Fig. 1: The mass balance calculation of the phase volumes in low water content conditions.

The red dots represent experimental results. a 16 GPa, phE: Mg2.3Si1.25H2.4O6, density and max water content of each phase. Wd, wadsleyite (3.5 g/cm3, 2.5 wt% H2O), En, clinoenstatite (3.28 g/cm3, 0.12 wt% H2O), phase E (2.92 g/cm3). The partition coefficient DWd/En = 3.8 (Detail calculation setting and data source in Supplementary Discussion). b 21.5 GPa, superhydrous phase B: Mg10Si3H4O18, ringwoodite (3.9 g/cm3, 2.8 wt% H2O), akimotoite (3.81 g/cm3, 0.133 wt% H2O), superhydrous phase B (3.3 g/cm3), stishovite (4.35 g/cm, 0 wt% H2O). The partition coefficient DRw/Ak = 21 (Detailed calculation setting data source in Supplementary Discussion).