Free-air gravity anomaly

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 sea level.[1]

Anomaly

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

g_{F} = g_{obs} - g_\lambda - \delta g_F

Here, g_F is the free-air gravity anomaly, g_{obs} is observed gravity, g_\lambda is the correction for latitude (because the Earth is not a perfect sphere), and \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]

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

At the equator, 2g/R = 0.3086 mGal/m.

The difference between gravity measurements at sea level and at an altitude of h above sea level is:

\delta g_F = -\frac{2g}{R} \times h .

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

See also

References

  1. ^ a b Fowler, C.M.R. (2005). The Solid Earth: An Introduction to Global Geophysics (2 ed.). Cambridge, UK: Cambridge University Press. ISBN 0521893070. 
  2. ^ Lillie, R.J. (1998). Whole Earth Geophysics: An Introductory Textbook for Geologists and Geophysicists. Prentice Hall. ISBN 0134905172.