Abstract
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.
Highlights
The orthometric height (OH), the height above the geoid along the gravity plumb line, plays an important role in geodesy, and has broad applications in various fields
The OH is determined by leveling with additional gravimetry [1], due to the fact that the leveling goes along the equigeopotential surface, and the non-parallel influences of different equigeopotential surfaces should be considered based on the measured gravity data
To conquer the mentioned drawbacks in conventional approach, Bjerhammar (1985) put forward an idea to determine the OH based on the general relativity theory (GRT) [2]: the OH might be determined by precise clocks
Summary
The orthometric height (OH), the height above the geoid along the gravity plumb line, plays an important role in geodesy, and has broad applications in various fields. Since the clock approach is based on the comparisons between precise atomic clocks between two stations by clock transportation approach [3], it is seriously constrained in practical applications due to the fact that atomic clocks are very expensive for general use and very difficult to control the normal work condition during their transportation. Just due to this reason, Shen et al (1993) suggested that the OH could be determined by gravity frequency shift, which is re-. This paper is an extension of Shen et al (2008b) [7]
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