Statistical characteristics of xenoliths in the Antioch kimberlite pipe, Marshall County, northeastern Kansas
Geometrical characteristics of xenoliths in the Antioch kimberlite pipe have been considered in statistical terms. A method of conversion of 2D intersections to 3D dimensions was used. It has been shown that the Rosin-Rammler distribution of mass leads to the Weibull distribution of sizes, whereas a fractal distribution of sizes can be expressed as the Pareto distribution. Lognormal, Weibull, and Pareto distributions have been tested as model distributions. The Pareto distribution could be the most appropriate model for the distribution of xenoliths. This conclusion is in agreement with the general concept that the xenoliths formed as a result of an underground explosion without additional breakage occurring during magma transport. The final distribution may be shifted from the initial model as a result of processes of redistribution and sorting of xenoliths in liquid-crystalline flows.