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

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.

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.

Cite this paper

Shen, W. , Ning, J. , Liu, J. , Li, J. and Chao, D. (2011) Determination of the geopotential and orthometric height based on frequency shift equation.*Natural Science*, **3**, 388-396. doi: 10.4236/ns.2011.35052.

Shen, W. , Ning, J. , Liu, J. , Li, J. and Chao, D. (2011) Determination of the geopotential and orthometric height based on frequency shift equation.

References

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[27] 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

[28] Pound, R. V. and Snider, J. R. (1965) Effect of gravity on gamma radiation. Physical Review, 140B, 788. doi:10.1103/PhysRev.140.B788

[29] 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.

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[31] 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

[32] 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

[33] 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.

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[37] Fischer, I. (1975) Does mean sea level slope or down toward north? Bulletin Geodesique, 49, 17. doi:10.1007/BF02523939

[38] Rapp, R. H. (1988) The geoid definition and determination. OSU Rep. 325.

[39] Torge, W. (1989) Gravimetry. Walfer de Cruyter, Berlin, New York.

[40] Vanicek, P. and Krakiwsky, E. (1986) Geodesy: The concepts. 2nd Edition, North-Holland Pub. Co., Amsterdam.

[41] Rapp, R. H. and Balasubramania, X. (1992) A conceptual formulation of a world height system. OSU Rep. No. 421.

[42] WGS84. http://en.wikipedia.org/wiki/World_Geodetic_System

[43] Grafarend, E. W. (1994) What is a geoid? In: Vani?cek P, Christou N T (eds), Geoid and Its Geophysical Interpretations, CRC Press, London.

[44] Misner, C. W., Thorne, K. S. and Wheeler, J. A. (1973) Gravitation. Freeman and Company, San Francisco.

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[46] 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

[1] Heiskanen, W. A. and Moritz, H. (1967) Physical geodesy. Freeman and Company, San Francisco.

[2] Bjerhammar, A. (1985) On a relativistic geodesy. Bulletin Geodesique, 59, 207-220. doi:10.1007/BF02520327

[3] 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

[4] Shen, W. B., Chao, D. and Jin, B. (1993) On the relativistic geoid. Bollettino di geodesia e scienze affini, 52, 207-216.

[5] 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

[6] Shen, W. B., Ning, J. and Chao, D. (2008a) Relativity and relativistic gravimetry. Wuhan University Press, Wuhan.

[7] 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.

[8] Moritz, H. (2000) Molodensky’s theory and GPS. Mitteil. Geod. Graz Technology University. Graz.

[9] Shen, W. B. (1996) On the separability of gravitation and inertia according to general relativity. Dissertation. Graz Technical University, Graz.

[10] Shen, W. B. (1998) Relativistic physical geodesy. Graz Technical University, Graz.

[11] Soffel, M. H. (1989) Relativity in astrometry, celestial mechanics and geodesy. Springer-Verlag, Berlin.

[12] Weinberg, S. (1972) Gravitation and cosmology. John Wiley & Sons, New York.

[13] 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.

[14] 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.

[15] Bjerhammar, A. (1986) Relativistic geodesy. NOAA Technical Report NOS 118 NGS 36, Rockville,.

[16] 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.

[17] 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.

[18] 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

[19] 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

[20] 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

[21] 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

[22] 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

[23] 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

[24] 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

[25] 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

[26] 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

[27] 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

[28] Pound, R. V. and Snider, J. R. (1965) Effect of gravity on gamma radiation. Physical Review, 140B, 788. doi:10.1103/PhysRev.140.B788

[29] 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.

[30] 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.

[31] 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

[32] 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

[33] 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.

[34] 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.

[35] Sturges, W. (1974) Sea level slope along continental boundaries. Journal of Geophysical Research, 79, 825. doi:10.1029/JC079i006p00825

[36] 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

[37] Fischer, I. (1975) Does mean sea level slope or down toward north? Bulletin Geodesique, 49, 17. doi:10.1007/BF02523939

[38] Rapp, R. H. (1988) The geoid definition and determination. OSU Rep. 325.

[39] Torge, W. (1989) Gravimetry. Walfer de Cruyter, Berlin, New York.

[40] Vanicek, P. and Krakiwsky, E. (1986) Geodesy: The concepts. 2nd Edition, North-Holland Pub. Co., Amsterdam.

[41] Rapp, R. H. and Balasubramania, X. (1992) A conceptual formulation of a world height system. OSU Rep. No. 421.

[42] WGS84. http://en.wikipedia.org/wiki/World_Geodetic_System

[43] Grafarend, E. W. (1994) What is a geoid? In: Vani?cek P, Christou N T (eds), Geoid and Its Geophysical Interpretations, CRC Press, London.

[44] Misner, C. W., Thorne, K. S. and Wheeler, J. A. (1973) Gravitation. Freeman and Company, San Francisco.

[45] Will, C. M. (1993) Theory and experiment in gravitational physics. Cambridge University Press, Cambridge.

[46] 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