Editing Physical geodesy

{{Short description|Study of the physical properties of the Earth's gravity field}}
{{Geophysics|all}}
{{Geodesy}}
[[Image:Ocean gravity map.gif|right|thumb|350px|Ocean basins mapped gravitationally. Seafloor features larger than 10 km are detected by resulting gravitational distortion of sea surface. (1995, [[NOAA]])]]
'''Physical geodesy''' is the study of the physical properties of [[Earth's gravity]] and its potential field (the [[geopotential]]), with a view to their application in [[geodesy]].

==Measurement procedure==
Traditional geodetic instruments such as [[theodolite]]s rely on the gravity field for orienting their vertical axis along the local [[plumb line]] or local [[vertical direction]] with the aid of a [[spirit level]]. After that, vertical [[angle]]s ([[zenith]] angles or, alternatively, [[elevation]] angles) are obtained with respect to this local vertical, and horizontal angles in the plane of the local horizon, perpendicular to the vertical.

[[Levelling]] instruments again are used to obtain [[geopotential]] differences between points on the Earth's surface. These can then be expressed as "height" differences by conversion to metric units.

===Units===

Gravity is commonly measured in units of m·s<sup>−2</sup> ([[metre]]s per [[second]] squared). This also can be expressed (multiplying by the [[gravitational constant]] '''G''' in order to change units) as [[newton (unit)|newton]]s per [[kilogram]] of attracted mass.

Potential is expressed as gravity times distance, m<sup>2</sup>·s<sup>−2</sup>.  Travelling one metre in the direction of a gravity vector of strength 1 m·s<sup>−2</sup> will increase your potential by 1 m<sup>2</sup>·s<sup>−2</sup>. Again employing G as a multiplier, the units can be changed to [[joule]]s per kilogram of attracted mass.

A more convenient unit is the GPU, or geopotential unit: it equals 10 m<sup>2</sup>·s<sup>−2</sup>. This means that travelling one metre in the vertical direction, i.e., the direction of the 9.8 m·s<sup>−2</sup> ambient gravity, will ''approximately'' change your potential by 1 GPU. Which again means that the difference in geopotential, in GPU, of a point with that of sea level can be used as a rough measure of height "above sea level" in metres.

==Gravity==
{{excerpt|Earth's gravity}}

==Potential fields==
{{excerpt|Geopotential}}

==Geoid==
{{main|Geoid}}
[[File:Earth_Gravitational_Model_1996.png|thumb|Map of the undulation of the geoid in meters (based on the [[EGM96]])]]
Due to the irregularity of the Earth's true gravity field, the equilibrium figure of sea water, or the [[geoid]], will also be of irregular form. In some places, like west of [[Ireland]], the geoid—mathematical mean sea level—sticks out as much as 100 m above the regular, rotationally symmetric reference ellipsoid of GRS80; in other places, like close to [[Sri Lanka]], it dives under the ellipsoid by nearly the same amount. 
The separation between the geoid and the reference ellipsoid is called the ''[[undulation of the geoid]]'', symbol <math>N</math>.

The geoid, or mathematical mean sea surface, is defined not only on the seas, but also under land; it is the equilibrium water surface that would result, would sea water be allowed to move freely (e.g., through tunnels) under the land. Technically, an ''equipotential surface'' of the true geopotential, chosen to coincide (on average) with mean sea level.

As mean sea level is physically realized by tide gauge bench marks on the coasts of different countries and continents, a number of slightly incompatible "near-geoids" will result, with differences of several decimetres to over one metre between them, due to the [[dynamic sea surface topography]]. These are referred to as ''[[vertical datum]]s'' or ''height [[datum (geodesy)|datum]]s''.

For every point on Earth, the local direction of gravity or [[vertical direction]], materialized with the [[plumb line]], is ''perpendicular'' to the geoid (see [[astrogeodetic leveling]]).

== 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]].

== See also ==
* [[Deflection of the vertical]]
* [[Dynamic height]]
* [[Friedrich Robert Helmert]]
* [[Geophysics]]
* [[Gravity of Earth]]
* [[Gravimetry]]
* [[LAGEOS]]
* [[Mikhail Molodenskii]]
* [[Normal height]]
* [[Orthometric height]]
* [[Satellite geodesy]]

==References==
{{Reflist}}

==Further reading==
* B. Hofmann-Wellenhof and H. Moritz, '''Physical Geodesy,''' Springer-Verlag Wien, 2005. (This text is an updated edition of the 1967 classic by W.A. Heiskanen and H. Moritz).

{{Authority control}}

[[Category:Geodesy]]
[[Category:Gravity]]
[[Category:Geophysics]]
[[Category:Gravimetry]]