# Gravity 4 Gravity Modeling. Gravity Corrections/Anomalies 1. Measurements of the gravity (absolute...

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Gravity 4Gravity Modeling

Gravity Corrections/Anomalies1. 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 approachDeveloped 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 sphereAnalogy 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 sphereTotal attraction at the observation pointdue to m

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

Gravity anomaly of sphere gravimeter measures only this componentR radius of the sphere - difference in density- distance between the centre of the sphere and the measurement point

Gravity anomaly of sphere

Gravity anomaly of a semi-infinite slabIncrease or decreaseof gravity1. 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 slabGravity 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 slabFundamental propertiesof gravity anomalies:

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 gradientBody away deep in the Earth - gentle gradient.

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

Gravity anomaly of semi-infinite slab(models using this approximation)Passive continental marginsWater 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 maxminEdge effect(only water contribution) (only mantle contribution)

Gravity anomaly of semi-infinite slab(models using this approximation)Passive continental marginsFree 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 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: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 RangeBatmananomaly(only topo contribution) (only root contribution) =c- m = -0.43 g/cm3 =c- a = +2.67 g/cm3gentle gradient

Bouguer Gravity Anomaly/CorrectionFor landgB = 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: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 ModelBlock of different densityThe same pressure from all blocks at the depth of compensation (crust/mantle boundary)Airy ModelBlocks of the same density but different thicknessThe base of the crust is exaggerated, mirror image of the topography

Gravity anomalies - exampleAiry type100% isostaticcompensationAiry type75% isostaticcompensationPratt type isostaticcompensationAiry type totally uncompensatedIsostatic anomaly the actual Bouguer anomaly minus the computed Bouguer anomaly for the proposed density model

Gravity Corrections/Anomalies1. 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 domesBouguer anomalyMap of the Mors salt domeJutland, Denmark

Reynolds, 1997

Feasibility study for safe disposal of radioactive waste in the salt dome24 20 16 12 8 4

Exploration of salt domesBouguer 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 domesBouguer anomaly profile compared with the corresponding sub-surface geology (Zechstein, northern Germany)

Hydrocarbon study

Reynolds, 1997

Salt domesNotice the axis direction

Mineral Exploration

Reynolds, 1997Some useful applications:

Discovery of Faro lead-zincdeposit in Yukon Gravity was the best geophysical method to delimit the ore bodyTonnage estimated (44.7 million tonnes) with the tonnage proven by drilling (46.7 million tonnes)

Mineral ExplorationBouguer anomaly profile across mineralized zones in chert at Sourton Tors, north-west Dartmoor (SW England) Reynolds, 1997No effectSome not very useful applications:

The scale of mineralization, was of the order of only a few meters wideThe 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 DeterminationResidual gravity profile across Salmon Glacier, British Columbia

Reynolds, 1997Some useful applications:

Gravity survey to ascertainthe glaciers 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 applicationsTo determine the extend of disturbed ground where other geophysical methods cant 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 elevationof the flanks of active volcanoes and predict next eruption

TextsLillie, 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)

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