Evidence supporting the approximation γρ = const for the Grüneisen parameter of the Earth's lower mantle

There has been no uniform acceptance of one theoretical formulation of the Grüneisen parameter formula over another. The application of a Grüneisen function to the earth's interior for temperature calculations by one author has been to some extent arbitrary, or at least held in doubt by others. In this paper, using only the seismic data of the earth, an argument is presented which supports the contention that an acceptable empirical law for the lower mantle is urn:x-wiley:01480227:media:jgrb2944:jgrb2944-math-0001 where γ is the Grüneisen parameter and ρ is the density, where q is close to unity. Because of the range of the compression, no great error is made by taking q to be exactly unity for simplicity in the empirical formulae. However, a value of q anywhere in the band 0.8 < q < 2.2 is acceptable on the basis of the seismic data. By assuming the rule γρ = const, it is shown that it follows that αK T is independent of temperature and pressure and therefore depth in the lower mantle. The term α is the volume thermal expansivity, and K T is the isothermal bulk modulus.