Gravity 4 Gravity Modeling. Gravity Corrections/Anomalies 1. Measurements of the gravity (absolute...
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Transcript of Gravity 4 Gravity Modeling. Gravity Corrections/Anomalies 1. Measurements of the gravity (absolute...
Gravity 4Gravity Modeling
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
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.
Gravity anomaly of sphere
2
22
r
VGg
VmVmr
mGg
R
GMg
Analogy with the gravitationalattraction of the Earth:
g g (change in gravity)M m (change in mass relative to
the surrounding material)R r
Gravity anomaly of a sphere
2r
VGg
22
3
222
2
33
2
3
zx
1
3
GR4g
zxr
r
1
3
GR4R
3
4
r
Gg
R3
4V
Total attraction at the observation pointdue to m
Gravity anomaly of sphere
)(cosgg
)(singg
g
g
g
ggg
y
x
y
x
yx
- 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
Gravity anomaly of sphere
- gravimeter measures only this component
2/322
3
22
222
22
3
02794.0
//cos
13
4
zxz
Rg
zxzrz
zxr
zxGR
g
z
cosgg
ggg
z
2y
2x
R – radius of the sphere - difference in density
- distance between the centre of the sphere and the measurement point
Gravity anomaly of sphere
2/322
3z
zx
zR02794.0g
Gravity anomaly of a semi-infinite slab
Increase or decreaseof gravity
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.
Gravity anomaly of semi-infinite slab
Gravity effect of infinite slab:
gz = 2()G(h) = 0.0419 ()(h)
Gravity effect of semi-infinite slab (depends on the position defined by ):
gz = ()G(h) (2)
=/2 + tan-1(x/z)
gz = 13.34 ()(h) (/2 + tan-1(x/z))
(~ Bouguer correction)
Gravity anomaly of semi-infinite slab
Gravity anomaly of semi-infinite slab
Fundamental propertiesof gravity anomalies:
1. The amplitude of the anomalyreflects the mass excess ordeficit (m=()V).
2. The gradient of the anomaly reflects the depth of the excessor deficient mass below the surface (z):- Body close to the surface – steep gradient- Body away deep in the Earth - gentle gradient.
Gravity anomaly of semi-infinite slab(models using this approximation)
Passive continental margins
km84.18h
km84.31)h(
m
cc
??
Airy (local) isostatic equilibrium
Gravity anomaly of semi-infinite slab(models using this approximation)
Passive continental margins
Water – mass deficit – (-m) = w - c = -1.64 g/cm3
Mantle effects – mass excess – (+m) = m - c = +0.43 g/cm3
FA gravity anomaly – sum of thecontributions from the shallow (water)and deep (mantle) effects
max
min
Edge effect
(only water contribution) (only mantle contribution)
Gravity anomaly of semi-infinite slab(models using this approximation)
Passive continental margins
Free Air anomaly:1. 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 massdeficit of the water ~ upper crust)1. Near zero over continental crust2. Mimics the Moho – parallel to the mantle topography3. Mirror image of the topography (bathimetry) over the water – increasing the anomaly – deepening of the water
Gravity anomaly of semi-infinite slab(models using this approximation)
Passive continental margins (Atlantic coast of the United States)
Free Air anomaly:1. Values are near zero (except for edge effects) (+m) = (-m)
2. The area under the gravity anomaly equals zero isostatic equilibrium
Gravity anomaly of semi-infinite slab(models using this approximation)
Mountain Range
??
Gravity anomaly of semi-infinite slab(models using this approximation)
Mountain Range
“Batman”anomaly
(only topo contribution) (only root contribution)
=c- m
= -0.43 g/cm3 =c- a
= +2.67 g/cm3
gentle gradient
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
Gravity anomaly of semi-infinite slab(models using this approximation)
Mountain RangeFree Air anomaly:1. 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 gradients3. The area under the gravity anomaly equals zero isostatic equilibrium
Bouguer anomaly (corrected for massdeficit of the water ~ upper crust)1. Near zero over continental crust2. Mimics the root contribution3. Mirror image of the topography – the anomaly increases where the topography of the mountains rises
Gravity anomaly of semi-infinite slab(models using this approximation)
Mountain Range (Andes Mountains)
Typical mountain anomalyNon-Typical anomaly
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
Gravity anomalies - example
Airy type100% isostaticcompensation
Airy type75% isostaticcompensation
Pratt type isostaticcompensationAiry type – totally uncompensated
Isostatic anomaly – the actual Bouguer anomaly minus the computed Bouguer anomaly for the proposed density model
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
Gravity Anomalies- Examples of application
Exploration of salt domes
Bouguer anomalyMap of the Mors salt domeJutland, Denmark
Reynolds, 1997
Feasibility study for safe disposal of radioactive waste in the salt dome
24 20 16 12 8 4
Exploration of salt domes
Bouguer anomalyprofile across the Mors salt dome, Jutland, Denmark
Reynolds, 1997
Modeling of the anomaly using a cylindrical body(fine details are not resolvable unambiguously)
Exploration of salt domes
Bouguer anomaly profile compared with the corresponding sub-surface geology (Zechstein, northern Germany)
Hydrocarbon study
Reynolds, 1997
Salt domes
Notice the axis direction
Mineral Exploration
Reynolds, 1997
Some useful applications:
- Discovery of Faro lead-zincdeposit 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)
Mineral Exploration
Bouguer anomaly profile across mineralized zones in chert at Sourton Tors, north-west Dartmoor (SW England)
Reynolds, 1997
No effect
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 andthe surrounding rocks
Gravimeter with better accuracy ~ Gals and smaller station intervals the zone of mineralization would be detectable
Glacier Thickness Determination
Residual gravity profile across Salmon Glacier, British Columbia
Reynolds, 1997
Some useful applications:
- Gravity survey to ascertainthe glacier’s basal profile priorto excavating a road tunnelbeneath 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 accuracythan other methods because of uncertainties in the sub-icetopography.
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
Texts
• Lillie, p. 223 – 261
• Fowler, p.193- 228 (appropriate sections only)
• Reynolds (1997) An introduction to applied and environmental geophysics, p.92 – 115 (this is only additional material about the applications)