Transient acoustic wave propagation in rigid porous media: a time-domain approach

Wave propagation of acoustic waves in porous media is considered. The medium is assumed to have a rigid frame, so that the propagation takes place in the air which fills the material. The Euler equation and the constitutive relation are generalized to take into account the dispersive nature of these media. It is shown that the connection between the fractional calculus and the behavior of materials with memory allows time-domain wave equations, the coefficients of which are no longer frequency dependent, to be worked out. These equations are suited for direct and inverse scattering problems, and lead to the complete determination of the porous medium parameters.