4. We present a set of 3-D numerical experiments on the mantle’s thermal evolution in a compressible spherical shell with Earth-like material parameters. The model is homogeneously heated from within. ( 238 U, 235 U, 232 Th, 40 K) ; Abundances according to McCulloch & Bennett (1994) Small additional heating from below (CMB)

5. What is new? [New in comparison with Walzer, U., Hendel, R., Baumgardner, J., 2003. Viscosity stratification and a 3-D compressible spherical shell model of mantle evolution. In: Krause, E., Jäger, W., Resch, M. (Eds.), High Performance Computing in Science and Engineering‘03, pp. 27-67, Springer-Verlag, Berlin, Heidelberg, New York, ISBN 3-540-40850-9] New model: Walzer, U., Hendel, R., Baumgardner, J., 2004. The effects of a variation of the radial viscosity profile on mantle evolution, Tectonophysics 384, 55-90. Newly derived melting curve of the mantle New viscosity profile with big jumps at the phase boundaries Viscoplastic yield stress  y Another thermal boundary condition at CMB: The CMB is assumed to be laterally isothermal at a particular time. Like other autors (Steinbach et al., 1993; Honda and Yuen, 1994) we adjust T cmb after each time step according to the heat transported from the core to the mantle.

6. The PREM values have been smoothed for each layer f=2 V.Z.; PREM P, K,  K/  P

8.  simplification

10. ALA The term is neglected. We obtain Conservation of mass Conservation of momentum Deviatoric stress tensor Adams-Williamson

11. This is the conservation of energy, where A less known expression of the conservation of energy is Equation of state

23. Thermal evolution of a 3-D compressible mantle with pressure- and temperature-dependent viscosity and time-dependent heating from within. Spherical shell Based on v p, v s,  of PREM, an experimental  (P) and solid-state physics, we derived the Grüneisen parameter, , the specific heats, c P and c v, and a new melting temperature, T m (r). A new radial viscosity profile, eta3, of the mantle with steep gradients at the known mineral phase boundaries High-viscosity transition layer, a second low-viscosity layer below the 660, a strong viscosity rise in the central part of the LM eta3 with its two low-viscosity layers plus viscoplastic yield stress facilitates the generation of stable, plate-tectonic behavior. I

24. Variation of non-dimensional numbers (Ra, Nu, Ur, r n ) Variation of the yield stress,  y, and Ra H (2) reveals four types of solutions. For intermediate values of  y and Ra H (2), we obtain plate-like movements along the surface with plate-like downwelling sheets. Solutions with infinite  y show only plate-like downwelling sheets but no plates near the surface.