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.
KeywordsEqui-Frequency GeoidGravity Frequency Shift EquationGPS SignalGeopotentialOrthometric HeightWorld Height Datum System Unification
Heiskanen, W. A. and Moritz, H. (1967) Physical geodesy. Freeman and Company, San Francisco.
Bjerhammar, A. (1985) On a relativistic geodesy. Bulletin Geodesique, 59, 207-220. doi:10.1007/BF02520327
Shen, W. B., Ning, J. S., Liu, J. N. and Chao, D. B. (2009) A proposal on the test of general relativity by clock transportation experiments. Advances in Space Research, 43, 164-166. doi:10.1016/j.asr.2008.04.001
Shen, W. B., Chao, D. and Jin, B. (1993) On the relativistic geoid. Bollettino di geodesia e scienze affini, 52, 207-216.
Shen, W. B. and Ning, J. (2005) The application of GPS technique in determining the Earth’s potential field. J. GPS, 4, 268-276 doi:10.5081/jgps.4.1.268
Shen, W. B., Ning, J. and Chao, D. (2008a) Relativity and relativistic gravimetry. Wuhan University Press, Wuhan.
Shen, W. B., Ning, J. S., Li, J. C., Liu, J. N. and Chao, D. B. (2008b) The concept of direct orthometric height determination based on frequency shift equation. International Conference on Earth Observation Data Processing and Analysis, 29 December 2008, 1-8.
Moritz, H. (2000) Molodensky’s theory and GPS. Mitteil. Geod. Graz Technology University. Graz.
Shen, W. B. (1996) On the separability of gravitation and inertia according to general relativity. Dissertation. Graz Technical University, Graz.
Shen, W. B. (1998) Relativistic physical geodesy. Graz Technical University, Graz.
Soffel, M. H. (1989) Relativity in astrometry, celestial mechanics and geodesy. Springer-Verlag, Berlin.
Weinberg, S. (1972) Gravitation and cosmology. John Wiley & Sons, New York.
Soffel, M. H., Herold, H., Ruder, H. and Schneider, M. (1988) Relativistic geodesy: The concept of asymptotically fixed reference frames. Manu. Geod., 13, 139-142.
Soffel, M. H., Herold, H., Ruder, H. and Schneider, M. (1988b) Relativistic theory of gravimetric measurements and definition of the geoid. Manu. Geod., 13, 143-146.
Bjerhammar, A. (1986) Relativistic geodesy. NOAA Technical Report NOS 118 NGS 36, Rockville,.
Shen, W. B., Chao, D. and Jin, B. (1994) The concept and application of the equi-frequency geoid. Journal of Wuhan Technical University, 19, 232-238.
Shen, W. B., Ning, J., Li, J. and Chao, D. (2004) On the relativistic geopotential and relativistic geoid. Journal of Wuhan University (Information Science), 29, 897-900.
Hanson, D. W. (1989) Fundamentals of two-way time transfer by satellite. 43rd Annual Frequency Control Symposium, 31 May - 2 June 1989, pp. 174-178. doi:10.1109/FREQ.1989.68861
Heavner, T. P., Jefferts, S. R., Donley, E. A., et al. (2005a) NIST-F1: Recent improvements and accuracy evaluations. Metrologia, 42, 411-422. doi:10.1088/0026-1394/42/5/012
Heavner, T. P., Jefferts, S. R., Donley, E. A., et al. (2005b) Recent improvements in NIST-F1 and a resulting accuracy of 0.61 × 10?15. IEEE Transactions on Instrumentation and Measurement, 54, 842-845. doi:10.1109/TIM.2005.843812
Parker, T. E., Heavner, T. P., Jefferts, S. R., et al. (2005) Operation of the NIST-F1 caesium fountain primary frequency standard with a maser ensemble, including the impact of frequency transfer noise. Metrologia, 42, 423- 430. doi:10.1088/0026-1394/42/5/013
Jones, D. J. (2000) Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis. Science, 288, 635-638. doi:10.1126/science.288.5466.635
