Power-law attenuation in acoustic and isotropic anelastic media

Power attenuation laws were originally introduced for phenomenological descriptions of attenuation in a large variety of materials. More recently they have been applied in viscoelastic inversion. Power-law models can be readily expressed in terms of scalar acoustic partial integro-differential equations. The restrictions on the exponent of the power law imposed by the assumptions of causality and dissipativity are discussed. An extension of power-law attenuation models from acoustic to isotropic anelastic media is proposed. The guiding principle is that the attenuation of longitudinal and transverse waves satisfies the power law. Restrictions imposed by thermodynamics and well-posedness considerations are discussed.