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In
geodesy Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equival ...
and
geophysics Geophysics () is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis. The term ''geophysics'' som ...
, the Bouguer anomaly (named after
Pierre Bouguer Pierre Bouguer () (16 February 1698, Croisic – 15 August 1758, Paris) was a French mathematician, geophysicist, geodesist, and astronomer. He is also known as "the father of naval architecture". Career Bouguer's father, Jean Bouguer, one ...
) is a
gravity anomaly The gravity anomaly at a location on the Earth's surface is the difference between the observed value of gravity and the value predicted by a theoretical model. If the Earth were an ideal oblate spheroid of uniform density, then the gravity meas ...
, corrected for the height at which it is measured and the attraction of terrain. The height correction alone gives a free-air gravity anomaly.


Definition

The Bouguer anomaly g_B defined as: g_B = g_ - \delta g_B + \delta g_T Here, * g_F is the free-air gravity anomaly. * \delta g_B is the ''Bouguer correction'' which allows for the gravitational attraction of rocks between the measurement point and sea level; * \delta g_T is a ''terrain correction'' which allows for deviations of the surface from an infinite horizontal plane The free-air anomaly g_F, in its turn, is related to the observed gravity g_ as follows: g_F = g_ - g_\lambda + \delta g_F where: * g_\lambda is the correction for latitude (because the Earth is not a perfect sphere; see
normal gravity In geodesy and geophysics, theoretical gravity or normal gravity is an approximation of the true gravity on Earth's surface by means of a mathematical model representing Earth. The most common model of a smoothed Earth is a rotating Earth ellipsoid ...
); * \delta g_F is the free-air correction.


Reduction

A Bouguer reduction is called ''simple'' (or ''incomplete'') if the terrain is approximated by an infinite flat plate called the Bouguer plate. A ''refined'' (or ''complete'') Bouguer reduction removes the effects of
terrain Terrain or relief (also topography, topographical relief) involves the vertical and horizontal dimensions of land surface. The term bathymetry is used to describe underwater relief, while hypsometry studies terrain relative to sea level. The ...
more precisely. The difference between the two is called the ''(residual) terrain effect'' (or ''(residual) terrain correction'') and is due to the differential gravitational effect of the unevenness of the terrain; it is always negative.


Simple reduction

The gravitational acceleration g outside a Bouguer plate is perpendicular to the plate and towards it, with magnitude ''2πG'' times the mass per unit area, where G is the
gravitational constant The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in th ...
. It is independent of the distance to the plate (as can be proven most simply with
Gauss's law for gravity In physics, Gauss's law for gravity, also known as Gauss's flux theorem for gravity, is a law of physics that is equivalent to Newton's law of universal gravitation. It is named after Carl Friedrich Gauss. It states that the flux (surface integr ...
, but can also be proven directly with
Newton's law of gravity Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distanc ...
). The value of G is , so g is times the mass per unit area. Using  =  () we get times the mass per unit area. For mean rock
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematica ...
() this gives . The Bouguer reduction for a Bouguer plate of thickness H is \delta g_B = 2\pi\rho G H where \rho is the density of the material and G is the constant of gravitation. On Earth the effect on gravity of elevation is 0.3086 mGal m−1 decrease when going up, minus the gravity of the Bouguer plate, giving the ''Bouguer gradient'' of 0.1967 mGal m−1. More generally, for a
mass distribution In physics and mechanics, mass distribution is the spatial distribution of mass within a solid body. In principle, it is relevant also for gases or liquids, but on Earth their mass distribution is almost homogeneous. Astronomy In astronomy mass d ...
with the density depending on one Cartesian coordinate ''z'' only, gravity for any ''z'' is 2π''G'' times the difference in mass per unit area on either side of this ''z'' value. A combination of two parallel infinite if equal mass per unit area plates does not produce any gravity between them.


See also

*
Earth's gravity The gravity of Earth, denoted by , is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation). It is a vector quantit ...
*
Physical geodesy Physical may refer to: * Physical examination, a regular overall check-up with a doctor * ''Physical'' (Olivia Newton-John album), 1981 ** "Physical" (Olivia Newton-John song) * ''Physical'' (Gabe Gurnsey album) * "Physical" (Alcazar song) (2004) * ...
*
Potential theory In mathematics and mathematical physics, potential theory is the study of harmonic functions. The term "potential theory" was coined in 19th-century physics when it was realized that two fundamental forces of nature known at the time, namely gravi ...
*
Vertical deflection The vertical deflection (VD) or deflection of the vertical (DoV), also known as deflection of the plumb line and astro-geodetic deflection, is a measure of how far the gravity direction at a given point of interest is rotated by local mass anom ...


Notes


References

* *{{cite book , last = Hofmann-Wellenhof , first = Bernard , last2 = Moritz , first2 = Helmut , title = Physical Geodesy , publisher =
Springer Springer or springers may refer to: Publishers * Springer Science+Business Media, aka Springer International Publishing, a worldwide publishing group founded in 1842 in Germany formerly known as Springer-Verlag. ** Springer Nature, a multinationa ...
, date = 2006 , edition = 2nd. , isbn=978-3-211-33544-4


External links


Bouguer anomalies of Belgium. The blue regions are related to deficit masses in the subsurface

Bouguer gravity anomaly grid for the conterminous US
by the nited States Geological Survey
Bouguer anomaly map of Grahamland
F.J. Davey (et al.), British Antarctic Survey
BAS Bulletins 1963-1988

Bouguer anomaly map
depicting south-eastern
Uruguay Uruguay (; ), officially the Oriental Republic of Uruguay ( es, República Oriental del Uruguay), is a country in South America. It shares borders with Argentina to its west and southwest and Brazil to its north and northeast; while bordering ...
's Merín Lagoon anomaly (amplitude greater than +100 mGal), an
detail of site


by the nited States Geological Survey Geophysics Gravimetry