On the dynamical effects of a heterogeneous and compressible liquid core in the theory of Chandler wobble

The general 3-D scalar equations of motion of the liquid core (with respect to the radial components of displacements and cubic dilatation) are constructed as a superposition of the solutions of ordinary differential equations describing the dynamics of a stably stratified, heterogeneous, compressible and inviscid rotating fluid inside thin spherical layers ( Molodensky & Sasao 1995 ). The estimation of dynamical effects of a homogeneous and incompressible liquid core on the Chandler period (Groten, Lenhardt & Molodensky 1991) is generalized for the case of a heterogeneous, compressible, inviscid and neutrally stratified liquid core.     

Geomagnetic effects of the Earth's ellipticity

We analyse the external field generated by a uniform distribution of magnetic susceptibility contained in an oblate spheroidal shell when it is magnetized by an internal magnetic field of arbitrary complexity. The situation is more relevant to the Earth than that of a spherical shell considered by Runcorn (1975a ) (in the context of lunar magnetism), because of the larger flattening of the Earth than that of the Moon. We find that, to first order in the susceptibility, each internal harmonic in a spheroidal harmonic expansion of the magnetic potential generates just one non-vanishing external field coefficient, unlike in the spherical case when all harmonics vanish identically. The field generated is proportional to the susceptibility, thickness of the shell and square of the Earth's eccentricity, and hence it appears that this field amplification mechanism will be very ineffective for the Earth.     

The change in Sq(H) amplitude on Abnormal Quiet Days

Summary. Analysis of geomagnetic data has shown that the superposed northward magnetic field, which reduces the S _q( H ) amplitude at northern mid-latitude stations on Abnormal Quiet Days, and increases the amplitude at stations on the equatorward side of the S _q focus, builds up in amplitude over four to five days before the AQD occurs, and subsides over a similar period after the AQD. It is inferred indirectly that the azimuthal component B_y of the interplanetary magnetic field varies similarly. Data for the opposite meridian show that the imposed field reverses to a southward direction at lower latitudes. The inferred currents to account for these fields are believed to flow in the ionosphere, but to arise from magnetospheric electric fields induced by the solar wind-transported IMF.     

Experiments on precessing flows in the Earth's liquid core

Experiments simulating flow in the Earth's liquid core induced by luni-solar precession of the solid mantle indicate, to a first approximation, that the core behaves like a rigidized fluid sphere spinning slower than the mantle and with its spin axis lagging the mantle spin axis in precession. Secondary flow patterns are always present. At low precession rates the fluid sphere is subdivided into a set of cylinders coaxial with the fluid spin axis, the cylinders rotating alternately at slightly faster and slower rates relative to the net retrograde motion of the fluid as a whole. Slow non-axisymmetric columnar wave patterns develop between the differentially rotating cylinders. Axial flows between the spheroidal cavity boundary and the interior are observed. Fluid motion becomes turbulent only at precession rates large enough to cause the fluid spin axis to align nearly with the precession axis. There is no evidence that the Earth's liquid spin axis direction departs more than a fraction of a degree from geographic north. Our observations suggest precession induces a complex variety of laminar flows, including slowly varying and/or periodic patterns, in the Earth's liquid core.     

Properties of iron at the Earth's core conditions

Summary. The phase diagram of iron up to 330 GPa is solved using the experimental data of static high pressure (up to 11 GPa) and the experimental data of shock wave data (up to 250 GPa). A solution for the highest triple point is found ( P = 280 GPa and T = 5760 K) by imposing the thermodynamic constraints of triple points. This pressure of the triple point is less than the pressure of the inner core–outer core boundary of the Earth. These results indicate that the density of iron at the inner core–outer core boundary pressure is close to 13 g cm⁻³, which lies close to the seismic solutions of the Earth at that pressure. It is thus concluded that the Earth's inner core is very likely to be virtually pure iron in its hexagonal close packed (hcp) phase.
It is shown that four properties of the Earth's inner core determined from seismology are close in value to the corresponding properties of hcp iron at inner core conditions: density, bulk modulus, longitudinal velocity, and Poisson's ratio. The density–pressure profile of hcp iron at inner core conditions matches the density–pressure profile of the inner core as determined by seismic methods, within the spread of values given by recent seismic models.
This indicates that the Earth is slowly cooling, the Earth's inner core is growing by crystallization, and the impurities of the core are concentrated in the outer core. The calculated temperature at the Earth's centre is 6450 K.