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Dynamics of the inner core wobble under mantle‐inner core gravitational interactions
Author(s) -
Chao Benjamin F.
Publication year - 2017
Publication title -
journal of geophysical research: solid earth
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.983
H-Index - 232
eISSN - 2169-9356
pISSN - 2169-9313
DOI - 10.1002/2017jb014405
Subject(s) - inner core , speed wobble , polar motion , mantle (geology) , hydrostatic equilibrium , physics , outer core , geology , geophysics , mechanics , geodesy , earth's rotation , classical mechanics , quantum mechanics
We investigate the dynamics of the inner core wobble (ICW), the Euler‐Liouville wobbling motion of the Earth's solid inner core, under the mantle‐inner core gravitational (MICG) torques within the Earth. Chao (2016) derived the full 3‐D equation of motion for the MICG dynamics in terms of the spherical‐harmonic multipoles of mass density and focused on the axial component for inner core's torsional libration. Here aiming for the ICW, we deduce the 2‐D equatorial component of the MICG torque owing to the oblateness of the mantle and the inner core. The period of the free Eulerian wobble of a hypothetical isolated rigid inner core would be a prograde +414 days. The action of the added MICG equatorial torque is found to be (negatively) strong enough to render the wobbling motion to become retrograde (with a negative frequency), which is further but slightly modified by the elastic yielding feedback of the inner core. Imposing yet further the passive effect of the hydrostatic pressure due to the fluid outer core greatly lengthens the natural period to become decadal. The final estimate of the ICW natural period in accordance with the (seismological) PREM Earth model is a retrograde P ICW ≈ −15.6 years, in contrast to a prograde +6.6 years supposed in the literature. The corresponding spring constant (per radian of wobble) is 5.5 × 10 22 N m. Our results instigate likely identification of the ICW with decadal wobbles observed in the Earth's polar motion.