板塊運動和地殼形變相關研究的資料以全球衛星定位系統（Global Positioning System，簡稱GPS）為基礎。在大部分GPS時間序列的研究中，資料誤差只考慮雜訊振幅與觀測時間無關的白雜訊（white noise）。但是近幾年來發現，如果不考慮雜訊振幅與時間相關的色雜訊（coloured noise），例如：flicker noise和random walk noise將會造成資料誤差的低估，準確度也受到影響。因此在本篇研究分析時間序列中的雜訊成分，並重新計算測站的速度誤差。本文考慮的GPS連續測站有541個，其中選用測站觀測長度大於2.5年的資料進行研究，觀測時間最長22年。這些測站具有各種不同的儀器基座，包括深錨淺錨柱式、屋頂型、淺錨柱式、水泥柱式等，在台灣淺錨柱式及屋頂式測站數量較多的基座型式，本研究找到519個測站的基座型式，其中淺錨柱式基座最多有227個測站（42%），其次為屋頂式基座203個測站（38%）。使用最大概似估計法（MLE）及功率頻譜（power spectrum）兩種方法進行分析，以了解時間序列中雜訊組成。結果顯示多數測站在南北向量的雜訊振幅最小，垂直向量的雜訊振幅最大，且W+F模型中white noise和flicker noise的雜訊振幅會呈正相關。針對不同基座型式的結果比較最佳雜訊模型、頻譜指數與速度誤差的穩定性，其中深錨柱式測站有較小的速度誤差，雜訊振幅大小也比其他基座型式更小、更穩定。

Global positioning system (GPS) is usually used for researches of plate tectonics and crustal deformation. In most studies, GPS time series considered only time-independent noises (white noise), but time-dependent noises (color noise: flicker noise, random walk noise) which were found by nearly twenty years are also important to the precision of data. The rate uncertainties of stations will be underestimated if the GPS time series are assumed only time-independent noise. Therefore, studying the noise properties of GPS time series is necessary in order to realize the precision and reliability of velocity estimates. The lengths of GPS time series are from 541 stations around Taiwan with time spans longer than 2.5 years up to 22 years. The GPS stations include different monument types such as deep drilled braced, roof, metal tripod, concrete pier etc., and the most common type in Taiwan are the metal tripod and roof. I investigated the noise properties of continuous GPS time series by using the spectral index and amplitude of the power law noise. During the process I first remove the data outliers, and then estimate linear trend, size of offsets, and seasonal signals, and finally the amplitudes of the power-law and white noise are estimated simultaneously. The results show that the noise amplitudes of the north component are smaller than that of the other two components, and the largest amplitudes are in the vertical. I also find that the amplitudes of white noise and power-law noises are positively correlated in three components. Amplitude of white noise do not change with time, called time-independent noise. Amplitude of flicker noise and random walk noise change with time, considered be time-dependent noise, called color noise. Comparisons of noise amplitudes of different monument types in Taiwan reveal that the deep drilled braced monuments have smaller velocity uncertainties and amplitudes, are more stable than other monuments.

Agnew, D. C. (1992), The time-domain behavior of power-law noises. Geophys. Res. Lett., 19(4), 333-336. doi: 10.1029/91gl02832
Akaike, H.(1974), A new look at the statistical model identification - IEEE Transactions on Automatic Control, https://ieeexplore.ieee.org/document/1100705/
Beavan, J. (2005), Noise Properties of continuous GPS data from concrete pillar geodetic monuments in New Zealand and comparison with data from U.S. deep drilled braced monuments. J. Geophys Res., 110 (B8), B08410. doi:10.1029/2005JB003642.
Bos, M. S., R. M. S. Fernandes, S. D. P. Williams, and L. Bastos (2013), Fast error analysis of continuous GNSS observations with missing data, Journal of Geodesy, 87(4), 351–360, doi:10.1007/s00190-012-0605-0.
Dmitrieva, K., P. Segall, and C. DeMets (2015), Network-based estimation of time-dependent noise in GPS position time series. Journal of Geodesy, 89(6), 591–606. https://doi.org/10.1007/s00190-015-0801-9
Dong, D., T. A. Herring, and R. W. King (1998), Estimating regional deformation from a combination of space and terrestrial geodetic data. J. Geod., 72, 200-214.
