共查询到20条相似文献,搜索用时 46 毫秒
1.
D.J. Stevenson 《Physics of the Earth and Planetary Interiors》1980,22(1):42-52
By use of the modern theory of liquids and some guidance from the hard-sphere model of liquid structure, the following new results have been derived for application to the Earth's outer core. (1) dK//K, where K is the incompressibility and P the pressure. This is valid for a high-pressure liquid near its melting point, provided that the pressure is derived primarily from a strongly repulsive pair potential φ. This result is consistent with seismic data, except possibly in the lowermost region of the outer core, and demonstrates the approximate universality of dK/dP proposed by Birch (1939) and Bullen (1949). (2) dlnTM/dlnρ = (γCV ? 1)/( is the melting point, ρ the density, γ the atomic thermodynamic Grüneisen parameter and CV the atomic contribution to the specific heat in units of Boltzmann's constant per atom. This reduces to Lindemann's law for CV = 3 and provides further support for the approximate validity of this law. (3) It follows that the “core paradox” of Higgins and Kennedy can only occur if . However, it is shown that , which cannot be achieved for any strongly repulsive pair potential φ and the corresponding pair distribution function g. It is concluded that and that the core paradox is almost certainly impossible for any conceivable core composition. Approximate calculations suggest that γ ~ 1.3–1.5 in the core. Further work on the thermodynamics of the liquid core must await development of a physically realistic pair potential, since existing pair potentials may be unsatisfactory. 相似文献
2.
Lowes (1966, 1974) has introduced the function Rn defined by are the coefficients of a spherical harmonic expansion of the scalar potential of the geomagnetic field at the Earth's surface. The mean squared value of the magnetic field B = ??V on a sphere of radius r > α is given by is the Earth's radius. We refer to Rn as the spherical harmonic spatial power spectrum of the geomagnetic field.In this paper it is shown that Rn = RMn = RCn where the components RnM due to the main (or core) field and RnC due to the crustal field are given approximately by . The two components are approximately equal for n = 15.Lowes has given equations for the core and crustal field spectra. His equation for the crustal field spectrum is significantly different from the one given here. The equation given in this paper is in better agreement with data obtained on the POGO spacecraft and with data for the crustal field given by Alldredge et al. (1963).The equations for the main and crustal geomagnetic field spectra are consistent with data for the core field given by Peddie and Fabiano (1976) and data for the crustal field given by Alldredge et al. The equations are based on a statistical model that makes use of the principle of equipartition of energy and predicts the shape of both the crustal and core spectra. The model also predicts the core radius accurately. The numerical values given by the equations are not strongly dependent on the model.Equations relating average great circle power spectra of the geomagnetic field components to Rn are derived. The three field components are in the radial direction, along the great circle track, and perpendicular to the first two. These equations can, in principle, be inverted to compute the Rn for celestial bodies from average great circle power spectra of the magnetic field components. 相似文献
3.
The dependence of bulk sound speed Vφ upon mean atomic weight and density ρ can be expressed in a single equation: Here B is an empirically determined “universal” parameter equal to 1.42, , a reference mean atomic weight for which well-determined elastic properties exist, and λ = 1.25 is a semi empirical parameter equal to where γ is a Grüneisen parameter. The constant c = (? ln VM/? ln , 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 GeSi substitutions and cCa ? 1.3 for CaMg 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. 相似文献
4.
Malcolm G. McLeod 《Physics of the Earth and Planetary Interiors》1980,23(2):P1-P4
An essentially arbitrary function V(θ, λ) defined on the surface of a sphere can be expressed in terms of spherical harmonics where the Pnm are the seminormalized associated Legendre polynomials used in geomagnetism, normalized so that The angular brackets denote an average over the sphere. The class of functions V(θ, λ) under consideration is that normally of interest in physics and engineering. If we consider an ensemble of all possible orientations of our coordinate system relative to the sphere, then the coefficients gnm and hnm will be functions of the particular coordinate system orientation, but where for any orientation of the coordinate system (Sn is invariant under rotation of the coordinate system). The averages are over all orientations of the system relative to the sphere. It is also shown that 〈gmnglp〉 = 〈hmnhlp〉 = 0 for l ≠ m or p ≠ n and 〈gmnhlp〉 = 0 fro all n, m, p, l. 相似文献
5.
Vladislav Babuška Jiří Fiala Mineo Kumazawa Ichiro Ohno Yoshio Sumino 《Physics of the Earth and Planetary Interiors》1978,16(2):157-176
The elastic constants of sixteen garnet specimens of wide variety in chemical composition are accurately determined by means of the rectangular parallelpiped resonance method. The dependence of the elastic properties on chemical composition is analyzed using the present data and those for seven garnets investigated by other authors. The property Xi of a garnet solid solution i is given by a linear addition law in terms of the mole fraction nij of component j; Xi = ΣnijXj where the Xj's are the properties of the end-members j (j = pyrope, almandine, spessartine, grossular and andradite). The Xj's are determined for density ρ, bulk modulus K, and shear moduli Cs = (C11 ? C12)/2 and C44. No systematic deviation is observed from the linear addition law for the elastic moduli nor for other quantities such as the elastic wave velocities. The extrapolated elastic moduli (Mbar) of the end-members are:
Almandine | Pyrope | Spessartine | Grossular | Andradite | |
1.779 ± 0.008 | 1.730 ± 0.009 | 1.742 ± 0.009 | 1.691 ± 0.008 | 1.379 ± 0.017 | |
0.981 ± 0.004 | 0.925 ± 0.004 | 0.964 ± 0.004 | 1.106 ± 0.004 | 0.979 ± 0.007 | |
0.958 ± 0.005 | 0.919 ± 0.005 | 0.937 ± 0.005 | 1.017 ± 0.006 | 0.827 ± 0.010 |