On the calculation of the seismic parameter ϕ at high pressure and high temperatures

Comparison of the Murnaghan equation of state with the Birch equation shows that, for a given value of pressure, the values of (p/po) calculated from the two equations differ by less than 1% to a pressure equal to 0.5 Ko (where Ko is the zero-pressure isothermal bulk modulus), but the corresponding values of the seismic parameter ϕ differ by 10%. The value of ϕ is extremely sensitive to the choice of the equation of state because ϕ is the derivative of pressure with respect to density. The good agreement between the two equations of state for pressure as a function of density observed for some materials does not imply the same agreement in the relationship between ϕ and pressure. Expressions for ϕ(P) that take into account the first order nonlinear dependence of the bulk modulus on pressure are presented, and their applications are discussed. Temperature correction of the pressure-dependent ϕ is also considered.

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