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.