Variation Diagrams and Indexes

Steven Dutch, Professor Emeritus, Natural and Applied Sciences, University of Wisconsin - Green Bay

To summarize relationships among igneous rocks, a wide variety of indexes and graphs are used. Indexes and variation diagrams can describe the state of a single rock or asuite of rocks. They can also help distinguish among rocks of different origins and histories.

Indexes

An index is a single number that describes where a rock plots along a continuum.

Felsic Index:: 100(Na₂O + K₂O)/(Na₂O + K₂O + CaO). This basically measures how rich the rock is in alkali. A syenite would have a very high felsic index, a tonalite a very low one, even if they both have identical silica contents.
Mafic Index:: 100(FeO + Fe₂O₃)/(MgO + FeO + Fe₂O₃) Since Fe-rich olivine and pyroxene form first, this index measures how much of the ferromagnesian component of the magma had been removed prior to crystallization of the rock.
Alkali-Lime Index:: Unlike the previous indices, this one measures not an individual rock but a suite. It is the silica percentage at which CaO equals (Na₂O + K₂O). Generally we'd expect CaO to exceed (Na₂O + K₂O) in an andesite, but (Na₂O + K₂O) to exceed CaO in a granite. In a suite of rocks with varying silica contents, this index measures exactly where the equality occurs.
Differentiation Index:: Weight percentage of normative Qz + Ab + Or + Ne + Le + Kp. That is, weight percentage of normative quartz, alkali feldspar, or alkali felspathoids (or foids). Obviously if either quartz or foids are positive the other will be zero.

Harker Plots

The simplest igneous rock variation diagram is simply to plot the content of some component against silica. This is a Harker Plot. Among the major elements, Fe and Mg tend to be extremely high in ultramafic rocks and decrease with silica content. Calcium peaks in mafic rocks, and aluminum in intermediate rocks. Potassium and sodium tend to increase with silica.

Among trace elements, chromium and nickel peak in the ultramafic range and copper peaks on the borderline with mafic rocks. Vanadium and cobalt peak in the mafic range, as do titanium and manganese at a bit higher silica content. Zinc and phosphorus peak near the mafic-intermediate boundary, strontium in the intermediate range (like calcium), zirconium at the felsic end of the intermediate range and barium in felsic rocks.

Other Simple Plots

Larsen Plot:: The horizontal axis is (Si/3 + K) - (Ca + Mg). This removes some of the systematic variation seen in Harker plots (Si and K go together and opposite to Mg) and reveals deviations from typical Harker plot patterns.
Nockolds-Allen Plot: The horizontal axis is (SiO₂/3 + K₂O) - (CaO + MgO + FeO). This also removes some of the systematic variation seen in Harker plots.
Felsic Index vs. Mafic Index:: One axis is 100(FeO + Fe₂O₃)/(MgO + FeO + Fe₂O₃), the other is 100(Na₂O + K₂O)/(Na₂O + K₂O + CaO).

Triangle Plots

Fe, Mg, Na+K

K, Na, Ca

(Na₂O + K₂O), (FeO + Fe₂O₃), MgO

Normative Qz, Ab, Or

Discrimination Diagrams

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Created 22 Sept 1997, Last Update

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