Upper Bound to Change in Incompressibility at the Earth's Mantle-Core Boundary

Abstract

A series of Earth models has been constructed in which the excess Δκ of the incompressibility at the top of the Earth'score over the value k at the bottom of the mantle has been given the assigned values 0, 0.05, 0.1,…, × 1012 dyn/cm2. The calculations indicate that unless the assumed seismic velocities and density gradients are more seriously in error than expected, Δk/k does not exceed 2 per cent. The most probable value of Δk/k is insignificantly different from zero. A comparison is made with results on the variation of k inside the Earth from Birch'sfinitestrain formulae; Birch'sresults appear to be wholly reconcilable only with difficulty with results on k on Bullen'sapproach. The present calculations suggest that one of three possibilities is the case: (i) Birch'sformulae fall a little short of fitting conditions near the Earth'smantle-core boundary; or (ii) the chemical compositions of the lower mantle and outer core are less different than Birch and some others have thought likely; or (iii) the average temperature gradient is rather higher and the average density gradient appreciably lower inside the lower mantle than has been considered likely in most earlier calculations of Bullen. To meet the numerical requirements of the present calculations, the possibility (iii) would appear to require a fairly extreme combination of circumstances.