Empirical Equations of State for the Earth's Lower Mantle and Core

Abstract

Summary A quadratic representation of the incompressibility k in terms of the pressure p for the materials of the Earth inside the pressure range 0.4 < p < 3.2 × 1012 dyn/cm2 was empirically derived some years ago on the basis of seismic and other evidence. The numerical coefficients in the representation have been revised in the present paper, taking account of recent observational evidence. The revised quadratic law applies to the whole Earth below 1000 km. The new evidence includes the recently revised estimate of the Earth's moment of inertia, revised seismic evidence on the lower core, and data from free Earth oscillations. The quadratic model is compared with linear models derived for the lower mantle and core separately. Attention is drawn to errors made when any of these models is applied at pressures less than 0.4 × 1012 dyn/cm2. It is pointed out that unqualified application of Birch's finite-strain formulae leads to some results for the Earth's deeper interior that are somewhat discordant with the empirical evidence here used.