Toward an understanding of chemical and isotopic heterogeneity in the Earth's mantle

We present models of the evolution of isotopic heterogeneity in the Earth's mantle to develop an understanding of the relationship between modern geochemical observables and physical processes through time.; Our basic model is 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.; In developing the model, we focus on the samarium-neodymium and rubidium-strontium parent-daughter systems, as these are the best behaved of the commonly-used systems. We then focus on the uranium-thorium-lead system, which introduces a significant degree of complexity not present in the simpler systems. We find that the removal of lead from the oceanic crust by subduction zone processes is critical in obtaining the observed slopes in lead-isotopic space.; We derive an internally consistent model of the Earth's isotopic evolution both in the bulk and statistical sense. We obtain a model of the Earth's mantle, heterogeneous on all length scales, which successfully reproduces the spectrum of heterogeneity observed in mid-ocean ridge basalts. This model leads us to a new version of the plum-pudding mantle in which relatively young, (<1 Gyr) depleted residua from continental crustal extraction form the plums and everything else mixes to form the pudding. This latter component may be identified with FOZO or C, the intermediate mixing endmember suggested previously by other authors.