When sound propagates in such media, there is always thermal consumption of energy caused by viscosity.
Sound attenuation may also be a result of heat conductivity in the media as has been shown by G. Kirchhoff in 1868.
[1][2] The Stokes-Kirchhoff attenuation formula takes into account both viscosity and thermal conductivity effects.
Acoustic attenuation in a lossy medium plays an important role in many scientific researches and engineering fields, such as medical ultrasonography, vibration and noise reduction.
[3][4][5][6] Many experimental and field measurements show that the acoustic attenuation coefficient of a wide range of viscoelastic materials, such as soft tissue, polymers, soil, and porous rock, can be expressed as the following power law with respect to frequency:[7][8][9] where
are real, non-negative material parameters obtained by fitting experimental data; the value of
In recent decades, increasing attention and efforts have been focused on developing accurate models to describe general power-law frequency-dependent acoustic attenuation.
[17] Szabo[8] proposed a time convolution integral dissipative acoustic wave equation.
On the other hand, acoustic wave equations based on fractional derivative viscoelastic models are applied to describe the power law frequency dependent acoustic attenuation.
[11] See [20] for a paper which compares fractional wave equations with model power-law attenuation.
This wave equation incorporates fractional time derivatives: See also[14] and the references therein.
Such fractional derivative models are linked to the commonly recognized hypothesis that multiple relaxation phenomena (see Nachman et al.[17]) give rise to the attenuation measured in complex media.
[24] describes a model-based method to attain causal power-law attenuation using a set of discrete relaxation mechanisms within the Nachman et al.
[17] In porous fluid-saturated sedimentary rocks, such as sandstone, acoustic attenuation is primarily caused by the wave-induced flow of the pore fluid relative to the solid frame, with