Precise estimation of pressure–temperature paths f

Authors: Tatsu Kuwatani Kenji Nagata Masato Okada Mitsuhiro Toriumi

Publish Date: 2011/09/16

Volume: 163, Issue: 3, Pages: 547-562

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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 petrologyWe thank the editors and two anonymous reviewers for constructive comments that improved an earlier version of this manuscript We also thank Mutsuko Inui and Atsushi Okamoto for helpful discussions This study was supported by the research project Evaluation and disaster prevention research for the coming Tokai Tonankai and Nankai earthquakes from the Ministry of Education Culture and Sports Science and Technology of Japan

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