Classical Physical Geodesy

Abstract

This chapter presents the basics of classical physical geodesy, starting from the definitions of the gravity potential and gravity. The normal gravity potential is derived as the potential of a level ellipsoid plus the rotational potential of the ellipsoid. Normal gravity, defined as the gradient of the normal gravity potential, is presented on and above the level ellipsoid. The basic concepts of the geoid, reference ellipsoid, disturbing potential and geoid height are defined, as well as the classical definitions of gravity anomaly and disturbing potential. After derivation of the fundamental equation of physical geodesy, the gravity field components of the disturbing potential, gravity anomaly and its radial derivative are presented in spherical harmonics, followed by Kaula’s power rule of the geopotential harmonics. The classical integral formulas of Poisson, Stokes, Hotine, Vening Meinesz and the vertical gradient of gravity anomaly are derived by spherical harmonics. Other spherical integral formulas are derived for determining the gravity anomaly and/or disturbing potential from deflections of the vertical (inverse Vening Meinesz formula) and gravity gradient components. The classical procedures in geoid determination, including direct and secondary indirect topographic effects and downward continuation of gravity and primary indirect topographic effect on the disturbing potential, are described. Finally, the chapter deals with common height systems, such as geopotential numbers, dynamic, orthometric and normal heights, as well as normal-orthometric heights. Some approximate formulas to correct normal-orthometric heights to orthometric or normal heights are also presented.