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 = 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 = x 2.67 x h =
= (0.112 mGal/m) x h
gB = gfa – (0.112 mGal/m) x h

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

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 – h
On land:
gB = gfa – (0.112 mGal/m) h
for  = +2.67
At sea:
gB = gfa + ( mGal/m) h
for  =
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 – h
On land:
gB = gfa – (0.112 mGal/m) h
for  = +2.67
At sea:
gB = gfa + ( mGal/m) h
for  =
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