The core-mantle boundary and the rotation of the Earth

摘要

We have modeled effects of topography at the core-mantle boundary (cmb) on variations in the earth's rotation. Topography will couple the core and mantle together, by causing restoring torques during differential rotation. For example, this coupling causes the Free Core Nutation (FCN) - a nearly diurnal normal mode that produces a resonance in the forced nutations and diurnal earth tides. The observed resonance has been used to determine the FCN frequency, which, in turn, has been used to constrain the ellipticity of the cmb. Our earth model for these studies consisted of a rigid mantle, a homogeneous and incompressible fluid core, and a slightly non-elliptical cmb. A convergent numerical technique was developed to solve the differential equations and boundary conditions for both the free and forced motions. In our solution, the fluid pressure was represented by a truncated sum of spherical harmonic functions in a special set of coordinates. By truncating this sum at large values of the spherical harmonic degree, we were able to include the effects of Coriolis coupling in the fluid core: effects that have been incompletely modeled in most previous studies for an elliptical cmb. We found that these effects are important when non-elliptical cmb terms are included. We retained second-order cmb topographic factors with the equatorial core rotation in our nutation calculations. Using the degree variances of a recent seismically-inferred cmb model (with non-elliptical cmb topography of about 3.5 km rms), we found that the rms contribution of the randomly generated nonelliptical topography to the retrograde annual nutation was about 0.2 mas. The effects depend on some cmb spherical harmonic components more than they do on others. For example, results as large as 0.77 mas are possible due to certain individual spherical harmonic cmb components with mean peak-to-peak amplitudes of 4-5 km. The effects grow quadratically with topography, so that perturbations in those components with amplitudes of 6-7 km would cause a 2 mas effect for the annual nutation, which is the approximate size of the discrepancy between the VLBI results and the 1980 IAU theory, the latter assuming a hydrostatic, elliptical cmb. The cmb topography is poorly known at present, but components of this magnitude may be unlikely. For the Chandler Wobble and the tidal variations in the length-of-day, we found that the effects of non-elliptical cmb topography are likely to be small. This argues that mantle anelasticity constraints based on observations of the CW period and damping and on the tidal length-of-day amplitudes, need not be corrected for topography.