台灣本島與離島之高程基準連結

Abstract

本論文結合長時間GPS觀測、水準正高資料與台灣區域之大地起伏模型，計算台灣本島與各離島，包括小琉球、綠島、蘭嶼及澎湖之高程基準差異。台灣本島與各離島之高程基準皆定義於當地之平均海水面，因此各地高程基準間之差異可視為各地之平均海水面與大地水準面之差異又稱為海面地形，亦可利用海洋學的理論來推導之。為了真實地反應台灣本島與各離島周圍的大地水準面，需要有高密度且分佈均勻的高精度重力資料，然而以往的船測重力資料或是測高衛星重力皆無法達到此要求。空載重力資料可有著分佈均勻的特性但因為航速快故空間解析度不比船測資料，本文中為了避免重力約化之基準點不一的情形，利用3-D Fourier series擬合空中的重力異常再向下延續至地形面上。 本文中利用小型漁船蒐集共五組近岸船測重力資料，施測時間為2006-2010年，可說是國際上第一次的經驗。利用現代空載測量的技術來處理船測重力資料，使用動態差分定位技術求解船隻的動態位置，解算軟體為Bernese 5.0，並分析由於過去船測資料定位的不精確產生的誤差量。為了得到最佳的重力資料，本研究對船測重力資料頻譜分析以確定各項濾波器的適用性，最後利用高斯濾波器來抑制高頻的雜訊，交叉點分析顯示本組近岸船測資料精度為1-2 mgal。最終的船測重力成果與測高資料相比顯示其在近岸區域更能精確地反應海底地形的變化，兩者最大差值超過30 mgal。 本研究利用去除回復法技術並將EGM08模型當作長波長參考場，利用修正的Stokes’函數積分計算殘餘大地起伏，用來消除重力資料中的系統誤差，得出的大地起伏模型在平地精度優於5公分，在基隆沿岸區域精度可達1公分。最終求得台灣本島高程基準TWVD2001與小琉球當地高程基準差異為24.6 2.1公分；與綠島之差異為50.4 9.3公分；與蘭嶼之差異為105.8 2.2公分；與澎湖之差異為44.1 2.4公分。

This study determines the vertical datum differences between Taiwan and its offshore islands, i.e., Liouciou, Lyudao, Lanyu and Penghu, based on a geodetic theory that converts potential differences to datum height differences. The local vertical datums (LVDs) of Taiwan and its offshore islands are the local mean sea levels derived from tide gauge records. The differences between the datums are the vertical datum offsets, which are closely related to the sea surface topography (SST) values that can also be derived by an ocean model. To determine the LVD offsets, determinations of ellipsoidal heights by GPS and geoidal undulations at points belonging to two different vertical datums are needed. For a precise geoid modeling, dense and evenly distributed high precision marine gravity data are needed. However, neither existing shipborne data nor altimeter-derived data can meet this requirement. Airborne gravity data can provide dense gravity coverage, but the corresponding spatial resolution is not competitive with that of shipborne data due to the high speed of the aircraft carrying out the airborne measurements. For the conversion of gravity values from one altitude to another, a 3-D Fourier series is used to fit the observed gravity anomalies at the flight altitude for downward continuation to the sea level or a desired altitude. From 2006 to 2010, small ships that are able to sail to the immediate coastal areas were used for the first time to collect shipborne gravity data around Taiwan's offshore islands. A popular procedure of airborne gravity data processing is used to process the offshore shipborne gravity data with some modifications. The Bernese 5.0 software is used for relative kinematic positioning of ships. For many existing ship gravity datasets, ship positions and velocities derived from GPS navigation solutions are used for gravity reductions, resulting in positioning-induced errors. Such errors are evaluated in this study. By assessing filter performances using spectrum analyses, an optimal low-pass Gaussian filter is designed to suppress the high frequency noises in ship gravity data. The quality of the offshore shipborne gravity data is assessed using crossover analysis, yielding RMS crossover differences of less than 2 mgal in all cases. Compared to the altimeter-derived DTU10 gravity model, the offshore shipborne gravity data reveal a detailed change of bathymetry. The maximum difference between the DTU10 and shipborne gravity values near the coast of Lanyu reaches 30 mgal. The gravimetric geoid modeling is based on the remove-compute-restore procedure, with the reference field being the EGM08 model. The residual geoid is computed by Stokes’ integral with a modified kernel to eliminate the long wavelength errors in the gravity data. The accuracy of the resulting geoid model is assessed using geoidal undulations at leveling benchmarks derived from ellipsoidal heights (GPS) and orthometric heights (precision leveling). The standard deviations of the differences between the gravimetric and GPS-derived geoid undulations in flat areas are mostly below 5 cm, and are about 1 cm along the coastal area of Keelung. An iterative method of geoid modeling is used that takes into account the LVD offsets in gravity reductions. With the gravimetric geoid model and 48-hour GPS observations collected at the vertical datum connection sites, the vertical datum differences with respect to the Keelung mean sea level (TWVD2001) are 24.6 2.1, 50.4 9.3, 105.8 2.2, and 44.1 2.4 cm for Liouciou, Lyudao, Lanyu and Penghu, respectively.