Effects of the spherical terrain on gravity and the geoid

The determination of the gravimetric geoid is based on the magnitude of gra vity observed at the topographical surface and applied in two boundary valu e problems of potential theory: the Dirichlet problem (for downward continu ation of gravity anomalies from the topography to the geoid) and the Stokes problem (for transformation of gravity anomalies into the disturbing gravi ty potential at the geoid). Since both problems require involved functions to be harmonic everywhere outside the geoid, proper reduction of gravity mu st be applied. This contribution deals with far-zone effects of the global terrain on gravity and the geoid in the Stokes-Helmert scheme. A spherical harmonic model of the global topography and a Molodenskij-type spectral app roach are used for a derivation of suitable computational formulae. Numeric al results for a part of the Canadian Rocky Mountains are presented to illu strate the significance of these effects in precise (i.e. centimetre) geoid computations. Their omission can be responsible for a long-frequency bias in the geoid, especially over mountainous areas. Due to the rough topograph y of the testing area, these numerical values can be used as maximum global estimates of the effects (maybe with the exception of the Himalayas). This study is a continuation of efforts to model adequately the topographical e ffects on gravity and the geoid, especially of a comparing the effects of t he planar topographical plate and the spherical topographical shell on grav ity and the geoid [Vanicek, Novak, Martinec (2001) J Geod 75: 210-215].