GRACE衛星於2002年發射，至今仍持續測量地球的時變重力場。我們透過GRACE資料研究時變重力場並分別討論以下兩個案例：(1)由地震斷層及其質量錯動所展生的重力變化，及(2)連結南極環流與南極震盪於空間與時間上所展生的重力變化。(1)應用於地震研究部份，由於GRACE所量測的時變重力訊號大多直接與地表變化相關，根本上也就是水循環部份，因此我們透過全球地表同化系統所提供之結果並以最小平方法計算季節性(年週期與半年週期)訊號移除陸地水的訊號。接著使用經驗正交函數分析出在震央地區由地震所產生的時變重力訊號在空間分佈的變化及隨時間的變動。從經驗正交函數的結果證實過去所發生的大地震不論是同震還是震後效應皆被記錄於GRACE時變重力訊號中。我們針對2004蘇門答臘－安達曼大地震(Mw 9.0)、2010智利大地震(Mw 8.8)和2011日本東北大地震(Mw 9.1)以及一些相對較小的地震，包括藏於2004蘇門答臘－安達曼大地震訊號下的2005尼亞斯地震(Mw 8.6)、2007明古魯地震(Mw 8.5)、2012印度洋(一天內有兩起地震，規模分別為Mw 8.2和8.6)其走向滑移斷層和2013深源的鄂霍次克海地震 (Mw 8.3)。同時我們也利用最小平方法在研究地區內擬合一同震階梯函數得每個資料點的同震跳躍，並將其與經驗正交函數之結果互相驗證。此外，假設地震為一點震源雙力偶的錯動且地球為球對稱的構造，因此將地震所造成的位移場透過球諧函數展開，級數大於2級的係數皆為0。我們採用正準座標將震央轉至北極點以求得所有球諧函數係數達60階和2級，並將此結果使用經驗正交函數及最小平方法分析求得點震源的同震效應。(2)應用於環南極洋流與南極震盪研究部份，我們藉由經驗正交函數分析GRACE資料從2003年到2015年在南大洋地區非季節性的海底壓力場，並發現其第一主成份反應海底壓力會隨著南極震盪一起變化且相關性高達0.77。此海底壓力變異會造成地轉流(也就是南極環流)的變異，此結果也顯示出一半環狀的最大向東流速變化出現於東半球的環南極洋流部份，同時其位於也重合於環南極洋流最南邊界，並證明在過去十年內此變化越發劇烈。;The twin-satellite mission - Gravity Recovery and Climate Experiment (GRACE) launched in 2002 measure the time-variable gravity (TVG) field. We analyze the GRACE data to study the TVG and find (1) earthquake faulting and the associated mass dislocations in the Earth and (2) unequivocal evidences linking the space-time variabilities of the entire Antarctic Circumpolar Current (ACC) with Antarctic Oscillation (AAO). (1) In application to co-seismic study, most GRACE TVG signals are directly related to changes in surface processes, primarily the water cycle. So we first strive to remove the terrestrial water signal using the Global Land Data Assimilation System model outputs and the seasonal (annual and semi-annual) signals by the least-squares estimation. Then we apply the method of Empirical Orthogonal Function (EOF) analysis to extract the earthquake-induced TVG signals in the epicentral region in terms of change pattern and time evolution. Our EOF results corroborate past findings of the GRACE TVG signals caused by the greatest recent earthquakes not only for co-seismic but also post-seismic behavior. We do so notably for the 2004 Sumatra-Andaman (Mw 9.1), 2010 Chile (Mw 8.9), and 2011 Tohoku (Mw 9.0) events, as well as somewhat smaller earthquakes including the 2005 Nias (Mw 8.5) event otherwise largely masked by the 2004 Sumatra-Andaman signals, the 2007 Sumatra (Mw 8.5) event, the 2012 Sumatra (double event of Mw 8.2 and 8.6 in one day) event which is largely strike-slip, and even possibly the 2013 deep-focused Okhotsk (Mw 8.3) event. We also conduct least-squares fitting with a co-seismic step function representing the earthquake for every grid point in the considered region, to augment to and confirm the EOF results. Furthermore, assuming a point-source double-couple dislocation and a spherically symmetrical Earth, the earthquake-induced displacement field is expanded by spherical harmonics where components of order greater than 2 vanish. We transform the epicenter to the North Pole in the canonical coordinates and could duplicate the whole TVG signal by spherical harmonics up to degree 60 but only order 2, which accentuates the EOF and least-squares fitting results that are approximated by co-seismic double-couple phenomena. (2) In application to the relation between ACC and SAM study, we solve for the method of EOF analysis of the non-seasonal ocean bottom pressure (OBP) field in the circum-Antarctica seas from GRACE data during 2003-2015. We find that the leading EOF mode of the observed GRACE OBP field represents a unison OBP oscillation around Antarctica with time history closely in pace with that of the AAO Index with broad-band correlation as high as 0.77. This OBP variation gives rise to a variation in the geostrophic flow field; the result for the same EOF mode shows in particular a half-ringed pattern for the maximum east-velocity variation that resides primarily in the eastern-hemispheric portion of ACC and coincided geographically with the southernmost boundary of ACC’s main stream. We also find evidences signifying that the said variation intensified over the past decade.
