The characterization of porous materials (e.g., sandstone) is very important for geotechnical and reservoir engineers. For this purpose, often use is made of acoustic waves that are sent through the medium. The desired material parameters can then be estimated from the measured signals. However, often only the velocity or the attenuation of the acoustic waves is employed, and much information that is carried by the waves remains untouched. Therefore, in this thesis we investigate the feasibility of the characterization of porous media using information contained in full acoustic waveforms as observed in different components (e.g., particle motion and fluid pressure). We subsequently address the mathematical description of pseudo interface waves, their experimental detection and the estimation of medium parameters. In the latter part, we show that it is possible to obtain unique and stable estimates of the permeability and porosity of a porous medium by simultaneously exploiting either different waveform attributes of a pseudo interface wave, or the reflection coefficients of different body waves.