不同扰动位泛函间的积分变换广义核函数  

General Kernel Functions Based on Integral Transformation among Different Disturbing Potential Elements

作　　者：程芦颖[1] 

机构地区：[1]西安测绘研究所,陕西西安710054

出　　处：《测绘学报》2013年第2期203-210,共8页Acta Geodaetica et Cartographica Sinica

摘　　要：基于物理大地测量边值问题的解,利用一阶边界算子定义,推导重力异常Δg、单层密度μ、大地水准面高N,垂线偏差ε、扰动重力δg等扰动场元的解。利用球谐函数的正交特性,通过对核函数的算子运算,可以得到上述扰动场元的有关逆变换公式。相对经典物理大地测量公式应用的边界面条件,笔者将含有因子r的对应扰动场元反演关系的公式称为广义积分公式。针对常用的重力异常Δg、大地水准面高N,垂线偏差ε、扰动重力δg计算,重点分析它们之间的变换关系,给出利用某个选定扰动场元计算其他扰动场元的广义积分公式。同时,通过对积分边界面的讨论,分析经典公式与广义积分公式的差异和联系。最后,给出所有外部扰动场元与核函数映射的关系表。According to the solutions of the physical geodesy boundary value problems and the definition of it＇s first order operator operations,the formulae for computing the gravity anomaly Δg,the single layer density μ,the geoidal height N,the deflection of the vertical ε and gravity disturbance δg are derived from the regeneration property of the kernel functions under the condition of the spherical approximation.Making use of the orthogonal characteristic of the spherical harmonics,the conversion relations among the disturbing potential elements are also derived,which integrate the operator operation in accordance with the kennel function computing.In this paper,the integral formulae with factor r are named as the general formulae,which relates to the conditions of the integral boundary surface in the classical physical geodesy formulae computation.The transformation relations among the gravity anomaly Δg,the geoidal height N,the deflection of the vertical ε and gravity disturbance δg are chiefly discussed,and the general integral formulae are derived from the given disturbing potential element.The differences and relations between the classical physical geodesy formula and the general integral formulae are compared on the integral boundary surface.Finally,the table of the relational expressions about the disturbing potential elements and the kernel functions is given.

关 键 词：物理大地测量 边值问题 扰动场元 算子运算 

分 类 号：P223[天文地球—大地测量学与测量工程]