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

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.