**1. Introduction**

The gravity effect of topography has been always intensively analyzed and modeled. In all the classical books of Geodesy and Geophysics there are sections devoted to this topic. Among the standard methods for modeling the gravity effect of topography one can enumerate the Bouguer reduction, the Helmert reduction and the isostasy reduction according to Airy-Heiskanen and Pratt-Hayford models (see e.g. [1]). In more recent years, the Residual Terrain Correction (RTC) has been devised as a method to be used in geodetic applications for gravity field and geoid estimation (see e.g. [2]).

In all these approaches, the gravity effect of topography is computed by using a Digital Terrain Model (DTM) at a given resolution, which is assumed to represent the actual shape of the Earth surface. Thus, the topography is discretized at the DTM resolution and the gravitational effect of each topography element is

computed. In doing so, different formulas can be applied. Usually, the single terrain element is modeled as a right parallelepiped (see e.g. [2]) or as a spherical or ellipsoidal tesseroid [3]. In this study, we compare the two aforementioned approach with that introduced by Tsoulis [4] in which the bottom and the top sides of the tesseroid are flat surfaces (flat tesseroid). This is done for the computation of the terrain correction in the framework of the Bouguer reduction.

The formulas giving the gravitational effect of a right parallelepiped, a spherical tesseroid and a flat tesseroid are given in Section 2. In Section 3, the Bouguer reduction is computed using these three different approaches in an area of the Alps, both on a grid of points and on a set of observed gravity values, and comments on the obtained results are given. Conclusions are then stated in Section 4.
