Glossary

Best central model

The central model that, among all successful tries made during the central model analysis, has either the minimum misfit (default) or maximum Bayes score. Whether misfit or Bayes score is used as the selection criterion is specified by the Bayes option.

Central model

An inversion result obtained with all known parameters set to their central values, i.e., most probable values. In MC_fit, the known parameters typically include analytical and thermodynamic data.

Composant

A phase with the same composition as a saturated component. If multiple component saturation constraints have been imposed, then the composant of the n’th saturated component is a phase that must contain component n, and may contain components 1 to n - 1, but does not contain any additional components ([Connolly1990]).

Compositional variable

An intensive state variable (e.g., molar fractions, molar properties, densities, specific properties, chemical compositions) that is a ratio of extensive variables ([Hillert1986], [Connolly1990]).

Excess Oxygen

The amount of oxygen component that must be added or subtracted from an oxide or metallic component to define the actual redox state of the metal represented by the oxide or metallic component (Appendix D).

Forward problem

The problem of predicting observations from a set of model parameters.

Generic fluid solution model

A method of modelling mixing behavior in fluids that parallels conventional petrological treatment of solid solutions ([Connolly2018]). In GFSM, the properties of each pure species are computed by an internal equation of state (EoS) specified by the user through perplex_option.dat and the non-ideality of the mixture is evaluated with an additional mixture EoS, typically the MRK. This contrasts with earlier treatments of complex fluids, Internal EoS, in which the fluid model was expressed entirely in terms of an internal algorithm ([Connolly1995]).

GFSM have the advantage of simplicity and flexibility over Internal EoS. Internal EoS are more precise and computationally efficient, but may involve assumptions about the components selected to represent the chemistry of a system and the chemistry itself (e.g., that the fluid is saturated in graphite).

GFSM are indicated by solution model code 39 in Perple_X solution model files. Internal EoS are indicated by solution model codes 0, 9, 20, 26, 40, 41, and 42.

GFSM

See generic fluid solution model.

Inverse problem

The problem of inferring model parameters from observations.

Inversion parameters

The unknown parameters that are to be inferred from the known parameters of an inverse problem, i.e., the parameters on the left-hand side of Eq 2. In the context of MC_fit, inversion parameters typically include temperature, pressure, and unmeasured compositional information.

Misfit function

A quantitative measure of the difference between observed data and model predictions.

Misfit imprecision

The amount by which the misfit of the Best central model varies due to uncertainty in the input analytical and thermodynamic data. Models with misfit values within the imprecision of the best central model misfit are statistically indistinguishable. The misfit imprecision is quantified by the standard deviation of the scatter of the misfit values obtained during the perturbation analysis and is denoted \(\epsilon_{\text{misfit}}\).

Monte Carlo sampling

A computational technique that uses random sampling to explore a parameter space. In MC_fit, Monte Carlo sampling is used to generate initial conditions for the central model analysis and to propagate analytical and thermodynamic uncertainties through the inversion process during the perturbation analysis.

MPP

In the inversion parameter space, the MPP is the centroid of the specified parameter ranges. If the ranges have been chosen rationally, the MPP represents the prior estimate of the most probable inversion parameter value. The MPP is also the average of the initial conditions generated for the Nelder-Mead optimizations of the central model analysis.

Potential variable

An intensive state variable (e.g., \(P, T, \mu_i, f_i, X_{CO2}^\text{fluid}\)) that is defined directly or indirectly by partial differentiation of a fundamental equation ([Callen1960], e.g., \(U(S,V,N)\)) with respect to an extensive variable (e.g., \(S, V, N\)) ([Tisza1961], [Callen1960], [Hillert1986], [Connolly1990]).

Try

A Nelder-Mead optimization to minimize the misfit between an observed phase assemblage and a thermodynamic model prediction as a function of the inversion parameters. Tries initiate from a random initial guess of the inversion parameters.