Journal de géologie et géophysique
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An Automatic Deconvolution Method for Modified Gaussian Model using the Exchange Monte Carlo Method: Application to Reflectance Spectra of Synthetic Clinopyroxene

Peng K Hong, Hideaki Miyamoto, Takafumi Niihara, Seiji Sugita, Kenji Nagata, James M Dohm and Masato Okada

Deconvolution analysis of reflectance spectra has been a useful method to infer mineral composition and crystal structure. Many of the recent deconvolution analyses of reflectance spectra of major rock-forming minerals, such as olivine and pyroxene, have been based on a modified Gaussian Model (MGM). The numerical algorithm of the widely used MGM, however, utilizes the steepest descent method, which has a local minima problem. With inaccurate initial parameters, the steepest descent method converges into a local minimum, thus the analyzer must manually adjust initial parameters and calculate the model repeatedly to obtain the desired solution. In order to avoid the local minimum problem, we utilized Bayesian spectral deconvolution with the exchange Monte Carlo method, which is an improved algorithm of the Markov chain Monte Carlo method, aimed to both avoid local minima traps and remove the arbitrariness originated from initial parameters. We applied the model to visible to near infrared reflectance spectra of 31 synthetic clinopyroxene samples with wide ranging Mg, Fe and Ca compositions (solid solution). We obtained results consistent with the previous studies based on conventional MGM analyses, suggesting that the exchange Monte Carlo method can yield results consistent with the conventional MGM analyses purely based on the observed data. We also find that the center wavelengths of 1 μm absorption bands of high-Ca pyroxene samples have a linear dependence on Fe/Mg component. Both 1 μm and 2 μm absorption bands seem to follow approximation lines in the three-dimensional spaces of center wavelengths, Ca and Fe components. The successful application of the exchange Monte Carlo method to a wide range of clinopyroxenes would have a potential to expand the applicability of MGM to a variety of space/ground-based observations, especially when we cannot rely on prior information of the mineralogy.