An end-member modelling approach to pseudo-Thellier palaeointensity data

Absolute palaeointensities are notoriously hard to obtain, because conventional thermal Thellier palaeointensity 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 palaeointensity 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 palaeointensities. Over the past years, attempts were made to calibrate pseudo-Thellier results into absolute palaeointensities 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 modelling approach (EMMA) allows for the calculation of absolute palaeointensities from pseudo-Thellier measurements. We tested our EMMA using a noise-free numerical data set, yielding a perfect reconstruction of the palaeointensities. When adding noise up to levels beyond what is expected in natural samples, the end-member model still produces the known palaeointensities well. In addition, we made a synthetic data set 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 palaeointensity and the known lab field is around 10 μT for the models with 2-4 end-members, while the palaeointensity of almost all flows can be retrieved within a deviation of ±20 μT. The deviations between the palaeointensities and the known lab fields are almost Gaussian distributed around the expected values. Although the two data sets in our study show that there is potential for using this end-member modelling technique for finding absolute palaeointensities from pseudo-Thellier data, these synthetic data sets cannot be directly related to natural samples. Therefore, it is necessary to compile a data set of known palaeointensities from different volcanic sites that recently cooled in a known magnetic field to find the universal end-members in future studies.