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Gravimetric Geoid

Gravimetric Geoid

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The gravimetric geoid is a model of the Earth's gravitational field that represents mean sea level as an equipotential surface. It is derived from gravity measurements and is used in geodesy to determine precise elevations and to study variations in the Earth's gravitational field.
lightbulbAbout this topic
The gravimetric geoid is a model of the Earth's gravitational field that represents mean sea level as an equipotential surface. It is derived from gravity measurements and is used in geodesy to determine precise elevations and to study variations in the Earth's gravitational field.

Key research themes

1. How can Global Geopotential Models be optimized and validated for accurate regional gravimetric geoid modeling?

This theme explores the enhancement, selection, and validation of global geopotential models (GGMs) such as GOCE-based models, EGM2008, and combined satellite-terrestrial data models, specifically in their application for regional gravimetric geoid determination. It addresses the importance of integrating satellite gravity missions with local data to improve medium and long wavelength components of the gravity field, and how model performance validation is carried out using terrestrial gravity and GPS/leveling datasets.

Improvement of GOCE-Based Global Geopotential Models for Gravimetric Geoid Modeling in Turkey
by Bihter Erol

2023, Geosciences

Key finding: Demonstrates that GOCE satellite missions significantly enhance the medium wavelength components of gravity field models, improving regional gravimetric geoid accuracy particularly in western Turkey where dense GNSS/leveling... Read more
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Study on the selection of optimal global geopotential models for geoid determination in Kuwait
by Mostafa Rabah

2024, Survey Review

Key finding: Performs a comprehensive evaluation of recent GGMs against terrestrial free-air gravity anomalies and GPS/levelling data in Kuwait, revealing that combined GGMs generally better fit ground data than satellite-only models due... Read more
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Evaluation of the Earth Gravitational Model 2008 in Turkey
by ALİ KILIÇOGLU

2024

Key finding: Provides an external assessment of the EGM2008 tide-free model's performance over Turkey, confirming its validity despite the absence of proprietary Turkish data in its computation. Statistical analyses indicate standard... Read more
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2. What methodological advancements enable precise local and regional gravimetric geoid determination in data-sparse or complex terrains?

This theme covers novel methodological approaches to gravimetric geoid modeling in regions where terrestrial gravity data are sparse or unevenly distributed, such as in developing countries or areas with complex topography. Emphasis is on techniques like airborne gravity surveys, Least Squares Collocation (LSC), Least Squares Modifications of Stokes' formula (KTH method), and remove-compute-restore procedures to integrate multi-source data for enhanced geoid accuracy.

Geoid Modelling of Kalimantan Island using Airborne Gravity Data and Global Geoid Model (EGM2008)
by Anas Osman

2021, IOP Conference Series Earth and Environmental Science

Key finding: Demonstrates improvement in local geoid accuracy using airborne gravity measurements combined with global models (EGM2008) and Shuttle Radar Topography Mission (SRTM) data through a remove-compute-restore procedure. The... Read more
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A High-Resolution Gravimetric Geoid Model for Kuwait Using the Least-Squares Collocation
by Mostafa Rabah

2022

Key finding: Develops a first accurate regional gravimetric geoid model for Kuwait (KW-FLGM2021) using Least Squares Collocation combined with GNSS/leveling and terrestrial gravity data. The model achieves an external accuracy in geoid... Read more
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The Uganda Gravimetric Geoid Model 2014 Computed by The KTH Method
by Ronald Ssengendo

2022, Journal of Geodetic Science

Key finding: Presents the first gravimetric geoid model over Uganda using the KTH method, which optimally incorporates sparse terrestrial gravity and GOCE satellite data. Despite ultra-sparse gravity sampling (one point per 65 km2), the... Read more
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Procedure for the Determination of Local Gravimetric
by Editor Ijasre and 
1 more
ETEJE SYLVESTER OKIEMUTE

2018

Key finding: Details a systematic approach for constructing local gravimetric-geometric geoid models by integrating gravity measurements with DGPS and leveling observations, and applying surface fitting techniques to derive accurate local... Read more
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3. How do topographic density distributions and corrections impact the accuracy and bias in gravimetric geoid determination?

Research within this theme investigates the influence of incomplete or approximated topographic density modeling on the gravimetric geoid, including biases introduced during analytical continuation and downward continuation to the geoid surface. It also explores theoretical and computational treatments of topographic and Bouguer shell effects, the distinctions between geoid and quasi-geoid systems, and how these factors affect orthometric height definitions and geoid-quasigeoid separations.

