Conditions for a density minimum in the upper mantle

A number of recent articles have indicated that there is a density minimum in the upper mantle. An example is the article by Clark and Ringwood, where the density minimum is based upon petrology. In this paper the conditions for a density minimum are established using the Mie-Gruneisen equation of state. It is shown that for a homogeneous mantle with a positive value of thermal expansivity, the sign of the density gradient is the same as the sign of the S velocity gradient, that is, d(ln υs)/d(ln ρ) > 0. The conditions for a density minimum in a nonhomogeneous upper mantle are also discussed.