A weighted equation based on the three-phase time-average and Wood equations is applied to derive a relationship between the compressional wave (P wave) velocity and the amount of hydrates filling the pore space. The proposed theory predicts accurate P wave velocities of marine sediments in the porosity range of 40--80% and provides a practical means of estimating the amount of in situ hydrate using seismic velocity. The shear (S) wave velocity is derived under the assumption that the P to S wave velocity ratio of the hydrated sediments is proportional to the weighted average of the P to S wave velocity ratios of the constituent components of the sediment. In the case that all constituent components are known, a weighted equation using multiphase time-average and Wood equations is possible. However, this study showed that a three-phase equation with modified matrix velocity, compensated for the clay content, is sufficient to accurately predict the compressional wave velocities for the marine sediments. This theory was applied to the laboratory measurements of the P and S wave velocities in permafrost samples to infer the amount of ice in the unconsolidated sediment. The results are comparable to the results obtained by repeatedly applying the two-phase wave scattering theory. The theory predicts that the Poisson's ratio of the hydrated sediments decreases as the hydrate concentration increases and the porosity decreases. In consequence, the amplitude versus offset (AVO) data for the bottom-simulating reflections may reveal positive, negative, or no AVO anomalies depending on the concentration of hydrates in the sediments.