2. Geoid Enhancement in the Gulf Coast Region
Physical Geodesy & Real-Time Network Observations
Cliff Mugnier & Ahmed Abdalla
Louisiana State University Center for GeoInformatics

4. Gravity – the “old way” Gravity – the “olriGravity – the “old way” of doing things … ty – the “old way”

5. WILD Heerbrugg T-4 Astronomical Theodolite used for observing for Deflection of the Vertical & Position

6. WILD Heerbrugg BC-4 Ballistic Camera used for Photogrammetric Geodetic positioning (1960s)

7. KERN Aarau DKM-3A Astronomical Theodolite used for observing for Deflection of the Vertical & Positions

8. Kern DKM-3A Striding Level Sensitivity & Precision

9. Pencil & paper way of doing things … (including Deflection of the Vertical)

10. Absolute Gravity Meter (FG-5)

11. Relative Gravity Meters (Scintrex CG5 on Left, LaXoste & Romberg G-meter on Right)

12. Vista-2 Digital Zenith Camera (University of Latvia, Institute of Geodesy & GeoInformatics) Serial #1

13. University of Latvia Astrometric Software for Deflection of the Vertical (± 0.1”)

14. Why Physical Geodesy? Geoid definition Geoid determination
GNSS data analysis
University of Latvia Astrometric Software for Deflection of the Vertical (± 0.1”)

15. Why Physical Geodesy?
It is one of the oldest natural sciences that concerns with studies of the
Size of the Earth
Shape of the Earth
Gravity field of the Earth
To precisely determine positions of points on/near the Earth surface with well defined geodetic reference system
University of Latvia Astrometric Software for Deflection of the Vertical (± 0.1”)

16. Geoid A surface that has overall equal potentials
Closely represents the mean sea level (MSL)
Vertical height measurements are referred
Complicated figure (density variations)
Rises above and below the ellipsoid
The geoid is very important for datum connection
High quality GNSS data need a precise geoid model combination
Different computation methods
University of Latvia Astrometric Software for Deflection of the Vertical (± 0.1”)

17. Geoid computation (gravimetric)
Stokes formula
Using terrestrial gravity measurements
The above formula has been modified because of the truncation error
Two modifications methods (deterministic and Stochastic)
High and low frequency combination to reduce it
Global geopotential models (GGMS)
Remove-compute-restore (RCR
University of Latvia Astrometric Software for Deflection of the Vertical (± 0.1”)

18. Geoid computation Geometrical geoid Orthometric Height (Levelling)
Ellipsoidal Height
(GPS)
University of Latvia Astrometric Software for Deflection of the Vertical (± 0.1”)
Geoid Height
(Geoid)
N = h - H

19. Geoid computation (gravimetric)
Least-squares modifications and additive corrections (LSMA)
Least-squares Collocation (LCC)
Boundary Element Method (BEM)
Some other approximations like
Fast Fourier Transform (FFT)
Spherical basis radial functions (SRBFs)
University of Latvia Astrometric Software for Deflection of the Vertical (± 0.1”)

20. Louisiana’s gravity datasets
We use three datasets to improve the gravity field over Louisiana as seen below
Terrestrial gravity data (green)
Airborne gravity data (red)
Marine gravity data (dark blue)

21. Methodology
The free-air gravity anomalies are computed from the global geopotential model (GGM) using the following equation
where GM is the Earth’s gravitational constant , (n,m) are the d/o of the spherical harmonic expansion, R and r are the mean earth’s and the geocentric radii of the Earth, are the spherical harmonics coefficients, is the surface spherical harmonics function.
University of Latvia Astrometric Software for Deflection of the Vertical (± 0.1”)

22. Methodology
The topography effect (TE) based on Poisson’s kernel is computed as follows
where ρ denotes the crustal density of the Earth, the spherical distance between the computation point P and the running point Q.
University of Latvia Astrometric Software for Deflection of the Vertical (± 0.1”)

23. Remove-Restore ehchique
Removing the topography and far-zone effects using the topographic correction and the GGM
Performing cross-validation for gross-error detection. The outliers are eliminated based on the cut-off the prediction error.
Restoring the removed quantities in step one.
University of Latvia Astrometric Software for Deflection of the Vertical (± 0.1”)

24. Remove-Restore ehchique
Removing the topography and far-zone effects using the topographic correction and the global geopotential model (GGM)
Performing cross-validation for gross-error detection. The outliers are eliminated based on the cut-off the prediction error.
Restoring the removed quantities in step one.
University of Latvia Astrometric Software for Deflection of the Vertical (± 0.1”)

25. EGM2008 and XGM2016
STD [mGal]
University of Latvia Astrometric Software for Deflection of the Vertical (± 0.1”)

26. Topographic effect
DTM TE

27. Cross-Validation 5 12 10

28. EGM2008 Validation 5 10

29. Airborne Gravity data
CS03
CS02
CROSS-OVERS

30. Airborne Gravity data
CS02
CS03

31. Conclusions
A two-step procedure (remove-restore) is conducted for refining the datasets
The cross-validation technique was conducted and data quality was assessed at ±5 mGal. The cut-off tolerance for the EGM2008 validation against terrestrial and marine data is ±5 mGal and ±10 mGal, respectively.
Differences as large as a hundred uGals are detected on cross-overs in block CS03.