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2016 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

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

Bringing the Power of R to a Geochemical Community

verfasst von: Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow

Verlag: Springer Berlin Heidelberg

Buchreihe : Springer Geochemistry

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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SUCHEN

Über dieses Buch

The aim of this book is to unlock the power of the freeware R language to advanced university students and researchers dealing with whole-rock geochemistry of (meta-) igneous rocks. The first part covers data input/output, calculation of commonly used indexes and plotting in R. The core of the book then focusses on the presentation and practical implementations of modelling techniques used for fingerprinting processes such as partial melting, fractional crystallization, binary mixing or AFC using major-, trace-element and radiogenic isotope data. The reader will be given a firm theoretical basis for forward/reverse modelling, followed by exercises dealing with typical problems likely to be encountered in real life, and their solutions using R. The concluding sections demonstrate, using practical examples, how a researcher can proceed in developing a realistic model simulating natural systems. The appendices outline the fundamentals of the R language and provide a quick introduction to the open-source R-package GCDkit for interpretation of whole-rock geochemical data from igneous and metamorphic rocks.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
In the beginning, this chapter briefly summarizes the historical development of ideas regarding the causes of chemical variations in magmatic suites, from mediaeval times to the present. It stresses the importance of current revolution driven by improving analytical techniques, providing large amounts of increasingly precise major- and trace-element analyses, as well as data on a growing number of isotopic systems. Later, it provides an overview of available PC programs for interpretation of whole-rock geochemical data from igneous rocks. Finally it outlines the importance of open-source software and introduces the R language and the Geochemical Data Toolkit (GCDkit), written in R. Both are used extensively throughout this book (for their fundamentals, see Appendices A and B).
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow

R/GCDkit at work

Frontmatter
Chapter 2. Data Manipulation and Simple Calculations
Abstract
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.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 3. Classical Plots
Abstract
In this chapter, plain R recipes are presented to produce the most common graphs used in igneous geochemistry, such as binary plots (simple and multiple, e.g. Harker plots), ternary plots or spiderplots. Practical exercises illustrating the general principles are also included. Special attention is given to dealing with spurious correlations in binary plots (closure effect). The fundamentals and implementation of classification and geotectonic diagrams in GCDkit are also mentioned, as are the relevant commands for drawing basic plot types (binary, ternary, spider and multiple) and their subsequent modification.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 4. Specialized Plots
Abstract
This chapter presents several less known (or newly designed) types of geochemical plots that are implemented in GCDkit. It does not aim at being systematic and comprehensive; instead it focuses on arguably the most useful or interesting among them that could be suitable for common applications in igneous geochemistry. These include log–log binary plots (for discussing ratios), spiderplots colour coded according some independent variables (such as silica), double-normalized spiderplots (stripping effects of fractional crystallization from a source-related variation produced by partial melting), spider boxplots and spider box and percentile plots (good to deal with large and/or noisy trace-element data sets), contour plots (serving to spot maxima in data distributions), anomaly plots (appropriate, for instance, for mineral exploration) and stripplots/strip boxplots (illustrating the variability in small datasets).
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 5. Radiogenic Isotopes
Abstract
The aim of this chapter is to explain basic numerical (R-language) approaches in interpreting radiogenic isotope data in igneous geochemistry, with particular emphasis on Sr–Nd–Hf–Os isotopic systems. The text is concerned with calculation of initial ratios, ages ε and γ values, single- and two-stage model ages and fitting of isochrons. Practical exercises illustrating the principles on real datasets are also included. Lastly, the SrNd plugin is introduced that takes care of such recalculations in the GCDkit system.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow

Modelling major elements

Frontmatter
Chapter 6. Direct Models
Abstract
In this chapter, we show how the major-element compositions of magmas are controlled by mass balance during their evolution through various processes such as crystallization, melting or mixing, including some variants thereof. Mass balance implies specific numerical and graphical relations (the “lever rule”) that can be used to predict the evolution of melt in any of these scenarios.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 7. Reverse Models
Abstract
This chapter presents numerical tools to “revert” the mass-balance relation (of Chap. 6), and explain the composition of a given igneous rock in terms of mixing between different components (solids or liquids). The proportions of each component can be constrained if their compositions are known. Thus it is possible to gain information on, e.g. the proportion of end-members involved in magma mixing, or the percentages of cumulative minerals formed during crystallization.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 8. Forward Modelling in R
Abstract
This chapter contains five solved exercises on forward modelling of the behaviour of major elements using R (see Chap. 6 for principles). These include: fractional crystallization of a single mineral and of a more complex cumulate assemblage, partial melting of a mantle peridotite and origin of basaltic magmas, and calculation of a bulk rock composition given the proportions and chemistries of its constituent minerals.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 9. Reverse Modelling in R
Abstract
This chapter contains four solved problems on reverse modelling of the behaviour of major elements using R (see Chap. 7 for principles). These include reverse modelling of fractional crystallization, partial melting of a paragneiss (yielding granitic magma) and calculation of a general “norm” given the composition of a bulk rock and its constituent minerals.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow

