Stirring in three-dimensional mantle convection models and mplications for geochemistry: Passive tracers

Numerical three-dimensional spherical models of stirring of passive tracers in a convective mantle incorporating plate tectonics, taking account of faster mantle overturning in the past and scaling the model to the Earth, show that the mean ages of MORB and OIB samples obtained from the models are ∼1.7 Ga for a 4.5 Ga Earth, close to the observed apparent lead isotopic age of ∼1.8 Ga. Only ∼3% of the mantle remains unprocessed. The processing time, which is the time for a mass equivalent to Earth's mantle to be processed through melting zones, is equal to the value estimated for the Earth (2.9 Ga). These results are consistent with previous results from two-dimensional models. A simple physical processing theory reveals that the degree of processing, the residence time of tracers in the mantle, and their age distribution are mainly controlled by the processing time. Comparison with analogous two-dimensional Cartesian models shows that the geometry, viscosity structure, and vigor of convection have only secondary influence on these results.