1. GEOID DETERMINAION
Presented by: Presented to :
Radhika Bhandari (05) Mr. Shangharsha Thapa
Prabha Dhital (09) Department of Civil and
Sudha Sapkota (26) Geomatics Engineering

2. What is geoid???
• The mean sea level at a particular location on Earth if extended in all
direction over the entire Earth would form an undulating spheroid,
called geoid.
• The geoid is the shape that the surface of the oceans would take
under the influence of Earth's gravity and rotation alone, in the
absence of other influences such as winds and tides.
• Geoidal surface is also called equipotential gravity surface.
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3. Fig1 : Geoid
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4. Characteristics of Geoid
• Dependent upon the irregular distribution of masses of the Earth
• Height measured from geoid to the Earth surface is Orthometric
height
• Levelling gives orthometric height
• Is the true physical figure of the Earth in contrast to the idealized
geometrical figure of a reference ellipsoid
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5. A little more…
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6. Why Geoid Determination?
• We determine the elevation of any point with reference to the
reference geoid at any time
• With the help of which we can complete the construction projects
(that require elevation data) faster and in less cost.
• Height of any prominent peaks can be determined accurately and
solve the controversies.
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7. A Gravimetric Approach For Geoid
Determination
• study of gravity field and gravitational potential field of the Earth is
simply called Gravimetry.
• Achieved by making different gravity measurements
• Gravimeter used to measure gravity value
• Gravity anomalies can be determined by a gravimeter by gravimetric
method
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8. Gravity Anamoly
• Difference between value of gravity as observed at a station after
applying correction to reduce it to the sea level and theoritical value
of gravity at a sea level
• Gravity anomalies helps in computing the deflection of vertical for
reduction of base lines from geoid to reference ellipsoid
• The separation of Geoid from reference ellipsoid can be determined
by using the value of gravity anomaly in stoke’s formula
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9. Stroke's Integral
The most general form of Stokes' integral formula is :
Where,
k = gravitational constant,
δM = difference in mass between real earth and normal earth,
δW = difference between gravity potential of real earth on the geoid
and the normal potential of model earth on the surface of this model,
R = 6371 km is radius of reference sphere approximating geoid,
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10. Δg = gravity anomalies downward continued to reference sphere
S(ψ) = Stokes' function
where ψ s the spherical distance
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11. Conditions required for stoke’s
integral
1.There is no mass above the geoid (topographic reduction, mean
density is often assumed)
2. Data given on the geoid (gravity reduction)
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12. Topographic reductions
• Removal of topography masses only (Bouguer reduction)
• large indirect effect
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13. Gravity reduction
Under gravity reduction we have the following sections:
1. Latitude reduction
2. Elevation/free air reduction
3. Bouguer/topographic reduction
4. Terrain reduction
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14. Modern Method: GRACE
• Stands for Gravity Recovery and Climate Experiment
• Is a pair of satellite that measures gravity field of the Earth
• Gravity field of the Earth is entirely mapped in every 30 days
• The twin satellites are 220 km apart and 460 km above the surface of
the Earth
• GRACE is part of NASA's Earth Science Enterprise, whose mission is to
understand and protect our home planet.
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15. How is gravity measured??
• gravity and mass are positively correlated
• lead satellite speeds up when passing over an area on Earth of slightly
stronger gravity that leads to increase in the distance between two
satellites and vice versa
• The distance between satellites is monitored by microwave K-band
ranging instrument.
• And then a gravity field map is prepared.
• Lastly geoid undulations(N) is calculated by series of calculations.
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16.  Pair of Grace satellites
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17. Application of Grace
Grace gives us our best opportunity to study time variable gravity effects
that provides detail information about:
• measuring the changing mass of polar ice caps
• measuring changes in water resources on land
• understanding shallow and deep ocean current transport
• understanding sea level change resulting from ocean temperature and
water mass changes
• understanding atmosphere-ocean mass exchange
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18. Conclusion
Thus in this presentation we discussed about:
• Gravimetric method (traditional) for determining Geoid.
• GRACE was used as a modern method for Geoid determination.
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19. References
• Chen, Y. and Yang, Z. (2001) “A Hybrid Method to Determine the Hong Kong
Geoid”, International Conference, FIG Working Week 2001, Seoul, Korea, 6-
11 May 2001
• Heiskanen, W. A., Moritz, H. (1967): Physical Geodesy W.H. Freeman and
Company San Francisco
• Hirvonen, R. (1960): New Theory of the Gravimetric Geodesy. Publications
of the Isostatic Institute of the IAG, 32, Helsinki
• Sanso, Fernando and Sideris, G. Michael (2013) “Geoid Determination”
• Wahr, J., 1997, Geodesy and gravity: Class notes: Samizdat Press
• Lecture slide of Shangharsha Thapa (Gravimetry)
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