Chandler Wobble Period and Q Derived by Wavelet Transform

We apply complex Morlet wavelet transform to three polar motion dataseries, and derive quasi-instantaneous periods of the Chandler and annual wobbleby differencing the wavelet transform results versus the scale factor, and then findtheir zero points. The results show that the mean periods of the Chandler (annual)wobble are 430.71±1.07 (365.24±0.11) and 432.71±0.42 (365.23±0.18) mean solardays for the data sets of 1900-2001 and 1940-2001, respectively. The maximumrelative variation of the quasi-instantaneous period to the mean of the Chandlerwobble is less than 1.5% during 1900-2001 (3%--5% during 1920-1940), and thatof the annual wobble is less than 1.6% during 1900--2001. Quasi-instantaneous andmean values of Q are also derived by using the energy density-period profile of theChandler wobble. An asymptotic value of Q = 36.7 is obtained by fitting polynomialof exponential of σto the relationship between Q and σ during 1940--2001.