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Data Fusion for Geoid Computation in Texas - Preliminary Results

This study explores methods for combining various gravity-related datasets to compute accurate geoid models in Texas. Preliminary results show promising outcomes, but further work is needed to refine parameters and validate the results against independent datasets.

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Data Fusion for Geoid Computation in Texas - Preliminary Results

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  1. Data fusion for geoid computation – numerical tests in Texas area(preliminary results) Yan Ming Wang & Xiaopeng Li National Geodetic Survey, NOAA, USA International Symposium on Gravity, Geoid and Height Systems October 9-12, 2012Venice, Italy

  2. Outline Objective of study Combination methods used Preliminary results Future work

  3. Objective of study Many types of gravity related data sets available today: - satellite gravity models (long wavelength) - Airborne gravity (medium wavelength) - Surface gravity (short wavelength) - High resolution digital elevation and density models (Ultra short wavelength) - Geopotential numbers from leveling (short wavelength) - Deflections of the vertical (short wavelength) Goal: To combine data in an optimal way (old topic, but a new challenge: can it reach 1 cm geoid accuracy?)

  4. Few words on the use of geopotential numbers C (1) The ellipsoidal height is NOT known at most historical leveling benchmarks, so that the disturbing potential can not be computed directly for all benchmarks To use the geopotential number C in determination of the gravity field, we compute initial disturbing potential as T0 = W0 – C – (U0 – γ0•h0) ≈ - C + γ0•h0 andh0 = H* + ζ = H + N

  5. Few words on the use of geopotential numbers C (2) Gravity anomaly can be computed from the geopotential numbers

  6. Combination methods(1) Over determined boundary values problems Least squares collocation Observation equation: l ... observation L … linear operator n … observation error The least squares solution:

  7. Combination methods(2) Use of harmonic (Eigen) functions Task: using observations l to determine coefficients . Solution in matrix form:

  8. Airborne and surface gravity Data

  9. Geopotential numbers The gravity anomaly dg can be computed from geopotential numbers as D(T0 )/Dh = g – γ0 = dg + (γ0 - γQ) γQnormal gravity on the telluroid.

  10. Empirical Covariance functions

  11. Residual gravity anomaly (LSC)

  12. Airborne Surface Air + Surface

  13. Residual disturbing potential

  14. Conclusions Surface data show rich high frequency of gravity field, but it shows also systematical difference from the airborne data. Airborne data is heavily smoother to remove high frequency dynamic errors. Preliminary results show the combination results are promising.

  15. Future Work Using truncated Stokes kernel to let satellite model controls the long wavelength Refine parameters used in both methods Include the geopotential numbers in the computations – if it helps to improve the solution Compare the results against independent data sets, such GSVS11 GPS/leveling data (1cm relative geoid accuracy along 300km line)

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