Fig. 9
a RMSR distributions between calculations with k = 1, 2, 4, and 8 and observations. The dashed lines separate the settling velocity classes. The box-and-whisker diagrams are based on the median (orange line), the 25–75th percentile (boxes), and the range of 1.5 times the box (whiskers), with outliers circled. b Frequency of optimal k among all cases for each settling velocity class. The numbers in the legend indicate the optimal k and NA (not applicable) indicates that the optimal k was not selected because the difference in RMSRs between k = 1, 2, 4, and 8 did not exceed the threshold. c The relationship between optimal k and frequency distribution of MR distribution for the settling velocity class 0.6–2.4 m s−1. Nvt is the number of total settling velocity classes among 39 eruptions