Internal Friction within the Earth and Seismic Attenuation

The existing theory of internal friction within the Earth uses viscosity for its fluids and "viscoelastic quality factor" (Q) for solids. Despite its broad acceptance, it is rarely noticed that this model also faces serious theoretical and practical difficulties. Such difficulties arise in cases of heterogeneous media, which are most important in seismology. For example, for a long-period Love wave, the viscoelastic model violates the energy balance and overestimates the attenuation by ~ 5-12 %. In all existing Q models, fluid layers such as the outer core unrealistically contribute zero dissipation of free oscillations, seismic waves, and tides. For fluids, internal friction (Q^-1) is directly proportional to viscosity, whereas from comparing seismic observations with geodynamics, this empirical correlation is opposite for the upper mantle. The viscoelastic model also produces nonphysical solutions and incorrect phases of acoustic impedances in heterogeneous media. These problems need to be addressed in order o understand the meaning of Q shown in many attenuation models. Fortunately, an alternate approach to internal friction is well known in continuum mechanics and thermodynamics. This approach is free from the above problems. Instead of Q and "material memory", it considers several specific mechanisms of energy dissipation: 1) viscosity for both solids or fluids, which can be Newtonian or non-Newtonian, 2) thermoelasticity, 3) scattering and variations of geometric spreading, and 4) kinetic transformations within the material. Here, we apply this approach to field and lab observations of seismic attenuation. As an example, we invert the Love-wave Q_L observed on the surface at 20-200-s periods for physical parameters 1)-3) above. With the exception of thermoelasticity on small heterogeneities, each of these mechanisms explains the observed frequency dependence of Q_L very closely. For several mechanisms, Love-wave attenuation is dominated by mantle layers at ~70-km depths, whereas for both types of viscosity, internal friction below 200-450 km is most important. Thus, seismic attenuation can be described by conventional mechanics, leading to constraints on physical parameters of the medium. However, distinguishing between different dissipation mechanisms within the mantle from surface-wave data remains a challenging problem. To solve it, we need to look beyond the viscoelastic Q and into the true physical models of internal friction.