We obtain the wave velocities of ice- and gas hydrate-bearing sediments as a function of concentration and temperature. Unlike previous theories based on simple slowness and/or moduli averaging or two-phase models, we use a Biot-type three-phase theory that considers the existence of two solids (grain and ice or clathrate) and a liquid (water), and a porous matrix containing gas and water. For consolidated Berea sandstone, the theory under-estimates the value of the compressional velocity below 0 degrees C. Including grain-ice interactions and grain cementation yields a good fit to the experimental data. Strictly speaking, water proportion and temperature are closely related. Fitting the wave velocity at a given temperature allows the prediction of the velocity throughout the range of temperatures, provided that the average pore radius and its standard deviation are known. The reflection coefficients are computed with a viscoelastic single-phase constitutive model. The analysis is carried out for the top and bottom of a free-gas zone beneath a gas hydrate-bearing sediment and overlying a sediment fully saturated with water. Assuming that the bottom-simulating reflector is caused solely by an interface separating cemented gas hydrate - and free gas-bearing sediments, we conclude that (1) for a given gas saturation, it is difficult to evaluate the amount of gas hydrate at low concentrations. However, low and high concentrations of hydrate can be distinguished, since they give positive and negative anomalies, respectively. (2) Saturation of free gas can be determined from the reflection amplitude, but not from the type of anomaly. (3) The P to S reflection coefficient is a good indicator of high amounts of free gas and gas hydrate. On the other hand, the amplitude-variation-with-offset curves are always positive for uncemented sediments.