Transport models for crust and mantle evolution

Abstract

The exact solutions for the isotopic compositions and the concentrations of two models for mantle—crust evolution are given for arbitrary rates of crustal growth and of backflow to the mantle. In Model I, continents are derived by melt extraction over the history of the earth from undepleted mantle. In Model II, new additions to the continents are derived from a mantle reservoir which becomes increasingly depleted through time by repeated extraction of melts. The key parameters are the chemical fractionation factors for crustal growth and refluxing and the integrated fractional mass removal rates from the crust and the mantle. The relationships between the mean age of the mass of the continents and the isotopic parameters are given. The models suggest that the pre-Archean era (prior to 3.8 AE) was dominated by rapid refluxing of crust to the mantle which during the early Archean gave way to a regime where transport from the mantle to the crust substantially dominated over refluxing of crust to the mantle. The mean age of the mass of the continents appears to be ~1.8 AE. Even for small amounts (~10%) of refluxing Model II shows that highly incompatible elements have very short residence times in the mantle. Mass balance considerations implies that the continents were derived from only a small fraction (~30%) of the mantle.

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