以卡爾曼濾波與主成分分析探討GNSS時間序列中的暫態變形訊號;Investigation of Transient Deformation Signals in GNSS Time Series Using Kalman Filtering and Principal Component Analysis

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題名:	以卡爾曼濾波與主成分分析探討GNSS時間序列中的暫態變形訊號;Investigation of Transient Deformation Signals in GNSS Time Series Using Kalman Filtering and Principal Component Analysis
作者:	詹鎧齊;Chan, Kai-Chi
貢獻者:	地球科學學系碩士班
關鍵詞:	GNSS位移時間序列;卡爾曼濾波;主成分分析;GNSS time series;Kalman filter;Principal component analysis
日期:	2026-01-28
上傳時間:	2026-03-06 18:29:26 (UTC+8)
出版者:	國立中央大學
摘要:	GPS位移時間序列中所含的暫態訊號可以反映地表諸多變形，如震後位移、火山作用及地下水位變化等，讓我們能夠以此研究地殼變形的性質並洞察災害發生的可能性。但在此連續位移紀錄中，存在著非常多的雜訊，導致較微弱的暫態訊號因低訊噪比而較難被觀察到。本研究參考Ji and Herring (2013)所提出的方法，將FOGM (First Order Gauss-Markov)隨機過程置入原始時間序列的狀態函數中，並以卡爾曼濾波器(Kalman filter)去除序列中固定振幅的趨勢(trend)、年週期、半年週期等狀態訊號以及白雜訊(white noise)，其所得的FOGM過程即包含了序列中各狀態分量的動態變化以及色雜訊(color noise)。最後將各站各分量的FOGM進行主成份分析(principal component analysis, or PCA)，以萃取其在時間與空間中的主要共同分量。相較於色雜訊，GPS測網中顯著的共同暫態地殼變形多來自位移趨勢中低頻且振幅較高的變化，因此將預期出現在PCA前面的幾項主成份。此方法可同時降低雜訊在時間域及空間域的影響，使微弱的暫態訊號能夠更容易被檢測。我們以位於美國西部Utah州Wasatch front區域的GPS測網資料作為範例(觀測時間>10年)，分析此區域可能出現的暫態地表變形，研究結果顯示在GPS的三分量的第一主成分皆出現佔比超過60%、空間分布均勻的共模分量(Common Mode Component, CMC)，而且垂直向的共模分量與水文訊號有相當高的相關性，顯示整體垂直向的暫態訊號受水文訊號影響。次要主成分則暗示著因乾旱而造成的以大鹽湖(Great Salt Lake)為中心向外擴張之暫態變形，我們也同時提取出該因素在水平分量在大鹽湖的位移。本研究也將此方法應用在臺北盆地，分析2019~2023年因旱季與濕季造成的暫態訊號。;Transient signals in GPS displacement time series reflect a wide range of surface deformation processes, including postseismic deformation, volcanic activity, and groundwater-related loading. However, continuous GPS records are often dominated by noise, making weak transient signals difficult to detect. In this study, we adopt the method of Ji and Herring (2013) in which a First-Order Gauss–Markov (FOGM) stochastic process is incorporated into the state vector and estimated using a Kalman filter to remove deterministic components with fixed amplitudes, including linear trends, annual and semiannual signals, as well as white noise. The resulting FOGM processes capture both dynamic variations in the displacement trend and colored noise. Principal component analysis (PCA) is then applied to the FOGM processes of all stations to extract dominant common spatiotemporal modes. Significant transient crustal deformation within a GPS network is expected to be characterized by low-frequency, high-amplitude signals and therefore to appear in the leading principal components. This combined Kalman filter–PCA approach effectively suppresses noise in both the temporal and spatial domains, enhancing the detectability of weak transient deformation. We apply this method to more than 10 years of GPS observations from the Wasatch Front region, Utah, western United States. The first principal components of all three displacement components account for more than 60% of the total variance and exhibit spatially coherent common-mode component (CMCs). The vertical CMC is strongly correlated with hydrological signals, indicating that transient vertical deformation is largely driven by hydrological loading. Secondary principal components reveal drought-induced transient deformation centered on the Great Salt Lake, with corresponding horizontal displacements identified around the lake. The method is further applied to the Taipei Basin to investigate transient deformation associated with seasonal hydrological variations during 2019–2023.
顯示於類別:	[地球物理研究所] 博碩士論文

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