Document Type : Original Research Paper
Authors
Department of Surveying Engineering, Faculty of Civil Engineering, Shahid Rajaee Teacher Training University, Tehran, Iran
Abstract
Background and Objectives: Vertical Skewness is a prevalent anomaly in the field of geodetic science, which arises due to the displacement of the vertical component on the geoid at various locations. This discrepancy directly impacts both horizontal and vertical angles that are observed, and indirectly influences measurements of lengths. When considering the adjustment of length conversions to the horizon, this phenomenon is adequately represented by vertical angles. Consequently, vertical angles assume a significant role in ameliorating the effects of geoid updrafts and ensuring the precision of length determinations.
The occurrence of refraction exerts a substantial influence on observations of angles. This impact, particularly on the vertical angle, possesses a considerable magnitude that gives rise to a substantial discrepancy when adjusting the transformation of lengths to the horizon. A prevalent approach employed to mitigate the influence of refraction involves the simultaneous measurement of vertical angles in both directions at two distinct endpoints of equivalent distances.
Methods: There exist two primary categories of coordinate system commonly employed to express the positions of points in geodesy. These categories are known as the geocentric coordinate system, which centers on the Earth, and the topocentric coordinate system, which also centers on the Earth. In the geocentric coordinate system, the origin of the coordinates coincides with the Earth's center of gravity, and the z-axis is defined in alignment with the Earth's epoch axis. On the other hand, in the topocentric coordinate system, the origin of the coordinates corresponds to a specific point on the Earth's surface, namely the location of the camera. Furthermore, the z-axis in this coordinate system corresponds to the surface of the parallel potential passing over the aforementioned point where the camera is situated, also known as the line of work passing over the point.
Geodetic measurements of both horizontal and vertical angles are conducted within topocentric coordinate systems. As indicated, the prevailing technique for mitigating the impact of refraction on vertical angles involves simultaneously reading said angles from both the initial and terminal positions along the lengths. Given that the starting and ending points of the lengths exhibit dissimilar vertical extensions on the potential surface, the measurement of the vertical angle, and consequently the correction of the length's conversion to the horizon, are subjected to a significant degree of error.
Findings: The current investigation comprehensively examines this error and its consequential impacts on the horizontal spacing of points within small-scale geodesic networks. To achieve this objective, four specific regions in Sweden characterized by accurate geoids were meticulously chosen, and an elliptical procedure was implemented on the geoid of these regions to determine the parameters of the geoid surface. Furthermore, the geoid surface was computed.
Conclusion: The findings of this investigation demonstrate that the significance of the skewness of geoid gauges is evident even in geodetic networks of small-scales, and should not be disregarded. It is important to consider that the assessment of the magnitude of the skewness effect of geoid perpendiculars is only feasible in areas where a precise geoid is present. Consequently, it becomes unfeasible to entirely eliminate this effect when observing vertical angles simultaneously in areas lacking accurate geoids. Consequently, an alternative approach must be employed to rectify the conversion to the mile-long horizon. Further examination of this alternative method is presented in subsequent sections of this scholarly article.
Keywords
- Vertical Skewness
- Occurrence of Refraction
- Topocentric Coordinate System
- Geocentric Coordinate System
Main Subjects
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© 2024 The Author(s). This is an open-access article distributed under the terms and conditions of the Creative Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)
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