Quoted from: https://doi.org/10.3389/feart.2020.00117

Authors consider thermal convection of mantle materials which is driven by a subducting and retreating motion of a cold slab in one eighth (azimuth θmin ≤ θ ≤ θmax where θmax-θmin=45∘) of a two-dimensional spherical annulus whose outer and inner radii are rmax = 6, 400 km and rmin = 4, 400 km, respectively. Authors take into account the effects of the phase transition from olivine to wadsleyite at around 410 km depth and that from ringwoodite to bridgmanite and ferro-periclase at around 660 km depth. The density contrasts associated with these phase transitions are taken to be 8.3 and 7.8%, respectively (Dziewonski and Anderson, 1981). The Clapeyron slope of the phase transition at 410 km depth is taken to be γ410 = +3 MPa/K, while that of 660 km depth γ660 is varied from −3 MPa/K or −1 MPa/K, based on the result of laboratory experiments (e.g., Ito and Takahashi, 1989; Katsura et al., 2003; Fei et al., 2004). The meanings and values of parameters used in this study are given in Table 1.