2 The various types of diagrams
Diagrams are often the key to understanding a text. They can convey a large amount of information, which makes learning how to read diagrams an essential skill. To interpret a diagram effectively, you need to recognize the type of diagram presented at and understand what it can show. Likewise, when presenting your own data, choosing the right type of diagram is crucial for communicating your message clearly. This section introduces the most common types of diagrams and explains what they are best used for.
Learning Goals
Knowing that various types of diagrams exist. Be able to recognise, read, and apply the various types of diagrams.
2.1 Making a Plot [04:38]
A brief guide outlining which important elements should or need to be included, i.e., need to appear in a plot.
Axes labelling, units, meaningful scaling with numbers, a legend.
Only information that could not sensibly be included in the figure itself. Resolving the used abbreviations. Alle explanations need to be placed in the text. Self-explanatories such as: ›The plot shows Mg vs. Ti‹ should not appear in the signature.
✓That the symbol colours are the same in all plots.
✗That both plots have a frame.
✗That both plots have similar figure captions.
✓That the symbols are the same.
✗That the plot is not unaesthetically ›open‹ in one direction.
✓It is easy to add specific lines.
✗A complete frame allows for more labelling-possibilities
✗The symbol names in alphabetic order from top to down.
✗All symbol names in the same colour.
✓The symbol names from top to down in the same sequence as the symbols themselves in the plot.
✓Heavy/dark colours more to the top.
2.2 Basics of Function Plots [04:25]
Functions are typically used for modelling. A function contains one free parameter plotted on the x-axis. This free parameter is used for modelling and might represent an abundance in mixing or amount of fractionated material from a melt or condensed from a vapour. It might represent an age in a reservoir evolution or the progession of time during element diffusion, and so on.
The y-axis displays a value that changes, i.e., is depended on the parameter plotted along the x-axis. The y-axis can be a simple value, a ratio, an inverse value, the logarithm of a value/ratio, …, while the parameter on the x-axis is typically a simple value that is often plotted across a limited interval (e.g., time or fraction).
It displays a dynamic content, as the variable on the x-axis changes. It is this dynamical change, what is usually the main interest of a function plot.
✓… is the compositional evolution of a reservoir over time.
✗… an isochron plot showing the chronological evolution of a reservoir over time.
✓… the compositional evolution of a reservoir relative to the amount of extracted material.
✓… the isotope fractionation in a reservoir relative to the amount of evaporative loss from a melt.
✗… the compositional evolution of a reservoir and over time, with a different element on each axis (e.g., Mg vs. Al).
✓… an element concentration
✗… the time
✓… the isotope composition
✗… a fraction (e.g., 0…1) of something that is added/removed
✓… an element concentration
✓… the time
✓… the isotope composition
✓… a fraction (e.g., 0…1) of something that is added/removed
✓True
✗False
2.3 Basics of Parametric Plots [04:07]
Parametric plots are typically used for modelling. A parametric plot contains one free parameter, but two functions that use this same one parameter. The result of these functions, i.e., the respective y-values are plotted along the two axis of a x-y plot. Hence, the free parameter itself is not plotted. The two functions might in fact be the same, i.e., the equation for mixing two reservoirs, however, the two mixing equations will contain different elements. The result of this calculation is then plotted in a scatter plot with the two elements on the respective axes.
Both axes display the resulting value of a function. Both functions have the same parameter that changes. Formally, this looks as follows: y1 = f(x) and y2 = g(x). Then, y1 and y2 are displayed along the two axis. f and g are two functions, and x is the common value that changes. An example is the isochron equation. Here, the function for the x-axis is the decay equation for the parent isotope, and the function for the y-axis is the ingrowth equation for the daughter isotope. The common parameter that changes is the time t. Another example would be the mixing of reservoirs displayed in a scatter plot, e.g., with two element concentrations on the axes (e.g., Si vs. Na). Here the function would in both cases be the mixing equation, but with Si in it for one axis and Na in it for the y-axis. The common parameter that changes would be the fraction of the reservoirs involved in the mixing.
It displays a dynamic content, as the common variable changes. It is this dynamical change that is the main interest of a parametric plot. It is typically used to model various processes. It is also manly combined with the scatter plot.
✓… is the compositional evolution of a reservoir over time.
✓… an isochron plot showing the chronological evolution of a reservoir over time.
✓… the compositional evolution of a reservoir relative to the amount of extracted material.
✓… the isotope fractionation in a reservoir relative to the amount of evaporative loss from a melt.
✓… the compositional evolution of a reservoir and over time, with a different element on each axis (e.g., Mg vs. Al).
