A Seismic Equation of State

Abstract

Birch's hypothesis of a close relationship between seismic velocity and density is extended and modified so as to be in accord with theoretical predictions concerning the form of the equation of state. Although developed as a simple method to assure consistency between the seismic velocities and densities in free oscillation calculations the resulting equation of state is of quite general utility in geophysical studies where the seismic velocities, rather than hydrostatic pressure and temperature, are the directly measured variables. A simplified form of the seismic equation of state is ρ= AMΦ^*
\nwhere ρ is the density, M is the mean atomic weight, n is a constant of the order of ¼ to ⅓ and is related to the Grüneisen constant γ, and Φ is the seismic parameter V_P^2 - (4/3)V_S^2. The exponent n is slightly different for constant temperature and constant pressure experiments but its magnitude, in both cases, can be estimated from lattice dynamics. On the other hand n is roughly the same number for compositional, structural and pressure effects.
\n
\nSince Φ also is (∂P/∂ρ)_S and KS/ρ, data from static compression and shock wave as well as ultrasonic experiments can be used to determine the parameters in the equation of state and to extend its range beyond that available from ultrasonic data. Static pressure and shock wave data extend to much higher pressures, or compressions, than the ultrasonic data used by Birch and many more materials have been tested.
\n
\nThe general tendency of density to increase with Φ can be used to determine the density in the C-region even if this is a region of phase changes. New density models for the Earth are constructed on these considerations.