3-D Grain Size

Abstract

Converting a size distribution of sectional circles to the corresponding size distribution of spheres is probably one of the oldest problems in stereology. It is not just an academic question but a serious practical problem whenever the grain size of loose sand or particulate matter is to be compared with the grain size of the corresponding rock type or solid material. When a mean grain size has to be determined from thin sections, it is common practice to convert a two-dimensional (2-D) mean to three dimensions by applying a multiplicative factor (of 1.3 or 1.5) to account for the fact that the cross section of a grain can always be smaller but never larger than the grain itself. However, there is no mathematical relationship between the statistical parameters (mean, variance, skewness, etc.) of the size distribution of sections and those of the size distribution of three-dimensional (3-D) grains. In particular, the mean size of the 2-D sections can be smaller than, equal to or larger than the mean size of the 3-D grains. This means that if we compare the means of 2-D grain size distributions, we may draw completely wrong conclusions with regard to the true (3-D) mean grain size.