Measuring Similarity between Calculated Paleomagnetic APWPs and the Fixed Hotspot Model Predicted APWP

Discussions about the spatiotemporal patterns and trends of apparent polar wander paths (APWPs) have focused on comparisons between different tectonic plates in order to look for clues that indicate they were part of the same supercontinent (e.g. Besse and Courtillot, 2002; Torsvik et al., 2008; Geuna et al., 2010; Domeier et al., 2011). However, before making these further advanced comparisons, we determined that the robustness of different algorithms that generate APWPs for an individual tectonic plate should be tested. This actually becomes a trajectory similarity measuring problem. The reference trajectory we chose is the Fixed Hotspot Model (Müller et al., 1993; Müller et al., 1999) predicted APWP, which is a known dataset. The subjects of comparison are the 60 paleomagnetic APWPs, which are produced using 60 algorithms (with more to come in the future) developed in this paper. These algorithms are based on different moving average methods, and also different weighting methods since not all paleomagnetic data are equal in quality. The data (from Global Paleomagnetic Database 4.6b) analyzed includes not only spatial (paleomagnetic pole longitude, latitude) and temporal (magnetic age) information, but also their errors (position error, age error, etc.). The question is what is the best way to turn a collection of individual poles, with different age constraints and uncertainties, into a smoothed APW path. Our goal is to get a reliable result, i.e. a path generated to approximate the "real" APWP with appropriate uncertainties. The result may help select the best APWP construction algorithm(s). As preliminary studies, the cratons of North America (PlateID 101; from Fig. 1 we actually can identify the general trend of its APWP), Australia (801) and India (501) are chosen as research objects to develop techniques we want to think about. First, the great circle distance between two poles (spatial) of the same age (temporal) respectively from the reference APWP and one paleomagnetic APWP is measured. The approach being developed to analyze the robustness of the smoothed and weighted APWPs, when compared with the predicted tectonic motion from seafloor spreading and hotspot data, is Monte Carlo simulation. This work is also relevant for comparing APWPs from different continents in future work.