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 equivale ...
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 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 account for the elevation at which a measurement is made. It does so by adjusting these ...
.
Definition
The Bouguer anomaly
defined as:
Here,
*
is the free-air gravity anomaly.
*
is the ''Bouguer correction'' which allows for the gravitational attraction of rocks between the measurement point and sea level;
*
is a ''terrain correction'' which allows for deviations of the surface from an infinite horizontal plane
The free-air anomaly
, in its turn, is related to the observed gravity
as follows:
where:
*
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 ...
);
*
is the
free-air correction 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 account for the elevation at which a measurement is made. It does so by adjusting these ...
.
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 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 Latin word ...
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
outside a Bouguer plate is perpendicular to the plate and towards it, with magnitude ''2πG'' times the mass per unit area, where
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 ...
. 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 integ ...
, 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 distan ...
). The value of
is , so
is times the mass per unit area. Using = () we get times the mass per unit area. For mean
rock
Rock most often refers to:
* Rock (geology), a naturally occurring solid aggregate of minerals or mineraloids
* Rock music, a genre of popular music
Rock or Rocks may also refer to:
Places United Kingdom
* Rock, Caerphilly, a location in Wales ...
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. Mathematical ...
() this gives .
The Bouguer reduction for a Bouguer plate of thickness
is
where
is the density of the material and
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 quantity ...
* Physical geodesy
Physical may refer to:
*Physical examination
In a physical examination, medical examination, or clinical examination, a medical practitioner examines a patient for any possible medical signs or symptoms of a medical condition. It generally co ...
* 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 anoma ...
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