Reichert, J., Niering, M. and Holzwarth, R. (2000) Phase coherent vacuum-ultraviolet to radio frequency comparison with a mode-locked laser. Physical Review Letters, 84, 3232-3235. doi:10.1103/PhysRevLett.84.3232
Diddams, S. A., Jones, D. J., Ye, J., et al. (2000) Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb. Physical Review Letters, 84, 5102-5105. doi:10.1103/PhysRevLett.84.5102
Diddams, S. A., Udem, T., Bergquist, J. C., et al. (2001) An optical clock based on a single trapped 199Hg+ ion. Science, 293, 825-828. doi:10.1126/science.1061171
Ye, J., Tai, H. Y. and John, L. H. (2000) Accuracy comparison of absolute optical frequency measurement between harmonic-generation synthesis and a frequency- division femtosecond comb. Physical Review Letters, 85, 3797-3800. doi:10.1103/PhysRevLett.85.3797
Ma, L., Bi, Z., Bartels, A., et al. (2004) Optical frequency synthesis and comparison with uncertainty at the 10?19 level. Science, 303, 1843-1845. doi:10.1126/science.1095092
Pound, R. V. and Snider, J. R. (1965) Effect of gravity on gamma radiation. Physical Review, 140B, 788. doi:10.1103/PhysRev.140.B788
Vessot, R. F. C., Levine, M. W., Mattison, E. M., et al. (1980) Test of relativistic gravitation with a space-borne hydrogen maser. Physical Review Letters, 45, 2081-2084.
Katila, T. and Riski, K. J. (1981) Measurement of the interaction between electromagnetic radiation and gravitational field using Zn67 M?ssbauer spectroscopy. Physics Letters, 83A, 51-54.
Turneaure, J. P., Will, C. M., Farrel, B. F., et al. (1983) Test of principle of equivalence by a null gravitational red-shift experiment. Physical Review D, 27, 1705-1714. doi:10.1103/PhysRevD.27.1705
Bauch, A. and Weyers, S. (2002) New experimental limit on the validity of local position invariance. Physical Review D, 65, Article ID R081101. doi:10.1103/PhysRevD.65.081101
Chao, D., Shen, W. B. and Wang, Z. (2007) The possibility and method investigations on the determination of the global centimeter level geoid. Acta Geodaetica et Cartographica Sinica, 36, 370-376.
Sturges, W. (1972) Comments on ocean circulation with regard to satellite altimetry. Sea Surface Topography from Space, Vol. 2, Tech. Rep. ERL228- AOML7 -2, The National Oceanic and Atmospheric Administration, Boulder.
Sturges, W. (1974) Sea level slope along continental boundaries. Journal of Geophysical Research, 79, 825. doi:10.1029/JC079i006p00825
Hamon, B. V. and Greig, M. A. (1972) Mean sea level in relation to geodetic land leveling around Australia. Journal of Geophysical Research, 77, 7157. doi:10.1029/JC077i036p07157
Fischer, I. (1975) Does mean sea level slope or down toward north? Bulletin Geodesique, 49, 17. doi:10.1007/BF02523939
Rapp, R. H. (1988) The geoid definition and determination. OSU Rep. 325.
Torge, W. (1989) Gravimetry. Walfer de Cruyter, Berlin, New York.
Vanicek, P. and Krakiwsky, E. (1986) Geodesy: The concepts. 2nd Edition, North-Holland Pub. Co., Amsterdam.
Rapp, R. H. and Balasubramania, X. (1992) A conceptual formulation of a world height system. OSU Rep. No. 421.
Grafarend, E. W. (1994) What is a geoid? In: Vani?cek P, Christou N T (eds), Geoid and Its Geophysical Interpretations, CRC Press, London.
Misner, C. W., Thorne, K. S. and Wheeler, J. A. (1973) Gravitation. Freeman and Company, San Francisco.
Will, C. M. (1993) Theory and experiment in gravitational physics. Cambridge University Press, Cambridge.
Brumberg, V. A. and Groten, E. (2002) On determination of height by using terrestrial clocks and GPS signals. Journal of Geodesy, 76, 49-54. doi:10.1007/s001900100219