水庫船載重力精進台灣大地起伏模型之可行性研究

A feasibility Study on Enhancing Taiwan geoid model with Shipborne Gravity on Reservoirs

本文模擬曾文水庫與石門水庫區域於枯水期及豐水期之重力異常模型，並計算大地起伏模型，以評估台灣實施水庫船載重力任務之必要性。依研究區域與不同水位分成8個案例，並分別以向上延續法模擬各案例在不同水位之重力異常模型，再藉由球諧展開式、剩餘地型模型理論及最小二乘配置法計算其長波長、短波長與殘餘波長之大地起伏，進而整合成各案例之最終大地起伏模型。結果顯示：（1）石門水庫之水位每上升10公尺，重力異常平均減少約0.2～0.3mgal；（2）石門水庫計算之大地起伏於枯水期與豐水期之差異平均約介於0.5～1.0公分，部分區域可達10公分；（3）曾文水庫之水位每上升20公尺，重力異常平均減少約0.1mgal；（4）曾文水庫計算之大地起伏於枯水期與豐水期之差異平均約低於0.5公分；（5）石門水庫實施水庫船載重力測量任務之重要性高於曾文水庫。 We simulate the Taiwan gravity anomaly models over the Tseng-Wen and Shihmen reservoir areas during the high and low water level periods, to assess necessity of shipborne gravity campaigns in Taiwan. Eight cases are tested based on study areas and water levels. The gravity anomaly model of each case is computed with the upward continuation method. We also use the methods of the harmonic expansion, the residual terrain model, and the least squares collocation to compute the long-, short- and residual- geoid undulations, and then integrate into a final geoid model for each case. The results of this paper include: (1) The average gravity anomaly is reduced by 0.2 ~ 0.3mgal while the water level rise by 10 m in the Tseng-Wen reservoir; (2) The difference value between the geoid undulations in the Shihmen reservoir during the high and low water level periods averages about 0.5 ~ 1.0 cm, but in some areas up to 10 cm. (3) If the water level rises by 20 meters in the TsengWen reservoir, the gravity anomaly is reduced by 0.1 mgal on average; (4) The difference value between the geoid undulations in the Tseng-Wen reservoir during the high and low water level periods averages about 0.5 cm; (5) The Shihmen reservoir is higher than the Tseng-Wen reservoir in necessity of shipborne gravity campaigns.