The multiple-frequency Chandler wobble.

Abstract

The problem of the excitation and damping of the Chandler wobble is reviewed and the conventional models analyzed. Using an axially near-symmetric and slightly triaxial Earth Model, a solution of the Liouville equation reveals that the Chandler wobble has multiple frequency and is rather a quasipermanent phenomenon in the Earth. The multiple Chandler frequency consists of a fundamental frequency attributable to the Earth's triaxiality, as well as series of small feedback frequencies arising from the Earth's instantaneous inertia, relative angular momentum, and inertia variation. After the introduction of the anelasticity of the mantle into the model, the Chandler wobble is found to be a combination of the Kelvin-Voigt and Maxwell oscillations with the former mechanism dominating the motion. The Chandler feedback comes mainly from the anelastic upper mantle, but it does not rule out fractional contributions from the oceans and atmosphere, the mantle-core coupling, or even large earthquakes; the Chandler wobble may behave like a multiple-coupling differential oscillation with the mantle as the major coupler. The feedback mechanism or frequency modulation gives the Chandler wobble a "beat" appearance. The quasi-permanency or the relaxation time of a multiple-frequency Chandler wobble is of the order of 104 to 106 years or higher, up to the contribution from the Maxwell feedback. The multiple-frequency model explains the Chandler amplitude and frequency variations as well as the persistence of the wobble beyond the damping relaxation time predicted by the single-frequency model.