High pressure equations of state with applications to the lower mantle and core

Empirical finite strain theories, currently favored by various authors for geophysical use, are critically reexamined. We focus attention on higher derivatives, especially K′=dK/dP (P is pressure and K is bulk modulus), which discriminate more sharply between alternative equations than do P(V) relationships. A thermodynamic analysis of the infinite pressure extrapolation is presented more rigorously than hitherto, confirming several crucial constraints: adiabatic and isothermal moduli, KS and KT, become equal, K∞′ has a limited admissible range and is an unambiguous parameter, applying to adiabats and isotherms at any temperature. At P→∞ Slater’s formula for the Grüneisen parameter, γ=K′/2−1/6, assumes the status of an identity and q=(∂ ln γ/∂ ln V)T→0. There is a strong advantage to using an equation relating K′ to P/K, making use of the condition K∞′=(P/K)∞−1 and avoiding difficulties with the commonly used Birch, logarithmic and Rydberg equations. On the P/K scale the infinite pressure asymptote is as close as the zero pressure limit for the lower mantle and much closer in case of the core, making it a powerful constraint. Equations of state for the lower mantle and core are developed using the PREM tabulations as starting models. For the lower mantle thermodynamic relationships link finite strain equations to thermal properties, permitting an assessment of the thermal contribution to tomographically observed seismic velocity anomalies. As we demonstrate by comparing the laboratory compression of iron with core data, Earth models offer much more effective tests of high pressure equations of state than do laboratory data and can be used to recalibrate laboratory pressure scales. A recalibration of the platinum pressure scale is presented.