**Abstract**

In this paper, three different methods for computing the terrain correction have been compared. The terrain effect has been accounted for by using the standard right parallelepiped closed formula, the spherical tesseroid and the flat tesseroid formulas. Particularly, the flat tesseroid approximation is obtained by flattening the top and the bottom sides of the spherical tesseroid. Its gravitational effect can be computed as the gravitational effect of a polyhedron, i.e. a three-dimensional body with flat polygonal faces, straight edges and sharp corners or vertices. These three methods have been applied in the context of a Bouguer reduction scheme. Two tests were devised in the Alpine area in order to quantify possible discrepancies. In the first test, the terrain correction has been evaluated on a grid of points on the DTM. In the second test, Bouguer gravity anomalies were computed on sparse observed gravity data points. The results prove that the three methods are practically equivalent even in an area of rough topography though, in the second test, the Bouguer anomalies obtained by using the tesseroid and the flat tesseroid formulas have slightly smaller RMSs than the one obtained by applying the standard right parallelepiped formula.

**Keywords:** Gravitational Terrain Effect, Bouguer reduction, Terrain Correction, Parallelepiped, Tesseroid, Polyhedron
