Mechanism of Anelasticity

Summary Access to modern vector processors—‘supercomputers’—now makes possible extremely large‐scale seismological computations, in which the anelasticity of the earth can be treated in an exact manner. For this exact formalism to be physically meaningful, it must be shown to be consistent with a convincing physical model of anelasticity. Such a model is investigated for unsaturated, solid‐earth materials. It is a scattering mechanism which is based on the nature of polycrystalline aggregates. For transverse waves, this linear mechanism of anelasticity is given bywhere φ, Φ, Φ are the fractional volumes of pores, crystalline inhomogeneities, and lubricated crystals. the Lamé constants, density, and crystal velocity, λ, μ, ρ, β c , describe the crystalline matrix exclusive of the pores and inhomogeneities; μ incl , ρ incl describe the inhomogeneities; and, if all these parameters are identified with a reference frequency ω 0 , the very simple approximation for the dispersion can be written. In this simple form, reasonably accurate predictions from the model are probably limited to values of the fractional scattering volumes that are individually no more than a few percent. Larger values of the fractional volumes appear to require either more detailed theoretical treatments, or empirically‐based scaling laws that reduce the true fractional scattering volumes to smaller, effective ones before the formulae above are used. the formulae are presented as constant‐ Q β representations of linear anelasticity; however, a Futterman type model, with Q β (ω) inversely proportional to the dispersive velocity, is also a reasonable result from the development. In this case, the multiplicative factor β(ω)/β c is added to the right‐hand side of the expression for 1/ Q β , and β(ω) ∽β(ω 0 )[1+(1/π Q β ) In (ω/ω 0 )].