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Determination of the geopotential and orthometric height based on frequency shift equation

Natural Science 2011年第5期3卷 388-396页

作者： Wenbin Shen Jinsheng Ning Jingnan Liu Jiancheng Li Dingbo Chao 不详

The orthometric height (OH) system plays a key role in geodesy, and it has broad applications in various fields and activities. Based on general relativity theory (GRT), on an arbitrary equi-geo- potential surface, there does not exist the gravity frequency shift of an electromagnetic wave signal. However, between arbitrary two different equi-geopotential surfaces, there exists the gra- vity frequency shift of the signal. The relationship between the geopotential difference and the gravity frequency shift between arbitrary two points P and Q is referred to as the gravity frequency shift equation. Based on this equation, one can determine the geopotential difference as well as the OH difference between two separated points P and Q either by using electromagnetic wave signals propagated between P and Q, or by using the Global Positioning System (GPS) satellite signals received simultaneously by receivers at P and Q. Suppose an emitter at P emits a signal with frequency f towards a receiver at Q, and the received frequency of the signal at Q is , or suppose an emitter on board a flying GPS satellite emits signals with frequency f towards two receivers at P and Q on ground, and the received frequencies of the signals at P and Q are and , respectively, then, the geopoten-tial dif- ference between these two points can be determined based on the geopotential frequen- cy shift equation, using either the gravity frequency shift ? f or ? , and the corresponding OH difference is further determined based on the Bruns’ formula. Besides, using this approach a unified world height datum system might be realized, because P and Q could be chosen quite arbitrarily, e.g., they are located on two separated continents or islands.

关键词： Equi-Frequency Geoid Gravity Frequency Shift Equation GPS Signal Geopotential orthometric Height World Height Datum System Unification

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Modelling orthometric Heights from a Combination of Ellipsoidal Heights and Gravimetric Geoid Model in Rivers State, Nigeria

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International Journal of Geosciences 2020年第4期11卷 184-196页

作者： Kurotamuno P. Jackson Elochukwu C. Moka Department of Surveying and Geomatics Rivers State University Port Harcourt Port Harcourt Nigeria Department of Geoinformatics and Surveying University of Nigeria Enugu Campus Enugu Nigeria

Many applications in geodesy, hydrography and engineering require geoid-related heights. Spirit leveling which is the traditional means of obtaining geoid- or mean sea level-related heights is slow, time-consuming and costly. Global Navigation Satellite Systems (GNSS) offer faster and relatively cheaper way of obtaining geoid-related heights when geoidal undulation is applied to ellipsoidal heights. However, difficulties involved in determining acceptable geoid height have seriously hampered the application of GNSS for leveling in Rivers State, thus necessitating the need to develop an acceptable geoid model which will serve as a means of conversion of GNSS-delivered ellipsoidal heights to their orthometric heights equivalent. In pursuance of this objective, a detailed gravimetric geoid has been evaluated for Rivers State, Nigeria. The computation of the geoid was carried out by the traditional remove-restore procedure. The Earth Geopotential Model 2008 (EGM08) was applied as the reference field for both the remove and restore parts of the procedures;spherical Fast Fourier Transform (FFT) was employed for the evaluation of the Molodenskii’s integral formula for the height anomaly, (ζ) to yield the quasi-geoid;while the Residual Terrain Modelling (RTM) was done by prism integration. The classical gravimetric geoid over Rivers State was obtained from the rigorously evaluated quasi-geoid by adding the quasi-geoid to geoid (N?- ζ) correction it. The minimum and maximum geoid height values are 18.599 m and 20.114 m respectively with standard deviation of 0.345 m across the study area. Comparison of the gravimetric geoidal heights with the GPS/Leveling-derived geoidal heights of 13 stations across Rivers State, Nigeria showed that the absolute agreement with respect to the GPS/leveling datum is generally better than 7 cm root mean squares (r.m.s) error. Results also showed that combining both GPS heights and the computed Rivers State geoid model can give orthometric heigh

关键词： Geoid Modelling Remove-Compute-Restore Fast Fourier Transform Residual Terrain Model Ellipsoidal Heights orthometric Heights

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Determination of geoid and elevation of the Mt. Qomolangma and discussion on the role of vertical gravity gradient

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Chinese Science Bulletin 1997年第20期42卷 1723-1725页

作者： ZHANG ChijunInstitute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China Institute of Geodesy and Geophysics Chinese Academy of Sciences Wuhan 430077 China

IT is known that the Mt. Qomolangma is the highest peak in the world. It was recorded in the'Map of Complete Territory of the Qin Dynasty' (published in 1717). As the highest peak,the Mt. Qomolangma not only provokes the interest of climbers but also arouses much atten-tion of geodesists. A significant cause is that the Mt. Qomolangma is located in the collisionbelt between the Indian Plate and the Eurasian Plate. According to the relative

关键词： geoid orthometric height the Mt. Qomolangma.

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Comparison of Different Height Systems

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Geo-Spatial Information Science 2008年第3期11卷 209-214页

作者： Nazan Yilmaz Department of Geodesy and Photogrammetry Engineering Karadeniz Technical University 61040 Trabzon Turkey.

Geopotential, dynamic, orthometric and normal height systems and the corrections related to these systems are evaluated in this paper. Along two different routes, with a length of about 5 kilometers, precise leveling and gravity measurements are done. One of the routes is in an even field while the other is in a rough field. The magnitudes of orthometric, normal and dynamic corrections are calculated for each route. orthometric, dynamic, and normal height differences are acquired by adding the corrections to the height differences obtained from geometric leveling. The magnitudes of the corrections between the two routes are compared. In addition, by subtracting orthometric, dynamic, and normal heights from geometric leveling, deviations of these heights from geometric leveling are counted.

关键词： geopotential dynamic orthometric normal ellipsoidal height gravity potential geoid

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