✓… an element concentration
✗… the time
✓… the isotope composition
✗… a fraction (e.g., 0…1) of something that is added/removed
✓… an element concentration
✗… the time
✓… the isotope composition
✗… a fraction (e.g., 0…1) of something that is added/removed
2.4 Basics of Scatter Plots [03:37]
The most typical plots to visualise data. Pairs of data ((x1,y1),(x2,y2),(…,…)) are required for this plot. Any dataset fitting this simple criteria can be presented in a scatter plot.
Both axes display a value, typically a simple value, a ratio, an inverse value, the logarithm of a value/ratio, etc.
It displays a static content. The displayed data show the current state of a system, for example the current composition of a rock.
✓… shows the composition of a rock with an element concentration or isotope composition on each axis (e.g., Mg vs. Al).
✗… shows REE compositions of rocks with various enrichment/depletion patterns.
✓… shows data an isochron plot.
✗… shows the isotope fractionation during evaporative loss from a melt.
✓… an element concentration
✓… normalised element concentration
✗… a sample name
✗… the time
✓… the isotope composition
✗… a chemical element
✓… an element concentration
✓… normalised element concentration
✗… a sample name
✗… the time
✓… the isotope composition
✗… a chemical element
2.5 Basics of Category Plots [05:47]
This typical plot has categories along its x-axis, sometimes also along its y-axis. Sub-types are for example histograms, line-plots, bar-charts, Caltech Plots, or box-whisker charts. A category might be an element, e.g., the REEs or something like chondrule type, shock class, etc.
The y-axis displays a value, typically a simple value, a ratio, an inverse value, the logarithm of a value/ratio, etc. The category is typically, but not necessarily, a description and not a value. For example, a sample name, a location name, the name of a chemical element, a classification name, etc. The category is usually plotted along the x-axis. Isotope compositions are, however, often displayed the other way round, with the categories on the y- and values on the x-axis.
It displays a static content. The displayed data show the current state of a system, for example the current composition of a rock.
✓… shows REE compositions of rocks with various enrichment/depletion patterns.
✓… shows the composition of a rock with an element concentration or isotope composition on each axis (e.g., Mg vs. Al).
✗… is the ›Caltech‹ plot, i.e., an e.g., isotope composition on the x-axis and the samples stacked along the y-axis.
✓… is a normalised plot showing the bulk chondrite compositions with the various chondrite groups along the x-axis.
✓… an element concentration
✓… normalised element concentration
✗… a sample name
✗… the time
✓… the isotope composition
✗… a chemical element
✗… an element concentration
✗… normalised element concentration
✓… a sample name
✓… the time
✗… the isotope composition
✓… a chemical element
2.6 Basics of Combining Plots [05:42]
For example, when data are combined with a model in a single plot, different types of plots need to be combined, e.g., a scatter plot with a parameteric plot.
Of course, any kind of values can be plotted. It is only important that when plots are combined that all the plots that are going to be combined have the same values on the same axes.
Combined plots are ideal to combine static and dynamic contents. For example, an x-y plot might display the static composition of a rock, and is then combined with a parametric plot showing e.g., a mixing or fractionation model. Another example would be a static x-y plot showing the isotope composition of many rocks, e.g., epsilon Hf vs. time, which is then combined with a dynamic evolution plot modelling the Lu-Hf system over time.
✓… is a static plot combined with another static plot.
✓… is a static plot combined with a dynamic plot.
✓… is a dynamic plot combined with another dynamic plot.
✗True
✓False
✓True
✗False
2.7 Basics of Ternary Plots [05:47]
This is used when triples of data ((x1,y1,z1),(x2,y2,z3),(…,…,…)) are visualised in triangular plots. Phase diagrams of chemographic triangles use this kind of presentation.
In principle, any type of value. These values can be absolute concentrations, when e.g., elements are at the corners. But often, components such as minerals are plotted at the corners, in which case the fractions of these components are often plotted along the axes. This means, the absolute abundances of each component is first re-normalised to 1 or 100.
Of course this is possible. It is basically possible to construct a ternary parametric plot that would add dynamic content such as mixing, fractionation, or even radiogenic evolution.
✓… is a phase diagram.
✗… shows REE compositions of rocks with various enrichment/depletion patterns.
✗… is the ›Caltech‹ plot, i.e., an e.g., isotope composition on the x-axis and the samples stacked along the two other axes.
✓… is a chemographic representation.
✗True
✓False
✓a/(a+b+c)
✗a/(b+c)
✗a/a+b+c c/(a+b+c)
✓b/(b+c)