地球自轉的變化可定義成三個方向向量改變，習慣上又分為兩部分：極移和日長變化。造成變動的主因為地球系統中的水文環流，如大氣和海洋，通過質量重新分佈和流動與地球角動量互換。第一部分，本論文採用小波頻譜來分析日長變化(1962-2009)的震盪信號。小波頻譜分析方法，可以揭開時間序列中的非穩定週期訊號。使用最小平方法去除日長變化中潮汐訊號並扣除大氣角動量貢獻後，針對仍保有的信號，如ENSO、準兩年和十年以上振盪，去與氣候學上的週期震盪訊號做比對。本研究結果除了與以往的研究預期具有良好的一致性，更進一步排除日長變化中準六年訊號與大氣角動量的關係，並推測十三年訊號來源於地球表面的大氣與海洋中。第二部分，極移中的Chandler wobble (CW)指地球本身自由振盪。本研究重新解算地球CW振幅與相位變化(1900-2009)，審視地球CW相位在1920年代出現反轉行為。本研究提出一個簡單的物理解釋說明，當物體運動能量小也就是幅度接近於零時容易發生相位跳躍(phase jump)。並根據Monte Carlo數值方法模擬長時間的極移運動，以振幅和相位行為的統計數據來驗證本研究的假設。結果顯示，1920年代地球並沒有任何的異常現象使地球CW發生相位反轉，只是該系統剛好在能量被抵消後又重新啟動，導致相位異常，其發生機率是偶然的。

The variation of Earth''s rotation, by definition a three-dimensional vectorial quantity, can be conveniently separated into two parts: polar-motion (X,Y) and the length of day (LOD). In the first part, we employ wavelet analysis on Earth''s rotation series to find the components of periodic signals and compare them to the excitation sources. The variable rotation of the Earth is produced and maintained by mass redistribution and movement within the Earth system in terms of angular momentum predominately by hydrological circulations such as atmosphere and ocean. The wavelet time-frequency spectrum has been proven as a powerful tool to reveal nonstationary periodicities in time series. Our results exhibit good consistency with previous studies as expected. After using least-square fits to remove the contributions due to tides and atmospheric angular momentum, the unknown signals, e.g. ENSO-like, quasi-biennial and some decadal oscillations are extracted. For the two strong periodic signals locate around 6 and 13 years, we are trying to confirm if they are associated to ENSO cycle. In the another part, the works primarily aim to retrieve the major amplitude and phase variations of Chandler wobble (CW) which is the normal-mode free oscillation of the rotating Earth, continuously excited by mass transports in Earth''s interior, surface, atmosphere, and ocean. It is well known that some close spectral peaks with comparable amplitudes exist in the CW band in the observed polar motion spectrum during the first half of the last century, which can actually be attributed to the unusual ~180◦ phase reversal of the CW during the 1920s–1930s. Although it was argued that the latter may be a manifestation of some dynamic changes of the Earth, it lacks specific evidences and geophysical interpretation. However, contrarily, we assert that the apparent phase reversal was simply a consequence of erratic excitation during a time when the amplitude happens to be rather small and hence easily altered. We simulate this assertion numerically by synthesizing long segments of polar motion, which are formed by convolving the free CW with Gaussian random noise meant to represent the external excitation. We do statistical examinations and indeed confirm our assertion above, indicating that the observed CW phase reversal during 1920-30 was nothing extraordinary.

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