Anderson, Don L. (1967) A Seismic Equation of State. Geophysical Journal of the Royal Astronomical Society, 13 (13). pp. 930. ISSN 00168009. https://resolver.caltech.edu/CaltechAUTHORS:20140501094548877

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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^* where 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. Since 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. The general tendency of density to increase with Φ can be used to determine the density in the Cregion even if this is a region of phase changes. New density models for the Earth are constructed on these considerations.
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Additional Information:  © 1967 Royal Astronomical Society. This work was supported by a Sloan Foundation Fellowship. I would like to acknowledge the assistance of Martin Smith in the calculations. Orson L. Anderson and R. G. McQueen kindly supplied me with preprints of some of their important experimental papers. I have profited greatly from conversations with Orson L. Anderson, Francis Birch and Dan McKenzie.  
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Issue or Number:  13  
Record Number:  CaltechAUTHORS:20140501094548877  
Persistent URL:  https://resolver.caltech.edu/CaltechAUTHORS:20140501094548877  
Official Citation:  Anderson, D. L. (1967), A Seismic Equation of State. Geophysical Journal of the Royal Astronomical Society, 13: 9–30. doi: 10.1111/j.1365246X.1967.tb02144.x  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  45401  
Collection:  CaltechAUTHORS  
Deposited By:  Ruth Sustaita  
Deposited On:  01 May 2014 17:57  
Last Modified:  03 Oct 2019 06:30 
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