Decadal variations in gravity caused by a tilt of the inner core

A tilt of the geometric figure of the inner core with respect to the mantle results in a global internal mass displacement. This comprises two parts: the redistribution of mass from the rigid equatorial rotation of the elliptical inner core; and that from global elastic deformations that occur to maintain the mechanical equilibrium. This global mass reorganization leads to changes in the moment of inertia tensor and, equivalently, to changes in the degree 2 component of the gravitational field. In this work, we compute the predicted changes in both gravity and in the moment of inertia tensor as a function of inner core tilt. We show that the inclusion of elastic deformations increases the amplitude of the gravity change at the surface by a factor 1.97. The Stokes coefficients that are the most affected are C-21, S-21: a tilt angle of 0.05 degrees leads to a change in these coefficients of similar to 4 x 10(-11), while leading to changes in other coefficients of degree 2 that are three orders of magnitude smaller. Observed changes in C-21, S-21 and in polar motion contain decadal variations of undetermined origin; in an effort to determine whether these could be caused by temporal changes in inner core tilt, we compute the changes in C-21, S-21 based on the observed polar motion and compare this prediction against observed variations as determined by satellite laser ranging (SLR) between 1985 and 2005. We show that observed decadal changes in C-21, S-21 and in polar motion suggest that both are predominantly driven by variations in the moment of inertia tensor. The source of these variations cannot be unambiguously determined, nor can we confirm whether they are of internal or surficial origin. Changes in inner core tilt are then not necessarily the cause of these variations, though if they are, our results show that motion in the fluid core must not play a significant role in the global angular momentum balance.