THE RELATIONSHIP BETWEEN SHEAR AND COMPRESSIONAL VELOCITIES AT HIGH-PRESSURES - RECONCILIATION OF SEISMIC TOMOGRAPHY AND MINERAL PHYSICS

The value of the parameter nu from low pressure laboratory measurements disagrees with the value from seismic observations. The parameter nu relates the isobaric change in shear velocity V(s) to the change in compressional velocity V(p). Seismic evidence indicates nu 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 nu 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 GAMMA = -(1/alpha-G)(partial derivative G/ partial derivative T)P, where G is the isotropic shear modulus and alpha is the volume thermal expansivity. Using measured values of thermoelastic parameters coupled with thermodynamic identities, we seek constraints on delta(s) = -(1/alpha-K(S))(partial derivative K(S)/ partial derivative T)P, where K(S) is the adiabatic bulk modulus, and confirm that P causes delta(S) to decrease. We find Poisson's ratio increases with P and T. Altogether these results show that for MgO, nu 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 nu does not require special assumptions about the state of the lower mantle.