Iterative thermodynamic modelling—Part 1: A theoretical scoring technique and a computer program (Bingo‐Antidote)

Abstract

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Iterative thermodynamic modelling—Part 2: Tracing equilibrium relationships between minerals in metamorphic rocks

“…The thermodynamic models presented in the following are all based on the internally consistent data set of and further updates collected in the Theriak-Domino database TC55_Bt distributed with Bingo-Antidote. The following solution models were used for feldspar (based on Baldwin, Powell, Brown, Moraes, & Fuck 2005;Holland & Powell, 2003); biotite (Tajčmanová, Connolly, & Cesare 2009); ilmenite, orthopyroxene, melt (White, Powell, & Holland, 2007); white mica (Coggon & Holland, 2002); chlorite (Holland, Baker, & Powell 1998); amphibole (Diener & Powell, 2012); garnet, staurolite, cordierite, epidote . The database TC55_Bt is the most robust database available to model the equilibrium relationships between garnet and biotite in amphibolite facies metapelites; the choice of this database is critical as the purpose of this work is to discuss possible equilibrium relationships between these two minerals.…”

“…Note that this is not possible for natural samples. The mineral modes corresponding to the bulk rock composition are generally unknown because modes are heterogeneous across the rock volume (Duesterhoeft & Lanari, 2020). Nevertheless, maps of the model‐quality factors Q asm , Q vol and Q cmp that quantify how the model reproduces the observed mineral assemblage, modes and mineral compositions as well as a map of a global evaluation criterion Q total1 were generated using Recipe #2 of Antidote ( P–T map of Q factors ) for a P–T range of 500–650°C and 0.4–1 GPa; results are shown in Figure 1.…”

“…Nevertheless, maps of the model‐quality factors Q asm , Q vol and Q cmp that quantify how the model reproduces the observed mineral assemblage, modes and mineral compositions as well as a map of a global evaluation criterion Q total1 were generated using Recipe #2 of Antidote ( P–T map of Q factors ) for a P–T range of 500–650°C and 0.4–1 GPa; results are shown in Figure 1. The formalism used by Bingo to calculate the model‐quality factors Q asm , Q vol , Q cmp and Q total1 is given in Duesterhoeft and Lanari (2020). Recipe #2 of Antidote is a simple mapping function producing P–T maps of model‐quality factors.…”

“…This mutual correspondence permits to build a fully quantitative comparison between model and observations as well as providing a statistical framework for evaluating model quality. This approach was implemented in the software solution Bingo‐Antidote, which is described in the companion paper (Duesterhoeft & Lanari, 2020). Two fundamental questions remain: (a) how do mineralogical variations at the thin‐section scale affect (or not) the result of ITMs?…”

An Algorithm for Thermodynamic Parameter Optimization: Application to the Martian Mantle

“…Therefore, it is important to refine thermodynamic parameters as new experimental data becomes available to ensure an improved local consistency. Existing methods of refining thermodynamic models such as Bayesian, iterative optimization and split combination approaches can be successful in improving thermodynamic model fit to new experimental data (Chatterjee et al., 1998; Duesterhoeft & Lanari, 2020; Li et al., 2020). However, these methods are limited in the number of parameters they can successfully refine concurrently and usually focus only on experimental uncertainty to constrain parameter values, rather than exploring model parameter uncertainty more directly.…”