Advertisement

Bulletin géodésique

, Volume 64, Issue 3, pp 231–246 | Cite as

The effect of topography on the determination of the geoid using analytical downward continuation

  • Y. M. Wang
Article

Abstract

The method of analytical downward continuation has been used for solving Molodensky’s problem. This method can also be used to reduce the surface free air anomaly to the ellipsoid for the determination of the coefficients of the spherical harmonic expansion of the geopotential. In the reduction of airborne or satellite gradiometry data, if the sea level is chosen as reference surface, we will encounter the problem of the analytical downward continuation of the disturbing potential into the earth, too. The goal of this paper is to find out the topographic effect of solving Stoke’sboundary value problem (determination of the geoid) by using the method of analytical downward continuation.

It is shown that the disturbing potential obtained by using the analytical downward continuation is different from the true disturbing potential on the sea level mostly by a −2πGρh 2/p. This correction is important and it is very easy to compute and add to the final results. A terrain effect (effect of the topography from the Bouguer plate) is found to be much smaller than the correction of the Bouguer plate and can be neglected in most cases.

It is also shown that the geoid determined by using the Helmert’s second condensation (including the indirect effect) and using the analytical downward continuation procedure (including the topographic effect) are identical. They are different procedures and may be used in different environments, e.g., the analytical downward continuation procedure is also more convenient for processing the aerial gravity gradient data.

A numerical test was completed in a rough mountain area, 35°<ϕ<38°, 240°<λ<243°. A digital height model in 30″×30″ point value was used. The test indicated that the terrain effect in the test area has theRMS value ±0.2−0.3 cm for geoid. The topographic effect on the deflections of the vertical is around1 arc second.

Keywords

Gravity Anomaly Topographic Effect Spherical Harmonic Expansion Geoid Undulation Terrain Correction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. W.A. HEISKANEN and H. MORITZ: Physical Geodesy. W.H. Freeman, San Francisco, 1967.Google Scholar
  2. H. MORITZ: Linear Solutions of the Geodetic Boundary-value Problem. Report No. 79, Department of Geodetic Science and Surveying, The Ohio State University, Columbus, 1966.Google Scholar
  3. H. MORITZ: On the Use of the Terrain Correction in Solving Molodensky’s Problem. Report No. 108, Dept. of Geodetic Science and Surveying, The Ohio State University, 1968.Google Scholar
  4. H. MORITZ: Advanced Physical Geodesy. Herbert Wichmann Verlag, Karlsruhe, Abacus Press, Tunbrige, Wells, Kent, 1980.Google Scholar
  5. R.H. RAPP: The Determination of High Degree Potential Coefficient Expansions from the Combination of Satellite and Terrestrial Gravity Information. Report No. 361, Dept. of Geodetic Science and Surveying, The Ohio State University, 1984.Google Scholar
  6. R.H. RAPP and J.Y. CRUZ: The Representation of the Earth’s Gravitational Potential in a Spherical Harmonic Expansion to Degree 250. Report No. 372, Department of Geodetic Science and Surveying, The Ohio State University, 1986.Google Scholar
  7. Y.M. WANG: Downward Continuation of the Free-Air Gravity Anomalies to the Ellipsoid Using the Gradient Solution, Poisson’s Integral and Terrain Correction—Numerical Comparison and the Computation. Report No. 393, Dept. of Geodetic Science and Surveying, The Ohio State University, 1988.Google Scholar
  8. Y.M. WANG and R.H. RAPP: Terrain Effects on Geoid Undulation Computation. Manuscripta geodaetica, 15, 1, 1990.Google Scholar
  9. C. WICHIENCHAROEN: The Indirect Effect on the Computation of Geoid Undulations. Report No. 336, Dept. of Geodetic Science and Surveying, The Ohio State University, 1982.Google Scholar

Copyright information

© Bureau Central de L’Association Internationale de Géodésie 1990

Authors and Affiliations

  • Y. M. Wang
    • 1
  1. 1.Department of Geodetic Science and SurveyingThe Ohio State UniversityOhioUSA

Personalised recommendations