重力梯度對大地起伏精度之影響

Impact of gravity gradient on geoid accuracy

吳夢伶(Meng-Ling Wu)

指導教授 ： 黃金維

國立交通大學/工學院/土木工程系所/碩士(2015年)

https://doi.org/10.6842/NCTU.2015.00836

摘要

本研究分別以正常重力梯度、觀測重力梯度與積分重力梯度約化陸測重力，並以求得之重力異常建構出台灣大地起伏模型。陸測重力資料為內政部2007年所測之一、二等重力點位值，經由三種重力梯度的約化來消弭正常重力值與自由空間重力效應，以求得海平面上之重力異常值。三種不同重力梯度的使用建構出不同的台灣大地起伏模型。
計算成果顯示，在高度大於 900公尺的地區，與傳統使用正常重力梯度所算得的大地起伏值相比，使用觀測重力梯度所算得的大地起伏值，精度提升了6.2 公分；使用積分重力梯度所計算得的大地起伏值，雖然在中橫路線有17.8公分的精度提升，但在中央山脈路線卻降低了0.3公分，顯示出積分重力梯度只有在局部地區有所助益。但在高度小於900公尺的地區，以不同重力梯度計算而得的大地起伏值並沒有太大的差異。在高海拔的地區，使用觀測重力梯度約化地表重力來求得大地起伏模型，可以獲得較好的精度。

關鍵字

重力梯度 ； 大地起伏模型 ； 重力異常 ； 台灣

並列摘要

This study determines Taiwan geoid models using gravity anomalies based on gravity reductions using three types of gravity gradients: normal gradient, observed gradient and integration-based gradient. Ground gravity values in the first and second order-networks, collected by Ministry of the Interior (MOI) in 2007, are reduced to free-air gravity anomalies at sea level by removing the normal gravity values and the free-air gravity effects using these three types of gradients. Use of different gradients results in three geoid models in Taiwan.
Compared with the geoid model based on normal gravity gradients, the overall geoid model accuracy improvement due to use of observed gravity gradients is 6.2 cm in areas with elevations > 900 m. With the integration-based gradients, the geoid model accuracy is improved by 17.8 cm along the Central Cross-Island Highway, but is degraded by 0.3 cm along a leveling route in Central Range. In areas under 900 m height, there is no significant difference between the accuracies for the geoid models based on normal and observed gravity gradients. In conclusion, use of observed gravity gradients improves the overall geoid model accuracy in high-elevation areas.

並列關鍵字

Gravity gradient ； Geoid model ； Gravity anomaly ； Taiwan

參考文獻

Bouman, J., Bosch, W., and Sebera, J. (2011). Assessment of systematic errors in the computation of gravity gradients from satellite altimeter data. Marine Geodesy, Vol. 34, pp. 85-107.

Bowin, C., Scheer, E., and Smith, W. (1986). Depth estimates from ratios of gravity, geoid, and gravity gradient anomalies. Geophysics, Vol. 51, pp. 123-136.

Hsiao, Y. S., and Hwang, C. (2010). Topography-assisted downward continuation of airborne gravity: application to geoid determination in Taiwan. Terrestrial, Atmospheric and Oceanic Sciences, Vol. 21, pp. 627-637.

Hwang, C. (1997). Analysis of some systematic errors affecting altimeter-derived sea surface gradient with application to geoid determination over Taiwan. Journal of Geodesy, Vol. 71, pp. 113-130.

Hwang, C., and Hsiao, Y. S. (2003). Orthometric correction from leveling, gravity, density and elevation data: a case study in Taiwan. Journal of Geodesy, Vol. 77, pp. 279-291.