Geoid Enhancement in the Gulf Coast Region

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Presentation transcript:

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

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

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

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

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

Kern DKM-3A Striding Level Sensitivity & Precision

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

Absolute Gravity Meter (FG-5)

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

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

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

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

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”)

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”)

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”)

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

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”)

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)

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”)

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”)

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”)

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”)

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

Topographic effect DTM TE

Cross-Validation 5 12 10

EGM2008 Validation 5 10

Airborne Gravity data CS03 CS02 CROSS-OVERS

Airborne Gravity data CS02 CS03

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.