Bouguer anomaly

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 (residual) terrain effect (or (residual) 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 ${\displaystyle g}$ outside a Bouguer plate is perpendicular to the plate and towards it, with magnitude 2πG times the mass per unit area, where ${\displaystyle G}$ 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 ${\displaystyle G}$ is 6.67×10⁻¹¹ N m² kg⁻², so ${\displaystyle g}$ 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 ${\displaystyle H}$ is $${\displaystyle \delta g_B=2\pi \rho GH}$$ where ${\displaystyle \rho }$ is the density of the material and ${\displaystyle G}$ 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 2πG 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.