Cluster analysis on a sphere: Application to magnetizations from metasediments of the Jack Hills, Western Australia

Abstract Metasediments of the Jack Hills contain the oldest known terrestrial minerals in the form of zircons nearly 4.4 billion years old. Paleointensity data from these zircons provide evidence for a Hadean geodynamo as old as 4.2 billion years old. Given the importance of these zircons for constraining the earliest history of the core, it is vital to understand the fidelity of the zircon record. A fundamental aspect providing context for the preservation of primary magnetic signals is the nature of overprints predicted to have been imparted on rocks of the Jack Hills due to Archean to Proterozoic metamorphic events. To be viable magnetic records of a Hadean geodynamo, zircon magnetization directions should differ from these secondary magnetizations. To evaluate these secondary magnetizations, we report paleomagnetic analyses of a comprehensive sampling of 68 quartzite cobble-sized clasts from the Jack Hills metasediments ∼0.5 to 1.0 km from the Discovery Site (which has yielded the oldest zircons and paleofield estimates). While application of standard paleomagnetic tests suggests that the ensemble of cobble directions cannot be distinguished from those drawn from a random distribution, a new cluster analysis of directions on a sphere and non-parametric resampling approaches reveal significant directions amongst subsets of the data. One, isolated at the lowest temperature analyzed [200 to 300 °C, Declination (Dec.) = 316.8°, Inclination (Inc.) = − 51.1 ° ] appears to be dominated by the present day field. Another, isolated at higher (but still relatively low unblocking temperatures that we call “intermediate”, of ∼350–500 °C, Dec. = 243.8°, Inc. = 9.5°) agrees with a magnetic overprint isolated from the secondary Cr–Fe mica fuchsite isolated from the Jack Hills Discovery site, passing a field test at the 80% confidence level. No evidence is found in our data, or in the data of others collected on similar Jack Hills lithologies, for a widespread 1 Ga remagnetization event. Instead, we interpret the most prevalent secondary magnetization of the quartzite (i.e., intermediate unblocking) and the fuchsite characteristic remanent magnetization to be ∼2.65 Ga in age, coincident with peak metamorphism (as high as ca. 475 °C) of the Jack Hills. The presence of this distinct secondary magnetization, its difference from that recorded by Jack Hills zircons at high unblocking temperatures, and the lack of a dominant remagnetization direction at high unblocking temperatures in the cobble data (the expected result for a primary magnetization), lends further support to the fidelity of the Hadean geomagnetic record. The presence of the secondary magnetization also lends support to the conclusion that most of the Jack Hills metasediments were deposited in the Archean, with only minor reworking and potential tectonic interleaving of Proterozoic components. Overall, the application of the new directional cluster analysis presented here has the potential to reveal magnetic directions in highly scattered data sets, typical of weakly magnetized coarse-grained sedimentary rocks