Modelling trace elements

Frontmatter
Chapter 10. Dilute Trace Elements: Partition Coefficients
Abstract
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.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 11. Direct (dilute) Trace-Element Models
Abstract
By combining the mass balance (Chap. 6) and partition coefficient (Chap. 10) concepts, it is possible to derive a range of laws that relate the trace-element composition of a melt to that of its source, the nature and proportion of solid phases (cumulate or restite), etc. Various laws are written to account for different situations (melting, crystallization, mixing; batch or fractional; etc.).
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 12. Reverse (dilute) Trace-Element Models
Abstract
Although the laws governing the trace-element behaviour are not linear, it is still possible, in some cases, to “invert” them and constrain the proportion of minerals present in a cumulate or a restite based on melt’s composition and partition coefficients. This chapter presents the relevant equations.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 13. Trace Elements as Essential Structural Constituents of Accessory Minerals: The Solubility Concept
Abstract
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.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 14. Forward Modelling in R
Abstract
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.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 15. Reverse Modelling in R
Abstract
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
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow

Radiogenic isotopes

Frontmatter
Chapter 16. Direct Models
Abstract
The best proofs for operation of open-system processes remain radiogenic isotope ratios, which are generally not fractionated during closed-system processes such as melting or crystallization. The magmas formed should preserve the isotopic characteristics of their source. In other words, the radiogenic isotope data are totally transparent to mechanisms of magmatic differentiation but are very sensitive to mixing or contamination. This chapter explains mathematical formulae governing binary mixing for a single isotopic ratio (in diagrams such as Sr vs. 87Sr/86Sr or 1/Sr vs. 87Sr/86Sr) and for their pairs (e.g., in 87Sr/86Sr vs. 143Nd/144Nd plots). The following text adds the theoretical treatment of the Assimilation and Fractional Crystallization (AFC) processes and their bearing on isotopic composition of the evolving magmas.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 17. Reverse Models
Abstract
This rather short chapter explains fundamentals of fitting binary mixing hyperbolae to real data arrays (e.g., in 87Sr/86Sr vs. 143Nd/144Nd plots). This is done by the least-square method, and the outputs are asymptotes with curvature. The second part of the text presents reverse solution of the AFC as described by Powell (1984), using the slope of the mixing line in the 1/C vs. I diagram (e.g., 1/Sr vs. 87Sr/86Sr plot).
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 18. Forward Modelling in R
Abstract
This chapter contains three solved problems on forward modelling of the behaviour of isotopes using R (see Chap. 16 for principles). The exercises deal with plotting mixing hyperbolae for a single isotope system (in the Sr vs. 87Sr/86Sr and 1/Sr vs. 87Sr/86Sr coordinates) and an Sr–Nd isotope pair (in the 87Sr/86Sr vs. 143Nd/144Nd plot). The last exercise simulates the effects of AFC processes in the 1/Sr vs. 87Sr/86Sr space.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 19. Reverse Modelling in R
Abstract
This chapter contains one solved problem on reverse modelling of the behaviour of isotopes using R (see Chap. 17 for principles). The exercise is concerned with fitting a binary mixing hyperbola to Pb–Hf isotopic data from lavas of the La Martinique Island (Lesser Antilles) by the least-square method.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow

Practical modelling

Frontmatter
Chapter 20. Choosing an Appropriate Model
Abstract
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.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 21. Semi-Quantitative Geochemical Approach
Abstract
Some numerical tools can be used to further constrain the processes shaping the geochemistry of a rock suite (see Chap. 20). The numerical form of the different laws established before (especially for trace elements, Chap. 11) is such that, in well-chosen diagrams, different processes will generate immediately distinguishable patterns. We discuss several such approaches including order of incompatibility, process identification, mixing test and fractionation vectors.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 22. Constraining a Model
Abstract
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.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 23. Numerical Tips and Tricks
Abstract
Although modelling is all about understanding a suite of rocks and relating observations to variables in a model (Chap. 22), some useful numerical tricks are important to keep in mind. Most relate to the fact that the composition of a rock can be seen as a vector in an n-dimension space (n being the number of elements in consideration). Some of these tricks are discussed here.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 24. Common Sense in Action
Abstract
As modelling is conducted with the specific purpose of understanding a series of igneous rocks, it is important to keep it firmly rooted in geological truth. This chapter discusses some of the limitations of the modelling exercise: some processes that may seem feasible from a geological point of view are physically unrealistic, for instance. We also discuss the uncertainties and the degree of confidence that may be attributed to a model.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow

Worked examples

Frontmatter
Chapter 25. Differentiation of a Calc-Alkaline Volcanic Series: Example of the Atacazo-Ninahuilca Volcanoes, Ecuador
Abstract
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.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Chapter 26. Progressive Melting of a Metasedimentary Sequence: the Saint-Malo Migmatitic Complex, France
Abstract
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.
Vojtěch Janoušek, Jean-François Moyen, Hervé Martin, Vojtěch Erban, Colin Farrow
Backmatter
Metadaten
Titel
Geochemical Modelling of Igneous Processes – Principles And Recipes in R Language
verfasst von
Vojtěch Janoušek
Jean-François Moyen
Hervé Martin
Vojtěch Erban
Colin Farrow
Copyright-Jahr
2016
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-662-46792-3
Print ISBN
978-3-662-46791-6
DOI
https://doi.org/10.1007/978-3-662-46792-3