Relative wobble of the Earth's inner core derived from polar motion and associated gravity variations

SUMMARY In this paper an explanation of the observed decadal variations of the polar motion of the Earth is presented. Recent investigations show that the contribution of surface processes is too small to excite the observed magnitudes of the decadal variations of polar motion. After removing the known effects of atmospheric variations from the observed polar motion, we obtain significant residuals that obviously can only be explained by processes in the core. In this paper, we investigate the effect of a relative inner-core rotation. In particular, we assume that the orientation of the figure axis of the inner core changes with respect to the outer core and mantle. Due to the flattening of the inner core and the density difference between the inner and outer core, these changes contribute to variations of the Earth's polar motion due to internal mass redistributions. The objective of this study is to determine those changes in the orientation of the figure axis of the inner core that produce mass redistributions necessary to excite the decadal variations of the observed polar motion minus the estimated atmospheric influence. Using polar motion data and the atmospheric excitation function, it is possible to determine the excitation function of the internal process superimposed on the free wobble of the Earth by linear approximation of the Liouville equation. On the other hand, provided that only the contribution of the mass redistributions is significant, we can express the time function obtained in terms of the orientation of the figure axis of the inner core. The final expression then contains the corresponding orientation angles as unknowns. Using this expression, we calculate the orientation angles from the numerically determined values of the excitation function. The calculation results in a mean tilt of 1°, and a mean eastward drift of 0.7° yr−1 of the figure axis of the inner core and quasi-periodic decadal variations of its orientation angles. The associated changes of the mass geometry in the core due to these variations of the figure axis of the inner core are then used to estimate their influence on the Earth's outer gravity field. Finally, we compare the magnitude of the resulting gravity field variations with the accuracy of recent and future gravity field models.