# Free-air gravity anomaly

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In geophysics, the free-air gravity anomaly, often simply called the free-air anomaly, is the measured gravity anomaly after a free-air correction is applied to correct for the elevation at which a measurement is made. The free-air correction does so by adjusting these measurements of gravity to what would have been measured at a reference level. For Earth, this reference level is commonly taken as the mean sea level.[1]

## Anomaly

The free-air gravity anomaly is given by the equation:[1]

${\displaystyle g_{F}=g_{obs}-g_{\lambda }+\delta g_{F}}$

Here, ${\displaystyle g_{F}}$ is the free-air gravity anomaly, ${\displaystyle g_{obs}}$ is observed gravity, ${\displaystyle g_{\lambda }}$ is the correction for latitude (because planetary bodies are not perfect spheres), and ${\displaystyle \delta g_{F}}$ is the free-air correction.

Gravitational acceleration decreases as an inverse square law with the distance at which the measurement is made from the mass. The free air correction is calculated from Newton's Law, as a rate of change of gravity with distance:[2]

{\displaystyle {\begin{aligned}g&={\frac {GM}{R^{2}}}\\{\frac {dg}{dR}}&=-{\frac {2GM}{R^{3}}}=-{\frac {2g}{R}}\end{aligned}}}

At 45° latitude, ${\displaystyle 2g/R=0.3086}$ mGal/m.[3]

The free-air correction is the amount that must be added to a measurement at height ${\displaystyle h}$ to correct it to the reference level:

${\displaystyle \delta g_{F}={\frac {2g}{R}}\times h}$

Here we have assumed that measurements are made relatively close to the surface so that R does not vary significantly. Also, there is an assumption that no mass exists between the observation point and the reference level. The Bouguer anomaly and terrain correction are used to account for this.