A LIMITATION OF THE BIOT-GARDNER THEORY OF EXTENSIONAL WAVES FLUID-SATURATED POROUS CYLINDERS

It is demonstrated that the Gardner theory of attenuation of extensional modes in porous fluid-saturated cylinders is not the low frequency limit of the Biot theory in that geometry. The calculated attenuation within the Gardner approximation is much less than that predicted by the full Biot theory unless the permeability is less than a specific crossover value which depends on the size of the rod: Typically kxc≈1 Darcy for water-saturated porous media of radius a = 1 cm having extensional speeds VE on the order of 1 km/s. For permeabilities larger than kxc the attenuation predicted by the full Biot theory can be orders of magnitude larger than that predicted by the Gardner approximation, even in the limit as the frequency tends to zero. © 1995, Acoustical Society of America. All rights reserved.