Iterative thermodynamic modelling—Part 1: A theoretical scoring technique and a computer program (bingo-antidote)

Abstract

This paper introduces the software solution bingo-antidote for thermodynamic calculations at equilibrium based on iterative thermodynamic models. It describes a hybrid strategy combining the strength of Gibbs energy minimization (GEM) and inverse thermobarometry models based on the comparison between the modelled and observed mineral assemblage, modes and compositions. The overall technique relies on quantitative compositional maps acquired by electron probe micro-analyser for obtaining a mutually consistent set of observed data such as bulk rock and mineral compositions. Thus it offers the opportunity to investigate metamorphic rocks on a microscale. The scoring part bingo integrates three statistical model quality factors

Qasm for the assemblage,

Qvol for the mineral modes,

Qcmp for the mineral compositions combined in a global evaluation criterion

Qtotal that quantifies how the model reproduces the observations for the investigated volume. The input parameters of GEM affecting the model quality such as pressure, temperature and eventually some components of the bulk composition (e.g. the molar amount of hydrogen, carbon or oxygen) or activity variables of fluids and gases (e.g.

aH2O,

aCO2, f(O2)) can be optimized by inversion in antidote using several mapping stages followed by a direct search optimization. Examples of iterative models based on compositional maps processed with bingo-antidote demonstrate the utility of the program. In contrast to the qualitative interpretation of phase diagrams, the inversion maximizes the benefits of GEM and permits the derivation of statistically ‘optimal’ pressure–temperature conditions for well-equilibrated samples. In addition, bingo-antidote opens new avenues for petrological investigations such as the generation of chemical potential landscape maps.