The Equivalent Source Method as an alternative tool for geoid modeling

M. E. GOMEZ; D. BAGÚ; D. DEL COGLIANO; R. PERDOMO; L. MENDOZA

Kiel

Congreso; 20 Lateinamerika Kolloquium der Geowisenschaften; 2007

Christian-Albrechts University

During the nineties geodetic networks were established in the Tierra del Fuego and Buenos Aires provinces. In both cases, they are materialized over the bench marks of the national altimetric network. This fact allowed to calculate geoid undulations and to build numerical models to transform ellipsoidal heights into orthometric heights. Particularly, for the case of Tierra del Fuego, besides geometric levelling, the Fagnano Lake was used like a level surface. This job was made in a joint effortwith the Dresden University (Technische Universität, Institut für Planetare Geodäsie). The result was a geoid model which differs fromEGM96 (Lemoine et al., 1998) and the EIGEN series (Reigber et al., 2005) in approximately 30 cm (standard deviation), and does not fitsuccessfully near the lake. This should be caused by a lack and bad distribution of information combined with global models deficiencies. In the same way, the observed geoid model for Buenos Aires province was compared with the global models previously mentioned. This showed a standard deviation of 15 cm for the EIGEN series and 24 cm withrespect to EGM96. In this region (Buenos Aires province) a height transformation model called FCAG98 (Perdomo & Del Cogliano,1999) was built taking into account about 200 observedgeoid undulations and their differences with EGM96. In the present decade several observation campaigns were carried out (Perdomo et al., 2002; Gomez et al., 2006; Bagú et al., 2006). With these new observations the FCAG98 model was tested and improved. The biggest differences between FCAG98 and new data were found in the north-west of Buenos Aires province and in Sierras de Tandil (a non flat region). In thefirst case (NW of the province), these differences were clearly due to the lack of data of the FCAG98 model. The inclusion of the new data improved significantly the knowledge of the geoid model behaviour in that region. In the case of the Sierras de Tandil (a moun-tainous region in the south of the province) it seems clear that there is not enough data, even including the recent campaigns, to solve theshort wavelengths satisfactorily. With the goal of solving this problem in this zone, a new study was done combining geometric undulations and gravimetric data by the Equivalent Source (ES) method (Del Cogliano, 2006). As it is well known, this technique consists in the computation of a set of point masses in order to reproduce gravitational field observ-ables, i.e. geoid heights, gravity anomalies and vertical deviations. While in Tandil zone the standard deviation of FCAG98 with respect to test data was about 10 cm, the deviation obtained adding gravity information and using ES to integrate it with the geometric undulations was considerably better (of the order of 3 cm). These results and the possibility to integrate easily different kind of data, makes the ES method an interesting tool to be applied in both regions (Tierra del Fuego and Buenos Aires). Considering the existence of gravity data in both regions, the new objective is to perform the integration of all the information to obtain improved geoid models. In a similar way, it will be very useful to add vertical deviation observations. A recent simulation(Guspí, 2004) has shown that to the level of accuracy of the present vertical deviation results, the use of ES to incorporate them to gravityand geometric undulations should produce excellent results. In this sense, a possible new field of cooperation between German and Argentine groups arises. The new digital zenith cameras (TZK 2D type), recently applied in Germany, has clearly shown the potential to get accurate vertical deviations in short time. It will be very interesting to apply this technique, not only in the regions described in this presentation, but in other projects related to vertical frames in South America.