A Seismic Equation of State
Abstract
where ρ is the density, M̄ 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 . 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. Since Φ also is (δP/δρ)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. The 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.
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