Evidence of nonlinearity of the Chandler wobble in the Earth’s pole motion

It is well known that rotational motions with annual and Chandler periods dominate in the dynamics of the location of the Earth’s poles. The nature of the Chandler wobble is not clear. It is most frequently attributed to elasticity and differential rotation of different internal spheres of the Earth [1, 2]. Recently, it was shown [3] that the Chandler-type motions are possible in a model of solid Earth if this model is nonlinear with an annual external influence (the deviation of the equatorial section of the Earth’s shape from the pure circular form is taken into account). Using the wavelet analysis of the time series of the North Pole coordinates, we have distinguished for the first time doubled and tripled Chandlerian oscillations with variable amplitudes. In addition, we have discovered some fingerprints of oscillations with periods close to the free Eulerian nutation of the Earth and its superharmonic 1 : 2. The existence of such oscillations can only be explained within the framework of the nonlinear approach. We used the initial data of the North Pole coordinates during the January 5, 1962‐July 18, 2004 period, which are more exact than the data of the previous years. The time discreteness of these data (5 days) is more detailed compared to the time series of the previous observations. In order to omit the trend, we applied a 6-yr-running averaging to the time series and subtracted the averaged series from the initial ones. The trajectory of the averaged component of the North Pole motion (NPM) on an ( x, y ) plane is shown in Fig. 1 (below). Since the positive direction of the X -axis corresponds to the southward displacement of the pole along the Greenwich meridian and the positive direction of the Y- axis corresponds to the displacement along 90 ° W, the figure suggests a general displacement (trend) of the pole toward Greenland. Thirty loops superimposed over the trend during the 36-yr-long period of the time-average series yields the mean period of the loop approximately equal to 1.2 yr (~14 months or 430 days), which coincides well with the known estimate of the Chandler period [2]. It is natural to suppose that the loops are actually related the Chandler wobble of the poles. Figure 1 (upper plot) shows a pure rotational component of the NPM. The rotation is counterclockwise (in the W‐E direction). The amplitude of the rotational component varies in time. Its time evolution is shown in Fig. 2 (upper plot). The graph in Fig. 2 (lower plot) shows the pattern of time evolution of this amplitude (abscissa) and the pattern over time scales (ordinate, logarithmic scale with base = 2). The plots are based on complex transformation of the time series of the amplitude of the rotational component using the Morlet function of wavelet transform (WT). The frequency characteristic of the Morlet function was taken so that the wavelet scale of the maximum response of the WT to any harmonic oscillation in the transformed series coincided exactly with the period of this harmonic. To our knowledge, the WT was used for the first time to study the motion of the Earth’s poles. However, this method has been used to study variations in the velocity of the Earth’s rotation in [4, 5]. The wavelet pattern in Fig. 2 is limited by the maximum scale equal to days, starting from which the wavelet amplitude (WA) becomes extremely large and reflects the prevalence of the ~6-yr-period oscillation, which is clearly seen in the initial WT-free time series. In the range of wavelet