MEDIDA DE ALTURAS CON GPS (medida sobre el nivel del mar) V. Corchete* Departamento de Física Aplicada Escuela Politécni

1. MEDIDA DE ALTURAS CON GPS (medida sobre el nivel del mar) V. Corchete* Departamento de Física Aplicada Escuela Politécnica Superior – CITE II (A) UNIVERSIDAD DE ALMERÍA. 04120 ALMERIA superficie de la Tierra Problema. Con GPS medimos la altura h sobre el elipsoide de referencia no la altura H sobre el nivel del mar (Figura 1). Solución. Si conocemos el valor de N(la altura del nivel mar medida sobre el elipsoide de referencia) podemos calcular H como: H = hGPS - N Para obtener el valor de N usamos un modelo de geoide, pues ese modelo es justo la medida del nivel del mar sobre el elipsoide de referencia (Figuras 2 y 3). Así, un programa de ordenador calcula el valor de N, pudiendo entonces obtener H con sólo efectuar la resta anterior. H hGPS nivel del mar N elipsoide de referencia Fig. 1. Relación que existe entre la altura medida sobre el elipsoide (h) y la altura medida sobre el nivel del mar (H). MODELOS DE GEOIDE PARA EL ÁREA IBÉRICA Fig. 2. Representación del valor de N medido en metros (http://airy.ual.es/www/nibgeo_spanish.htm). Fig. 3. Representación del valor de N medido en metros (http://airy.ual.es/www/sosgis_spanish.htm). *e-mail: corchete@ual.es

2. The use of the gravimetric GEOid of TUNisia: GEOTUN V. Corchete*1, C. Jallouli2, M. Chourak3,4and N. Rebai2 1Higher Polytechnic School, University of Almeria, 04120 ALMERIA, Spain 2Faculté des Sciences de Tunis, University Tunis El Manar, TUNIS, Tunisia 3Faculté Polidisciplinaire d'Errachidia, University of Moulay Ismaïl, B.P. 509 BOUTALAMINE, Morocco 4NASG (North Africa Seismological Group) AECI The relation between orthometric height (H) and ellipsoidal (h) is the undulation of the geoid (N): H = h - N Surface of the Earth The use of the GPS for levelling requires a geoid model to get orthometric heights from ellipsoidal heights. GEOid model for TUNisia: GEOTUN A Surface of the Earth B H Geoid C h NA NB Ellipsoid HA = hA- NA DHBA = DhBA-DNBA HB = hB- NB DNBA = NB – NA 0 DHBADhBA Acknowledgements. The authors are grateful to the National Geophysical Data Center (NGDC), the Bureau Gravimetrique International (BGI) and the United States Geological Survey (USGS); who have provided the data used in this study. NGDC and USGS have supplied the elevation data required to compute the necessary terrain corrections, through the databases: ETOPO2 and SRTM 90M (available by FTP internet protocol). The Agency of International Cooperation (AECI, Spain) supported this research partially, through the project A/5830/06. *Corresponding author: Fax +34 950 015477; e-mail: corchete@ual.es

