In a compressible mantle, there is a strong variation in material properties with pressure, hence depth. Although these have been included in most of the studies discussed in this paper, only a few authors have performed systematic investigations aimed at determining their effect on the phase-change modulated dynamics. Variations in other parameters such as internal heating rate and aspect ratio are also considered in these studies. Zhao et al. [1992] find that both depth-dependent thermal expansivity and greater internal heating increase the propensity to layering. The latter effect was later confirmed by Solheim and Peltier [1994]. Ita and King [1994] investigated the effect of thermodynamic formulation and equation of state on the degree of layering, finding that strictly depth-dependent parameters lead to increased layering, whereas when a fully self-consistent thermodynamic model including the temperature-dependence of thermodynamic parameters was used, the degree of layering is reduced. They also find that in small boxes and at low Rayleigh numbers, the final flow pattern and degree of layering is strongly affected by initial conditions.
The influence of depth-dependent parameters on cooling Earth models (discussed later) was investigated by Steinbach and Yuen [1994b] and Honda and Yuen [1994].