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The cost of assuming a lateral density distribution in corrections to Helmert orthometric heights

The cost of assuming a lateral density distribution in corrections to Helmert orthometric heights. 1 Department of Geodesy and Geomatics Engineering, University of New Brunswick, Fredericton, New Brunswick E3B 5A3. Robert Kingdon 1 , Artu Ellmann 1 , Petr Vanicek 1 , Marcelo Santos 1.

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The cost of assuming a lateral density distribution in corrections to Helmert orthometric heights

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  1. The cost of assuming a lateral density distribution in corrections to Helmert orthometric heights 1Department of Geodesy and Geomatics Engineering, University of New Brunswick, Fredericton, New Brunswick E3B 5A3 Robert Kingdon1, Artu Ellmann1, Petr Vanicek1, Marcelo Santos1 AGU Joint Assembly / May 23-26, 2006

  2. Orthometric Height Bouguer Shell Terrain Plumbline Geoid AGU Joint Assembly / May 23-26, 2006

  3. Evaluating Mean Gravity e.g. Helmert’s method: Surface Gravity Corrective Terms (for Bouguer plate and normal gravity) Converting Helmert mean gravity to rigorous mean gravity: Additional Corrective Terms Each correction takes the form: Corrections may be made for topographical or non-topographical masses. We will only discuss corrections for topographical effects. AGU Joint Assembly / May 23-26, 2006

  4. Models of Topography Terrain + Bouguer Plate/Shell Bouguer Plate/Shell (used by Helmert) Real Topodensity Distribution 3D Density Distribution (more rigorous corrections?) 2D Density Distribution (used for rigorous corrections) AGU Joint Assembly / May 23-26, 2006

  5. Shortcomings of the 2D Density Model Rigorous with 3D Density Distribution Rigorous with 2D Density Distribution Residual Anomalous Density AGU Joint Assembly / May 23-26, 2006

  6. Additional Correction Accounting for 3D Density Distribution AGU Joint Assembly / May 23-26, 2006

  7. Test Area Test area: 50° to 51° N latitude, and 236° to 237° E longitude. Heights from 0 (green) to 2862 (white) m. AGU Joint Assembly / May 23-26, 2006

  8. Simulation B1 Cone Values from 0 (red) to 5.7 (blue) cm, 1 cm contours. AGU Joint Assembly / May 23-26, 2006

  9. Simulation B2 Slab Values from 0 (red) to 6.9 (blue) cm, 1 cm contours. AGU Joint Assembly / May 23-26, 2006

  10. Simulation B3 Wedge Values from 0 (red) to 7.9 (blue) cm, 1 cm contours. AGU Joint Assembly / May 23-26, 2006

  11. Simulation A1 θ=45° Values from -1.2 (green) to 1.2 (red) cm, 1 cm contours. AGU Joint Assembly / May 23-26, 2006

  12. Simulation A2 θ=30° Values from -1.7 (green) to 1.6 (red) cm, 1 cm contours. AGU Joint Assembly / May 23-26, 2006

  13. Simulation A3 θ=15° Values from -2.3 (green) to 2.6 (red) cm, 1 cm contours. AGU Joint Assembly / May 23-26, 2006

  14. Summary of Results AGU Joint Assembly / May 23-26, 2006

  15. Conclusions – Shortcomings are largest for regional phenomena. – Shortcomings are only significant close to their source. – More realistic estimates of shortcomings reach up to ~3 cm, but are only > 1 cm (in the test area) at elevations above ~1500 m. – There do exist limited areas where these shortcomings may be significant, in terms of rigorous orthometric heights. Effects on e.g. geoid heights have yet to be evaluated. AGU Joint Assembly / May 23-26, 2006

  16. Acknowledgements We would like to acknowledge NSERC and for their funding of this research. AGU Joint Assembly / May 23-26, 2006

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