最佳化重力資料處理及整合以建構公分級台灣大地起伏模式

Abstract

大地起伏模式的精度取決於重力資料的品質、空間密度及整合，本文的主要目的為最佳化處理空載、測高及陸測重力資料及整合所有重力資料以建構台灣區域的大地起伏模型。空載重力資料的處理，吾人提出一個消除殘留於交叉點平差後空載重力之 biases、tilts 的方法，經過高斯濾波及移除高階球諧地球重力場的有限頻譜 (band-limited)空載重力經過向下延續至地面後，利用數值地形模型計算布格重力異常並整合陸測及海洋重力，再以數值地形模型及地形改正重建地表的重力異常，最後將該重力異常向上延續至航高位置與空載重力進行比較以偵測並消除空載重力的 biases、tilts，重複疊代上述的程序至收斂為止。數值分析的結果顯示吾人提出的方法可以消除殘留於交叉點平差後空載重力的 biases、tilts，而且整合向下延續的空載重力及地面重力可有效避免重力缺乏之區域受到外插誤差的影響。高頻誤差受到Eötvös改正量之速度項誤差的影響殘留於東西向的測線中。本文也試驗該程序搭配不同資料，例如只使用空載重力及DEM資料(沒有使用陸測重力)、EGM2008及GOCE-TIM4，卻都得不到同樣的效果。經過與GOCE的比較分析，顯示交叉點統計對於空載重力而言非永遠是可靠的精度指標，特別是當交叉點分布不均勻時。測高重力資料的處理，吾人自行發展衛星測高海洋重力模型，考慮並比較多種不同波形重定技術，試圖找出此區域最理想之波形重定來改善沿岸因波形不佳導致測距精度不良的情形。使用的測高資料除了包括Geosat/GM、ERS–1/GM、Geosat/ERM、ERS-1/35d、ERS-2/35d、T/P之外，還另外蒐集目前最新的Jason-1/GM及Cryosat-2測高資料。採用的波形重定演算法分別有次波形門檻值、門檻值及 beta-5 等，以沿軌跡海水面高梯度的標準偏差當作選取指標來篩選此研究區最理想的波形重定演算法，結果顯示Geosat/GM、ERS-1/GM及Jason-1/GM以次波形門檻值演算法分別搭配門檻值為0.3、0.2及0.2可得到台灣區域最佳的重力異常網格。分別測試Inverse Vening Meinesz (IVM)及最小二乘配置法並搭配去除回復法計算測高重力異常網格。測高重力與船測重力比較的結果顯示，吾人發展的測高海洋重力模型精度略優於Sandwell V18.1及DTU10。陸測重力則是分別對重力值及重力點高程進行處理，本文以加權約制平差求解內政部於2004-2012年間蒐集的陸測重力，相對重力觀測量共17852筆資料，其中約制14個絕對重力點，反覆進行重力網平差及粗差偵測，共偵測並移除其中67筆觀測量粗差，最後通過整體測試的平差後未知重力點共有6498筆，平均精度約0.034 mGal。重力點高程資料的處理，則是採用交叉驗證法偵測出共26個高程為粗差。為了建構公分級的大地起伏模型，本文以有限頻譜的最小二乘配置法(Band-limited LSC)搭配以先移除地形重力效應再進行整合的程序，成功的整合所有經過處理的重力資料並計算布格重力及自由空間重力異常網格。此外，還發現台灣東部山區(或近岸)的布格重力異常計算如沒同時考慮陸地地形及海洋質量的貢獻時將導致低估的情形。重力法大地起伏模式採用以快速傅立葉變換(Fast Fourier Transform, FFT)為基礎的stokes積分理論來計算，過程中搭配傳統去除-計算-回復法，長波長分量使用地球重力模型(Earth gravitational model 2008, EGM2008)展開至2190階。新一代大地起伏模型使用14條幾何法大地起伏來進行精度評估，整體平均精度約7公分，混合型大地起伏模型透過整合重力法及幾何法大地起伏值計算而得，本文所發展的新一代大地起伏模型已廣泛在產官學界應用於橢球高與正高間的轉換。

