利用空載，地面重力與測高資料計算台灣大地起伏: 研究向上/向下延續與地形效應計算

Abstract

本論文的內容是結合地面、船載、測高與空載重力資料計算台灣與周邊海域的大地起伏模型。空載重力資料是在平均高度5156公尺下利用LaCoste and Romberg (LCR) System II 空載/船載重力儀所測得。為了得到最佳的大地起伏模型，本文研究兩個主要的課題。第一，考慮三種計算剩餘地形效應的方法，這三種方法分別為快速傅立葉轉換、柱狀體法與高斯求積法。在柱狀體法中，將考慮二維地質密度模型的影響。第二，快速傅立葉轉換與最小二乘配置法應用於向下延續的計算。在快速傅立葉轉換計算時，高斯與維納濾波將用平滑向下延續的重力值。最小二乘配置法則分為直接與間接大地起伏計算方法。此外，本文大地起伏計算策略為去除回覆法並搭配最小二乘配置法。 空中重力異常與地表重力比較後發現，兩者間較大的差值分部於高山地區，其主要原因為此區域缺乏地面重力資料。在交叉點分析方面，在bias-only改正前後的交叉點差值的均方根分別為4.92 和 2.88 mgal。在重複分析比較方面，150秒的濾波寬度是平滑空載重力值的最佳濾波寬度。在剩餘地形效應的研究方面，用快速傅立葉轉換計算此效應的大地起伏模型具有最佳的精度。此外，雖然考慮地質密度變化後，大地起伏面會比僅考慮地質密度常數的大地起伏模型有著4公分的變化量，但對改善大地起伏精度卻非常有限。在向下延續分析方面，先把重力向下延續到海水面(包括利用高斯與維納濾波的快速傅立葉轉換與最小二乘配置法)，再計算大地起伏的方法，所表現出的大地起伏模型很相似。然而採用最小二乘配置法直接計算大地起伏所得到的模型與其他方法所計算的比較，在某些區域有著30公分的差值。大致上來說，結合地面與空載重力所計算得到的大地起伏，其精度要比僅用地面重力所計算得的要佳，在部分山區可達到10公分以內的精度。

This dissertation is aimed at geoid modeling over Taiwan and the surrounding seas by land-based, shipborne, altimeter, and airborne gravity data. Airborne gravity data was obtained from an airborne gravity survey over Taiwan using a LaCoste and Romberg (LCR) System II air-sea gravimeter at an average altitude of 5156 m. In order to model the best geoid, two main topics are studied. First, three computational methods of the residual terrain model (RTM) effects are considered. The three methods are the fast Fourier transform (FFT), prism, and Gaussian quadrature methods. A 2-D density model of terrain is used in the prism method. Second, the FFT and least squares collocation (LSC) methods are adopted for the computation of the downward continuation (DWC). Both Gaussian and Wiener low-pass filters are used to smooth the downward-continued data by using FFT. Direct and indirect geoid computations are studied in LSC DWC. The methodology of the geoid modeling is mainly based on the remove-compute-restore (RCR) procedure by using LSC. The airborne gravity anomalies are compared with the surface values. Large discrepancies are found to occur over high mountains due to the sparse surface gravity data coverage. The RMS crossover differences before and after a bias-only adjustment are 4.92 and 2.88 mgal. A filter width of 150 s is the optimal width for filtering the airborne gravity data, according to a repeatability analysis. In the investigation of the RTM, the FFT method in the RTM-derived effect computation produces the best geoid accuracy. Although the density variation considered in the geoid modeling yields a 4-cm change in the geoid surface from that using a geological constant, the improvement in the geoid accuracy is extremely small. In the DWC analysis, the methods of DWC to sea level, including FFT with the Gaussian and Wiener filters and LSC, perform similar in geoid modeling. The method of direct geoid determination by LSC provides an obviously different geoid result due to the 30-cm differences of geoid surface from the other geoid models over some areas. Generally, the accuracies of the geoid models from the surface and airborne gravity data outperform the surface-gravity-only geoid models. The improvement in geoid accuracy reaches 10 cm over some high mountainous areas.