Table 1. Values of physical parameters and constants.
| Parameters with physical units | |
|---|---|
| Earth's radius | 6.371 × 106 m |
| Mantle thickness | 2.870 × 106 m |
| Initial volume (small plume) | 1.22 × 108 km3 |
| Initial volume (intermediate plume) | 2.47 × 108 km3 |
| Initial volume (large plume) | 3.71 × 108 km3 |
| Thickness of the bottom thermochemical BL (thermochemical models) | 430 km |
| Thickness of the bottom thermochemical BL (thermal models) | 100 km |
| Temperature difference surface—CMB ΔT | 3,500 K |
| surface temperature TS | 273 K |
| Temperature increase across the top thermal boundary layer | 1,220 K |
| Temperature increase across the bottom thermal boundary layer | 1,200 K |
| Surface density ρ0 | 3,400 kg m−3 |
| Reference viscosity η0 | 8.44 × 1021 Pa s |
| Gravitational acceleration g | 10 m s−2 |
| Thermal diffusivity (surface) κ0* | 7 × 10−7 m2 s−1 |
| Thermal expansivity (surface) α0 | 4.2 × 10−5 K−1 |
| Specific heat cp | 1,000 J kg−1 K−1 |
| Radiogenic heat production rate H | 5.9 × 10−12 W kg−1 |
| Mantle compressibility χ† | 5.124 10−12 Pa−1 |
| Clapeyron slope of the 410-km phase transition γ410 | 1 MPa K−1 |
| Clapeyron slope of the 660-km phase transition γ660 | −1 MPa K−1 |
| Prefactor in the temperature dependence of viscosity A‡ | 3.9473 × 10−3resp.1.3 × 10−2 |
CMB, core-mantle boundary.
*The thermal diffusivity increases linearly from the surface to the core-mantle boundary by a factor of 2.18 (from ref. 27).
†We use the Adams–Williamson equation of state, resulting in a depth-dependent density in the form of ρ(z)=exp(ρ0g χz). Density changes caused by phase transitions are applied additionally.
‡We use a viscosity law27 in the form of η(T,z)=ηr(z) exp(−A(T-Tadi(z))), with η(z) for the average mantle temperature being the viscosity profile shown in Supplementary Fig. 1(e). A=3.9473 × 10−3 (as in ref. 27) corresponds to a viscosity range of six orders of magnitude for ΔT=3,500 K (temperature difference surface—CMB). To examine the effect of a higher temperature dependence of viscosity on plume dynamics, we also performed computations with a three times higher activation energy (that is, A=1.3 × 10−2).