An end-member modeling approach (EMMA) to pseudo-Thellier paleointensity data

Absolute paleointensities are notoriously hard to obtain, because conventional thermal Thellier paleointensity experiments often have low success rates for volcanic samples. The thermal treatments necessary for these experiments potentially induce (magnetic) alteration in the samples, preventing a reliable paleointensity estimate. These heating steps can be avoided by pseudo-Thellier measurements, where samples are demagnetized and remagnetized with alternating-fields. However, pseudo-Thellier experiments intrinsically produce relative paleointensities. Over the past years attempts were made to calibrate pseudo-Thellier results into absolute paleointensities for lavas by mapping laboratory induced Anhysteretic Remanent Magnetizations (ARMs) to the thermally acquired Natural Remanent Magnetizations (NRMs). Naturally occurring volcanic rocks, however, are assemblages of minerals differing in grain size, shape, and chemistry. These different minerals all have their own characteristic mapping between ARMs and thermal NRMs Here we show that it is possible to find these characteristic mappings by unmixing the NRM demagnetization and the ARM acquisition curves into end-members, with an iterative method of non-negative matrix factorization. In turn, this end-member modeling approach (EMMA) allows for the calculation of absolute paleointensities from pseudo-Thellier measurements. We tested our end-member modeling approach using a noise-free numerical data set, yielding a perfect reconstruction of the paleointensities. When adding noise up to levels beyond what is expected in natural samples, the end-member model still produces the known paleointensities well. In addition, we made a synthetic dataset with natural volcanic samples from different volcanic edifices that were given a magnetization by heating and cooling them in a controlled magnetic field in the lab. The applied fields ranged between 10 and 70 μT⁠. The average absolute difference between the calculated paleointensity and the known lab-field is around 10 μT for the models with 2 to 4 end-members, while the paleointensity of almost all flows can be retrieved within a deviation of ± 20 μT⁠. The average difference between calculated paleointensities for the 3 end-member model is -1.7 μT⁠. The deviations between the paleointensities and the known lab-fields are almost Gaussian distributed around the expected values. To assess whether the end-members produced by our analysis have a physical meaning, we measured the Curie temperatures of our samples. These Curie measurements show that there is a relationship between the abundances of the end members of the 3 end-member model in the samples and their dominant Curie temperatures. This indicates that even whilst the spectrum of Curie temperatures and hence composition of iron-oxides in the sample set is continuous, and the magnetization is also related to mineral size and shape, the calculated end-members of the 3 end-member model are somewhat related to magnetic mineral composition present in the samples. Although the two datasets in our study show that there is potential for using this end-member modeling technique for finding absolute paleointensities from pseudo-Thellier data, these synthetic datasets cannot be directly related to natural samples. Therefore, it is necessary to compile a dataset of known paleointensities from different volcanic sites that recently cooled in a known magnetic field to find the universal end-members in future studies