Crystal size distributions derived from 3D datasets: Sample size versus uncertainties

Crystal size distributions (CSD) are the most commonly studied character in quantitative textural investigations of igneous rocks. The quality of CSD depends fundamentally on the sample size (i.e. total number of crystals). Here we use 3D X-ray tomographic datasets of two early erupted Bishop Tuff pumice clasts (comprising 849 and 446 quartz crystals) to investigate the effect of sample size on the quality of the quartz size distributions. Because CSD are obtained using a counting procedure, uncertainties related to counting statistics can be used as minimum estimates of error. Given that most natural samples are characterized by a decreasing number of crystals with increasing crystal size, uncertainties tend to increase markedly with crystal size, and the number of small crystals to be counted grows very quickly with increasing sample size. Accordingly, with as few as 100 crystals in total, it is possible to properly estimate the population densities for small size bins (20-80 mu m). However, to obtain meaningful estimates across four bin sizes (20-320 mu m), at least similar to 250 crystals, but preferably > 400 crystals are needed. To minimize the total number of crystals counted, and keep the uncertainties on the larger size ranges within reasonable values, it becomes necessary to study multiple volumes at variable spatial resolution.