Geophysical and geochemical evidence suggests that Earth's core is predominantly made of iron (or iron-nickel alloy) with several percent of light elements. However, Earth's solid inner core transmits shear waves at a much lower velocity than expected from mineralogical models that are consistent with geochemical constraints. Here we investigate the effect of hydrogen on the elastic properties of iron and iron-silicon alloys using ab initio molecular dynamic simulations. We find that these H-bearing alloys maintain a superionic state under inner-core conditions and that their shear moduli exhibit a strong shear softening due to the superionic effect, with a corresponding reduction in VS. Several hcp-iron-silicon-hydrogen compositions can explain the observed density, VP, VS, and Poisson's ratio of the inner core simultaneously. Our results indicate that hydrogen is a significant component of the Earth's core, and that it may contain at least four ocean masses of water. This indicates that the Earth may have accreted wet and obtained its water from chondritic and/or nebular materials before or during core formation
