The relationship between shear and compressional velocities at high pressures: Reconciliation of seismic tomography and mineral physics

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Abstract
The value of the parameter ν from low pressure laboratory measurements disagrees with the value from seismic observations. The parameter ν relates the isobaric change in shear velocity Vs to the change in compressional velocity Vp. Seismic evidence indicates ν exceeds 2.0 in the lower mantle, whereas data on a variety of minerals at high temperature T and ambient pressure P result in lower values. We reconcile these differences. Our ab initio model calculations on MgO show that ν increases with P and is 2.0–2.5 at lower mantle pressures. There is no need to assume partial melting to explain the seismic data. These calculations also provide insight into the P and T dependence of the dimensionless parameter Γ ≡ −(1/αG)(∂G/∂T)p, where G is the isotropic shear modulus and α is the volume thermal expansivity. Using measured values of thermoelastic parameters coupled with thermodynamic identities, we seek constraints on δs ≡ −(1/αKs)(∂Ks/∂T)p, where Ks is the adiabatic bulk modulus, and confirm that P causes δs to decrease. We find Poisson's ratio increases with P and T. Altogether these results show that for MgO, ν increases from 1.3 at ambient conditions to over 2 at lower mantle conditions. We expect other mantle minerals to behave similarly. Therefore we find that reconciliation of the mineral physics approach with that of seismic tomography concerning ν does not require special assumptions about the state of the lower mantle.

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