A comparison of classical and Sjoberg's approaches to terrain corrections in gravimetric geoid determination

This paper investigates three approaches for compting the terrain effects in the gravimetric geoid determination. First method is the classical approach which is documented by Moritz. The second classical approach is developed by Vanicek and Kleusberg. Direct terrain effect in Moritz appraoch has been reduced to a surface with constant elevation, i.e., geoid whereas in Vanicek and Kleusberg approach this effect has been reduced to a varying surface depending on topography but in a different way. A different way has been used to compute terrain effects in Sjoberg's approach. This third method is based on spherical harmonic theorems. Direct terrain effect in Sjoberg's approach has been derived at the topographical surface of the Earth. Numerical investigations has been carried out in two regions A and B in Sweden. The region A has a smooth topography where region B has a rugged topography. Comparison of these there approaches show large differences in test region B. The range of the Vanicek and Kleusberg direct terrain correction (-66 to 21 mGal) was substantially larger than in the Moritz (0 to 17 mGal) and Sjoberg's (-540 to 250 MicroGal) approaches. The range of the indirect effect in Moritz (or Vanicek and Kleusberg) approach was -4 to 8 cm where it was 4 to 6 cm for the sjoberg's approach.