General relationships among sound speeds II. Theory and discussion

Details General relationships among sound speeds II. Theory and discussion General relationships among sound speeds II. Theory and discussion

Mar 1974

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974pepi....8..121s&link_type=abstract

Physics of the Earth and Planetary Interiors, Volume 8, Issue 2, p. 121-129.

Physics

7

Scientific paper

The dependence of bulk sound speed Vφ upon mean atomic weight m and density ρ can be expressed in a single equation: Vφ=Bρλ(m0/m[1/2+λ(1-c)](km/sec) Here B is an empirically determined ``universal'' parameter equal to 1.42, m0 = 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 - 1/3 where γ is a Grüneisen parameter. The constant c = (∂ ln VM/∂ ln m)X, where VM is molar volume, is in general different for different crystal structure series and different cation substitutions. However, it is possible to use cFe = 0.14 for Fe2+-Mg2+ and Ge-Si substitutions and cCa ≅ 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 VM-4.

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