Directional Cluster Analysis on a Sphere: Retrieval of Archean Magnetic Directions from Data with High Dispersion

Magnetic directions from coarse clastic rocks are typically highly scattered, to the point that the null hypothesis that they are drawn from a random distribution, using the iconic test of Watson (1956), cannot be rejected at a high confidence level (e.g. 95%). Here, we use an alternative approach of searching for directional clusters on a sphere. When applied to a new data set of directions from quartzites from the Jack Hills of Western Australia, we find evidence for distinct and meaningful magnetic directions at low (200 to 300 degrees C) and intermediate ( 350 to 450 degrees C) unblocking temperatures, whereas the test of Watson (1956) fails to draw a distinction from random distributions for the ensemble of directions at these unblocking temperature ranges. The robustness of the directional groups identified by the cluster analysis is confirmed by non-parametric resampling tests. The lowest unblocking temperature directional mode appears related to the present day field, perhaps contaminated by viscous magnetizations. The intermediate temperature magnetization matches an overprint recorded by the secondary mineral fuchsite (Cottrell et al., 2016) acquired at ca. 2.65 Ga. These data thus indicate that the Jack Hills carry an overprint at intermediate unblocking temperatures of Archean age. We find no evidence for a 1 Ga remagnetization. In general, the application of cluster analysis on a sphere, with directions confirmed by nonparametric tests, represents a new approach that should be applied when evaluating data with high dispersion, such as those that typically come from weak coarse-grained clastic sedimentary rocks, and/or rocks that have seen several tectonic events that could have imparted multiple magnetic overprints.