1On first principles of viscoelasticity

Fundamental principles of the viscoelastic theory are compared to those of theoretical mechanics, classical theory of elasticity, and also to Biot’s theory of saturated porous rock. This comparison shows that viscoelasticity lacks the physical foundation of the variational dynamic principle, which is standard in mechanics. In addition, viscoelasticity does not address the actual physical mechanisms of energy dissipation but uses mathematical generalizations that allow bypassing the detailed physics and encoding the observed attenuation coefficients of P- and S waves into the elastic moduli of the medium. Therefore, viscoelasticity can be viewed not as a physical theory but rather as a mathematical model of general linear processes. This model is accurate for several known end-member cases, such as the P- and S-wave propagation in uniform media. However, its predictions for heterogeneous media are based on strong mathematical assumptions and still need to be verified from full physical considerations. At the same time, it appears clear that such assumptions should fail in the general case. Viscoelastic medium properties, such as the generalized bulk and shear moduli, are phenomenological by nature. In each specific case, these properties should be related to combinations of various physical factors. Unfortunately, for deep-Earth conditions, such factors still remain to be identified, and true physical theories of wave attenuation still need to be developed. The development of such theories should affect the existing interpretation of seismic attenuation, as well as its forward and inverse models. Key words: Anelasticity; seismic attenuation; mechanics; theory