The influence of the aspect ratio in the determination of CSD slopes: comparing 2D versus 3D

Abstract Crystal size distribution (CSD) slopes are used to calculate magma residence times, based on the principle that the slope is inversely proportional to the product of crystal residence times and growth rate. Most CSD studies are based on two-dimensional (2D) data, relying on statistical calculations and stereological corrections of the analyzed data to estimate three-dimensional (3D) size distributions using specialized software. However, the effect of this estimation on the actual CSD distributions and their slopes remains unclear. To evaluate the effect of this CSD slope calculation/estimation on crystal residence times, we compare CSD slopes estimated from 2D and directly measured from 3D data. A 2D data set of pyroxene microlites from a glassy lava sample from Mount Ruapehu (New Zealand) was used to generate CSD (2D-CSD) applying three different aspect ratios. These aspect ratios were calculated using known databases (i.e., CSDSlice and ShapeCalc), and the average aspect ratios from a 3D dataset. The CSD slopes between 10 – 20 μm were extracted and compared to the slope obtained from a true CSD using synchrotron radiation X-ray computational tomography (3D-CSD). Our results show differences in the shape determination by the two databases compared to the average 3D aspect ratio, mainly impacting the intermediate/long axes ratio (I/L) showing a I/L ratio difference of 0.18 between both databases, that translate in slope differences of ±0.03 μm-1 compared to the 3D-CSD. The slopes were applied to the determination of crystal residence times using a known growth rate (i.e., 1.80 × 10−11 m/s), finding differences of approximately 31 h between those CSD determined with the databases, and nearly 17 h comparing the 2D-CSD to the 3D-CSD. Our results contribute to the discussion about which is the best shape estimate to use for 2D stereological conversions, highlighting the uncertainties derived from the statistical calculations of the aspect ratios, and the difficulties in replicating true 3D crystal distributions. We conclude that limitations can be circumvented by using 3D datasets.