Hervé Martin

Geochemical Modelling of Igneous Processes – Principles And Recipes in R Language

Provides basics of R language syntax and its application to geochemical problems; gives a comprehensive introduction to the GCDkit system Explains fundamentals of numerical modelling of igneous processes (including not only formulae, but also showing the successful modelling strategies) Includes numerous worked examples indicating how geochemical modelling helps us to understand geological problems

Data Manipulation and Simple Calculations

This chapter will demonstrate the practical use of the R language (for overview of its syntax, see Appendix A) and GCDkit (Appendix B) to solve common problems in igneous geochemistry. We shall follow the basic procedure from loading the data into the system, through their subsetting, calculation of basic indexes (such as mg# or A/CNK values) or cationic parameters (after Niggli, Debon & Le Fort and De la Roche), to normative recalculations (e.g., CIPW norm). Briefly mentioned are also statistical applications of the R language, such as obtaining simple descriptive statistics and use of factors-based grouping to deal with complex geochemical data sets.

Constraining a Model

This chapter shows how information can be gleaned from various sources to con-strain the parameters needed to build a full model. Some of the parameters come from observations of the petrology or the geochemical patterns of the rocks stud-ied. In other cases, information must be sought from the literature. The remaining parameters can be calculated based on the previous information. The art of modelling consists in assembling this disparate information in a consistent set.

Progressive Melting of a Metasedimentary Sequence: the Saint-Malo Migmatitic Complex, France

This chapter shows a worked example, modelling the crustal anatexis to form a migmatitic complex. Starting with geological and petrological data, we describe the main geochemical features of the lavas and model their evolution. In this environment, the melts are not well extracted from their solid residue. They are poorly homogenised and their composition largely reflects the variations of the particular source lithologies. Fortunately, field relations allow to directly constrain the local melt amount. Increasing melt fractions correspond to successive melting reactions, and thus a residue with an evolving composition. We propose, therefore, a strategy based on describing the evolution of melt’s composition for a given source as a function of the melt amount (and therefore of the nature of the residue), and of the source’s composition. Finally, we bracket the possible range of melts between the compositions derived from two end-member sources.

Dilute Trace Elements: Partition Coefficients

This chapter presents the key concept of the partition coefficient (applied to igneous systems). The partition coefficient is the ratio between the composition in a mineral phase, and the concentration in the melt, for a given element. Whereas major-element composition of the mineral is known or it can be assumed (see Chap. 6), for trace elements the best constrained parameter is the partition coefficient. We explore some of the factors that control its value, as well as, in turn, the way this coefficient controls the distribution of elements between liquid and solid phases.

Differentiation of a Calc-Alkaline Volcanic Series: Example of the Atacazo-Ninahuilca Volcanoes, Ecuador

This chapter presents a worked example, based on the evolution of a calc-alkaline differentiation series, from recent volcanoes in Ecuador (Andes). Starting with geological and petrological data, we describe the main geochemical features of the lavas and model their evolution. We show that fractional crystallization was the dominant process, and that all the lavas in the volcano are related by fractionation from a common parent. The differentiation story is modelled here as a two-step process, with two successive cumulate compositions. We also explore some uncertainties of the modelling exercise and discuss the range of possible solutions permissible by geochemistry.

Choosing an Appropriate Model

This chapter presents a range of geological and petrological evidence that can be used to decide on the process shaping the geochemistry of a rock suite. In turn, we discuss the evidence for crystallization, melting and mixing (and assimilation), and we show which of the laws discussed in Chaps. 6 and 11 are more appropriate for each situation.

Reverse Modelling in R

This chapter contains two solved problems on reverse modelling of the behaviour of trace elements using R (see Chap. 12 for principles). One concerns fractionation of tonalitic magma (given the compositions of primitive and fractionated melt and partition coefficients of the principal mineral phases). The other is a reverse problem of garnet lherzolite melting, yielding a basaltic melt

Forward Modelling in R

This chapter contains five solved problems on forward modelling of the behaviour of trace elements using R (see Chaps. 11 and 13 for principles). They include theoretical treatment of batch and fractional crystallization equations, development of REE during tonalite magma fractionation, partial melting of primitive mantle or depleted mantle reservoirs, construction of a binary mixing hyperbola, plotting zircon saturation isotherms and calculation of zircon saturation temperatures.

Trace Elements as Essential Structural Constituents of Accessory Minerals: The Solubility Concept

The concept of partition coefficient becomes useless for elements that form a significant (stoichiometric) portion of a mineral. Such is the case for many accessory minerals including zircon (controlling Zr) and monazite (controlling LREE and Th). In this case, a more appropriate concept is that of solubility (of the accessory mineral). This chapter presents several (empirical) solubility laws for various accessory minerals, and discusses how this concept will affect the evolution of melts during common processes such as melting or crystallization.