Uses and misuses of compositional data in sedimentology

This paper serves two goals. The first part shows how mass evolution processes of different nature become undistinguishable once we take a size-limited, noisy sample of its compositional fingerprint: processes of exponential decay, mass mixture and complementary accumulation are simulated, and then samples contaminated with noise are extracted. The aim of this exercise is to illustrate the limitations of typical graphical representations and statistical methods when dealing with compositional data, i.e. data in percentages, concentrations or proportions. The second part presents a series of concepts, tools and methods to represent and statistically treat a compositional data set attending to these limitations. The aim of this second part is to offer a state-of-the-art Compositional Data Analysis. This includes: descriptive statistics and graphics (the biplot); ternary diagrams with confidence regions for the mean; regression and ANalysis-Of-VAriance models to explain compositional variability; and the use of compositional information to predict environmental covariables or discriminate between groups. All these tools share a four-step algorithm: (1) transform compositions with an invertible log-ratio transformation; (2) apply a statistical method to the transformed scores; (3) back-transform the results to compositions; and (4) interpret results in relative terms. Using these techniques, a data set of sand petrographic composition has been analyzed, highlighting that: finer sands are richer in single-crystal grains in relation to polycrystalline grains, and that grain-size accounts for almost all compositional variability; a stronger water flow (river discharge) favors mica grains against quartz or rock fragment grains, possibly due to hydrodynamic sorting effects; a higher relief ratio implies shorter residence times, which may favor survival of micas and rock fragments, relatively more labile grains.

Figure optionsDownload high-quality image (370 K)Download as PowerPoint slideHighlights
► Different mass evolution processes may have the same compositional fingerprint.
► The reasons for this fact: noise, lack of time information, relative information.
► The theoretical and statistical tools behind Compositional Data Analysis (CoDa).
► a CoDa analysis of sand petrographic data from Grantham and Velbel (1988).
► How to graphically assess dependence with other variables in ternary diagrams.