The crystallization of a magma ocean (MO) early in Earth's history shaped the entire evolution of our planet. The buoyancy relations between the forming crystals and the residual melt is the most important but also the most unknown parameter affecting the large-scale structure and evolution of the MO. The accumulation of crystals, near the depth of neutral buoyancy between crystals and the coexisting melt, if happening at mid-depths, can separate convecting regions within the MO. Here we use jointly first-principles molecular-dynamics calculations and diamond-anvil cell experiments to obtain the density relations between the molten bulk silicate Earth and the bridgmanite crystals during the crystallization of the MO. The chemical evolutions of the liquid and the coexisting solid during progressive crystallization were constrained by experiments, and the relevant densities were calculated by molecular dynamics. We find that the first crystal of bridgmanite that is formed in a fully molten mantle is Fe-poor, and becomes neutrally buoyant at 110-120 GPa. Since the cooling of the deep MO is fast, and related convection is vigorous, however, first crystals remain entrained. As crystallization advances, the relative Fe content increases in the melt, and the pressure of neutral buoyancy decreases. At 50% solidification, close to the rheological transition, the pressure of the density crossover moves to ∼50 GPa. At this pressure, crystals form an interconnected network and block global convection currents, which in turn leads to the separation of the partly crystallized MO into a surficial MO and a basal MO through melt-solid segregation. Such a shallow segregation of a crystal mush at mid-mantle depth has important implications for the dynamics and timescales of early mantle differentiation. Moreover, the shallow segregation should have promoted the formation of a voluminous basal MO that evolves into a large geochemically enriched reservoir. Accordingly, the seismically observed residues of basal MO crystallization in the present-day mantle may host an unmixed reservoir for the missing budget of highly incompatible elements.