Editing Physical geodesy (section)

== Gravity anomalies ==<!-- This section is linked from [[Divergence theorem]] -->

{{main|Gravity anomaly}}

Above we already made use of ''gravity anomalies'' <math>\Delta g</math>. These are computed as the differences between true (observed) gravity <math>g=\|\vec{g}\|</math>, and calculated (normal) gravity <math>\gamma=\|\vec{\gamma}\|=\|\nabla U\|</math>. (This is an oversimplification; in practice the location in space at which γ is evaluated will differ slightly from that where ''g'' has been measured.) We thus get

:<math>
\Delta g = g - \gamma.\,
</math>

These anomalies are called [[free-air anomaly|free-air anomalies]], and are the ones to be used in the above Stokes equation.

In [[geophysics]], these anomalies are often further reduced by removing from them the ''attraction of the topography'', which for a flat, horizontal plate ([[Bouguer plate]]) of thickness ''H'' is given by

:<math>
a_B=2\pi G\rho H,\,
</math>

The [[Bouguer reduction]] to be applied as follows:

:<math>
\Delta g_B = \Delta g_{FA} - a_B,\,
</math>

so-called [[Bouguer anomaly|Bouguer anomalies]]. Here, <math>\Delta g_{FA}</math> is our earlier <math>\Delta g</math>, the free-air anomaly.

In case the terrain is not a flat plate (the usual case!) we use for ''H'' the local terrain height value but apply a further correction called the [[terrain correction]].