基于面积分的重力地形改正方法研究及应用

Research and application on gravity terrain correction method based on surface integral

在重力勘探中,地形改正对重力总精度影响较大,尤其在地形条件相当复杂的山区和丘陵地区,地形对重力观测异常的影响特别大。这里研究并分析了传统方域积分(体积积分)的不足:1方域对实际地形拟合(方柱拟合)不好;2传统方法采用的梯形数值积分的地改精度低且不能满足目前高精度重力测量的要求。模拟研究了基于对地形表面的面积分,然后用精度比较高的高斯数值积分代替原来的梯形积分。结果表明,高斯数值积分不但实现了对任意地形的最佳拟合,而且使得地改精度有了明显地提高,实际应用证明了基于面积积分的地改方法优于传统的方域地改方法。

In gravity prospecting,terrain correction has a great impact on the overall accuracy of gravity survey.The ter-rain correction has an awfully great influence on the observed anomaly of gravity especially in areas of fairly complex terrain condition as mountainous and hilly regions.Different methods of terrain correction have different precision.The disadvantages of traditional square-domain integral （volume integral）are studied and analyzed in this study as follow：on the one hand,the square-domain cannot fit the actual terrain well because of its square columns fitting;on the other hand,the terrain correction precision of the numerical integral employed in traditional methods is too low to meet the demand of high- precision gravity survey.In this article the surface integral based on the ground surface is simulated,and then replace the original trapezoidal in-tegral with Gauss numerical integral of relatively high precision.The result shows that the Gauss numerical integral not only realizes the best fitting to arbitrary terrain but also obviously enhances the precision of terrain correction,which is verified by the practical application.The results,finally,prove that the terrain correction methods on surface integral are better than tra-ditional ones based on square domain.