EVIDENCE SUPPORTING THE APPROXIMATION GAMMA-RHO= CONSTANT FOR THE GRUNEISEN-PARAMETER OF THE EARTHS LOWER MANTLE

There has been no uniform acceptance of one theoretical formulation of the Gruneisen parameter formula over another. The application of Gruneisen 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 gamma rhoq = const, where gamma is the Gruneisen parameter and rho is the density, where q is the 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 less than q less than 2.2 is acceptable on the basis of the seismic data. By assuming the role gamme rho = const, it is shown that it follows that alpha KT is independent of temperature and pressure and therefore depth in the lower mantle. The term alpha is the volume thermal expansivity, and KT is the isothermal bulk modulus.-Author