In this work we interpret the data showing unusually strong velocity dispersion of P-waves (up to 30%) and attenuation in a relatively narrow frequency range. The cross-hole and VSP data were measured in a reservoir, which is in the porous zone of the Silurian Kankakee Limestone Formation formed by vertical fractures within a porous matrix saturated by oil, and gas patches. Such a medium exhibits significant attenuation due to wave-induced fluid flow across the interfaces between different types of inclusions (fractures, fluid patches) and background. Other models of intrinsic attenuation (in particular squirt flow models) cannot explain the amount of observed dispersion when using realistic rock properties. In order to interpret data in a satisfactory way we develop a superposition model for fractured porous rocks accounting also for the patchy saturation effect. In this work we interpret the data showing unusually strong dispersion of P-waves (up to 30%) and attenuation in a relatively narrow frequency range. The cross-hole and VSP data were measured in a reservoir, which is in the porous zone of the Silurian Kankakee Limestone Formation formed by vertical fractures within a porous matrix saturated by oil, and gas patches. Such a medium exhibits significant attenuation due to wave-induced fluid flow across the interfaces between different types of inclusions (fractures, fluid patches) and background. Other models of intrinsic attenuation (in particular squirt flow models) can not explain the amount of observed dispersion when using realistic rock properties. In order to interpret data when a satisfactory way we develop a superposition model for fractured porous rocks accounting also for the patchy saturation effect.