利用地形数据计算重力梯度张量的直接积分法

The Direct Integral Method to Calculate Gravity Gradient Tensor with Terrain Data

为了获取重力梯度中的高频信息，基于DEM数字高程数据，利用直接积分法建模计算重力梯度张量，并与利用棱柱法建模的计算结果进行对比；建立了与DEM数据相同分辨率的重力梯度图，与已知的重力梯度图进行比较。结果表明：基于地形数据利用直接积分法建模解算重力梯度全张量与利用棱柱法解算具有相当的精度，但前者解算速度更快且它的平均相对误差百分比为4．16％；建立的重力梯度图与实测重力梯度图具有相同的变化趋势和特征，符合实际情况。在重力梯度测量相对落后和重力资料欠缺的情况下，利用地形数据计算重力梯度以获取高频信息是可行的。因此，在一定的精度要求下，直接积分法可以作为一种有效计算重力梯度张量高频信息的方法。

In order to obtain high frequency information in gravity gradient, the direct integral method is used to calculate gravity gradient tensor with DEM digital elevation data, and the calculation results are compared with that calculated using prism method. Gravity gradient map with the same resolution of DEM data is set up, and compared with the known one. Results show that based on terrain data, the accuracy of gravity gradient tensor calculated using direct integral method is almost the same with that of prism method, but the calculation speed of the former is faster and the percentage of average relative error is 4.16% ; the gravity gradient map has the same change tendency and features with the measured gravity gradient map, which is in line with the actual situation. When the gravity gradient measurement is relatively backward and gravity data is lacking, it is feasible to obtain high frequency information by calculating gravity gradient with terrain data. Therefore, the direct integral method can be used as an effective method for gravity gradient tensor calculation to satisfy certain accuracy requirement.