Unmixing Multi-Component Magnetic Mixtures in Geologic Materials Using First Order Reversal Curve Diagrams

Abstract:

We have developed a magnetic unmixing method based on principal component analysis (PCA) of first-order reversal curve (FORC) diagrams. PCA provides an objective and robust statistical framework for unmixing, because it represents data variability as a linear combination of a limited number of principal components that are derived purely on the basis of natural variations contained within the dataset. For PCA we have resampled FORC distributions on grids that capture diagnostic signatures of magnetic domain states. Individual FORC diagrams were then recast as linear combinations of end-member (EM) FORC diagrams, located at user-defined positions in PCA space. The EM selection is guided by constraints derived from physical modeling, and is imposed by data scatter. To test our model, we have investigated temporal variations of two EMs in bulk North Atlantic sediment cores collected from the Rockall Trough and the Iberian Continental Margin. Sediments from these sites contain a mixture of magnetosomes and granulometrically distinct detrital magnetite. We have also quantified the spatial variation of three EM components in surficial sediments along the flow path of the North Atlantic Deep Water (NADW). These samples were separated into granulometric fractions, which also assisted in constraining EM definition. The unmixing model reveals systematic variations in EM relative abundance as a function of distance along NADW flow. Finally, we have applied PCA to the combined dataset of Rockall Trough and NADW sediments, which can be recast as a four-EM mixture, providing enhanced discrimination between components. Our method forms the foundation of a general solution to the problem of unmixing multi-component magnetic mixtures, a fundamental task of rock magnetic studies.