Phase reversals are commonly observed during exploration seismic amplitude-versus-offset analysis, and usually modelled with the Zoeppritz equations. In practice, when multiple fluids are present we often deal with reflections from interfaces having a contrast in both elastic and anelastic properties. In this paper, we present a new phenomenological model for phase reversals in cases in which velocity dispersion and attenuation are present. We demonstrate strong qualitative differences in behaviour between the elastic and anelastic cases, influencing both the amplitude and phase of the reflection coefficient. Analysis of seismic data showing a phase reversal from a gas reservoir in the Vienna basin shows a striking agreement with the modelling. We conclude that the influence of fluid-induced dispersion on reflection data is a significant and measurable phenomenon in cases of practical interest, that recognition of the phenomena may be used as a novel fluid indicator and that frequency-dependent rock physics analysis may be an important tool for both industrial geophysics and seismic monitoring of CO2 storage.