應用重力法推求台灣最佳大地起伏模型之研究

Abstract

隨著衛星科技之日漸成熟，GPS已廣泛的應用在物理大地測量學中，其提供了取得高精度幾何高差的機會，亦改變了傳統高程測量的方法及概念，因此如何將GPS觀測資料應用於高程系統中，已成為近年來一個重要的研究課題。然而應用GPS所測得之橢球高h與傳統高程基準所使用的正高H其高程之基準並不一致，因此有賴一與地球重力位有關的物理量以為橢球高與正高之間提供適當的轉換媒介，此物理量即為大地起伏(N=h-H)。若能以重力數據建立台灣之大地水準面模型，且其精度若能與GPS的測高精度相當者，那麼藉由兩者的結合即可求得精確的正高值，則GPS將可成為一極為經濟的測定正高之方法。 本研究將針對數種不同的重力法，包括Stokes’積分式之二維平面快速傅立葉轉換、一維球面快速傅立葉轉換以及最小二乘配置法，並針對全球大地位模式EGM96及剩餘地形模型理論以去除回復技術實行之，以推求台灣地區之重力法大地起伏值。另外將配合所收集之各筆不同時期、不同分佈、不同密度所測得之台灣重力資料，計算台灣30〞×30〞之大地起伏模型，並進行比較分析。再以重力資料結合一等水準測量與GPS高程推求之大地起伏值檢核所計算得之重力法大地水準面之精度，以期提供一最佳求定台灣大地起伏之計算模式與重力數據組合。 由本研究實驗分析可知，以中研院603個重力點所計算出來之重力法大地起伏值之相對精度較單獨由其他三筆資料來得好，其結果與檢核值之相對差值的均方根值僅約5公分。另外，以Stokes’積分式之一維球面快速傅立葉轉換計算台灣之大地起伏較優於二維平面快速傅立葉轉換之計算方法，而以最小二乘配置法計算所得之大地起伏值之精度又優於Stokes’積分式之一維球面快速傅立葉轉換與於二維平面快速傅立葉轉換。本研究最後所建立之台灣最佳重力法大地起伏模型在台灣地區最大值可達28.564公尺，最小值為12.933公尺，其與台灣西部26座一等水準點之幾何法大地起伏之差值最大值為5.8公分、最小值為-9.5公分、標準偏差為2.56公分、均方根值為4.78公分。

Due to the rapid development of GPS technique these years, it has been extensively applied to physical geodesy. GPS technique can obtain high-accuracy ellipsoidal heights, and change the face and concept of traditional heighting procedure. However, leveling height is orthometric and GPS height is ellipsoidal, so geoid undulation is essential for relating the two. If we can build up a high-accuracy geoid model, then GPS will be an inexpensive method to measure orthometric. The geoid model has been strictly computed for Taiwan area in this research using Stokes’ formula with two-dimensional plane fast fourier transform (2D Plane FFT), one-dimensional spherical fast fourier transform (1D Spherical FFT) techniques and least square collocation (LSC) methods by remove-compute-restore technique. The computations of geoid undulations were carried out using data from EGM96 spherical harmonic model and residual terrain model for Taiwan. We use some gravity anomaly data, which are measured in different time, different distribution and different density, to compute the best Taiwan geoid model, and checked the accuracy of these models by GPS/Leveling observations. The numerical analysis results show that the result using gravity anomaly collected by Academia Sinica (Yen et al., 1990) is better than other three items. The root mean square of the difference between the geoid undulations computed by gravimetric and GPS/Leveling methods is about 5 cm. According to the results, Stokes’ formula with 1D Spherical FFT is better then 2D Plane FFT method, and LSC is the best one. Moreover, the best Taiwan geoid computed by gravimetric is about 12.993 m to 28.564 m. The maximum, minimum, standard deviation, and root mean square of the difference between the geoid undulations computed by gravimetric and GPS/Leveling methods are 5.8, -9.5, 2.56 and 4.78 cm.