Editing Free-air gravity anomaly (section)

== Calculation ==

The free-air gravity anomaly <math>g_F</math> is given by the equation:<ref name="Fowler" />

:<math>g_{F} = (g_{obs} + \delta g_F) - g_\lambda </math>

Here,  <math>g_{obs}</math> is observed gravity, <math>\delta g_F</math> is the ''free-air correction'', and <math>g_\lambda</math> is [[theoretical gravity]].

It can be helpful to think of the free-air anomaly as comparing observed gravity to theoretical gravity adjusted up to the measurement point instead of observed gravity adjusted down to the geoid. This avoids any confusion of assuming that the measurement is made in free air.<ref>{{Cite journal|last=Ervin|first=C. Patrick|date=December 1977|title=Theory of the Bouguer Anomaly|url=https://doi.org/10.1190/1.1440807|journal=Geophysics|volume=42|issue=7|pages=1468|doi=10.1190/1.1440807|bibcode=1977Geop...42.1468E|issn=0016-8033|url-access=subscription}}</ref> Either way, however, the Earth mass between the observation point and the geoid is neglected. 
The equation for this approach is simply rearranging terms in the first equation of this section so that reference gravity is adjusted and not the observed gravity:

:<math>g_{F} = g_{obs} - (g_\lambda - \delta g_F)  </math>

=== 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:<ref name=Lillie>{{cite book|first=R.J.|last=Lillie|title=Whole Earth Geophysics: An Introductory Textbook for Geologists and Geophysicists|year=1998|publisher=[[Prentice Hall]]|isbn=978-0-13-490517-4}}</ref>

:<math>\begin{align} g &=\frac{GM}{R^2}\\
\frac{dg}{dR} &= -\frac{2GM}{R^3}= -\frac{2g}{R} \end{align}</math>
At 45° latitude, <math>2g/R = 0.3086</math> [[mGal]]/m.<ref name="Telford1990">{{cite book | title=Applied Geophysics | url=https://archive.org/details/appliedgeophysic00telf | url-access=limited | publisher=Cambridge University Press | first1=W.M. | last1=Telford | first2=L.P. | last2=Geldart | first3=R.E. | last3=Sheriff | year=1990 | location=Cambridge | pages=[https://archive.org/details/appliedgeophysic00telf/page/n22 11]–12 | isbn=978-0-521-32693-3| edition=2nd }}</ref>

The free-air correction is the amount that must be added to a measurement at height <math>h</math> to correct it to the reference level:
:<math>\delta g_F = \frac{2g}{R} \times h </math>

Here we have assumed that measurements are made relatively close to the surface so that R does not vary significantly. The value of the free-air correction is positive when measured above the geoid, and negative when measured below. There is the assumption that no mass exists between the observation point and the reference level.  The Bouguer and terrain corrections are used to account for this.