- Bouguer plate
A Bouguer plate is an infinite, flat plate, used as a model in
gravity andgravity anomaly computations.Gravity outside the plate is perpendicular to the plate, towards it, with magnitude "2πG" times the mass per unit area, where "G" = 6.67 × 10−11 N m² kg-2, hence we have 4.191 × 10−10 N m² kg-2 times the mass per unit area.
Using 1 Gal = 0.01 m/s² we get 4.191 × 10−5 mGal m² kg-1 times the mass per unit area.
For mean rock
density (2.67 g/cm³) this gives 0.1119 mGal/m.This is independent of the distance to the plate. (This can be proven most simply with
Gauss's law for gravity , but can also be proven directly with Newton's law of gravity.)Bouguer gradient
On Earth the effect on gravity of elevation is 0.3086 mGal/m decrease when going up, minus the gravity of the Bouguer plate, giving the "Bouguer gradient" of 0.1967 mGal/m.
General
More generally, for a
mass distribution with the density depending on one Cartesian coordinate "z" only, gravity for any "z" is 2π"G" times the difference in mass per unit area on either side of this "z" value.In particular, a combination of two equal parallel infinite plates does not produce any gravity inside.
ee also
*
divergence theorem ,potential theory
* gravity anomalies
*Gauss's law for gravity References
External links
Wikimedia Foundation. 2010.
