Propagation of transient acoustic waves in layered porous media: Fractional equations for the scattering operators

Acoustic waves scattering from a rigid air-saturated porous medium is studied in the time domain. The medium is one dimensional and its physical parameters are depth dependent, i.e., the medium is layered. The loss and dispersion properties of the medium are due to the fluid-structure interaction induced by wave propagation. They are modeled by generalized susceptibility functions which express the memory effects in the propagation process. The wave equation is then a fractional telegraphist's equation. The two relevant quantities are the scattering operators-transmission and reflection operators-which give the scattered fields from the incident wave. They are obtained from Volterra equations which are fractional equations for the scattering operators.