Constructing modal mineralogy from geochemical composition: A geometric-Bayesian approach

Modal mineralogical composition is known to carry more information than major element geochemistry, though the latter is far easier to determine in the lab. Constructing mineral compositions from geochemistry can be seen as a typical end-member problem, where one assumes that some multivariate observations are generated by a convex linear mixture of a few pure end-members: these end-member characteristics as well as the coefficients of the linear mixture for the observations can be then estimated from geochemical data. We propose a mixed geometric-probabilistic solution to this problem. First, we assume known end-members, in number and properties, and study the set of solutions from a purely geometric perspective. Second, we discuss how to select representative solutions from this space, in particular under some distributional assumptions. Third, we allow the end-member properties to randomly vary in a controlled, interpretable fashion. Finally we build a Bayesian model, with a parsimonious parametrization characterizing each of these three steps, that can be treated by conventional Markov-Chain Monte Carlo techniques. In the illustration case study, we apply the method to reconstruct the mineralogy of a set of fluvio-glacial monomictic sediments from an Alpine granitoid massif. Results suggest a trend of enrichment in chlorite, muscovite and Ti-bearing minerals, along with depletion in quartz and feldspar. This is tentatively interpreted as an effect of comminution combined with differential mechanical properties. Moreover, mineral chemistry is estimated to exhibit very low Na in muscovite, Fe-rich garnet, Na-rich plagioclase, K-feldspar with up to 10% Na-component (albite), and biotite with Mg>FeMg>Fe. The reconstructed modal mineralogy stays in a reasonable agreement with quantitative XRD phase analyses.