TY - JOUR
T1 - Precise estimation of pressure-temperature paths from zoned minerals using Markov random field modeling
T2 - Theory and synthetic inversion
AU - Kuwatani, Tatsu
AU - Nagata, Kenji
AU - Okada, Masato
AU - Toriumi, Mitsuhiro
PY - 2012/3
Y1 - 2012/3
N2 - 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.
AB - 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.
KW - Bayesian estimation
KW - Chemical equilibrium
KW - Chemical zoning
KW - Markov random field
KW - P-T path
UR - http://www.scopus.com/inward/record.url?scp=84857363250&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84857363250&partnerID=8YFLogxK
U2 - 10.1007/s00410-011-0687-3
DO - 10.1007/s00410-011-0687-3
M3 - Article
AN - SCOPUS:84857363250
VL - 163
SP - 547
EP - 562
JO - Contributions of Mineralogy and Petrology
JF - Contributions of Mineralogy and Petrology
SN - 0010-7999
IS - 3
ER -