HR: 0800h
AN: DI41A-0349    [Abstracts]
TI: Constraining Parameters of the Reciprocal K-Primed Equation of State Using Normal Modes
AU: * Davis, P M
EM: pdavis@ess.ucla.edu
AF: Paul M. Davis, Department of Earth and Space Sciences, UCLA, Los Angeles, CA 90095, United States
AU: Stacey, F D
EM: frank.stacey@csiro.au
AF: Frank D. Stacey, CSIRO Exploration and Mining, Kenmore, Qld Q4069, Australia
AB: Most equations of state predict that K', the pressure derivative of bulk modulus, K, decreases with pressure, but there is considerable variation in the infinite pressure limit, K'_infinity. Although this limit can never be attained physically, since phase transitions as pressure increases invalidates the use of a single EOS, K'_infinity represents a fitting constant for EOS valid over pressure ranges where the material has constant phase. Thermodynamic arguments have been used to place constraints on K'_infinity. The reciprocal K-primed equation of state RKp_EOS (GJI 143, 621-628, 2000; PEPI 142, 137-184, 2004) relates K' to the variation of P (normalized by K) by two parameters K'₀ and K'_infinity, with density, ρ, variation governed a third parameter, ρ₀. It describes a smooth decrease of K' and ρ with pressure, and the limit satisfies the thermodynamic constraint, and so is useful for determining other thermodynamic parameters that require (smooth) higher order derivatives. The parameters of the RKp-EOS are determined by fitting to standard Earth models such as PREM. However the PREM K' variation does not exhibit smooth decrease in K' with P and so the fit has been through a widely fluctuating curve. This fluctuation not unexpected, as the PREM parameters were expressed in polynomial expansions of radial distance adjusted to fit seismic data with no constraints on smoothness of K'. In order to estimate the RKp_EOS parameters in the outer core, we use non-linear least squares to fit spheroidal mode frequencies using the PREM polynomial expansion in the mantle and inner core, but the RKp_EOS parameters in the outer core. The resulting constants give a core EOS that satisfies the mode data, the thermodynamic constraint, and smooth decrease of K' with P.
DE: 3919 Equations of state
SC: Study of the Earth's Deep Interior [DI]
MN: 2007 Fall Meeting