The existence of geochemically distinct reservoirs in the Earth's mantle is inferred from the observation of worldwide rather homogeneous mid-ocean ridge basalts (MORB) on the one side and heterogeneous ocean island basalts (OIB) on the other side. How can these observations be reconciled with geophysically favoured large-scale convection? ... is an unresolved problem of global geodynamics. In this thesis stirring properties of 3-D spherical models of convection in the Earth's mantle are investigated numerically. Attempts to make the models more earthlike are described. It is proposed as a working assumption for future, more detailed investigations that there may have been a change from small-scale to large-scale convection during the evolution of the mantle.