The structures,elasticities,sound velocities,and electronic properties of anhydrous and hydrous fayalite (Fe2SiO4 and Fel.75Ho.sSiO4) under high pressure have been investigated by means of the density functional theory within the generalized gradient approximation (GGA) with the on-site Coulomb energy being taken into account (GGA+U).The optimized results show that H atoms prefer to substitute Fe atoms in the Fel site.Compared with the anhydrous fayalite Fe2SiO4,the mass density,elastic moduli,and sound velocities of Fel.75Ho.sSiO4 slightly decrease.According to our data,adding 2.3 wt％ water into fayalite leads to reductions of compressional and shear wave velocities (Vp and Vs) by 3.4％-7.5％ and 0.3％-3.4％ at pressures from 0 GPa to 25 GPa,respectively,which are basically in agreement with the 2％-5％ reductions of sound velocity obtained by the experimental measurement in the low velocity zones (LVZ).Based on the electronic structure,the valence and conduction bands are slightly broader for hydrous fayalite.However,hydrous fayalite keeps the insulation characteristics under the pressures up to 30 GPa,which indicates that hydration has little effect on its electronic structure.