有限范围的重力层间改正算法

The Bouguer Correction Algorithm for Gravity with Limited Range

层间改正是重力归算的一项重要内容,传统的平面层层间改正、球面层层间改正与地形改正的范围不一致,因此均存在远区虚拟地形引入的近似误差,且计算点高度越高,此误差越大。本文提出使用有限范围的层间改正进行重力归算的方法,使其区域范围与地形改正的范围一致。然后给出了有限范围层间改正的简便计算方法,该算法与通过地形改正严密积分法演化来的算法具有较好的一致性。内插试验说明当计算点地形高于1000m时,内插应使用基于有限范围层间改正的重力归算方法。

The Bouguer correction is an important item in gravity reduction, while the traditional Bouguer correction, whether the plane Bouguer correction or the spherical Bouguer correction, exists approximation error because of far-zone virtual terrain. The error grows as the calculation point gets higher. Therefore gravity reduction using the Bouguer correction with limited range, which was in accordance with the scope of the topographic correction, was researched in this paper. After that, a simplified formula to calculate the Bouguer correction with limited range was proposed. The algorithm, which is innovative and has the value of mathematical theory to some extent, shows consistency with the equation evolved from the strict integral algorithm for topographic correction. The interpolation experiment shows that gravity reduction based on the Bouguer correction with limited range is prior to unlimited range when the calculation point is taller than 1000 m.