Grain-shaped indices and isometric graphs

ABSTRACT Plotting of grain-shape data on a conventional ternary composition diagram, with long (L), intermediate (I), and short (S) axes of clasts as end members, has advantages over triangular diagrams that employ geometric ratios as primary scales. The isometric (linear) nature of the conventional ternary scale facilitates plotting and interpretation, and the plot provides a basis for comparing the three components over a common denominator (100). Consequently, the graph preserves the information on individual axial values (as a percentage of their sum). The triangle serves as a compilation diagram on which the L-I-S phase space can be subdivided in any number of ways, one of which is the use of selected contour lines of percentage values. In addition, the graph is capable of accommodating t e various grain-shape diagrams (e.g., those of Zingg, Krumbein, and Sneed and Folk) by superposition; this allows for direct, graphic comparison of all such diagrams, and evaluation of their relative efficacy for shape classification. The percentage triangle can be subdivided using a variety of additional functions, such as those that express relative axial uniformity (an entropy-like function), or any other parameter derived from the basic axial values. Employing a scale of percentage values of S versus the form index (L-I) in Cartesian coordinates, superimposed on a conventional isometric composition diagram, yields a ternary plot of great simplicity and high information content.