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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 sea level.<ref name=Fowler>{{cite book|first=C.M.R.|last=Fowler|title=The Solid Earth: An Introduction to Global Geophysics|year=2005|edition=2|publisher=[[Cambridge University Press]]|location=[[Cambridge, UK]]|isbn=0-521-89307-0|pages=205&ndash;206}}</ref>
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==Anomaly==
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The free-air gravity anomaly is given by the equation:<ref name=Fowler/>
 
:<math>g_{F} = g_{obs} - g_\lambda + \delta g_F</math>
 
Here, <math>g_F</math> is the free-air gravity anomaly, <math>g_{obs}</math> is observed gravity, <math>g_\lambda</math> is the correction for latitude (because the Earth is not a perfect sphere), and <math>\delta g_F</math> 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:<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=0-13-490517-2}}</ref>
 
:<math>\begin{align} g &=\frac{GM}{R^2}\\
\frac{dg}{dR} &= -\frac{2GM}{R^3}= -\frac{2g}{R} \end{align}</math>
At the equator, <math>2g/R = 0.3086</math> mGal/m.
 
The free-air correction is the amount that must be added to a measurement at height <math>h</math> to correct it to sea level:
:<math>\delta g_F = \frac{2g}{R} \times h </math>.
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==
* [[Earth's gravity]]
 
==References==
<references/>
 
 
[[Category:Gravimetry]]
{{geophysics-stub}}

Latest revision as of 11:27, 17 December 2014

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>


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