The high-accuracy of geoid model is dependent on the quality, spatial density and combination of gravity data. The purpose of this thesis is to optimize gravity data processing and combination for cm-geoid in Taiwan. For the airborne gravity data processing, we present a method to reduce biases and tilts in Taiwan airborne gravity surveys that have not been removed completely by a crossover adjustment at flight height. Band-limited airborne gravity anomalies, after low-pass filtering and removal of a high-degree spherical harmonic Earth gravitational model, are downward-continued to the topographic surface and converted to Bouguer anomalies using a digital elevation model. These are merged with land and marine gravity data and ‘reconstructed’ with a digital elevation model and terrain corrections added to give gravity anomalies on the topography. These are upward-continued to the flight height and compared with the airborne gravity to detect and reduce biases and tilts in the airborne data. These airborne gravity data are then subjected to the above procedures in an iterative manner. Numerical results from an airborne gravity survey over Taiwan show that the method detects then reduces biases and tilts that were not removed by the crossover adjustment. There is a need to supplement the terrestrial data with the downward-continued airborne data to avoid spurious extrapolation of the Bouguer anomalies in areas devoid of terrestrial data. High-frequency noise remains in the east-west flight lines because of uncertainties in the velocity term of the Eötvös correction. This leads us to recommend different geometries for flight patterns. We also trialled the method with no terrestrial data, EGM2008 and a fourth-generation GOCE model, but none were as effective. Using the independent GOCE data, we show that crossover statistics are not always reliable indicators of the precision of airborne gravity, especially when the crossovers are distributed unevenly. For the altimeter-derived gravity data processing, we developed our marine gravity grid from retracked Geosat/GM, retracked ERS-1/GM, repeat Geosat/ERM, ERS-1/35d, ERS-2/35d, ENIVSAT, and TOPEX/POSEIDON altimeter data. In addition, the latest geodetic mission: Jason-1/GM and Cryosat-2 were also used. Several retrackers were tested and the sub-waveform threshold retracker based on a correlation analysis method outperforms the Beta-5 and full-waveform threshold retrackers over this region. The least-squares collocation (LSC) and inverse Vening Meinesz (IVM) methods were used to compute gravity anomalies from along-track geoid gradients, in a remove-restore procedure with the EGM2008 gravity model to degree 2190 as the reference field. Comparisons of our altimeter-derived gravity anomalies with shipborne gravity anomalies results in RMS differences of few mgal, and our result outperforms other recent gravity fields such as Sandwell.V18.1 and DTU10. For the land gravity, we focused on processing the relative gravity measurements and the elevation of gravity station, respectively. This study adjusts land gravity from the effort of MOI collected during 2004-2012 using least-squares with weighted constraints. There are 17852 relative gravity measurements with 14 absolute gravity stations for network-adjustment. There are 67 outliers were detected and excluded after adjustment. There are 6498 gravity station pass the global model test and give an overall accuracy around 0.034 mGal. For the elevation of gravity station, there are 26 elevation of gravity station regarded as outlier using cross-validation technique. For the cm-geoid modeling, a band-limited LSC was applied with a procedure that first removed the terrain gravity effect before combination. All processed datasets were combined by the band-limited least-squares collocation in a one-step procedure. In addition, In the eastern mountainous (or offshore) region, Bouguer anomalies and density contrasts without considering the oceanic (or land) topographic contribution are underestimated. The Stokes formula based on the FFT technique was used to compute the geoid model with the standard remove-computation-restore procedure. The EGM2008 to degree 2190 is used as the long wavelength part of the geoid. The new geoid model is evaluated using “observed” geoidal heights at Taiwan’s first-order leveling benchmarks along 14 major routes. The overall accuracy of this geoid model is around 7cm. A hybrid geoid model is determined by merging GPS-derived and gravimetric geoidal heights. The geoid model is now widely used in Taiwan for ellipsoidal height-orthometric height conversion.