我們在連續 GPS 3-D 位移觀測中找尋－由 2011 年 Mw 9.0 東北大地震所激發的地球自由振盪。一項前人研究展示了這種偵測的可行性，我們在這裡進行更全面、更詳細的研究。我們使用的GPS數據來自三個獨立觀測網：(i) 日本 GEONET 觀測網，約 1000 個測站； (ii) 美國西部 PBO 觀測網，約 600 個測站； (iii) 覆蓋全球的 IGS 觀測網，約 140 個台站；以 30 秒採樣率求解並解算出 21 小時長的記錄。我們使用了多記錄疊加方法：降低噪聲方差的頻率域功率譜疊加，以及提高目標模態信噪比和抑制非目標模態的時間域疊加。我們發現最佳序列估計 (OSE) 的時間域疊加方法是最有效的，它對於頻譜中的自由震盪正交模態，清楚地顯示出高靈敏度和可偵測性。在近場的GEONET，所有激發模態都處於反節點 (anti-nodes)，低於 5 mHz 的所有 spheroidal fundamental modes (0S9 – 0S43) 和部分 lower-degree overtones 以及大多數的 lower-degree toroidal fundamental modes 都在 PREM 模型特徵頻率上出現顯著的譜峰(peak)。 PBO 看到的譜峰強度較弱（遠場且通常不為反節點），但仍然可以清楚地識別fundamental modes的頻譜譜峰。全球 IGS 網由於其測站分布稀疏和測站數量少，較弱地偵測了這些模態。因此，我們的研究展示 GPS 確實記錄了微小的地震信號，可以通過多記錄疊加方法揭示之，這可能有助於研究激發normal modes的震源機制。;We search in the continuous GPS 3-D displacement data for the signals of the normal modes of Earth’s free oscillation that were excited by the 2011 Mw 9.0 Tohoku earthquake. A previous study has reported such a detection; we here conduct a more comprehensive and detailed study. We use GPS data from three separate networks: (i) about 1000 stations from the Japan GEONET; (ii) about 600 stations from the western USA PBO; and (iii) about 140 stations of the global IGS, and solve and form records of 21 hours long at 30-second sampling rate. We conduct various multiple-record stacking methods: the frequency-domain power spectrum stacking that reduces the variance of the noises, and the time-domain stackings that boost the SNR of target modes and suppressing the non-target modes. We find the time-domain stacking method of optimal sequence estimation (OSE) to be the most effective, which show clearly high sensitivity and detectability of the modes in the spectrum. For the near-field GEONET where all excited modes have anti-nodes, all the spheroidal fundamental modes 0S9 – 0S43 below 5 mHz and some of the lower-degree overtones as well as most of the low-degree toroidal fundamental modes show up as prominent spectral peaks against the PREM model eigenfrequencies. The PBO sees less strong (being far-field and generally off-antinodes) but still clearly identifiable spectral peaks of the fundamental modes. The global IGS network data detect barely a handful of these modes because of its sparsity and small numbers of stations. We thus demonstrate that GPS does actually record the tiny seismic signals that can be revealed by means of multiple-record stacking methods, potentially useful for studying earthquake source mechanisms exciting the normal modes.
