Fig. 3

a The plot of L (the thickness of the lithosphere normalized by the mantle depth) against M_p. The dotted line shows the plot that is expected from the Boussinesq approximation \( L (M_{\text{p}} = 1 )\cdot M_{\text{p}}^{ - 0.346} \) where \( L (M_{\text{p}} = 1 ) \) is the normalized thickness at M_p= 1 (for details, see the main text). b The dependence of the thickness of the lithosphere h = Ld^* on M_p, where d^* is the mantle depth that depends on M_p as \( d^{*} = d_{ \oplus } \left( {M_{\text{p}} } \right)^{0.28} \); the thickness is normalized by its value at M_p= 1. The dashed line shows the dependence suggested earlier from the Boussinesq approximation (Valencia et al., 2007); the thickness depends on M_p as \( M_{\text{p}}^{ - 0.45} \) in their models. c The dimensional root-mean-square average velocity V ^*_rms of the convection plotted against M_p. The dashed line shows the relationship of \( V_{\text{rms}}^{ *} (M_{\text{p}} = 1 )\cdot M_{\text{p}}^{1.19} \) suggested in Valencia et al. (2007). (Here, V ^*_rms (M_p= 1) is the value of V ^*_rms at M_p= 1.)