Figure 3. Effect of the size of the k-cutoff on a) the number of sites (N) remaining in the dataset, and the b) A95, c) K, and d) S of the acquired paleopole. Commonly applied cutoff sizes of 50 and 100 are indicated with gray dashed lines.
4.2 Effect of the number of samples per site (n)
Next, we analyze the benefits of collecting multiple samples per site to average within-site or between-sample errors. To this end, we studied the influence of the number of samples per site (n) on the mean paleopole of a dataset (Figure 4) and its angular distance to the reference pole with n=7 (or 6, in case of Antarctica), A95, K, and S (Figure 5). For each n, we performed the calculations 1000 times, each repetition collecting n different samples from the total number of samples per site. The paleopole position calculated with n=1 falls within the A95 of the mean pole calculated with n=7 in 100% of the calculations for the datasets from Mongolia, Turkey, and Antarctica (Figure 4). For the Norwegian dataset, this is the case for 91% of the calculations. In other words, the pole position is barely influenced by the number of samples per site (Figure 5a) and stays within the 95% confidence interval. The influence on the A95 is small, but there is a slight decrease in the A95 when within-site scatter is averaged by increasing n (Figure 5b). This varies from less than 0.5° to 1.5°, with the largest effect occurring for the dataset from Norway, whose sites have the largest within-site scatter. We find that the number of samples per site has a minor influence on K and S (Figure 5c, d). Only Norway shows an increase in K from approximately 14 to 29 and in S from 23° to 16°. This experiment shows that the effect of the number of samples per site on determining a pole position is surprisingly small, even if between-site scatter is somewhat decreasing.