Variation of G with latitude

# Variation of G with latitude

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## Variation of G with latitude

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1. Variation of G with latitude gp =983.2 Gal ge = 978.0 Gal Radius gprad-gerad= 6.6 Gal Excess mass gpem-geem = -4.8 Gal Rotation gprot-gerot= 3,4 Gal

2. Variation of G with latitude • In the long-term, the earth behaves like a fluid • Reference ellipsoid (approximation to geoid) • The scalar potential verifies the Laplace equation and the solution can be expanded on Legendre polynomials degree 0 degree 2 rotation

3. Variation of G with latitude We then get for the normal gravity (uniform density) due to position only We are interested in the gravity anomaly gobs -gn

4. Variation of G with latitude

5. Free air correction At the Earth’s surface z is the elevation from sea level. The gravity anomaly is then (brings gravity to sea level) Units: mGal, m

6. Bouguer correction We also need to correct for the mass between sea level and elevation z. Bouguer assumes an infinite slab of density ρ and thickness z Units: mGal, m, g/cm3

7. Bouguer correction The difficulty is to choose the right density ρ (average crustal rock has a density of 2.67

8. Terrain correction

9. Terrain correction (hammer)

10. Terrain correction (laborious)

11. other corrections and precautions • Isostatic correction: due to deeper sources regional trend  correct or filter • Tidal correction  correct or drift if short time sales • Elevation • Latitude • Drift • Base

12. Gravity of simple shapes

13. Gravity of simple shapes

14. Gravity of simple shapes Bedrock density 2.3, ore density 3.0, half cylinder at depth 100m radius for precision 0.1 mGal?

15. Gravity of simple shapes

16. Regionals and residuals

17. Regionals and residuals

18. Regionals and residualsgeological knowledge andexperience

19. Regionals and residualstrend surfaces

20. Regionals and residualstrend surfaces

21. Regionals and residualstrend surfaces

22. Regionals and residualsupward continuation

23. Regionals and residualssecond derivatives

24. Regionals and residualssecond derivatives

25. Gravity interpretationhalf-maximum technique

26. Gravity interpretationhalf-maximum technique

27. Gravity interpretation2nd derivatives technique

28. Gravity interpretation2nd derivatives technique

29. Gravity interpretation2nd derivatives technique

30. Detection of cavities

31. Bedrock depths