The topographic bias in gravimetric geoid determination revisited
by Lars Sjöberg

2023, Journal of Geodetic Science

Key finding: The study derives that the topographic potential bias during analytical continuation for geoid determination can be precisely expressed as the sum of two Bouguer shell components, with the spherical symmetric Bouguer shell... Read more
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Remarks on the Terrain Correction and the Geoid Bias
by Lars Sjöberg

2023, International Association of Geodesy Symposia

Key finding: Quantifies that topographic bias arising from incomplete terrain mass reduction in gravimetric geoid computations originates only from mass within a confined dome-shaped volume centered at the computation point, while... Read more
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On the Consistency between a Classical Definition of the Geoid-to-Quasigeoid Separation and Helmert Orthometric Heights
by Albertini Nsiah Ababio

2024, Sensors

Key finding: Provides theoretical and numerical confirmation that the classical definition of geoid-to-quasigeoid separation, based on the planar Bouguer gravity anomaly, is consistent with Helmert's definition of orthometric heights... Read more
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Geoid or Quasi-Geoid? A Short Comparison
by Majid Abrehdary

2023, International Association of Geodesy Symposia

Key finding: Summarizes the fundamental differences between geoid and quasigeoid concepts and associated height systems, explicating how topographic density assumptions influence the choice of using orthometric or normal heights.... Read more
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Related Topics

