Bifurcation of the Biot slow wave in a porous medium

The propagation of the Biot slow wave in a fluid-saturated porous medium at low frequencies is investigated by asymptotic methods. It is proven that the Biot wave has a bifurcation behavior depending on its wave number. The bifurcation occurs in a neighborhood of the critical value k(cr), which depends on the permeability of a medium and the viscosity of a fluid. The P2 wave is fully attenuated if its wave number is smaller than k(cr) and it becomes propagatory with wave numbers bigger than k(cr). Asymptotic formulas for the phase velocity and attenuation of the Biot wave are derived.