Rheological anisotropy of the Earth’s mantle and attenuation of seismic waves

The nonlinear integral (having memory) model previously proposed by the author for the description of the dislocation rheology of mantle rocks is generalized to the case of crystals with anisotropic rheology. The latter is caused by a large difference between the effective viscosities associated with dislocation glide and dislocation climb (in the crystallographic coordinate system, the dislocation glide governs simple shear, whereas the dislocation climb governs pure shear). Since the mantle is polycrystalline and crystal grains an order of a millimeter in size are oriented chaotically, anisotropy vanishes with volume averaging. However, convective flows in the mantle produce large strains and lead to a preferred orientation of grains and, thereby, anisotropy of the upper mantle. The lower mantle is dominated by diffusion rheology, which cannot cause anisotropy. The mantle rheological anisotropy gives rise to anisotropic attenuation of seismic waves. It is shown that the attenuation depends on the polarization and direction of seismic waves and on the parameters of the rheological model.