absorption bands with gaussians and we fitted a linear combination of those to a continuum – removed version of the original spectra. Continuum Removal: One technique we propose removes the complete upper convex hull from the spectra. We use this approach when we do not want to treat absorption bands individually because some of the minerals of interest show features that are considered diagnostic if taken in pairs (e.g. pyroxene). The continuum removal is performed by subtraction in log reflectance, unlike a similar technique in [7] and [8] in which the operation is carried out by division in reflectance. We choose the log domain because we find that in reflectance the effect of artifacts produced by the removal process is more evident. In cases where the continuum removal procedure creates spurious bands in the spectrum (for the high convexity of the convex hull) we make use of an alternative approach in which the user is free to choose the anchor points (the tangential points) on the spectral curve and then the algorithm fits user defined functions between these points.