Ali Onceloncel@kfupm.edu.sa

Department of Earth SciencesKFUPM

Gravity Methods 2

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Introduction to GeophysicsIn

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Previous Lecture

Gravity Methods Earth's Gravity Potential Field Earth's Magnetic Potential Field Differences in Earth's Potential Fields Earth's Gravity Field Earth's Gravitational Acceleration Theoretical Gravity Free Air Gravity Correction Gravity Anomaly Free Air Gravity Anomaly Bouguer Correction

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Recall: Theoretical Gravity

2 42978.03185 1 0.005278895sin 0.000023463sinn

cmgs

The average value of gravity for a given latitude is approximated by the International Association of Geodesy in 1967.

gn =Normal Gravity: Gravitational acceleration

expected for a rotating ellipsoidal earth without any geologic complications and no surface features.

Ф=latitudeGravitation increase from the equator (Ф =0)

=978,03185 mGal to the pole (Ф =90)=983,217.72 mGalIn

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Recall: Gravity Anomaly

• What is an anomaly?• Difference between observed gravity and

International Gravity Formula (IGF) for same location or relative to local base

station, termed the gravity anomaly, Dg

Dg = gobs - gn

• difference is the result of density contrasts in the subsurface below the measurement point

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Δgfa= g – gt + FAC

g = gravitational acceleration observed at stationgt= theoretical gravityIn

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Δgfa = free gravity

anomaly

Recall: Free Air Gravity Correction

•The free air correction (FAC) accounts for the extended radius to an observation point, elevated h meters above a sea level datum.

• The above equation illustrates that, for every 3 m (about 10 feet) upward from the surface of the Earth, the acceleration due to gravity decreases by about 1 mGal.

•The basis of this correction is that it makes allowance for the reduction in magnitude of gravity with height above the geoid (pp.55, Reynolds, 2005).

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Bouguer Correction

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•The extra mass of mountains results in higher gravity relative to areas near sea level.

• The Bouguer Correction (BC) accounts for the gravitational attraction of the mass above the sea-level datum.

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Bouguer Correction

•Thus, to account for the excess mass above a sea level datum, the Bouguer correction assumes an infinite slab of density (ρ), with thickness (h) equal to the station’s elevation.

BC= 2 π ρ G hG=Universal Gravitational Constant (6,367,000 m)

H= thickness of the slab (station elevation)

Substituting the values of G and 2 π yields:

BC= 0.419 ρ h

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The extra mass of mountains results in higher gravity relative to the near sea level.

To account for the excess mass above a sea level datum, The BC assumes an infinite slab of density (ρ), with thickness (h) equal to the station’s elevation.

Bouguer CorrectionBC= 0.419 ρ h

To determine the Bouguer correction, the density of the infinite slab (ρ) is needed to assumed as a reduction density of 2.67 g/cm, which is equal to typical density of granite.

Bouguer Gravity Anomaly on Land

ΔgB= Δgfa-BC

The simple Bouguer gravity anomaly results from subtracting the effect of the infinite slab (BC) from the free air gravity anomaly:

BC= 0.419 ρ h =0.419 (2.67g/cm3) h=(0.112 mGal/m)*h (m)

ΔgB= Δgfa-(0.112 mGal/m) hIn

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Bouguer Gravity Anomaly on Sea

ΔgB= Δgfa- 0.419 ρ h Station elevations (h) are zero,

Then, ΔgB= Δgfa

Thus, if a type of Bouguer correction is applied, then equation (see page 233 of Lillie) is:

ΔgB= Δgfa + (0.0687 mGal/m)hw

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Bouguer Gravity Anomaly on SeaIn

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Δgfa= g – gt + FAC

ΔgB= Δgfa-BC BC= 0.419 ρ h

FAC= h x (0.308 mGal/m)