MODELING THE DISTRIBUTION OF ISOTOPIC RATIOS IN GEOCHEMICAL RESERVOIRS

Abstract

We present an extension of the conventional geochemical reservoir model for the evolution of the Earth's crust-mantle system in which we calculate not only the mean isotopic ratios, but also the distribution of those ratios within the reservoirs. Owing to low chemical diffusion rates, subreservoirs that are created by mass transport into and out of the mantle effectively exist as distinct geochemical entities for all time. By tracking these subreservoirs, we obtain a model of the full range of isotopic values represented in the mantle. Using results from numerical calculations of mixing, we also track the length scales associated with each subreservoir. Applying simple statistics, we obtain the distribution of expected measurements as a function of the stirring time, effective melt fraction, sampling volume, and mass transport history. We present calculations of isotopic heterogeneity for two simple mantle evolution models and explore the sensitivity of geochemical observables to the variables mentioned. We focus on the Rb-Sr and Sm-Nd systems and are able to reproduce much of the observed complexity of oceanic basalts. We infer that the stirring time of the mantle falls between 250 and 750 Myr, and that the initial length scale of mantle heterogeneity before stirring is of the same order as the length scale of sampling. We also conclude that the differences between isotopic data from mid-ocean ridge basalts and ocean island basalts cannot simply be due to differences in sampling volume, but must also reflect differences in the source reservoirs and/or melting processes. Increasing the size of the ocean island basalt source region by 45% with respect to the mid-ocean ridge basalt source region reproduces the offset between the two distributions, but still fails to explain the more isotopically extreme measurements. Our results show that the argument suggesting that the absence of samples with a primitive isotopic signature indicates that no primitive material remains in the mantle is not valid.