Theory of pulse propagation in fluid saturated porous layers

A theory for ultrasonic pulses in a porous solid layer immersed in a fluid was developed. Biot's mixture theory describes the constitutive equation of a fluid saturated porous solid. Since fast and slow waves exist in a Biot solid, there is mode conversion at the interface even at normal incidence and the transmission and reflection coefficients are 2 x 2 matrices. Matrix methods are used in developing the solution of the wave propagation problem. A generalized ray expansion algorithm is obtained by using the Gauss-Seidel matrix iterative method. The arrivals of the fast and the slow waves are easily identified. A compact computational algorithm is developed using combinatorial analysis and the Cayley-Hamilton theorem. The computed solution is compared with Plona's experiment on pulses originating in water and striking normally at a porous disk.