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Application of compositional data analysis to geochemical data of marine sediments

In an earlier investigation (Burger et al., 2000) five sediment cores near the Rodrigues 
Triple Junction in the Indian Ocean were studied applying classical statistical methods 
(fuzzy c-means clustering, linear mixing model, principal component analysis) for the 
extraction of endmembers and evaluating the spatial and temporal variation of 
geochemical signals. Three main factors of sedimentation were expected by the marine 
geologists: a volcano-genetic, a hydro-hydrothermal and an ultra-basic factor. The 
display of fuzzy membership values and/or factor scores versus depth provided 
consistent results for two factors only; the ultra-basic component could not be 
identified. The reason for this may be that only traditional statistical methods were 
applied, i.e. the untransformed components were used and the cosine-theta coefficient as 
similarity measure. 
During the last decade considerable progress in compositional data analysis was made 
and many case studies were published using new tools for exploratory analysis of these 
data. Therefore it makes sense to check if the application of suitable data transformations, 
reduction of the D-part simplex to two or three factors and visual 
interpretation of the factor scores would lead to a revision of earlier results and to 
answers to open questions . In this paper we follow the lines of a paper of R. Tolosana- 
Delgado et al. (2005) starting with a problem-oriented interpretation of the biplot 
scattergram, extracting compositional factors, ilr-transformation of the components and 
visualization of the factor scores in a spatial context: The compositional factors will be 
plotted versus depth (time) of the core samples in order to facilitate the identification of 
the expected sources of the sedimentary process. 
Kew words: compositional data analysis, biplot, deep sea sediments