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General relationships among sound speeds: II. Theory and discussion

Authors:	TJ Shankland DH Chung

Institution:	1. Weston Observatory, Boston College, Weston, Mass., U.S.A.;2. Massachusetts Institute of Technology, Cambridge, Mass. U.S.A.

Abstract:	The dependence of bulk sound speed V_φ upon mean atomic weight $m$ and density ρ can be expressed in a single equation: $V_{φ} =Bρ^{λ} (m_{0} m^{12+λ(1?c)]} (km/sec)$ Here B is an empirically determined “universal” parameter equal to 1.42, $m_{0} = 20.2$ , a reference mean atomic weight for which well-determined elastic properties exist, and λ = 1.25 is a semi empirical parameter equal to $γ ? 13$ where γ is a Grüneisen parameter. The constant c = (? ln V_M/? ln $m)_{X}$ , where V_M is molar volume, is in general different for different crystal structure series and different cation substitutions. However, it is possible to use c_Fe = 0.14 for Fe²⁺Mg²⁺ and GeSi substitutions and c_Ca ? 1.3 for CaMg substitutional series. With these values it is pos to deduce from the above equation Birch's law, its modifications introduced by Simmons to account for Ca-bearing minerals, variations in the seismic equation of state observed by D.L. Anderson, and the apparent proportionality of bulk modulus K to V_M^?4.

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