地形改正与地形直接影响的转化关系

传统的第三边值问题的解算方法有Molodensky算法和Stokes-Helmert算法两种。在Molodensky算法中使用的地形改正和Stokes-Helmert算法中使用的直接影响均由大地水准面外地形产生,因而必然存在关系。本文通过推导给出了直接影响是地形改正、层间改正与压缩地形影响3项之和的结论。在此基础上,给出了直接影响的质量线平面积分算法、质量棱柱平面积分算法和地形改正的球面积分算法。此外本文还推导了布格球冠层间改正算法。通过实验得出,直接影响的质量线平面积分算法和质量棱柱平面积分算法与传统球面积分算法的差异分别为3.81和1.64 m Gal;地形改正球面积分算法与传统质量线、质量棱柱平面积分的差异分别为3.92和1.69 m Gal。该结果说明,本文推导的直接影响与地形改正的关系式是正确有效且实用的。

Transformation Relation between the Topographic Correction and the Direct Topographic Effect

The calculating methods of the traditional third boundary value problem include Molodensky algorithm and Stokes-Helmert algorithm.The topographic correction used in the Molodensky method and the topographic direct effect used in the Stokes-Helmert method are both generated by the terrain outside the geoid,and therefore they should have some transformation relations.A formula was put forward that the topographic direct effect is the sum of the topographic correction,the bouguer layer correction and the gravitation of the condensed terrain.Subsequently,three algorithms were achieved which included the line-quality and prism-quality planar integral formula of the direct topographic effect and the spherical integral formula of topographic correction.Besides,the bouguer layer correction for spherical cap was also deduced in this paper.The experiment shows that the differences of the direct effect between the traditional spherical integral formula and the line-quality and the prism-quality planar integral algorithms are 3.81 mGal and 1.64 mGal respectively,while the difference of the terrain correction between the prism-quality planar and spherical integral algorithms is 1.69 mGal,which climbs up to 3.92 mGal for the linequality case.The results fully illustrate the transformation relation between the topographic correction and the direct effect is correct and practical.