  • Geoid Determination
  • Geodesy
  • Geophysics
  • Remote Sensing

    • All papers in Gravimetric Geoid

    Enhancement of Global Geopotential Harmonic Models for Egypt
    by Abdelrahim Ruby and 
    1 more
    Maher M Amin
    The aim of this research is to develop a new precise and high-resolution geoid model for Egypt by refining the Global Geopotential Models (GGMs) through a process named tailoring, where the existing spherical harmonic coefficients of... more
    shows the statistics of this heights without marine areas. In this study, the DTM2006.0 model, complete to degree and order 190, has been used to create a 5’x5’ mean heights for Egypt Fig. (4.6) by sing harmonic synth program (Holmes & Pavlis, 2006), in the area ounded by latitudes 212 to 332 and longitudes 24° and 382, and Table (4.6) haAtare tha ectatchre nf thic haimhte waithait marina araac
    Figure (4.8): Distribution of NRIAG Gravity Data.
    Table (4.3): Statistics of the 5 Arc-minute Anomaly Data Selected by the Merging Procedure Used to Develop the EGM2008 Model, Unit is mGal [source: Pavlis et al., 2012, Table (2)]. Over areas where only lower resolution gravity data were available
    Figure (5.28): Difference Gravimetric minus Combined Geoid Solution Computed by Using Tailored Geopotential Model EG1GOC5s in Remove-Restore Technique. Contour interval 5 cm.
    Table (4.2): Parameters of Earth Gravity Field Model EGM2008. The available gravity anomaly data that were necessary for the computation of the 5 arc-minute area mean values to develop the EGM2008 model, divide into three sub-divisions (see Pavlis et al., [2012, sections 3.5]), as shown in Fig. (4.1a):- a) Areas without any restrictions [are colored green in Fig. (4.1a)], most of this area is ocean areas, where the altimetry-derived gravity anomalies data.
    Figure (1.1): Research Methodology
    Figure (2.1): Attraction and Centrifugal Force.
    Figure (2.5): Terrain Correction (Hofmann-Wellenhof & Moritz 2005, p. 136)
    Figure (2.7): Pratt-Hayford Isostatic Compensation Model (Sanso &Sideris, 2013, p.349) A anrnminn tn BUnfmann_W allanhnaf and Manty (INN n1A1) tha
    Figure (2.8): The geometry of the RTM reduction
    Figure (2.9): The Reference Surfaces and Height Systems.
    a) For gravity anomalies:
    Figure (2.10): Signal (thick lines) and error (thin lines) amplitudes per degree in terms of gravity anomaly for the geopotential harmonic model EGM 2008 (Dotted), EGM96 (Dashed) and GOCO05s (Dash-dot).
    Figure (2.11) Cumulative RMS of Gravity Anomaly and Geoid Error.
    Figure (2.12): Essential parameters of covariance function
    Figure (2.14): The First-order Levelling Network in Egypt (Saad, A., 1993).
    the n = m location. We have: Then, the diagonal elements corresponding to the diagonal passing through
    Figure (4.1): Geographic Display of the 5 Arc-minute Anomalies Used to Develop the EGM2008 model: (a) Data Availability. (b) Data Source Identification [source: Pavlis et al., 2012, Fig.(3)].
    Figure (4.2): Data Availability for Egypt Used to Develop The EGM2008 Model [source: subset from Fig. (4.1)].
    Figure (5.29): Difference Gravimetric minus Combined Geoid Solution Computed by Using Tailored Geopotential Model EGTM0818 i Remove-Restore Technique. Contour interval 5 cm.
    Figure (4.3): Geographic Locations and Identification of Merged 30 Arc- minute Gravity Anomalies Used to Develop The EGM96. (Source: Lemoine et al., 1998, p.8-21).
    Figure (5.24): Gravimetric Geoid Norav-a for Egypt. Contour interval 1.0 m.
    Figure (5.25): Gravimetric Geoid Norav-8 for Egypt. Contour interval 1.0 m.
    Figure (4.5): Distribution of Egyptian Gravity Data in A frican Gravity Project. [Source: Fairhead at el., 1997, subset from Fig. (1)].
    Table (2.2): Numerical Values of Some Parameters of WGS 84 Ellipsoid.
    Table (4.1): Parameters of Earth Gravity Field Model GOCO05s.
    Table (4.4): Parameters of Earth Gravity Field Model EGM96.
    Hence, each gravity stations of the ENGSN97 precisely have a three-dimensional geodetic position (latitude, longitude, and geodetic height) from GPS data, as well as vertical position made by the orthometric height from precise levelling. The standard deviation of the final solution of the ENGSN97 network is range from 0.002 to 0.048 mGal (Dawod, 1998). Figure (4.9) Egyptian National Gravity Standardization Network 1997. (Dawod, 1998)
    Figure (4.12): Distribution of Available Measurements of Gravity in the Database of BGI. (Balmino G.at el., 1999).
    Figure (4.13): Distribution of BGI Gravity Data.
    Figure (4.14): Geographic Locations of Available Gravity Data for Egypt.
    Figure (4.16): Components of Deflections of The Vertical Data in Egypt.
    In each of the above three GPS project, the WGS84 reference frame was utilized to be the basic datum of the produced coordinates which were gained directly from GPS.
    Table (4.11): Statistics of The Egyptian 5'x5' Mean Free-air Gravity Anomalies. Figure (4.21): The Egyptian 5'x5' Mean Free-air Gravity Anomalies Interpolated by Least Squares Collocation.
    Figure (4.23): Components of Deflections of The Vertical Used for The Computation.
    Differences between tide-free and mean tide system for the ellipsoidal heights er a Figure (4.24): Differences between tide- Free and mean tide system for the ellipsoidal heights of HARN stations
    Figure (5.1): Iteration Scheme for Tailored geopotential Model.
    Figure (5.3): (a) Difference between The Egyptian 5’ x 5’ Mean Gravity Anomalies and The Computed Gravity Anomalies Using The Oniginal Model GOCO05s (b) Histogram of These Differences in 10 mGal bins. (Iteration Number =0)
