The use of seismic anisotropy for the characterization of fracture systems in the subsurface is based upon equivalent medium theories that describe the average elastic response of a fractured material in the long wavelength limit. Traditional equivalent medium models predict a seismic response that is independent of frequency and insensitive to the size of the fractures. Recent observations from seismic data challenge these assumptions. The interpretation of attenuation and velocity dispersion in laboratory data acquired in the kHz to GHz frequency range is based on the concept of squirt flow in porous fluid-saturated rock. A number of studies have also found effects of dispersion in the seismic frequency band, particularly in connection with fracture zones. However, these observations have been lacking quantitative explanation in terms of petrophysical processes, and with regard to wave-induced fluid motion in porous rock seismic data are generally assumed to represent the low frequency limit. Recent work on equivalent medium theories for fractured rock address these issues by incorporating wave-induced uid motion into the modelling, which predicts seismic anisotropy to depend on frequency. I analyse VSP data from five different sedimentary basins that contain naturally fractured hydrocarbon reservoirs. I design processing techniques to investigate whether frequency-dependent anisotropy can be detected in the seismic frequency band. I find broad evidence in support of the concept. Three different attributes are extracted from the data that give evidence of anisotropic dispersion: P-wave attenuation anisotropy, the frequency dependence of the time delay between split shear waves, and attenuation of the slow shear wave compared to the fast one. The measured effects correlate with information on the presence of fractures in the reservoirs of the respective oil and gas fields. For one of the data sets where no anisotropic dispersion is detected, fracture-induced anisotropy is very weak and dominated by polar anisotropy. The observations can be explained by a squirt-flow model for fractured rock. The sensitivity of the modelled response to fluid type and fracture length scales is consistent with the real data results and geological evidence. It may not always be possible to detect frequency-dependent anisotropy in real data depending on data quality and the symmetry of the equivalent anisotropic medium. Nevertheless, the quantitative evidence of anisotropic dispersion from the majority of the VSPs and the correlation with the presence of fractures in the subsurface suggest that it is worthwhile considering these effects in analyses of seismic anisotropy.