Bouguer anomaly

In geodesy and geophysics, the Bouguer anomaly (named after Pierre Bouguer) is a gravity anomaly, corrected for the height at which it is measured and the attraction of terrain. The height correction alone gives a free-air gravity anomaly.
Definition.
The Bouguer anomaly formula_1 defined as:
Here, 
The free-air anomaly formula_3, in its turn, is related to the observed gravity formula_7 as follows:
where:
Reduction.
A Bouguer reduction is called "simple" (or "incomplete") if the terrain is approximated by an infinite flat plate called the "Bouguer plate". A "refined" (or "complete") Bouguer reduction removes the effects of terrain more precisely. The difference between the two is called the "terrain effect" (or "terrain correction") and is due to the differential gravitational effect of the unevenness of the terrain; it is always negative.
Simple reduction.
The gravitational acceleration formula_11 outside a Bouguer plate is perpendicular to the plate and towards it, with magnitude "2πG" times the mass per unit area, where formula_12 is the gravitational constant. It is independent of the distance to the plate (as can be proven most simply with Gauss's law for gravity, but can also be proven directly with Newton's law of gravity). The value of formula_12 is 6.67 × 10−11 N m2 kg−2, so formula_11 is 4.191 × 10−10 N m2 kg−2 times the mass per unit area. Using 1 Gal = 0.01 m s−2 (1 cm s−2) we get 4.191 × 10−5 mGal m2 kg−1 times the mass per unit area. For mean rock density (2.67 g cm−3) this gives 0.1119 mGal m−1.
The Bouguer reduction for a Bouguer plate of thickness formula_15 is
where formula_17 is the density of the material and formula_12 is the constant of gravitation. On Earth the effect on gravity of elevation is 0.3086 mGal m−1 decrease when going up, minus the gravity of the Bouguer plate, giving the "Bouguer gradient" of 0.1967 mGal m−1.
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. A combination of two parallel infinite if equal mass per unit area plates does not produce any gravity between them.