The geochemical consequences of mixing melts from a heterogeneous mantle

Binary mixing is one of the most common ways of describing the relationships between incompatible element concentrations and Sr-Nd-Pb isotopic ratios in oceanic basalts. Apparent binary mixing trends are seen in a wide variety of data sets, both at a local-scale and globally. Here we focus on data from Iceland where isotopic variations in whole-rock samples and olivine-hosted melt inclusions demonstrate the presence of high-amplitude, short lengthscale mantle heterogeneity. Binary mixing models fail to provide an adequate fit to data for moderately incompatible and compatible elements, which provides evidence that some of the variation in melt compositions arises from the fractional melting process itself. To explore the role of mixing in determining the geochemical systematics of oceanic basalts we have developed a new model of the mixing of fractional melts from a bi-lithological mantle source where small enriched fusible heterogeneities are embedded in a refractory depleted matrix. This model is a statistical model, based on the Dirichlet distribution, that allows us to determine the expected statistical distributions of melt compositions. The Icelandic data appears to provide evidence that the mixing process is not uniform with depth, and that the deepest melts appear to have undergone a greater degree of homogenisation than the shallower melts. The model most closely resembles the data when all melts beneath a depth corresponding to ∼5% melting of the refractory lithology are homogenised. We speculate that this depth marks the transition between diffuse and channelised melt flow. This new statistical model of mixing challenges some of the conventional interpretations of trace element-isotope systematics. Notably, picking mantle end-members from apparent binary mixing arrays in isotope ratio plots is fraught with difficulty: in our models the apparent binary mixing arrays do not point towards the isotopic compositions of their mantle sources (with the exception of Pb-Pb)