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The Krauklis waves are highly dispersive and greatly attenuating waves arising in thin fractures at low frequencies. This makes these waves very attractive for identification of fractured zones that contain hydrocarbon. We apply the effective medium theory to incorporate the Krauklis wave effect in anisotropic viscoelastic properties of carbonate rocks containing aligned fractures filled with fluids of different viscosity (oil and brine). We analyze frequency dependence of the group velocities of P-, Sv-, and Sh-waves, propagating at different angles to the fracture normal, and their attenuation. It is shown that “frequency-angular” dependences of velocities and attenuation are nonlinear and different for different waves and saturating fluids. The calculated patterns of velocities and attenuation versus frequency and ray direction can be used to design observation systems (seismic and VSP surveys) aimed to recognize fractured zones, estimate fracture orientation and type of saturating fluids.