alexa An Automatic Deconvolution Method for Modified Gaussian
ISSN: 2381-8719

Journal of Geology & Geophysics
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Research Article

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

Peng K Hong1*, Hideaki Miyamoto1-3, Takafumi Niihara1,4, Seiji Sugita2, Kenji Nagata5, James M Dohm1 and Masato Okada5
1The University Museum, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
2Department of Earth and Planetary Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
3Planetary Science Institute, 1700 East Fort Lowell, Tucson, AZ 85719-2395, USA
4Lunar and Planetary Institute, Universities Space Research Association, 3600 Bay Area Boulevard, Houston, TX 77058, USA
5Department of Complexity Science and Engineering, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8561, Japan
*Corresponding Author : Peng K Hong
The University Museum, The University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
Tel: +81338176842
E-mail: [email protected]
Received: March 08, 2016 Accepted: March 31, 2016 Published: April 05, 2016
Citation: Hong PK, Miyamoto H, Niihara T, Sugita S, Nagata K, et al. (2016) An Automatic Deconvolution Method for Modified Gaussian Model using the Exchange Monte Carlo Method: Application to Reflectance Spectra of Synthetic Clinopyroxene. J Geol Geophys 5:243. doi:10.4172/2381-8719.1000243
Copyright: © 2016 Hong PK, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
 

Abstract

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.

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