Scientific Research and Essay Vol.4 (12), pp. 1438-1444, December, 2009 Available online at http://www.academicjournals.org/SRE ISSN 1992-2248 © 2009 Academic Journals Full Length Research Paper Determination of the deflection of vertical components via GPS and leveling measurement: A case study of a GPS test network in Konya, Turkey Ayhan Ceylan Selcuk University, Faculty of Engineering and Architecture, Department of Geomatic Engineering, Konya, Turkey. E- mail: [email protected]. Accepted 20 October, 2009 Deflection of the vertical is used in reducing geodetic measurements related to geoid networks (vertical and horizontal directions observations and length measurement, etc.) to ellipsoid plane and in geoid modeling processes. Generally, it is obtained by Astro-Geodetic and gravimetric techniques. These techniques are very complex and time-consuming. Ellipsoidal coordinates of points are easily obtained thanks to the widespread use of Satellite Positioning Techniques (GNNS) such as GPS in geodesy. When the orthometric heights of points are determined via geometric leveling, geoid height differences and deflection of the vertical components can be measured faster and much more easily by using GPS and leveling measurements than the other techniques. This study discusses the calculation of the deflection of vertical components via GPS and leveling measurements. The deflection of the vertical components obtained from GPS and leveling measurements were compared with global (EGM96 and CG03C) and local (TG03) geoid models. Deflection of the vertical components (north-south) and (east-west) were calculated as = -4.15” ± 0.61”, = 8.75” ± 0.69” via a GPS and leveling model; as = -5.64”, = 1.95” via the EGM96 geoid model; as = -4.85”, = 1.82” via the CG03C geoid model; as = -7.47”, = -0.51” via the TG03 model; and as = -3.9”, = 4.6” via Astro-Geodetic deflection of a vertical map of Turkey produced by Ayan (1976). When the values obtained from GPS and leveling measurements were compared with the values produced by the other techniques, the north-south component was found to be approximately consistent, while east-west component differed to same extent. Since very little data on the terrestrial gravity of Turkey was present in the EGM96 and CG03C global geoid models, it was not anticipated that the results obtained via these models would be comparable with other methods. Key words: Deflection of the vertical, deflection of the vertical components, GPS/Leveling, EGM96, CG03C. INTRODUCTION Since the physical earth has a highly complex surface, defined in mathematical terms. In country measurements, measurements typically substitute simpler surfaces, in the geodetic coordinates of points are calculated on an order to facilitate the evaluation of measurements and ellipsoid converging to the shape and size of the making of calculations. These surfaces are ellipsoid measurement area. On the other hand, measurements surfaces, which are defined in geometric terms and geoid made of the physical earth surface by using surfaces, which are defined in physical terms and measurement tools are related to the actual leveling constitute one of the equapotential leveling surfaces. A surface passing though the point and the plumb line geoid is a sea-level surface with homogenous gravity direction. An ellipsoid is a simple surface, defined in potential and is always vertical to the direction of the geometric terms. Although an ellipsoid is designed as a plumb line. It is a part of the leveling surface, which surface converging to a geoid, these two surfaces do not passes partially through the solid earth surface. The overlap. The difference between the two surfaces is curvature of this surface exhibits discontinuity in the called geoid height, symbolized by the letter N. As well as places where density changes suddenly. Therefore, this mapping purposes, practical problems (for instance, the is not a simple analytical surface which can be easily direction of water flow) require geoid knowledge. The Ceylan 1439 position of the geoid in relation to the reference surface other hand, local geoid models vary, depending on the can be determined via not only geoid height but also geodetic data resources of the country they are used in. “deflection of the vertical” that can be converted in both For regions with no gravity information, the orthometric directions. Geoid height and deflection of the vertical are heights obtained via geometric leveling and the ellipsoidal two components of disturbed gravity fields. heights obtained via GPS can be used in combination. In Deflection of the vertical is defined as the angle previous studies carried out by Soler et al. (1989); between the geodetic zenith direction of a point and the Vandenberg (1999); Magilevsky and Melzer (1994); Acar local astronomical zenith direction (Gürkan, 1979). and Turgut (2005); Tse and Iz (2006) and Akkul (2007), it Deflection of the vertical is an important parameter of the was shown that traditional measurement techniques and local gravity field; it is therefore used in various fields, new measurement techniques can be used in including the following: combination to calculate the deflection of the vertical components. The present study aimed to determine (1) Transformation of astronomical coordinates into geo- whether or not deflection of the vertical components of an detic coordinates. existing Leveling Network, in the Konya Province of (2) Transformation of astronomical azimuth into geodetic Turkey, could be calculated via GPS measurements and azimuth. geometric leveling measurements. Konya province is a (3) Reduction of horizontal and vertical angles to a rich application area in terms of the large amount of spheroid (ellipsoid surface). leveling and GPS heights data produced by many (4) Net calculations of geodetic networks: positioning of previous studies and the potential to therefore calculate geodetic theodolites and leveling instruments according deflection of the vertical components using these data. to the real vertical. This study also aimed to introduce the techniques used (5) Geoid detection: Current, high-level global geo- in the calculation of the deflection of vertical components potential models have reached a level where they can be and to compare the deflection of the vertical components used in local applications. Geoid heights and deflection of obtained via GPS/leveling in a selected test network with the vertical components (, ) can be calculated at a the values obtained via global geoid models (EGM96 and specific level of accuracy, depending on the local capa- CG03C) and a local geoid (TG03) model. cities of the model (whether or not it includes gravimetric data). (6) Transformation from ellipsoidal heights to local Deflection of the vertical (orthometric, normal) height systems: Satellite measure- ments are based on a geometric reference ellipsoid Deflection of the vertical is the angular difference (WGS-84). However, continental heights are related to between the real plumb line direction and the normal to a geoid. Since heights from the sea-level are preferred in surface (that is, “mathematical plumb line direction”) of a practice, ellipsoidal heights have to be converted into reference surface (Figure 1). Deflection of the vertical has geoid-based height systems. two dimensions: north-south () and east-west () (Figure (7) Geophysics studies: Deflection of the vertical and 1). geoid heights are directly affected by the mass (density) distribution of the earth. Geodesists try to model the earth surface, while applied geophysicists use such data in Calculation of deflection of the vertical components exploration for crude oil, natural gas and mineral ores via GPS and geometric leveling (Acar, 1999; Turgut and Acar, 2005). (8) Deflection of the vertical (generally defined in terms of The relationship between geoid height and deflection of two components: north-south and east-west direction) is the vertical is presented in Figure 2. obtained via astro-geodetic and gravimetric techniques. The differential relationship between geoid height and Astro-geodetic technique adopts astronomical coordi- deflection of the vertical is defined through the following nates (, ) and geodetic coordinates (, ) while formulae (Heiskanen and Moritz, 1984): gravimetric technique is based on Stokes formula, using abnormalities of the earth’s gravitational field as the input dN = −ε.ds (1) data (Ayan, 1978; Arslan and Yılmaz, 2005). Or dN In addition to the two techniques mentioned above, global ε = − (2) geo-potential and local gravimetric models, as well as ds combined techniques (GPS-Leveling, GPS-Gravimetric etc.), can be used to obtain such figures. Global geoid Deflection of the vertical on any geodetic azimuth () models, such as CG03C and EGM96, are developed by direction can be calculated as follows, by using north- using the gravitational information of the whole world. south and east-west components: Geoid heights can be calculated by using the potential harmonic coefficients of the global geoid models. On the ε = ξ.cos α + η.sin α (3) 1440 Sci. Res. Essays Figure 1. Deflection of the vertical and its components (Üstün, 2006). Figure 2. Relationship between geoid height and deflection of the vertical (Heiskanen and Moritz, 1984). When formulae (2) and (3) are combined, following result When the differential elements in formula (4) are replaced is obtained; by the difference values obtained in geodetic measure- ments, the result will be as follows; dN ∆N − = ξ.cos