The present study investigates novelties brought about into the classicBiot's theory of propagation of elastic waves in a fluid-saturated porous solidby inclusion of non-Newtonian effects that are important, for example, forhydrocarbons. Based on our previous results (Tsiklauri and Beresnev: 2001,Phys. Rev. E, 63, 046304), we have investigated the propagation of rotationaland dilatational elastic waves, through calculating their phase velocities andattenuation coefficients as a function of frequency. We found that thereplacement of an ordinary Newtonian fluid by a Maxwell fluid in thefluid-saturated porous solid results in: (a) an overall increase of the phasevelocities of both the rotational and dilatational waves. With the increase offrequency these quantities tend to a fixed, higher, as compared to theNewtonian limiting case, level which is not changing with the decrease of theDeborah number $\alpha$. (b) the overall decrease of the attenuationcoefficients of both the rotational and dilatational waves. With the increaseof frequency these quantities tend to a progressively lower, as compared to theNewtonian limiting case, levels as $\alpha$ decreases. (c) Appearance ofoscillations in all physical quantities in the deeply non-Newtonian regime.
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