AN ANALYSIS OF UNCERTAINTY IN NON-EQUILIBRIUM AND EQUILIBRIUM GEOTHERMOBAROMETRY

Abstract

In statistically optimised P–T estimation, the contributions to overall uncertainty from different sources are represented by ellipses. One source, for a diffusion-controlled reaction at non-equilibrium, is diffusion modelling of the reaction texture. This modelling is used to estimate ratios, Q, between free-energy differences, ΔG, of reactions among mineral end-members, to replace the equilibrium condition ΔG = 0. The associated uncertainty is compared with those already inherent in the equilibrium case (from end-member data, activity models and mineral compositions). A compact matrix formulation is introduced for activity coefficients, and their partial derivatives governing error propagation. The non-equilibrium example studied is a corona reaction with the assemblage Grt–Opx–Cpx–Pl–Qtz. Two garnet compositions are used, from opposite sides of the corona. In one of them, affected by post-reaction Fe, Mg exchange with pyroxene, the problem of reconstructing the original composition is overcome by direct use of ratios between chemical-potential differences, given by the diffusion modelling. The number of geothermobarometers in the optimisation is limited by near-degeneracies. Their weightings are affected by strong correlations among Q ratios. Uncertainty from diffusion modelling is not large in comparison with other sources. Overall precision is limited mainly by uncertainties in activity models. Hypothetical equilibrium P–T are also estimated for both garnet compositions. By this approach, departure from equilibrium can be measured, with statistical uncertainties. For the example, the result for difference from equilibrium pressure is 1.2 ± 0.7 kbar.