In
geodesy
Geodesy or geodetics is the science of measuring and representing the Figure of the Earth, geometry, Gravity of Earth, gravity, and Earth's rotation, spatial orientation of the Earth in Relative change, temporally varying Three-dimensional spac ...
and
geophysics
Geophysics () is a subject of natural science concerned with the physical processes and Physical property, properties of Earth and its surrounding space environment, and the use of quantitative methods for their analysis. Geophysicists conduct i ...
, the Bouguer anomaly (named after
Pierre Bouguer
Pierre Bouguer () (16 February 1698, Le 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, ...
) 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
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);
*
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 (), alternatively relief or topographical relief, is the dimension and shape of a given surface of land. In physical geography, terrain is the lay of the land. This is usually expressed in terms of the elevation, slope, and orientati ...
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 is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general relativity, theory of general relativity. It ...
. 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 describes gravity as a force by stating 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 sq ...
). 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 Wale ...
density
Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...
() 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 ...
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
*
* Gravity map
A gravity map is a map that depicts Standard gravity, gravity measurements across an area of space, which are typically obtained via gravimetry. Gravity maps are an extension of the field of geodynamics. Readings are typically taken at regular ...
*
*
*
Notes
References
*
*{{cite book
, last1 = Hofmann-Wellenhof
, first1 = 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, 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 the Río de la Plata to the south and the A ...
's Merín Lagoon anomaly (amplitude greater than +100 mGal), an
detail of site
by the nited States Geological Survey
Geophysics
Gravimetry