3. The first high-resolution gravimetric GEOid for TUNisia: GEOTUN V. Corchete*1, C. Jallouli2, M. Chourak3,4and N. Rebai2 1Higher Polytechnic School, University of Almeria, 04120 ALMERIA, Spain 2Faculté des Sciences de Tunis, University Tunis El Manar, TUNIS, Tunisia 3Faculté Polidisciplinaire d'Errachidia, University of Moulay Ismaïl, B.P. 509 BOUTALAMINE, Morocco 4NASG (North Africa Seismological Group) AECI Computation of the geoid We have followed the computation method detailed by Corchete et al. (2005) for the calculation of the gravimetric geoid shown in Figure 6. Following this method, a complete data set consisting of: free-air gravity anomalies, a geopotential model and a high precision DTM; is necessary. The gravity data used have been 8628 points, distributed over the study area as it is shown in the Figure 1. The EIGEN-GL04C model (Förste et al., 2006) represents a major advance in the modelling of the Earth’s gravity and geoid (Figure 2). Therefore, this geopotential model has been considered in this study. Any gravimetric geoid computation must use anomalies that have been reduced to the geoid. This involves the computation of the terrain correction (Figure 4) and the indirect effect (Figure 5) on the geoid, which are computed from a DTM (Figure 3). This DTM is based on the SRTM (Shuttler Radar Topography Mission) and ETOPO2. Figure 1. Gravity data. Figure 2. EIGEN-GL04C geoid. Figure 4. Terrain correction. Figure 5. Indirect effect. Acknowledgements. The authors are grateful to the National Geophysical Data Center (NGDC), the Bureau Gravimetrique International (BGI) and the United States Geological Survey (USGS); who have provided the data used in this study. NGDC and USGS have supplied the elevation data required to compute the necessary terrain corrections, through the databases: ETOPO2 and SRTM 90M (available by FTP internet protocol). The Agency of International Cooperation (AECI, Spain) supported this research partially, through the project A/5830/06. Figure 6. Gravimetric GEOid of TUNisia (GEOTUN). REFERENCES Corchete, V., M. Chourak and D. Khattach. The high-resolution gravimetric geoid of Iberia: IGG2005. Geophys. J. Int., 162, 676–684, 2005. Förste, C., F. Flechtner, R. Schmidt, R. König, U. Meyer, R. Stubenvoll, M. Rothacher, F. Barthelmes, H. Neumayer, R. Biancale, S. Bruinsma, J.-M. Lemoine and S. Loyer. A mean global gravity field model from the combination of satellite mission and altimetry/gravimetry surface data: EIGEN-GL04C. Geophysical Research Abstracts, Vol. 8, 03462, 2006. Figure 3. Digital Terrain Model (DTM). *Corresponding author: Fax +34 950 015477 e-mail: corchete@ual.es

4. Bouguer anomaly map of the Moroccan area V. Corchete*1, M. Chourak2,3 and D. Khattach4 1Higher Polytechnic School, University of Almeria, 04120 ALMERIA, Spain 2Faculté Polidisciplinaire d'Errachidia, University of Moulay Ismaïl, B.P. 509 BOUTALAMINE, Morocco 3NASG (North Africa Seismological Group) 4Faculté des Sciences, University of Mohamed I, OUJDA, Morocco AECI Computation of the Bouguer anomalies Since the gravity data set consisting of point data anomalies distributed randomly (Figure 1), we need to interpolate these data to obtain a regular data grid (Corchete et al. 2007). Before the interpolation, the short-wave effects that appear in the gravity anomaly field, associated to the short-wave topography and bathymetry, must be corrected (Corchete et al., 2005). Thus, we can compute a regular grid of free-air gravity data, as it is shown in Figure 3. When we have obtained the free-air gravity anomalies gridded, we can compute the Bouguer complete anomalies, as it shown in Figure 5, considering the terrain correction (Figure 4) previously obtained from a DTM of the study area (Figure 2). This DTM is based on the SRTM (Shuttler Radar Topography Mission) and ETOPO2. Figure 1. Gravity data. Figure 2. Digital terrain model (DTM). Figure 3. Free-air anomaly map. Figure 4. Terrain correction. Acknowledgements. The authors are grateful to the National Geophysical Data Center (NGDC), the Bureau Gravimetrique International (BGI) and the United States Geological Survey (USGS); who have provided the data used in this study. NGDC and USGS have supplied the elevation data required to compute the necessary terrain corrections, through the databases: ETOPO2 and SRTM 90M (available by FTP internet protocol). The Agency of International Cooperation (AECI, Spain) supported this research partially, through the project 4/04/P/E. Figure 5. Bouguer anomaly map of the Moroccan area. REFERENCES Corchete, V., M. Chourak and D. Khattach. The high-resolution gravimetric geoid of Iberia: IGG2005. Geophys. J. Int., 162, 676–684, 2005. Corchete, V., M. Chourak, D. Khattach and E. H. Benaim. The high-resolution gravimetric geoid of Morocco: MORGEO. Journal of African Earth Sciences, 48, 267-272, 2007. *Corresponding author: Fax +34 950 015477; e-mail: corchete@ual.es