Analysis of seismic data suggests that hydrocarbon deposits are often associated with higher than usual values of attenuation, but this is generally ignored during amplitude versus offset (AVO) analysis. The effect can be modelled with equivalent medium theory based on the squirt flow concept, but the excess attenuation is associated with strong velocity dispersion. Consequently, when we study reflections from the interface between such an equivalent medium and an elastic overburden we find that the reflection coefficient varies with frequency. The impact of this variation depends on the AVO behaviour at the interface; class I reflections tend to be shifted to higher frequency while class III reflections have their lower frequencies amplified. We calculate synthetic seismograms for typical models using the reflectivity method for materials with frequency dependent velocities and attenuations, and find that these effects are predicted to be detectable on stacked data. Two field data sets show frequency anomalies similar to those predicted by the analysis, and we suggest that our modelling provides a plausible explanation of the observations.