On the importance of advection in determining the local isotopic composition of the mantle

The equations for isotopic evolution in a deforming medium are derived and used to show that the local isotopic composition of the mantle depends primarily on the advection of heterogeneities by the flow field. Various examples of the role of advection are given using a two-scale model of mantle convection. The effect of small-scale flows, which have dimensions smaller than the plates themselves, is to convert any initially localized heterogeneity into thin spiral sheets. The isotopic properties of erupted lavas will depend on the relative size of the zone of partial melt to the spacing between such sheets. An idealized model for⁸⁷Sr/⁸⁶Sr variations from Pacific islands and the covariation of¹⁴³Nd/¹⁴⁴Nd-⁸⁷Sr/⁸⁶Sr is based on the combined effect of isotopic fluxes at subduction zones and advection by the return flow under the moving lithospheric plates.