Free Vibrations of the Earth and the Properties of its Deep Interior Regions Part 1: Density†

Summary Density in the Earth has been determined by a new method. Near the base of the mantle the new model predicts densities about 10 per cent lower than the Bullen A' value and constant densities have been found for depths between 1600 km and 2800 km from the surface. This density model does not depend upon prior assumptions of homogeneity or the Adams‐Williamson equation for any region except the outer core. It is based on the following independent sets of data: periods of torsional and spheroidal free oscillations; travel times of P and S waves; total mass; moment of inertia derived from the satellite value of flattening. Torsional and spheroidal free periods and phase velocities have been calculated for many models of density and shear velocity in a heterogeneous spherical Earth. For the gravest free modes, the changes in computed phase velocity caused by variations in shear velocity consistent with S wave travel times are about an order of magnitude less than those caused by variations in density consistent with the total mass and moment of inertia. Alteration of density rather than shear velocity in the lower mantle has been made in order to satisfy both observations of free oscillations and of S wave travel times. Comparison of calculated phase velocities with those derived from free vibration measurements shows that densities for model Ml are very close to the Bullen A' distribution down to depths of about 500 km, slightly lower to 1100 km and then slightly higher to 1800 km depth. The region between depths of 1600 km and 2800 km was found to have essentially constant density. A super‐adiabatic temperature gradient of about 2°C/km, combined with a depletion of iron in the high temperature region of the lower mantle is a possible explanation of this result. The mass removed from the mantle because of the free period observations has been transferred nearer to the centre of the Earth, subject to the requirements of mass, moment of inertia and, for model M1, the core densities of Bullen and Bolt. The resulting outer core densities are about 2 per cent higher than those of the Bullen A model; the central density is about 15.42 g/cm 3 . If, as for model M3, the Adams‐Williamson equation is used throughout the core (taken to be entirely fluid), outer core densities are about 4 per cent higher than those for Bullen's model A' the central density is about 12.63 g/cm 3 .