Observed multiple frequencies of the Chandler wobble

Two time spans of up-to-date polar motion observations [Gross, R.S., 2005. Combinations of Earth Orientation Measurements: SPACE2004, COMB2004, and POLE2004. JPL Publication 05-6. Pasadena, CA, 20 pp.], (1) POLE2004 series, span 20 January 1900 to 20 January 2005 at 30.4375-day intervals, and (2) COMB2004_noon series, span 20 January 1962 to 22 January 2005 at daily intervals, are studied using a newly developed spectral analysis and digital filtering technique [Pan, C., 1998. Spectral ringing suppression and optimal windowing for attenuation and Q measurements, Geophysics 63, 632-636; Pan, C., 2001. Gibbs phenomenon removal and digital filtering directly through the fast Fourier transform, IEEE Trans. Sig. Process. 49, 444-448] to remove the spectral smear due to finite data truncation from the spectra and to suppress incoherent background noises. The older polar motion observations before 1962 are found much noisier but are still reliable measurements for the Chandler and annual wobbles. Results from both spectral analysis and digital filtering of the polar motion data indicate that the Chandler wobble possesses multiple frequencies to exhibit the envelope characteristics of resonant coupled oscillations. The appearance of apparent single Chandler peak is because the length of the polar motion data chosen for analysis is shorter than the main resonance cycle of the Chandler wobble and in a time span within the modulation envelope of the oscillations; the close splits of the Chandler frequency are hence concealed. Using the five Chandler frequency components found from analysis of the 105-year POLE2004 series and the annual wobble, synthetic simulation equivalent to same lengths of the polar motion observations is made. The simulation demonstrates the application of the new technique in the spectral analysis and digital filtering, and also confirms the relationship between the Chandler frequency split and data length, time span and time sampling interval shown by the observations. This factual finding raises a serious question on the conventional modeling of the Earth's rotation that gives only a single Chandler frequency. The theoretical aspects of the problem are briefly reviewed. The linearization of the Liouville equation has over-neglected the contribution to the Chandler frequency excitation from the same motion and mass redistribution that excite the Chandler amplitude. This leaves out the coupling of different parts of the Earth and the main Earth body that will cause the Chandler frequency to split, while the Chandler wobble is still kept with a single frequency like that of a rigid Earth. (c) 2007 Elsevier Ltd. All rights reserved.