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Propagation of transient acoustic waves in layered porous media: Fractional equations for the scattering operators. (English) Zbl 1099.74035
Summary: 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 telegraph equation. Two relevant scattering operators – transmission and reflection operators – give the scattered fields from the incident wave. They are obtained from Volterra equations which are fractional equations for the scattering operators.

74J20 Wave scattering in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
26A33 Fractional derivatives and integrals
Full Text: DOI
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