All materials show some deviation from perfect elasticity particularly at low frequencies and/or high temperatures. In geophysics, this effect can be seen as the attenuation of seismic waves, but it can also be seen as a reduction in seismic wave velocities. Many of the physical processes causing this effect involve the motion of crystalline defects (dislocations, grain boundaries) and are sensitive to temperature, grain size and the chemical environment such as the fugacity of water. This chapter provides a review of the solid-state mechanisms of seismic wave attenuation as well as those involving partial melt. Understanding the physical mechanisms of anelasticity (or visco-elasticity) is critical for the inference of distribution of temperature, grain size, water content and other variables describing physico-chemical environment such as the presence of partial melt from seismic wave attenuation (Chapters 18, 20).

Key words anelasticity, visco-elasticity, Q, velocity dispersion, Maxwell model, Voigt model, standard linear solid, Burgers model, absorption band model, melt squirt, Walsh model, Zener mechanism (thermoelasticity), Bordoni peak, Snoek peak, Kê peak, bulk attenuation.