Gravity 4 Gravity Modeling. Gravity Corrections/Anomalies 1. Measurements of the gravity (absolute or relative) 2. Calculation of the theoretical gravity

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


)(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


- 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


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)



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



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)



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


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


Mountain Range

??


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


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


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


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)


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)

Documents

Gravity 4 Gravity Modeling. Gravity Corrections/Anomalies 1. Measurements of the gravity (absolute or relative) 2. Calculation of the theoretical gravity