Yoder-Tilley basalt tetrahedron

Figure 3.28 Normative nepheline-oUvine-diopside-hypersthene-quartz projection after Thompson (1984), showing the compositions of initial melts in the CMAS system, MORE source and fertile anhydrous mantle at a range of pressures (in kb). The inset shows the relationship of the diagram to the surface of the Yoder-Tilley basalt tetrahedron.

Fi re 3.29 The low-pressure tholeiidc basalt phase diagram after G)X ef a/. (1979). The inset shows that the projection is from normative quartz onto the critical plane of silica undersaturation modihed to olivine-plagioclase-ciinopyroxene in the Yoder-Tilley basalt tetrahedron. 

Table 3.9 Projection procedures for basaltic compositions within the Yoder-Tilley tetrahedron...

Phase relations and rock compositions of andesitic and related magmas of the calc-alkaline suite can also be represented by the diopside-olivine-albite-quartz tetrahedron — the silica-saturated part of the Yoder-Tilley (1962) basalt tetrahedron. 

The concept of metric tensor becomes central whenever distances and projections are considered, particularly when least-square criterion are used, a point that will be discussed in Chapter 5. Let us ask the frequently raised question of how to find an expression in terms of old coordinates (e.g., oxide proportions) for a projection made in the non-Euclidian space. This could be the case for finding oxide abundances of a basalt composition projected in the Yoder and Tilley tetrahedron, or the oxide abundance of a metamorphic rock composition projected into an ACF diagram assuming that quartz is present. 

The normative nepheline-diopside-olivine-quartz tetrahedron (Figure 3.26a) originally propo by Yoder and Tilley (1962) for the classification of basalts has been extensively used for comparing the results of experimental studies on basalts with rock analyses. Various projection procedures are in use. 

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