NDLI: Precise estimation of pressure–temperature paths from zoned minerals using Markov random field modeling: theory and synthetic inversion

Content Provider	Springer Nature Link
Author	Kuwatani, Tatsu Nagata, Kenji Okada, Masato Toriumi, Mitsuhiro
Copyright Year	2011
Abstract	The chemical zoning profile in metamorphic minerals is often used to deduce the pressure–temperature (P–T) history of rock. However, it remains difficult to restore detailed paths from zoned minerals because thermobarometric evaluation of metamorphic conditions involves several uncertainties, including measurement errors and geological noise. We propose a new stochastic framework for estimating precise P–T paths from a chemical zoning structure using the Markov random field (MRF) model, which is a type of Bayesian stochastic method that is often applied to image analysis. The continuity of pressure and temperature during mineral growth is incorporated by Gaussian Markov chains as prior probabilities in order to apply the MRF model to the P–T path inversion. The most probable P–T path can be obtained by maximizing the posterior probability of the sequential set of P and T given the observed compositions of zoned minerals. Synthetic P–T inversion tests were conducted in order to investigate the effectiveness and validity of the proposed model from zoned Mg–Fe–Ca garnet in the divariant KNCFMASH system. In the present study, the steepest descent method was implemented in order to maximize the posterior probability using the Markov chain Monte Carlo algorithm. The proposed method successfully reproduced the detailed shape of the synthetic P–T path by eliminating appropriately the statistical compositional noises without operator’s subjectivity and prior knowledge. It was also used to simultaneously evaluate the uncertainty of pressure, temperature, and mineral compositions for all measurement points. The MRF method may have potential to deal with several geological uncertainties, which cause cumbersome systematic errors, by its Bayesian approach and flexible formalism, so that it comprises potentially powerful tools for various inverse problems in petrology.
Starting Page	547
Ending Page	562
Page Count	16
File Format	PDF
ISSN	00107999
Journal	Contributions to Mineralogy and Petrology
Volume Number	163
Issue Number	3
e-ISSN	14320967
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-09-16
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	P–T path Chemical equilibrium Chemical zoning Bayesian estimation Markov random field Geology Mineral Resources Mineralogy
Content Type	Text
Resource Type	Article
Subject	Geochemistry and Petrology Geophysics

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