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NEW ANALYTIC APPROACHES TO THE CONSTRUCTION OF A SPHERICAL HARMONIC GEOPOTENTIAL MODEL

NEW ANALYTIC APPROACHES TO THE CONSTRUCTION OF A SPHERICAL HARMONIC GEOPOTENTIAL MODEL. Sten Claessens and Will Featherstone Western Australian Centre for Geodesy Curtin University of Technology Perth, Australia. Dynamic Planet 2005, 25 August. Introduction.

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NEW ANALYTIC APPROACHES TO THE CONSTRUCTION OF A SPHERICAL HARMONIC GEOPOTENTIAL MODEL

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  1. NEW ANALYTIC APPROACHES TO THE CONSTRUCTION OF A SPHERICAL HARMONIC GEOPOTENTIAL MODEL Sten Claessens and Will Featherstone Western Australian Centre for Geodesy Curtin University of Technology Perth, Australia Dynamic Planet 2005, 25 August

  2. Introduction COMPUTATION OF GEOPOTENTIAL COEFFICIENTSFROM GRAVITY ANOMALIES (Block-Diagonal) Least Squares estimation Numerical Quadrature based on analytic solutions

  3. Introduction COMPUTATION OF GEOPOTENTIAL COEFFICIENTSFROM GRAVITY ANOMALIES (Block-Diagonal) Least Squares estimation  prone to aliasing effects in higher degrees Numerical Quadrature based on analytic solutions

  4. Introduction COMPUTATION OF GEOPOTENTIAL COEFFICIENTSFROM GRAVITY ANOMALIES • (Block-Diagonal) Least Squares estimation •  prone to aliasing effects in higher degrees • Numerical Quadrature based on analytic solutions • Ellipsoidal harmonics conversion (Jekeli) • Weighted summation over spherically approximated coefficients

  5. Analytic approaches (1/4) ellipsoid space domain

  6. Analytic approaches (1/4) ellipsoid space domain SHS frequency domain solid harmonics

  7. Analytic approaches (1/4) ellipsoid sphere space upward continuation domain SHS frequency domain solid harmonics

  8. Analytic approaches (1/4) ellipsoid sphere space upward continuation domain SHS SHA frequency domain solid harmonics

  9. Analytic approaches (1/4) ellipsoid sphere space upward continuation domain SHS SHA frequency domain solid harmonics

  10. Analytic approaches (2/4) ellipsoid sphere space upward continuation domain SHS ellipsoidal integration SHA frequency domain solid harmonics

  11. Analytic approaches (3/4) ellipsoid sphere space upward continuation domain SHA SHS ellipsoidal integration SHA frequency domain surface harmonics solid harmonics

  12. Analytic approaches (3/4) ellipsoid sphere space upward continuation domain SHA SHS ellipsoidal integration SHA frequency coefficient transformation domain surface harmonics solid harmonics

  13. Analytic approaches (4/4) COEFFICIENT TRANSFORMATION

  14. Analytic approaches (4/4) COEFFICIENT TRANSFORMATION

  15. Analytic approaches (4/4) COEFFICIENT TRANSFORMATION

  16. Analytic approaches (4/4) COEFFICIENT TRANSFORMATION

  17. Analytic approaches (4/4) COEFFICIENT TRANSFORMATION

  18. Analytic approaches (4/4) COEFFICIENT TRANSFORMATION

  19. Analytic approaches (4/4) COEFFICIENT TRANSFORMATION

  20. Analytic approaches (4/4) COEFFICIENT TRANSFORMATION

  21. Analytic approaches (4/4) COEFFICIENT TRANSFORMATION

  22. Analytic approaches (4/4) COEFFICIENT TRANSFORMATION

  23. Numerical comparison (1/3) Weights for zonal harmonics

  24. Numerical comparison (1/3) Weights for zonal harmonics

  25. Numerical comparison (1/3) Weights for zonal harmonics

  26. Numerical comparison (1/3) Weights for zonal harmonics

  27. Numerical comparison (1/3) Weights for zonal harmonics

  28. Numerical comparison (2/3)

  29. Numerical comparison (2/3)

  30. Numerical comparison (2/3)

  31. Numerical comparison (2/3)

  32. Numerical comparison (2/3)

  33. Numerical comparison (2/3)

  34. Numerical comparison (3/3) Geoid height errors – spherical approximation Min: -5.84m difference in geoid height (m) (n=20-360) Max: 7.85m

  35. Numerical comparison (3/3) Geoid height errors – Cruz/Sjöberg Min: -3.19m difference in geoid height (m) (n=20-360) Max: 2.60m

  36. Numerical comparison (3/3) Geoid height errors – Petrovskaya et al. Min: -0.65m difference in geoid height (m) (n=20-360) Max: 0.81m

  37. Numerical comparison (3/3) Geoid height errors – ellipsoidal integration Min: -0.065m difference in geoid height (m) (n=20-360) Max: 0.069m

  38. Numerical comparison (3/3) Geoid height errors – coefficient transformation Min: -0.0021m difference in geoid height (m) (n=20-360) Max: 0.0026m

  39. Numerical comparison (3/3) Geoid height errors – Jekeli Min: -0.00018m difference in geoid height (m) (n=20-360) Max: 0.00016m

  40. Summary and conclusions • Three methods for the computation of geopotential coefficients have been derived rigorously • The accuracy of these methods is significantly higher than existing methods • Numerical tests have shown that the Coefficient Transformation approach performs best, improving on Jekeli’s approach for coefficients of low order m

  41. Acknowledgements Thanks are extended to Dr. Simon Holmes of Raytheon ITSS, USA, for providing test data and Jekeli’s solution

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