The Variable Period Hypothesis and Q of the Chandler Wobble Reexamined

The Chandler wobble is one of the elastic-gravitational normal modes of the Earth. The eigenperiod is about 435 sidereal days, larger than the other modes by a factor 104, which gives the Chandler wobble an exotic status in the group of normal modes. The quality factor of the Chandler wobble, Qw, plays a critically important role in discussing the mantle rheology since the frequency dependence of the mantle Q is affected more seriously by the low frequency Chandler Qw than by the other seismic Q's. A problem should be resolved in advance so as to estimate Qw safely from the spectral analysis of the polar motion. Namely, significance of the variable Chandler period hypothesis. We test the hypothesis in two ways. First, we reexamine throughly the observational grounds of the hypothesis by applying the same scheme as employed by the proponents of the hypothesis to synthetic polar motion of a constant Chandler period. It is revealed that most of the evidence for the hypothesis is not definitive and it is also explained by the invariant Chandler period model as well. Next, we trace the time variation of the spectral structure of the Chandler wobble. For this purpose, we extend the high-resolution Instantaneous Frequency Analysis to be applicable to a complex-valued time series. Applying the technique to IPMS and BIH polar motion data, we find that the result favors the time-invariant Chandler period model. After confirming that there is no observational difficulty in the time-invariant Chandler period model, we estimate Qw by critically applying Maximum Entropy Spectral Analysis (MESA) to ILS and IPMS data. It is found that Qw lies in the range of 50≦Qw≦100 and Graber's result of Qw=600 is due to the erroneous choice of the length of the prediction error filter. Finally, we discuss the effect of the mantle anelasticity upon the period and Q of the Chandler wobble. We calculate the complex Love number k for the realistic Q models by Rayleigh's principle and relate it to Qw. The ratio of Qw to lower mantle Qm is found to be about 1.5 and it is shown to be consistent with the energy budget arguments. If the Chandler wobble energy is totally dissipated in the mantle, Qm should be frequency-dependent to account for the observed Qw of 50～100. If the frequency dependence of Qm is the power law, the power exponent is found to be 0.1～0.2. Anelasticity of the mantle is shown to lengthen the theoretical Chandler period by 7～11 days due to physical dispersion. Adding 29.8 days of ocean effect to the theoretical period of oceanless Earth yields 438～443 sidereal days as the Chandlerian period, in excellent agreement with the observed one.チャンドラー極運動は地球のelastic-gravitationalな自由振動の一つのモードであり,瞬間自転軸が形状軸のまわりを反時計回りに回転する極運動である.その周期は約435日であり,他の地震学的なモードの周期よりも104倍以上も長いという特徴がある.したがって,そのQ値はマントルの非弾性的性質,とりわけ周波数依存性を議論する上できわめて重要となる.また地球科学の諸分野(地震学,海洋学,気象学,地球電磁気学)とチャンドラー極運動の関りの上でもQを確定することは大切になってくる