**4. Conclusions**

the EGM96 geoid undulations when computing the terrain correction with the TC

In Eq. (4), as previously stated, the orthometric height *H* is derived via the EGM96 geoid undulation and the Bouguer plate is accounted for by using Eq. (1).

Given the three different terrain corrections, by applying Eq. (4), three different

and the normal gravity in a point *Q* of latitude *φ<sup>Q</sup>* on the ellipsoid is given by the

Although this formula has an accuracy of 0.1 mGal (see [16]), it can be used in the context of this relative comparison among different terrain correction compu-

**Table 7** summarizes the statistics of the Bouguer anomalies obtained with the

Comments similar to those given on **Table 3** hold for the Bouguer values in **Table 7**. The Bouguer anomalies obtained by applying the three methods have quite similar statistics. Those computed via TC-GRAVSOFT software have the smallest standard deviation and the highest mean while those obtained with the other two methods have smaller mean and higher standard deviations. If the RMSs are considered, one can see that the Bouguer anomalies based on the flat tesseroid have the smallest value. However, as pointed out before, even the largest difference among

**Δ***gB* **μ [mGal] σ [mGal] RMS [mGal] Min [mGal] Max [mGal]** TC (GRAVSOFT) �137.846 16.131 138.786 �168.873 �90.511 TESSEROID (UNIPOL) �137.074 16.205 138.028 �166.337 �90.299 FLAT TESSEROID (FT) �136.894 16.221 137.852 �166.262 �90.069

*<sup>∂</sup><sup>h</sup>* ¼ �0*:*<sup>30877</sup> *mGal=<sup>m</sup>* (14)

2*φ<sup>Q</sup>*

*<sup>φ</sup><sup>Q</sup>* � <sup>0</sup>*:*<sup>0000058</sup> *sin* <sup>2</sup>

*mGal* (15)

software of the GRAVSOFT package.

GRS80 normal gravity formula [16]:

three terrain correction methods.

*The statistics of the Bouguer anomalies.*

*<sup>γ</sup>*ð Þ¼ *<sup>Q</sup>* <sup>978032</sup>*:*7 1 <sup>þ</sup> <sup>0</sup>*:*<sup>0053024</sup> *sin* <sup>2</sup>

We further assumed that

**Figure 7.**

tation methods.

**Table 7.**

**54**

sets of Bouguer anomalies have been derived.

*The DTM (AREA\_2) and the points for TC computation.*

*Geodetic Sciences - Theory, Applications and Recent Developments*

*∂γ*

Three different methods for terrain correction have been compared in two areas over the Alps. The standard computation given by the TC-GRAVSOFT program has been compared with the terrain corrections evaluated via spherical tesseroid and flat tesseroid formulas. In the first test, the SRTM DTM was clipped in a 1° 1° window and *TC* effect was computed in a set of gridded points in the same area. In the second test, observed gravity values in a 1° 1° area have been used in the computation of Bouguer anomalies considering the 3° 3° SRTM DTM values centered on the area containing the gravity data. Despite the fact that the topography in the two selected DTM windows is quite rough, no significant differences among the methods have been revealed. The statistics of the values obtained by modeling in different ways the shape of the discretized topography elements are practically equivalent. Differences among *TC* effects and Bouguer anomalies computed with parallelepiped, spherical tesseroid and flat tesseroid amount to maximum values that are around 1 and 3 mGal respectively. As a matter of fact, there are other error sources (e.g., density heterogeneities, DTM and gravity point heights mismatch) that can have impacts on the terrain correction computation larger than 3 mGal. However, if in the second test on Bouguer computation we consider the values *per se*, spherical tesseroid and flat tesseroid models perform slightly better when RMS values are compared, i.e. the spherical tesseroid and flat tesseroid based Bouguer anomalies are smoother.

Finally, we remark that the concept applied in the flat tesseroid modeling can be adapted to the terrain effect computation when shaping the topography according to the Triangulated Irregular Network model [17]. In this way, a more detailed terrain effect evaluation will be possible, particularly in the neighbor of the computational points, by better modeling the terrain slopes.
