GEOID-DETERMINAION

1. GEOID DETERMINAION Presented by: Presented to : Radhika Bhandari (05) Mr . S hangharsha T hapa Prabha D hital (09) Department of Civil and Sudha S apkota (26) Geomatics Engineering

2. What is geoid??? T he 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. 2

3. Fig1 : Geoid 3

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 4

5. A little more… 5

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. 6

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 7

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 8

9. Stroke's Integral The most general form of Stokes' integral formula is : Where, k = gravitational constant, δ M = difference in mass between real earth and normal earth , δ W = 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, 9

10. Δ g = gravity anomalies downward continued to reference sphere S (ψ) = Stokes' function where ψ s the spherical distance   10

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) 11

12. Topographic reductions Removal of topography masses only (Bouguer reduction) large indirect effect 12

13. Gravity reduction Under gravity reduction we have the following sections: Latitude reduction Elevation/free air reduction Bouguer/topographic reduction Terrain reduction 13

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. 14

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. 15

16. Pair of Grace satellites 16

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 17

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. 18

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) 19

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