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Gravity 3

Gravity 3. Gravity Corrections/Anomalies. Gravity survey flow chart: 1. Measurements of the gravity (absolute or relative)  2. Calculation of the theoretical gravity (reference formula)  3. Gravity corrections 4. Gravity anomalies 5. Interpretation of the results. Theoretical Gravity.

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Gravity 3

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  1. Gravity 3

  2. Gravity Corrections/Anomalies Gravity survey flow chart: • 1. Measurements of the gravity (absolute or relative)  • 2. Calculation of the theoretical gravity (reference formula)  • 3. Gravity corrections • 4. Gravity anomalies • 5. Interpretation of the results

  3. Theoretical Gravity • Gravity is a function of: • Latitute of observation () • Elevation of the station (R – the difference for R) • Mass distribution in the subsurface (M)

  4. Theoretical Gravity For a Reference Oblate Spheroid: • – latitude of observation • (sometime you can see  instead of )

  5. Free Air Gravity Anomaly/Correction • Accounts for the elevation For g  980,625 MGal, and R  6,367 km = 6,367,000 m • Average value for the change • in gravity with elevation

  6. Free Air Gravity Anomaly/Correction FAC – Free Air Correction (mGal); h – elevation above sea level (m) gfa = g – gt + FAC

  7. Free Air Gravity Anomaly/Correction Example of free air gravity anomaly across areas of mass excess and mass deficiency

  8. Bouguer Gravity Anomaly/Correction • Accounts for the gravitational attraction of the mass above sea level datum Attraction of a infinite slab with thickness h = elevation of the station: BC = 2Gh BC = 0.0418h BC – Bouguer Correction (mGal); h – elevation above sea level (m)  - density (g/cm3)

  9. Bouguer Gravity Anomaly/Correction For land gB = gfa – BC • in BC must be assumed (reduction density) For a typical  = 2.67 g/cm3 (density of granite): BC = 0.0419 x 2.67 x h = = (0.112 mGal/m) x h gB = gfa – (0.112 mGal/m) x h

  10. gB = gfa + (0.0687 mGal/m) x hw Bouguer Gravity Anomaly/Correction For sea For a typical w = 1.03 g/cm3 (water) and c = 2.67 g/cm3 (crust): BCs = 0.0419 x (w - c) x hw = 0.0419 x (-1.64) x hw = -0.0687 (mGal/m) x hw gB = gfa – BCs gB = gfa – 0.0419h h = 0  gB = gfa

  11. Bouguer Gravity Anomaly/Correction FAC vs. BC: • BC < FAC (always for stations above sea level) • Mass excesses result in “+” anomalies, and deficiencies in “-” anomalies for both • Short-wavelength changes in FAC due to abrupt topographic changes are removed by BC.

  12. Terrain Correction • For rugged areas – additional correction For low relief the BC is okay but for rugged terrain it is not gBc = gB + TC

  13. Free Air and Bouguer Gravity Anomalies (summary) 3. Bouguer Gravity Anomaly gB = gfa – BC = gfa – 0.0419h On land: gB = gfa – (0.112 mGal/m) h for  = +2.67 At sea: gB = gfa + (0.0687 mGal/m) h for  = - 1.64 In rugged terrain: gBc = gB + TC • Theoretical Gravity • Free Air Gravity Anomaly gfa = g – gt + (0.308 mGal/m) h Bs – Bouguer – simple; Bc – Bouguer – complete

  14. Free Air and Bouguer Gravity Anomalies (summary) 3. Bouguer Gravity Anomaly gB = gfa – BC = gfa – 0.0419h On land: gB = gfa – (0.112 mGal/m) h for  = +2.67 At sea: gB = gfa + (0.0687 mGal/m) h for  = - 1.64 In rugged terrain: gBc = gB + TC • Theoretical Gravity • Free Air Gravity Anomaly gfa = g – gt + (0.308 mGal/m) h Bs – Bouguer – simple; Bc – Bouguer – complete

  15. Gravity Corrections/Anomalies • 1. Measurements of the gravity (absolute or relative)  • 2. Calculation of the theoretical gravity (reference formula)  • 3. Gravity corrections  • 4. Gravity anomalies • 5. Interpretation of the results

  16. Gravity modelling - 2-D approach • Developed by Talwani et al. (1959): • Gravity anomaly can be computed as a sum of contribution of individual bodies, each with given density and volume. • The 2-D bodies are approximated , in cross-section as polygons.

  17. Gravity anomaly of sphere Analogy with the gravitational attraction of the Earth: g  g (change in gravity) M  m (change in mass relative to the surrounding material) R  r

  18. Gravity anomaly of sphere Total attraction at the observation point due to m

  19. Gravity anomaly of sphere - Total attraction (vector) • Horizontal component of • the total attraction (vector) • Vertical component of • the total attraction (vector) • Horizontal component • Vertical component • Angle between a vertical component • and g direction

  20. Gravity anomaly of sphere • a gravimeter measures • only this component R – radius of a sphere  - difference in density

  21. Gravity anomaly of sphere

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