Challenging equilibrium in metamorphic systems: computational, statistical, and chemical–textural approaches to thermodynamic modelling

Forward thermodynamic modelling represents one of the most powerful approaches for providing quantitative constraints on pressure–temperature conditions of metamorphic rocks. However, the reliability of the obtained results depends on the validity of the equilibrium assumptions and the precision of the input data. In metamorphic systems where disequilibrium textures, kinetic barriers, and diffusion processes can be significant, these assumptions may introduce uncertainties to the interpretation of thermobarometric results. This PhD project investigates the reliability of thermodynamic modelling based on equilibrium assumptions by explicitly quantifying uncertainties related to problem definition and improving the integration between microstructural, chemical, and statistical information. Three complementary approaches were applied to metamorphic rocks from the Himalayan belt, an ideal natural laboratory, as it records a wide range of metamorphic conditions. IntersecT, an open-source Python package, was developed to statistically propagate compositional uncertainties in isopleth thermobarometry from Perple_X models. The method assesses the quality of fit between the modelled and measured mineral chemical compositions and incorporates reduced χ² statistics to identify and down-weight outlier data or disequilibrium features. IntersecT provides a quantitative basis for interpreting phase equilibrium modelling results and particularly isopleth thermobarometry. The sectioning bias in garnet-bearing micaschists was quantitatively assessed to evaluate how two-dimensional analyses may influence the reconstruction of early metamorphic conditions. Simulations using MnO zoning profiles from three Himalayan samples show that there is a 50% probability of missing the initial garnet core at the sample scale by an offset of ~10% for samples with homogeneous grain sizes and of up to 25% for samples with heterogeneous crystal size distributions. This bias becomes even more significant when considering trace elements. The initial garnet core is of great importance for investigating departure from equilibrium due to kinetic barriers to nucleation. Further investigations demonstrate that while sectioning bias introduces nonnegligible uncertainty, the dominant source of error in estimating the departure from equilibrium in such investigations lies in the position of the modelled equilibrium garnet-in curve due to the choice of dataset and solution models. II The integration of microstructural and trace element investigations was applied to kyanite-bearing migmatites to improve the interpretation of hightemperature metamorphic processes, when chemical information of major elements can be erased by diffusion. Cathodoluminescence and trace element mapping of kyanite revealed three distinct growth domains: sub-solidus Ky1, Cr–V-enriched peritectic Ky2 as a product of muscovite dehydration melting, and Cr–V-depleted magmatic Ky3 associated with cooling. The trace element distributions (Cr/V ratio >1 in Ky2 and <1 in Ky3) provide insights into the partitioning behaviour between kyanite and melt, also reflecting the evolution of the residual melt composition during progressive melting. Overall, this PhD project highlights that combining forward thermodynamic modelling with statistical treatment of compositional uncertainties and microstructural–geochemical integrated investigations enhances the robustness of metamorphic interpretations