Multivectors: Nine components represented on a ternary diagram

Abstract

Methods of graphical representation of data need to keep pace with increasingly complex data manipulation. Conventional ternary diagrams allow the presentation of three components as a point in a plane. Multivector diagrams allow plotting of up to nine components in one ternary diagram by representing compositions not as points but as vectors sharing a “triple-point”. The triple point represents the composition of three sets of three components (triads). The vector arms represent the composition within triads. Multivector diagrams can be used to illustrate individual samples or multiple samples. The techniques for computing, plotting, reading and interpreting multiple vectors follow the same rules as a conventional ternary diagram such that any of the nine components or groups of components can be compared directly or with the aid of simple projections. Although the mathematical and statistical implications of this graphical representation are not presented, it is demonstrated that the technique is useful for visual assessment of compositions and key compositional ratios. Multivector diagrams can be applied to any system where a graphical representation of up to nine components may be useful. Multivectors are applied to examples from whole rock geochemistry, whole rock modal mineralogy, mineral alteration, chemical weathering and groundwater chemistry.