A more general expression for the mantle vorticity equation is proposed for convection using axisymmetrical spherical geometry. Both the main mantle phase changes and radial and lateral variations of viscosity due to temperature and pressure. Four series of computations have been performed with (1) both the latent heat releases of the 400 km exothermic and the 670 km endothermic phase change and uniform and constant mantle viscosity; (2) the 670 km phase change alone and viscosity jumps of 10 or 30 between upper and lower mantle phases; (3) the 670 km endothermic phase change, a viscosity contrast of 30, and temperature and pressure dependent viscosity law; and (4) both 400 km and 670 km phase changes, a viscosity jump of 30, and a temperature and pressure dependent viscosity. The 400 km exothermic phase change modifies the global structure from partly layered to whole mantle convection. This effect is opposite to the effect obtained by increasing the viscosity jump at 670 km. However, both effects induce unrealistic thermal behavior which will not appear with temperature dependent laws for viscosity. The mantle avalanches which suddenly inject huge quantities of cold material into the lower mantle have effects at the surface and at the core-mantle boundary (CMB). They induced heat flow crises which explain the huge volcanic events, high rates of mid-oceanic ridge accretion, and periods of low-frequency magnetic reversal. The surface heat flow proceeds directly from the upper mantle return flow along with the avalanches. The temperature dependent viscosity tends to decrease the strength of the avalanches. The bottom heat flow and the birth of CMB plumes may be considered as the consequences of cold upper mantle material arrival at the CMB. The lower mantle and the upper mantle transit times depend on the thickness of upper and lower mantles but also on the phase changes and on the viscosity. The CMB and surface perturbations may be simultaneous (to a few tens of million years). The temporal evolution of the convection pattern during an avalanche allows us to propose self-consistent mechanisms for slab migration above the 670 km discontinuity for the birth and disappearance of ridges, the rising of powerful plumes from the CMB, and the creation of low-viscosity zones which may act as a lubricant under continents for fast migration. These results show that the main mantle phase changes, combined with temperature and pressure dependent viscosity, induce convective behavior which provides an explanation for most of the past and present large-scale dynamic behavior of the Earth's global tectonics. ¿ 1998 American Geophysical Union