How Many Components? A New Statistical Approach for Fitting Complex Paleodirections.

Paleomagnetic specimens acquire a magnetization in a direction parallel to the magnetic field they cool in. If a paleomagnetic specimen is reheated to a lower temperature, moves during cooling, or is present in a magnetic field at ambient temperature for a sufficient time, then grains within the specimen with lower blocking temperatures will also record a secondary direction. On a Zijderveld plot, this appears as a change in the magnetization vector direction at a particular temperature, with the new direction starting at the vector endpoint of the old one. Each constituent direction is referred to as a component". Paleodirections with multiple components can be difficult to analyze. For older specimens which have undergone multiple reheating events, determining the number of vector components is not always trivial, and may require more detailed statistical analysis (e.g. doi: 10.1016/j.epsl.2017.12.007). The temperature at which the paleomagnetic direction changes may also be of interest. This is not always easy to determine as the boundary between paleomagnetic directions is not always sharp, the change may occur over a range of temperatures. We present a new Bayesian method which uses a probabilistic framework to fit paleomagnetic directions with any number of components to data. This allows the method to automatically detect the number of components for a specimen, with an uncertainty on both the direction vectors and the number of components. Uncertainty estimates are useful as they allow for objective assessment of the quality of a fit to multi-component data, and can indicate when there may be alternative interpretations. A site mean direction can be obtained by bootstrapping pseudosamples from the probability distribution for each specimens direction, avoiding a reliance on Fisherian statistics. Our method also incorporates the temperature information from thermally demagnetized data to determine the temperatures of inflection points between vector components, with uncertainty. This has applications for emplacement temperatures of pyroclastic deposits, cooling rates for intrusive bodies, and for automatically choosing temperature ranges for paleointensity data based on vector directions. We hope that our method will be useful for objectively analyzing hard to interpret directional data.