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Natural Resources Canada > Earth Sciences Sector > Geological Survey of Canada > Gravity
Gravity Gravity reduction formulae
| go |
= |
observed gravity |
| gt |
= |
theoretical gravity at the surface of the reference ellipsoid |
| θ |
= |
latitude (degrees) |
| δg/ δz |
= |
+ 0.3086 mGal m-1 (average vertical gravity gradient per metre of elevation above sea level) |
| G |
= |
6.672 x 10-11m3kg-1s-2
or
6.672 x 10-6m2kg-1mGal (constant of gravitation adopted by IAG, 1975) |
| h |
= |
station elevation above mean sea level (metres) |
| dw |
= |
depth of underwater station or depth below surface observation (metres) |
| di |
= |
thickness of ice cover (metres) |
| ρc |
= |
2670 kg m-3 (density of crustal rock) |
| ρw |
= |
1030 kg m-3 (density of sea water) |
| = |
1000 kg m-3 (density of fresh water) |
| ρi |
= |
900 kg m-3 (density of ice) |
| TC |
= |
terrain correction (mGals) |
The formula for computation of the theoretical value of gravity at the surface of the reference ellipsoid :
| gt (θ) |
= |
978032.7 [1.0 + 0.0053024 sin2(θ) - 0.0000058 sin2(2θ)] mGal |
is based on the 1980 Geodetic Reference System. This formula is used to calculate anomalies for observations referred to NAD83.
- Free Air Anomaly
The computation of the free air anomaly incorporates a correction for the difference in elevation between the observed station and the reference ellipsoid :
FA = go - gt + (δg/δz)h
- Bouguer Anomaly
The Bouguer anomaly includes a further correction for the mass between the station and the reference ellipsoid :
| BA |
= |
go - gt + (δg/δz - 2πGρc)h + TC |
| |
= |
FA - 2πGρch + TC |
- Free Air Anomaly
If the station is observed on a lake or ocean bottom with an underwater meter, the free air anomaly is :
| FA |
= |
go - gt + (δg/δz)h - (δg/δz - 4πGρw)dw |
- Bouguer Anomaly
The corresponding Bouguer anomaly is :
| BA |
= |
go - gt + (δg/δz -
2πGρc)h +
2πG(ρc -
ρw)dw
- (δg/δz - 4πGρw)dw
|
| |
= |
FA - 2πG(ρch - ρcdw + ρwdw) |
| Ice or Water Surface Stations |
- Free Air Anomaly
For stations observed with a dynamic gravimeter from a ship or with a standard gravimeter on the ice surface, the free air anomaly is :
FA = go - gt + (δg/δz)h
- Bouguer Anomaly
The corresponding Bouguer anomaly is :
| BA |
= |
go - gt + (δg/δz - 2πGρc)h + 2πG(ρc - ρw)dw
- (δg/δz - 4πGρw)dw |
| |
= |
FA - 2πG(ρch - ρcdw + ρwdw) |
- Free Air Anomaly
If the gravity station is observed on the surface of a significant body of ice which covers the land surface, the free air anomaly is identical to that for the land station :
FA = go - gt + (δg/δz)h
- Bouguer Anomaly
The Bouguer anomaly includes a correction for the ice below the station as well as the standard land corrections :
| BA |
= |
go - gt + (δg/δz - 2πGρc)h + 2πG(ρc - ρi)di + TC |
| |
= |
FA - 2πG(ρch - ρcdi + ρidi) |
|
