On the Physics of the Inner-Core Wobble; Corrections to “Dynamics of the Inner-Core Wobble Under Mantle-Inner-Core Gravitational Interactions” by B. F. Chao

Abstract

The original paper by Chao (2017, https://doi.org/10.1002/2017JB014405), denoted C17, derived the period of the Earth's free inner-core wobble (ICW) with a result which was both retrograde and substantially longer than the prograde period derived by previous authors. Here we correct major errors in C17, bringing the result into better agreement with previous derivations, and clarify the role of the various torques on the Earth's inner core (IC) as presented in C17. One serious discrepancy was the magnitude of (Formula presented.), the zonal quadrupole of the mantle mass distribution, which is incorrectly evaluated in C17, with a value too large compared to those that have been previously well established for a hydrostatic Earth model. Moreover, an error in the kinematics of the ICW in C17 leads to a wrong sign for the gravitational torque exerted by the mantle on the IC. The combination of these errors led to the erroneous conclusion that the ICW is retrograde, with a much longer period (−15.6 yr) compared to previous derivations, which showed it to be prograde with a period of about +7 yr. In correcting C17, we elucidate the complete torque balance involved in the ICW.