Functional PCA of measures for investigating the influence of bioturbation on sediment structure

After describing the main characteristics of grain-size curves, we recall previous results about Principal Components Analysis of absolutely continuous measures, in connection with grain-size curves analysis. This method simultaneously takes into account a chosen reference probability (r.p.) μ (associated with a Radon-Nikodym derivation operator), and the imposed sampling mesh Tp. The point is that it amounts to usual PCA in some metrics M − (Tp;μ); consequently, analyzing a set of grain-size curves in reference to different r.p.s amounts to carry out PCA with different metrics. Three complementary r.p.s were chosen to analyze a set of 552 grain-size curves issued from an experiment designed for investigating the influence of a Polychaetes, Nereis diversicolor , on the sediment structure. The obtained results show that this worm is actually able to alter the sediment. Furthermore, it is shown that its influence depends on its density in the sedimentary column, but not on its position.