关键词: 物理大地测量, 边值问题, 扰动场元, 算子运算

Abstract: According to the solution of the physical geodesy boundary value problem and the definition of the 1st order operator operations, under the condition of the spherical approximation, the formulae for computing the gravity anomaly , the single layer density , the geoidal undulation , the deflection of the vertical , gravity disturbance are derived from the regeneration property of the kernel functions in this paper. Making use of the orthogonal characteristic of the spherical harmonics, the conversion relations among the disturbing potential elements are also derived，which integrates the operator operation in accordance with the kennel function computing. In this paper, the integral formulae with factor are named as the general formulae, which relatives to the conditions of the integral boundary surface in the classical physical geodesy formulae computing. The alternate relations among the gravity anomaly , the geoidal undulation , the deflection of the vertical , gravity disturbance are chiefly discussed. The general integral formulae are derived from the given disturbing potential element to others disturbing potential element. Through the classical physical geodesy formula compared with the general integral formulae, the differences and relations are analyzed on the integral boundary surface. Finally, the table of the relational expressions about the disturbing potential elements and the kernel functions is given.

Key words: physical geodesy, boundary value problem, disturbing potential elements, operator operation