梯度法在球谐综合中的适用性分析

Applicability analysis of gradient method in spherical harmonic synthesis

针对地球表面球谐综合过程中要求考虑高程信息的问题,在球谐综合过程中,基于地形模型DTM2006.0和超高阶的重力场模型EGM2008,分别在椭球坐标系与球坐标系下,利用梯度法对球谐综合过程中的重力场泛函进行一定阶次扩展,分析梯度法在椭球坐标系与球坐标系下的适用性.在实验区域,计算结果表明,在球谐综合过程中,利用梯度法计算重力场泛函,它能够将高程信息带来的近似误差减少到对实际应用无关紧要的程度,可计算任意密集网格点上的表面重力场泛函.

Aiming at the problem of considering elevation information in the process of spherical harmonic synthesis of the earth’s surface,based on the topographic model DTM2006.0 and the ultra-high-order gravity field model EGM2008,the gravity field function in the spherical harmonic synthesis process is extended by gradient method in ellipsoid coordinate system and spherical coordinate system,respectively.Analyzing the applicability of gradient method in ellipsoidal coordinate system and spherical coordinate system.In the experimental region,the calculation results show that the gradient method can reduce the approximate error caused by elevation information to the degree of irrelevance significance for practical application,and can calculate the surface gravity field function at any dense grid point.