A dynamic 3-D spherical-shell model for the chemical evolution of the Earth's mantle is presented. Chemical differentiation, convection, stirring, and ther-mal evolution constitute an inseparable dynamic system. Our model is based on the solution of the balance equations of mass, momentum, energy, angular momentum, and four sums of the number of atoms of the pairs ~(238)U-~(206)Pb, ~(235)U-~(207)Pb, ~(232)Th-~(208)Pb, and ~(40)K-~(40)Ar. Similar to the present model, the continental crust of the real Earth was not produced entirely at the start of the evolution but developed episod-ically in batches. The details of the continental distribution of the model are largely stochastic, but the spectral properties are quite similar to the present real Earth. Fig. 6 reveals that the modelled present-day mantle has no chemical stratification but we find a marble-cake structure. If we compare the observational results of the present-day proportion of depleted MORB mantle with the model then we find a similar order of magnitude. The MORB source dominates under the lithosphere. In our model, there are nowhere pure unblended reservoirs in the mantle. It is, how-ever, remarkable that, in spite of 4500 Ma of solid-state mantle convection, certain strong concentrations of distributed chemical reservoirs continue to persist in certain volumes, although without sharp abundance boundaries. Section 4 presents results regarding the numerical method, implementation, scalability and performance.
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