An Inverse Method for Quantifying Petrological Parameters and Uncertainty in Phase Equilibrium Modelling

Journal article

Phase equilibrium modelling offers a powerful quantitative framework for understanding petrological processes. Yet, many studies still rely on qualitative comparisons between natural datasets and these forward modelled predictions to constrain model parameters, commonly pressure–temperature (P–T) conditions. Compounding this, uncertainties from the observed data or within the modelled predictions are rarely quantified, limiting confidence in the estimated P–T conditions and resulting petrological interpretations. We introduce LinaForma, an inverse modelling workflow that determines best‐fit P–T conditions (or other petrological parameters) and their associated uncertainties for a given rock system by minimizing the misfit between observed data (e.g., mineral compositions or modal proportions) and their forward modelled predictions. Uncertainty is quantified by resampling of the observed data with replacement. Diagnostic metrics identify poorly performing variables and assess the sensitivity of the inversion result to variable uncertainty. Applied to an amphibolite‐facies pelite and metabasite from the Greater Himalayan Sequence (Zanskar Himalaya, NW India), the approach proves effective across contrasting model systems that require different sets of solution models and variables, and it produces P–T estimates consistent with classical thermobarometry. The workflow offers several advantages: compatibility with outputs from any forward modelling software; flexible variable selection; systematic grid‐search inversion in multidimensional space; a robust L1‐norm misfit function resistant to outliers; and sensitivity and uncertainty analysis via bootstrap resampling. Limitations include the increasing computational demands for high‐dimensional grids (N > 2) and the absence of explicit quantification of uncertainties inherited from the thermodynamic dataset and solution models. Alongside other emerging quantitative methods, LinaForma enables petrologists to make more informed interpretations of complex metamorphic systems and target improvements to thermodynamic datasets.

Authors: Mackay‐Champion, T; Cawood, I

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Wiley
• Journal: Journal of Metamorphic Geology
• Publication date: 2025-12-05
• Acceptance date: 2025-10-02
• DOI: 10.1111/jmg.70016
• EISSN: 1525-1314
• ISSN: 0263-4929
• Language: English