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

Abstract

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.

Electromagnetic torques in the core and resonant excitation of decadal polar motion

“…• yr −1 (Greiner-Mai et al 2000;Greiner-Mai & Barthelmes 2001;Greiner-Mai et al 2003). As noted by those authors, this inner-core tilt would produce a gravity signature that should soon be detectable by the GRACE and CHAMP satellite missions.…”

The gravity field variation caused by inner core super rotation

“…Other geophysical parameters used in the present study are listed in Table 1. Flattening of inner core f = 1/412.88 [2] Mean radius of inner core r 0 = 1 221.5 km [3] Density of inner core at ICB ρ inner = 12 763.60 kg/m 3 [3] Density of outer core at ICB ρ outer = 12 763.60 kg/m 3 [3] Longitude of inner core's figure axis (1980) 280° [ 16] Tilt of inner core figure axes 0.07° [ 17] Rate of inner core super rotation 0.27 ~ 0.53°/yr [15] The variation of the gravity field on the ground is of great significance since the gravity observations might provide another clue besides seismic observations to determine the differential rotation of the inner core. Here we will first work out the magnitude and distribution of the variation, and then give an estimation of the temporal variation ratio of the second order of the fully-normalized spherical harmonic coefficients.…”

“…The orientation of the inner core figure axis was 280°E in 1980 [16] , under the assumption that the super rotation rate is 0.27~0.53°/yr [15] , and the inner core tilt 0.07° [ 17] holds invariable during the periods discussed. Then, only the longitude of the inner core figure axis varies with the super rotation angle, which leads to the corresponding gravity variation.…”

“…Besides, the inner core seems to be a little tilted relative to the mantle which explains the decadal variation of the polar motion [16,17] . Due to the ICSR, the tilted inner core figure axis would progress relative to the mantle and give rise to a variation of the gravity field.…”

“…A uniform inner core model doesn't coincide with the fact that the inner core density increases with the depth, as described by PREM (Preliminary reference Earth model [3] ). Furthermore, recent studies [16,17,19] suggest that the inner core tilt should not exceed 1°. Consequently, a more accurate model for the gravity variation caused by the ICSR is significant for providing a gravimetric method to detect or even determine the ICSR.…”