在多數時間序列及隨機過程的研究中，僅將誤差視為與時間無關的白雜訊（white noise），這是因為白雜訊的數值模型及計算較為容易。但根據前人研究指出，若不考慮與時間相關的色雜訊（color noise）的存在將會低估時間序列觀測值的誤差。在本研究中，我利用白雜訊及色雜訊的數學模型來嘗試分析及計算各GPS時間序列中的雜訊振幅值，並希望以此為基礎估計合理的地殼形變速度誤差。
本研究所使用的GPS觀測資料來自於美國的EBAR（54站）及YSRP（60站）觀測網，使用兩種方法來進行資料的雜訊分析，分別是時間域上的最大概似估計法以及頻率域上的頻譜分析法。假設每筆GPS時間序列中僅含有兩種雜訊，對應兩個雜訊模型：一是白雜訊加閃爍雜訊模型，二是白雜訊加隨機走動雜訊模型。以此兩模型為基礎計算出各別雜訊的振幅並找出最適合本研究區域內GPS時間序列的雜訊模型。結果指出兩個觀測網中白雜訊加閃爍雜訊均為較好的雜訊模型，而其中都閃爍雜訊雜訊的振幅值都高於0.5 mm/yr^0.25。兩區域中PBO測站的閃爍雜訊振幅值都比非PBO測站低，可能是由於PBO的測站儀器設計較新，相對之下較不容易產生閃爍雜訊，且PBO測站的時間序列較短，較不容易偵測到色雜訊的存在。除此之外，YSRP觀測網的閃爍雜訊振幅平均值比EBAR觀測網來的大，可能是由於YSRP區域的氣候變化較大且緯度較高，因此與EBAR區域相比較，GPS觀測易受到模擬不完整的殘餘大氣對流層效應或電離層效應影響而有較高的閃爍雜訊振幅。另外根據速度誤差的比例參數分析，指出在計算地表運動時若將誤差來源僅視為白雜訊，將會低估速度誤差約1-13倍。

Most researches on geodetic measurements considered only time-independent noises (white noise), while time-dependent noises (color noises) are also important factors that affect the precision of geodetic data. Previous analysis of GPS time series found that the color noises (for example, flicker noise and random-walk noise) are significant components and ignoring their contributions would underestimate the errors of velocity estimation. In this study, I calculated amplitudes of different noises of GPS time series and evaluate more accurate crustal deformation rates and errors than that considered only the white noise.
This study used GPS time series spanned at least 2 years from 54 stations in EBAR and 60 stations in YSRP networks in the western U.S. with most sites on bed rock, Two methods were applied to estimate the amplitudes of different noise models associated with each time series: The spectral analysis that is used to determine the underlying character of the observations in frequency domain, and the maximum likelihood method that does the analysis in time domain. We assume that there are only two sources of noise in the time series and apply two models, white noise plus flicker noise (WHFN) and white noise plus random-walk noise (WHRW), to evaluate the amplitudes of each noise model. At last we will compare the results of these two methods. My results indicate that the WHFN model is preferred for most of the GPS time series from the two networks, with amplitudes of flicker noise larger than 0.5 mm/yr^0.25. The amplitudes of flicker noise of PBO stations in two regions are larger than other stations. It is likely that the monument and antenna design of PBO stations are better than other stations, and other stations have longer time series. In this study, the amplitudes of flicker noise from YSRP are larger than EBAR network. It is likely that YSRP have intense climate and located at higher latitude, the atmospheric and ionospheric effects will be larger than EBAR. In addition, this study suggests that considering only time-independent noises in GPS measurements would underestimate the errors of velocity estimation by a factor of 1-13.

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