    Figure (5.4): (a) Difference between The Egyptian 5’ x 5’ Mean Gravity Anomalies and The Computed Gravity Anomalies Using The EG1GOC5s Tailored Model (b) Histogram of These Differences in 10 mGal bins. (Iteration Number =5)
    Figure (5.5): The Egyptian 5'x5' Mean Gravity Anomalies Derived by Using EG1GOC5s Model Completed to Degree and Order 280.
    Figure (5.7): (a) Difference between The Egyptian 5’ x 5’ Mean Gravity Anomalies and The Computed Gravity Anomalies Using The Original Model EGM2008 (till degree 360) (b) Histogram of These Differences in 10 mGal bins.(Iteration Number =0)
    Figure (5.8): (a) Difference between The Egyptian 5’ x 5’ Mean Gravity Anomalies and The Computed Gravity Anomalies Using The EGM08F Tailored Model (b) Histogram of These Differences in 10 mGal bins.(Iteration Number =5)
    Figure (5.9): (a) Difference between The Egyptian 5’ x 5’ Mean Gravity Anomalies and The Computed Gravity Anomalies Using The Original Model EGM2008 (Max. degree. 2190) (b) Histogram of These Differences in 15 mGal bins.
    Figure (5.10): (a) Difference between The Egyptian 5’ x 5’ Mean Gravity Anomalies and The Computed Gravity Anomalies Using The EGTM0818 Tailored Model (Max. degree. 2190) (b) Histogram of These Differences ir 15 mGal bins.
    Figure (5.11): The Egyptian 5’x5’ Mean Gravity Anomalies Derived By Using EGTM0818 Model Complete to Degree and Order 2190.
    Table (5.10) shows the differences between the geoid heights derived from 17 GPS/levelling stations of HARN project and those derived from the fitted geoid models after removing trend surface.
    Figure (5.16): Geoid Model for Egypt Derived from Tailored Geopotential Model EG1GOC5s (till degree and order 280) after Removing Trend Surface Using The 4-parameter Model and The Weighted-Mean. Contour interval 1.0 m
    jure (5.17): 3D - Fitted Geoid Model for Egypt Derived from Tailored Geopotential Model EG1GOC5s.
    Figure (5.18): Geoid Model for Egypt Derived from Tailored Geopotential Model EGTM0818 (till degree and order 2190) after Removing Trend Surface Using The 4-parameter Model and The Weighted-Mean. Contour interval 1.0 m
    Figure (5.19): 3D - Fitted Geoid Model for Egypt Derived from Tailored Geopotential Model EGTM0818.
    Now all tools available for using 3D LSC for geoid solutions; the residual quantities, the covariance function, and the predictions surface area. The rest is to establish the normal equations Eq. (3.52) and compute predictions and error estimates, Eq. (3.53) and (3.56) without parameters (X) i.e. the output of 3D LSC called absolute solution. This may be done using GRAVSOFT program GEOCOL.
    Figure (5.22): Difference in Geoid Heights between The Gravimetric Geoid Norav-a and The GPS/Levelling Geoid before Removing Trend Surface. Contour interval = 30 cm.
    Figure (5.23): Difference in Geoid Heights between The Gravimetric Geoid Nerav-s and The GPS/Levelling Geoid before Removing Trend Surface. Contour interval =30 cm.
    Accordingly, from Fig. (4.3), and referring to Table (4.5), most of Egypt is located in green area file (A), blue area file (B) and a small part in gray area file (D) as shown in Fig. (4.4). This data obtained from African Gravity Project (AGP) (Fairhead & Watts, 1989; Merry, 2003; Merry et al., 2005).
    ‘7&é PyGravsoft Launcher - Gravity field programs Figure (4.19) Main Programs Package of GRAVSOFT Software.
    Table (4.10): Statistics of the selection Egyptian Point Gravity Anomalies.
    Figure (4.22): Histogram of Residual between The Gravity Anomalies Derived from Original Points and 5 Arc-minute Gravity Anomalies 4.8.4 Preparation of Deflections of the vertical Data
    Figure(5.2): RMS of The Differences of The Egyptian 5 Arc-minute Mean Gravity Anomalies Using EG1GOC5s Tailored Model with respect to The Iteration Number.
    Figure(5.6): RMS of The Differences of The Egyptian 5 Arc-minute Mean Gravity Anomalies Using EGMO8F Tailored Model with respect to The Iteration Number.
    Table (5.10): Differences between The Geoid Models and The 17 GPS/Levelling of HARN Stations after Removing Trend Surface. In order to validate an external check of the quality of the fitted geoid models, the 9 GPS/levelling stations were used Table (5.11), which was not used for the geoid fitting in the previous section. In addition, the EGM96 geopotential model (cf. Fig. 4.5), complete to degree and order 360, has also been used to compute geoid model for Egypt for comparison
    The result of check points shows that the geoid models derived from
    Finally, Fig. (5.16) and Fig. (5.18) show the geoid model for Egypt derived from harmonic coefficients of both EG1GOC5s and EGTM0818 tailored geopotential models, respectively, while Fig. (5.17) and Fig. (5.19) show their 3D fitted geoid model for both geoid models Negcicocss and Necrmosis- Table (5.12): Statistics of The 5'x5' Fitted Geoid Models for Egypt.
    After the remove-step, the residual height anomalies, as well as residual gravity anomalies, are estimated at the surface of the Earth from the residual gravity Table (5.13) or a combining between a residual gravity
    Table (5.20): Statistics of Gravimetric Geoid Ncray-g for Egypt. Table (5.19): Statistics of Gravimetric Geoid Ncrav-a for Egypt.
    From Table (5.21), the accuracy of both combined geoids is about
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    Validation of recent GOCE/GRACE geopotential models over Khartoum state - Sudan
    by Ahmed Abdalla

    2012, Journal of Geodetic Science

    This paper evaluates a number of latest releases of GOCE/GRACE global geopotential models (GGMs) using the GPS-levelling geometric geoid heights, terrestrial gravity data and existing local gravimetric models. We investigate each global... more
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