Simple Reduction
The gravitational acceleration outside a Bouguer plate is perpendicular to the plate and towards it, with magnitude 2πG times the mass per unit area, where 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 is 6.67 × 10−11 N m² kg−2, so is 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.
The Bouguer reduction for a Bouguer plate of thickness is
where is the density of the material and is the constant of gravitation. 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.
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 equal parallel infinite plates does not produce any gravity inside.
Read more about this topic: Bouguer Anomaly
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