Bayesian probabilistic reconstruction of metamorphic P–T paths using inclusion geothermobarometry

Abstract

Geothermometry and geobarometry are used to study the equilibration of mineral inclusions and their zoned host minerals, which provide information on the P–T conditions of inclusions at the time of their entrapment. However, reconstructing detailed P–T paths remains difficult, owing to the sparsity of inclusions suitable for geothermometry and geobarometry. We developed a stochastic inversion method for reconstructing precise P–T paths from chemically zoned structures and inclusions using the Markov random field (MRF) model, a type of Bayesian stochastic method often used in image restoration. As baseline information for P–T path inversion, we introduce the concepts of pressure and temperature continuity during mineral growth into the MRF model. To evaluate the proposed model, it was applied to a P–T inversion problem using the garnet–biotite geothermometer and the garnet–Al₂SiO₅–plagioclase–quartz geobarometer for mineral compositions from published datasets of host garnets and mineral inclusions in pelitic schist. Our method successfully reconstructed the P–T path, even after removing a large part of the inclusion dataset. In addition, we found that by using a probability distribution of the most probable P–T path, rather than a single solution, an objective discussion of the validity of the thermodynamic analysis is possible.