Dong D., P. Fang, Y. Bock, M. K. Cheng, S. Miyazaki (2002), Anatomy of apparent seasonal variations from GPS-derived site position time series. J Geophys Res. https://doi.org/10.1029/2001JB000573
Feigl, K., R. King, and T. Jordan. (1990), Geodetic measurement of tectonic deformation in the Santa Maria Fold and Thrust Belt, California. J. Geophys. Res., 95(B3), 2679-2699. doi: 10.1029/JB095iB03p02679
Hackl, M., R. Malservisi, U. Hugentobler, and R. Wonnacott (2011), Estimation of velocity uncertainties from GPS time series: Examples from the analysis of the south african TrigNet network. Journal of Geophysical Research.Solid Earth, 116(11) doi:http://dx.doi.org/10.1029/2010JB008142
Herring, T., J. Davis, and I. Shapiro (1990), Geodesy by radio interferometry: The application of Kalman Filtering to the analysis of very long baseline interferometry data. J. Geophys. Res., 95(B8), 12561-12581. doi: 10.1029/JB095iB08p12561
Hosking J. R. M. (1981), Fractional differencing. Biometrika 68(1):165–176
Johnson, H. O., and F. K. Wyatt (1994), Geodetic network design for fault mechanics studies, Manuscr. Geod, 19,309-323.
Langbein, J. (2004), Noise in two-color electronic distance meter measurements revisited. J. Geophys. Res., 109(B4), B04406. doi: 10.1029/2003jb002819
Langbein, J. (2008), Noise in GPS displacement measurements from Southern California and Southern Nevada. J. Geophys. Res., 113(B5), B05405. doi: 10.1029/2007jb005247
Langbein, J., and Y. Bock (2004), High-rate real-time GPS network at Parkfield: Utility for detecting fault slip and seismic displacements. Geophysical Research Letters, 31(15). https://doi.org/10.1029/2003GL019408
Langbein, J., and H. Johnson (1997), Correlated errors in geodetic time series: Implications for time-dependent deformation. J. Geophys. Res., 102(B1), 591-603. doi: 10.1029/96jb02945
Mao, A., C. G. A. Harrison, T. H. Dixon (1999), Noise in GPS coordinate time series. J Geophys Res 104: 2797–2816
Nikolaidis, R.(2002), Observation of geodetic and seismic deformation with the Global Positioning System, Ph.D. thesis, Univ. of Calif., San Diego.
Schwarz, G. (1978), Estimating the Dimension of a Model. The Annals of Statistics, 6(2):461–464.
Williams, S. D. P. (2003), The effect of coloured noise on the uncertainties of rates estimated from geodetic time series, Journal of Geodesy, 76(9–10), 483–494, doi:10.1007/s00190-002-0283-4.
Williams, S. D. P. (2004), Error analysis of continuous GPS position time series. Journal of Geophysical Research, 109(B3). doi: 10.1029/2003JB002741
Williams, S. D. P., Y. Bock, P. Fang, P. Jamason, R. Nikolaidis, L. Prawirodirdjo, M. Miller, and D. Johnson (2004), Error analysis of continuous GPS position time series, J. Geophys. Res., 109, B03412, doi:10.1029/2003JB002741.
Wyatt, F. (1982), Displacement of Surface Monuments: Horizontal Motion. J. Geophys. Res., 87(B2), 979-989. doi: 10.1029/JB087iB02p00979
Wyatt, F. K. (1989), Displacement of Surface Monuments: Vertical Motion. J. Geophys. Res., 94(B2), 1655-1664. doi: 10.1029/JB094iB02p01655
Yu, S.-B., Y.-J. Hsu, L.-C. Kuo, H.-Y. Chen, and C.-C. Liu (2003), GPS measurement of postseismic deformation following the 1999 Chi-Chi, Taiwan, earthquake. Journal of Geophysical Research: Solid Earth, 108(B11), 2520. https://doi.org/10.1029/2003JB00239
Zhang, J., Y. Bock, H. Johnson, P. Fang, S. Williams, J. Genrich, S. Wdowinski, and J. Behr (1997), Southern California Permanent GPS Geodetic Array: Error analysis of daily position estimates and site velocities. J. Geophys. Res., 102(B8), 18035-18055. doi: 10.1029/97jb01380
余水倍、郭隆晨、陳宏宇、蘇宣翰、許雅儒（2002）臺灣GPS密集連續觀測網之規劃與建立（II）。交通部中央氣象局技術報告彙編，第33卷，第301-318頁。
余水倍、郭隆晨、陳宏宇、蘇宣翰、許雅儒（2003）臺灣GPS密集連續觀測網之規劃與建立（III）。交通部中央氣象局技術報告彙編，第36卷，第259-274頁。
余水倍、郭隆晨、陳宏宇、蘇宣翰、蔡旻倩（2004）臺灣GPS密集連續觀測網之規劃及時間序列分析。交通部中央氣象局技術報告彙編，第39卷，第277-292頁。
余水倍、郭隆晨、陳宏宇、蘇宣翰、蔡旻倩（2004）臺灣GPS密集連續觀測網之規劃及時間序列分析（II）。交通部中央氣象局技術報告彙編，第42卷，第249-266頁。
李炘旻（2005），2003年台東成功地震之同震變形模式研究。國立中央大學地球物理研究所碩士論文，中壢市，共118頁。
饒瑞鈞、許麗文、陳燕玲、許文偉（2014）GPS觀測之雜訊分析研究（II）。交通部中央氣象局技術報告彙編，第64卷，第281-327頁。