Editing Gravity anomaly (section)

==The model field and corrections{{anchor|Computation}}==
[[File:Gravity anomaly gn.png|thumb|Hypothetical gravity measurement. The value of gravity is measured at the red point marked <math>g_m</math>. The green point is the normal gravity <math>g_n</math>, which lies on the reference ellipsoid.]]
[[File:Gravity anomaly tidal.png|thumb|Hypothetical gravity measurement corrected for tidal forces]]
[[File:Gravity anomaly terrain.png|thumb|Hypothetical gravity measurement corrected for tides and terrain]]
[[File:Gravity anomaly fa.png|thumb|Hypothetical gravity measurement with free-air corrections]]
[[File:Gravity anomaly bouger.png|thumb|Hypothetical gravity measurement with Bouguer correction]]
The starting point for the model field is the International Reference Ellipsoid, which gives the normal gravity ''g''<sub>n</sub> for every point on the Earth's idealized shape. Further refinements of the model field are usually expressed as corrections added to the measured gravity or (equivalently) subtracted from the normal gravity. At a minimum, these include the tidal correction △''g''<sub>tid</sub>, the terrain correction △''g''<sub>T</sub>, and the free air correction △''g''<sub>FA</sub>. Other corrections are added for various gravitational models. The difference between the corrected measured gravity and the normal gravity is the gravity anomaly.{{sfn|Lowrie|2007|pp=77–78}}

===The normal gravity===
{{main|Normal gravity}}

The normal gravity accounts for the bulk gravitation of the entire Earth, corrected for its idealized shape and rotation. It is given by the formula:
<math display="block">g_n = g_e(1 + \beta_1 \sin^2\lambda + \beta_2 \sin^2 2\lambda)</math>
where <math>g_e</math> = {{val|9.780327|u=m.s-2}}; <math>\beta_1</math> = {{val|5.30244|e=-3}}; and <math>\beta_2</math> = {{val|−5.8|e=-6}}. This is accurate to 0.1 [[gal (unit)|mgal]] at any latitude <math>\lambda</math>. When greater precision is needed, a more elaborate formula gives the normal gravity with an accuracy of 0.0001 mgal.{{sfn|Lowrie|2007|pp=65–66}}

===The tidal correction===
The Sun and Moon create time-dependent tidal forces that affect the measured value of gravity by about 0.3 mgal. Two-thirds of this is from the Moon. This effect is very well understood and can be calculated precisely for a given time and location using astrophysical data and formulas, to yield the tidal correction △''g''<sub>tid</sub>.{{sfn|Lowrie|2007|p=54}}

===The terrain correction===
The local [[topography]] of the land surface affects the gravity measurement. Both terrain higher than the measurement point and valleys lower than the measurement point reduce the measured value of gravity. This is taken into account by the terrain correction △''g''<sub>T</sub>. The terrain correction is calculated from knowledge of the local topography and estimates of the density of the rock making up the high ground. In effect, the terrain correction levels the terrain around the measurement point.{{sfn|Lowrie|2007|p=77}}

The terrain correction must be calculated for every point at which gravity is measured, taking into account every hill or valley whose difference in elevation from the measurement point is greater than about 5% of its distance from the measurement point. This is tedious and time-consuming but necessary for obtaining a meaningful gravity anomaly.{{sfn|Lowrie|2007|p=79}}

===The free-air correction===
{{main|Free-air anomaly}}
The next correction is the free-air correction. This takes into account the fact that the measurement is usually at a different elevation than the reference ellipsoid at the measurement latitude and longitude. For a measurement point above the reference ellipsoid, this means that the gravitational attraction of the bulk mass of the earth is slightly reduced. The free-air correction is simply 0.3086 mgal m<sup>−1</sup> times the elevation above the reference ellipsoid.{{sfn|Lowrie|2007|pp=79–80}}

The remaining gravity anomaly at this point in the reduction is called the ''free-air anomaly''. That is, the free-air anomaly is:{{sfn|Lowrie|2007|pp=83–84}}
<math display="block">\Delta g_F = g_m + (\Delta g_{FA} + \Delta g_T + \Delta g_\text{tide}) - g_n</math>

===Bouguer plate correction===
{{main|Bouguer anomaly}}
The free-air anomaly does not take into account the layer of material (after terrain leveling) outside the reference ellipsoid. The gravitational attraction of this layer or plate is taken into account by the Bouguer plate correction, which is {{val|−0.0419|e=-3}} ρ ''h'' mgal m<sup>2</sup> kg<sup>−1</sup>. The density of crustal rock, ρ, is usually taken to be 2670&nbsp;kg m<sup>−3</sup> so the Bouguer plate correction is usually taken as −0.1119 mgal m<sup>−1</sup> ''h''. Here ''h'' is the elevation above the reference ellipsoid.{{sfn|Lowrie|2007|p=80}}

The remaining gravity anomaly at this point in the reduction is called the ''Bouguer anomaly''. That is, the Bouguer anomaly is:{{sfn|Lowrie|2007|pp=83–84}}
<math display="block">\Delta g_B = g_m + (\Delta g_{BP} + \Delta g_{FA} + \Delta g_T + \Delta g_\text{tide}) - g_n</math>

===Isostatic correction===
{{see also|Isostasy}}
The Bouguer anomaly is positive over ocean basins and negative over high continental areas. This shows that the low elevation of ocean basins and high elevation of continents is compensated by the thickness of the crust at depth. The higher terrain is held up by the buoyancy of thicker crust "floating" on the mantle.<ref>{{cite book |last1=Kearey |first1=P. |last2=Klepeis |first2=K.A. |last3=Vine |first3=F.J. |title=Global tectonics. |date=2009 |publisher=Wiley-Blackwell |location=Oxford |isbn=9781405107778 |edition=3rd |page=42}}</ref>

The '''isostatic anomaly''' is defined as the Bouger anomaly minus the gravity anomaly due to the subsurface compensation, and is a measure of the local departure from isostatic equilibrium, due to dynamic processes in the viscous mantle. At the center of a level plateau, it is approximately equal to the free air anomaly.{{sfn|Kearey|Klepeis|Vine|2009|pp=45–48}} The isostatic correction is dependent on the isostatic model used to calculate isostatic balance, and so is slightly different for the Airy-Heiskanen model (which assumes that the crust and mantle are uniform in density and isostatic balance is provided by changes in crust thickness), the Pratt-Hayford model (which assumes that the bottom of the crust is at the same depth everywhere and isostatic balance is provided by lateral changes in crust density), and the Vening Meinesz elastic plate model (which assumes the crust acts like an elastic sheet).{{sfn|Lowrie|2007|pp=103–104}}

''Forward modelling'' is the process of computing the detailed shape of the compensation required by a theoretical model and using this to correct the Bouguer anomaly to yield an isostatic anomaly.{{sfn|Kearey|Klepeis|Vine|2009|p=46}}