1. Gravity 4
Gravity Modeling

2. 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

3. 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.

4. 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

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

6. 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

7. Gravity anomaly of sphere
gravimeter measures
only this component
- distance between the centre of the sphere and the measurement point
R – radius of the sphere
 - difference in density

8. Gravity anomaly of sphere

9. Gravity anomaly of a semi-infinite slab
1. No gravity effects far away from
truncation.
2. Increasing/decreasing of gravity
crossing the edge of the slab.
3. Full (positive/negative) effects
over the slab but far from the edge.
Increase or decrease
of gravity

10. Gravity anomaly of semi-infinite slab
Gravity effect of infinite slab:
gz = 2()G(h) = ()(h)
Gravity effect of semi-infinite slab (depends on the position defined by ):
gz = ()G(h) (2)
=/2 + tan-1(x/z)
(~ Bouguer correction)
gz = ()(h) (/2 + tan-1(x/z))

11. Gravity anomaly of semi-infinite slab

12. Gravity anomaly of semi-infinite slab
Fundamental properties
of gravity anomalies:
The amplitude of the anomaly
reflects the mass excess or
deficit (m=()V).
2. The gradient of the anomaly
reflects the depth of the excess
or deficient mass below the
surface (z):
Body close to the surface –
steep gradient
Body away deep in the Earth -
gentle gradient.

13. Gravity anomaly of semi-infinite slab (models using this approximation)
Passive continental margins ? ?
Airy (local) isostatic equilibrium

14. Gravity anomaly of semi-infinite slab (models using this approximation)
Passive continental margins
(only water contribution) (only mantle contribution)
Water – mass deficit – (-m)
 = w - c = g/cm3
Mantle effects – mass excess –
(+m)
 = m - c = g/cm3
FA gravity anomaly – sum of the
contributions from the shallow (water)
and deep (mantle) effects
max
Edge effect
min

15. Gravity anomaly of semi-infinite slab (models using this approximation)
Passive continental margins
Free Air anomaly:
Values are near zero (except for
edge effects) (+m) = (-m)
2. The area under the gravity
anomaly equals zero 
isostatic equilibrium
Bouguer anomaly (corrected for mass
deficit of the water ~ upper crust)
1. Near zero over continental crust
2. Mimics the Moho – parallel to the
mantle topography
3. Mirror image of the topography
(bathimetry) over the water –
increasing the anomaly – deepening
of the water

16. Gravity anomaly of semi-infinite slab (models using this approximation)
Passive continental margins (Atlantic coast of the United States)
Free Air anomaly:
Values are near zero (except for
edge effects) (+m) = (-m)
2. The area under the gravity
anomaly equals zero 
isostatic equilibrium

17. Gravity anomaly of semi-infinite slab (models using this approximation)
Mountain Range ? ?

18. Gravity anomaly of semi-infinite slab (models using this approximation)
Mountain Range
(only topo contribution) (only root contribution)
=c- m
= g/cm3
=c- a
= g/cm3
gentle
gradient
“Batman”
anomaly

19. 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

20. Gravity anomaly of semi-infinite slab (models using this approximation)
Free Air anomaly:
Values are near zero (mass
excess of the topography equals
the mass deficit of the crustal roots
(+m) = (-m)
2. Significant edge effects occur
because shallow and deep
contributions have different gradients
3. The area under the gravity
anomaly equals zero 
isostatic equilibrium
Bouguer anomaly (corrected for mass
deficit of the water ~ upper crust)
1. Near zero over continental crust
2. Mimics the root contribution
3. Mirror image of the topography –
the anomaly increases where the
topography of the mountains rises
Mountain Range

21. Gravity anomaly of semi-infinite slab (models using this approximation)
Mountain Range (Andes Mountains)
Non-Typical anomaly
Typical mountain anomaly

22. Local Isostasy (Pratt vs Airy Model)
Pratt Model
Block of different density
The same pressure from all blocks at the depth of compensation (crust/mantle boundary)
Airy Model
Blocks of the same density but different thickness
The base of the crust is exaggerated, mirror image of the topography

23. Gravity anomalies - example
Airy type
100% isostatic
compensation
Airy type
75% isostatic
compensation
Pratt type isostatic
compensation
Airy type – totally
uncompensated
Isostatic anomaly – the actual Bouguer anomaly minus the computed
Bouguer anomaly for the proposed density model

24. 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 

25. - Examples of application
Gravity Anomalies
- Examples of application

26. Exploration of salt domes
Bouguer anomaly
Map of the Mors salt dome
Jutland, Denmark
Reynolds, 1997
Feasibility study for safe disposal of radioactive waste in the salt dome

27. Exploration of salt domes
Bouguer anomaly
profile across the
Mors salt dome,
Jutland, Denmark
Reynolds, 1997
Modeling of the anomaly using a cylindrical body
(fine details are not resolvable unambiguously)

28. Exploration of salt domes
Notice the
axis direction
Bouguer anomaly profile compared with the corresponding sub-surface geology (Zechstein, northern Germany)
Hydrocarbon study
Reynolds, 1997

29. Mineral Exploration Some useful applications:
Discovery of Faro lead-zinc
deposit in Yukon
Gravity was the best
geophysical method to
delimit the ore body
Tonnage estimated
(44.7 million tonnes) with the tonnage proven by drilling
(46.7 million tonnes)
Reynolds, 1997

30. Mineral Exploration Some not very useful applications:
The scale of mineralization,
was of the order of only a few
meters wide
The sensitivity of the
gravimeter was insufficient to
resolve the small density
contrast between the
sulphide mineralization and
the surrounding rocks
Gravimeter with better accuracy ~ Gals and smaller station intervals the zone of mineralization would be detectable
No effect
Bouguer anomaly profile across mineralized zones in chert at Sourton Tors, north-west Dartmoor (SW England)
Reynolds, 1997

31. Glacier Thickness Determination
Some useful applications:
Gravity survey to ascertain
the glacier’s basal profile prior
to excavating a road tunnel
beneath it – anomaly 40 mGal
Error in the initial estimate
for the rock density  10%
error in the depth
Gravity measurements over
large ice sheets can have
considerably less accuracy
than other methods because of
uncertainties in the sub-ice
topography.
Residual gravity profile across Salmon Glacier, British Columbia
Reynolds, 1997

32. Engineering applications
To determine the extend of disturbed ground where
other geophysical methods can’t work:
Detection of back-filled quarries
Detection of massive ice in permafrost terrain
Detection of underground cavities – natural or artificial
Hydrogeological applications (e.g. for buried valleys,
monitoring of ground water levels
Volcanic hazards – monitor small changes in the elevation
of the flanks of active volcanoes and predict next eruption

33. Texts
Lillie, p. 223 – 261
Fowler, p (appropriate sections only)
Reynolds (1997) An introduction to applied and environmental geophysics, p.92 – 115 (this is only additional material about the applications)