The incorporation mechanisms and elastic properties of hydrous Bridgmanite (Brg) and post-Perovskite (PPv) are investigated by using first principles calculations at the lower mantle pressures. The elastic properties calculations in both (Al, Fe)-free and (Al, Fe)-bearing systems give evidences that hydrogen has less effect on the elastic wave velocities and moduli in (Al, Fe)-free and Al-bearing system. However, the elastic wave velocities and moduli, especially the shear velocity V-S and the shear modulus G, are remarkably sensitive to the presence of hydrogen in the Fe-bearing system. The calculated shear velocity anomaly (dV(S)) are -2.9% for FeSi3+H-Brg and -3.1% for FeSi3+H-PPv, which are very close to the average anomaly value of LLSVPs. This result may imply the Ferric-bearing hydrous MgSiO3 is likely a dominated mineral in LLSVPs. Density functional perturbation theory (DFPT) and QHA calculation have also been performed to determine the P-T phase diagram for different hydrous systems. The phase transition boundary between Brg and PPv shifts to higher or lower pressures when the hydrogen atom substitutes in the Mg or Si sites in the lattice, respectively. The existence of volatiles such as hydrogen may account for the strong lateral chemical heterogeneity in lowermost mantle. (C) 2019 Elsevier B.V. All rights reserved.