Abstract
This paper presents new theoretical expressions for the elastic velocities (of a cubic or isotropic homogeneous solid) as functions of density and temperature (equations 7 and 8). These equations have been derived within the fourth-order anharmonic theory, i.e., the extension of the theory of lattice dynamics into the regime of finite strain, and they include implicitly the effects of noncentral forces, distant-neighbor interaction, and thermal vibration. Application of the equations to garnet, spinel, and olivine (considered as Voigt-Reuss-Hill isotropic bodies) confirms and lends rigor to the present consensus on the elasticity of the mantle. The equations indicate further that the observed instabilities of these materials under upper mantle conditions are not directly related to vanishing of an elastic modulus.
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