On the indirect effect in the Stokes–Helmert method of geoid determination

Abstract.

The classical integral formula for determining the indirect effect in connection with the Stokes–Helmert method is related to a planar approximation of the sea level. A strict integral formula, as well as some approximations to it, are derived. It is concluded that the cap- size truncated integral formulas will suffer from the omission of some long-wavelength contributions, of the order of 50 cm in high mountains for the classical formula. This long-wavelength information can be represented by a set of spherical harmonic coefficients of the topography to, say, degree and order 360. Hence, for practical use, a combination of the classical formula and a set of spherical harmonics is recommended.