Amplitude-versus-offset, AVO, approximations allow the estimation of various properties from pre-stack seismic gathers. Recently it has been suggested that fluid mobility is a controlling factor in pore pressure equalisation and can result in anomalous velocity dispersion in the seismic bandwidth. However, current approximations all assume an elastic subsurface and are unable to account for velocity dispersion. I have applied existing methodologies to a real dataset to qualitatively detect and interpret spectral amplitude anomalies. Three areas had AVO and spectral signature consistent with frequency-dependent AVO theory. The results suggest that it is feasible to measure such effects on real data in the presence of random noise. It would imply that the relaxation parameter, tau, is larger in the field than has been measured in water-saturated real and synthetic sandstones in the laboratory. I extended a two-term AVO approximation by accounting for velocity dispersion and showed how the resultant reflection coefficient becomes frequency-dependent. I then used this to measure P- and S-wave reflectivity dispersion using spectrally-balanced amplitudes. The inversion was able to quantify the affect of the P-wave velocity dispersion as an instantaneous effect on the reflection. NMO stretch was an issue at the far offsets and I limited myself to the near offsets and effectively measured only the P-wave reflectivity dispersion. I showed how the P-wave reflectivity dispersion signs depend on the AVO classification of the reflection whilst the magnitude depends on the crack density of my model. I showed how the effect of noise and thin-bed tuning can enter uncertainties into the interpretation of spectral anomalies. Whilst it is possible to detect frequency-dependent AVO signatures on pre-stack gathers, the interpretation remains non-unique. I have quantitatively measured a new physical property, reflectivity dispersion, from pre-stack seismic data. I have presented a method of detecting and measuring velocity dispersion in pre-stack gathers but there remain ambiguities in the interpretation of such results. The approach incorporates spectrally decomposed data in an extended AVO inversion scheme. Future work should investigate the application of the methodology to a real seismic dataset.