高精度GPS衛星測量在地殼變形觀測之研究

Abstract

本文將介紹測站座標與速度之誤差傳播，藉由推導理論公式方式切入，依誤差傳播之原理，推導帶有速度之座標值其最佳推定時間點為觀測期間中點。探討如何由單次量測的座標值及其精度，推展到計算速度時，可能獲得的精度；並且導出一可作為規畫與評估的實用公式。在經由觀測所得之座標精度依理論公式間接推估到預期的速度精度，與直接推估之速度精度比較，兩者是非常吻合的，差異僅在3﹪以內，印證該公式能精確地將實測座標精度傳播到速度之精度上。提昇速度之精度，除拉長觀測年限外，還需提高每一單次量測的座標精度。 在研究對流層折射誤差對GPS高程之影響時，經由模擬GPS資料之分析顯示，在高溫、高濕之氣象條件下，以及採用較低角度觀測資料，氣象誤差所造成的 GPS高程偏差較大。進一步分析其影響GPS高程的情形，將其相應關係整理成函數之形態，用來描述氣象誤差與GPS高程偏差之關係。為改善殘留之對流層誤差，在處理GPS資料時，使用較低角度之觀測量，並引用Niel mapping function，考量觀測量之權隨天頂距而變，配合每2小時附加1個天頂向和水平梯度折射修正參數，可有效地改善對流層殘留之系統誤差，大幅提升量測的座標精度。 分析1992-1999年重複觀測GPS資料，測站之平面向精度約5-6 ㎜，垂直向精度約16 ㎜；在連續運轉固定站上，可獲3-5 ㎜的水平精度和11-15 ㎜之垂直向精度。從分析測站速度之經驗中，無論測站是連續運轉或定期重複觀測型態，若想獲±2∼3 ㎜/y之測站速度估值，則較理想的觀測期是3年左右。

Based on the least squares theory, the error propagation between the site coordinate and velocity are derived and discussed in the thesis. The best quality of site coordinates with estimated velocities are determined at the middle epoch of the observation period. The uncertainty in site velocity can be expressed as a function of the single measurement position accuracy. This function can be used for the planning of an experiment, we can easily know how long it should take to acquire a data set with a given rate accuracy, or how offen an experiment must be repeated within a fixed period to obtain that accuracy. The analysis of a repeated experiment reveals that the rate uncertainties derived directly from covariance are comparable with that from the function, and the difference is less than 3%. The function is proved to be correct and useful by using the analysis of real data in the repeated campaigns. Longer period experiment and higher single measurement accuracy is the most efficient way to reduce the uncertainty in a site velocity estimate. Collecting GPS data under the weather condition of high temperature, high humidity and using observables of lower elevation angle result in larger tropospheric refraction errors on GPS height. The relationships between the meterological errors and the resulting bias on GPS height are derived theoretically and expressed as functions by using analytical and regressive analysis. It is found that applying the method of troposphere zenith delay estimates, considering the elevation-dependent weighting of observations, estimating the troposphere gradients, using Niel mapping function, and including low-elevation angle GPS data into the processing would be able to improve the precision of coordinates effectively. Analyzing annually repeated GPS data from 1992 to 1999, we found the baselines repeatabilities are 5-6 mm in horizontal component, and 16 mm in vertical component. The expected precision of site velocity at 4-5 mm/y can be reached within 2-3 years. Repeatabilities of 3-5 mm in horizontal vector and 11-15 mm in vertical component are found at the continuously recording stations. To obtain the site velocity of either campaign-surveyed or continuous GPS stations with an accuracy of 2∼3 mm/y, the optimal total time span of observations is about 3 years.