Explicit expressions for the frequency dependence of the velocity and attenuation of shear waves in a periodic system of flat solid and viscous fluid layers have been derived by solving exact Rytov's dispersion equation in the long-wavelength approximation. The dispersion and attenuation are related to the well known mechanisms of dissipation in porous media: viscoelastic mechanism (viscous shear relaxation) and visco-inertial Biot's mechanism. The expressions describing the effects of these two mechanisms in a broad frequency range have been derived from the same standpoint. The asymptotic expresslons for various limiting cases coincide with the results of previous studies.


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