GNSS Geodesy Innovation Interviews UAV/UAS Positioning Surveying Applications Perspective Time Navigation Mapping Policy Land Administration News Archives LBS GIS SDI Imaging E-Zine
 Geodesy

# Measuring geopotential difference between two points

Dec 2005 | Comments Off on Measuring geopotential difference between two points

frequency shift. This is referred to as the equi-frequency geoid (Shen 1998). Now, suppose the light signal emitter E is located in a satellite, and two light signal receivers at P and Q receive the light signals coming from E corresponding to an emitting time t (Cf. Fig.2). Further suppose the received signals’ frequencies corresponding to time t are recorded by receivers at P and Q in some way, respectively, i.e., fP and fQ corresponding to time t are recorded by receivers at P and Q, respectively. Note that the time at which the signal is received by P is generally different from that by Q. By comparing the received frequencies fP and fQ it could be determined the geopotential difference ?WPQ = WQ – WP (Shen et al., 1993), which is just given by Eq. (1).

By the above mentioned way, the geopotential on the Earth’s whole surface could be determined based on the geopotential frequency shift approach by receiving the light signals emitted by satellites. Once the geopotential W on the Earth’s surface is determined, the potential field V outside the Earth could be determined, and as a result, the geoid could be more precisely determined.

The emitter could be a distant stable star. The receivers at P and Q could be designed in such a way that the received light signals might be recorded on diskettes at P and Q in details. Then, comparing the recorded diskettes at a centre process system. In this way, the frequency shift information between P and Q might be drawn out.

In the case that the emitter is located on the Earth’s surface, the potential difference between the two points P and Q could be also directly determined based on the same principle, as long as the the receivers at these two points could simultaneously receive the light signals emitted by the emitter.

It is noted that the accuracy for determining the potential difference by using the geopotential frequency shift approach is becoming more and more prospective for the goal of determining the centimeter-geoid, which is mainly depending on the frequency stability of the receiver. More than 10 years ago, the frequency stability was around 10-14, which is very poor for determining the geoid with an adequate accuracy. At present however, the frequency stability is around 10-15 – 10-16 (HMC Project 2005), which corresponds to the height variation about 1 m. In the next ten years, it is prospective that the frequency stability 10-17 – 10-18 could be achieved, which corresponds to the height variation 1cm.

The great advantage by using the geopotential frequency shift approach lies in that a uni?ed global datum system could be established: two receivers located at two datum points A and B which belong to two separated continents could simultaneously receive the signals emitted by a satellite source emitter, and consequently the frequency shift between A and B is determined; then, based on the geopotential frequency shift equation the geopotential difference between A and B is determined.

With satellite technique (e.g. CHAMP mission, Cf. Gerlach 2003), the potential on the satellite surface could be determined, and consequently it could be determined the Earth’s could be determined the Earth’s external potential field, which is quite accurate for the long and middle wave-length of the field, but not for the short wave-length of the field.

The will-be launched GOCE system could provide a 10 x 10 global gravity model with accuracy level around 1cm. However, concerning a single datum point A, the accuracy of the potential at A determined based on the global gravity model is far from centimeter level. To get more precise result, local measurements (gravimetry and leveling) are needed. Hence, with the goal of determining the global centimeter-geoid, the connections between different datum points located on different continents should be precisely established, which might be completed by geopotential frequency shift approach.

## Acknowledgements

This study is funded in parts by Natural Science Foundation China (No.40574004), and the Foundation of the Key Lab. of Geospace Environment and Geodesy, Ministry of Education China (03-04-13).

## References

Bjerhammar A (1985) A relativistic geodesy. Royal Institute of Technology, Geodesy Division, Stockholm. Gerlach Ch., Földvary L., Svehla D., Gruber Th., Wermuth M., Sneeuw N., Frommknecht B., Oberndorfer H., Peters Th., Rothacher M., Rummel R., Steigenberger P. (2003) A CHAMP-only gravity field model from kinematic orbits using the energy integral. Geophysical Research Letters 30(20), 2037. Heiskanen W.A., Moritz H. (1967) Physical Geodesy. Freeman and Company, San Francisco. HMC Project (2005) http://cfawww. harvard.edu/hmc/

Katila T., Riski Q. (1981) Measurement of the interaction between electromagnetic radiation and gravitational field using 67Zn Mössbauer spectroscopy. Physics Letters, 83A: 51-54.

Pound R.V., Snider J.L. (1965) Effect of gravity on gamma radiation. Physical Review, 140(3B): 788-803.

Rummel R., Sansó F., van Gelderen M., Brovelli M., Koop R., Miggliaccio
F., Schrama E., Sacerdote F. (1993)

Spherical harmonic analysis of satellite gradiometry. Netherlands Geodetic Commission, Publications on Geodesy, New Series No. 39

Shen W.B. (1998) Relativistic physical geodesy. Habilitation Thesis, Graz Technical University, Graz, Austria.

Shen W.B. (2004) The fictitious compress recuperation method for gravitational potential. Geomatics and Information Science of Wuhan University 29(8): 720-724

Shen W.B., Chao D.B., Jin B.R. (1993) On the relativistic geoid. Bollettino di Geodesia e Scienze Affini, 52: 207-216.

Vessot R.F.C., Levine M.W., Mattison E.M., Blomberg E.L., Hoffman T.E.,
Nystrom G.U., Farrel B.F., Decher R., Eby P.B., Baugher C.R., Watts J.W., Teuber D.L., Wills F.D. (1980) Test of relativistic gravitation with a
space-borne hydrogen maser. Physical Review Letters, 45: 2081-2084.

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