New Mexico Geological Society Annual Spring Meeting — Abstracts

Normative treatment of geologically pertinent grain-size distributions generally dictates comparison of mass-percent data with log-Normal distributions through the use of phicumulative probability diagrams, graphical moment statistics, mass-percent moment statistics, or fitted mixtures of log-Normal distributions. None of these techniques fits the original data particularly well and the higher moment measures can not be used to generate approximations of original distributions. As an alternative, log-hyperbolic distributions closely approximate grain-size distributions of many transported clastic sediments. As shown previously by BarndorffNielsen, log-hyperbolic distributions are described by four parameters that can be used to generate model curves. Thus the four parameters are much more powerful descriptors of log-hyperbolic distributions than are normative statistics. In order to explore the relationships between log-hyperbolic distributions and normative treatments, we compared exact moment statistics calculated from theoretical distributions with moments and curves derived from normative procedures. The results suggest that calculation of normative statistics be limited to historical comparisons only.