Dynamics of axial torsional libration under the mantle-inner core gravitational interaction

The aims of this paper are (i) formulating the dynamics of the mantle-inner core gravitational (MICG) interaction in terms of the spherical-harmonic multipoles of mass density. The modeled MICG system is composed of two concentric rigid bodies (mantle and inner core) of near-spherical but otherwise heterogeneous configuration, with a fluid outer core in between playing a passive role. We derive the general equation of motion for the vector rotation but only focus on the polar component that describes the MICG axial torsional libration. The torsion constant and hence the square of the natural frequency of the libration is proportional to the product of the equatorial ellipticities of the mantle and inner-core geoid embodied in their multipoles (of two different types) of degree 2 and order 2 (such as the Large Low-Shear-Velocity Provinces above the core-mantle boundary) and (ii) studying the geophysical implications upon equating the said MICG libration to the steady 6year oscillation that are observed in the Earth's spin rate or the length-of-day variation (LOD). In particular, the MICG torsion constant is found to be (Gamma) over tilde (z) = C-IC sigma(2)(z) approximate to 6.5 x 10(19) N m, while the inner core's (B-IC - A(IC)) approximate to 1.08 x 10(31) kg m(2) gives the inner core triaxiality (B-IC - A(IC))/C-IC approximate to 1.8 x 10(-4),about 8 times the whole-Earth value. It is also asserted that the required inner-core ellipticity amounts to no more than similar to 140m in geoid height, much smaller than the sensitivity required for the seismic wave travel time to resolve the variation of the inner core.