Bouguer anomaly
Encyclopedia
In geodesy
and geophysics
, the Bouguer anomaly (named after Pierre Bouguer
) is a gravity anomaly
, corrected for the height at which it is measured and the attraction of terrain. The height correction alone gives a free-air anomaly
.
, the height of the gravity measurement location above sea level, we speak of a simple or incomplete Bouguer reduction. The difference between the two, the differential gravitational effect of the unevenness of the terrain, is called the terrain effect. It is always negative.
The equation for the simple Bouguer reduction is
where
is the density of the material, 
is the constant of gravitation and 
is the thickness of the plate.
computations.
Gravity outside the plate is perpendicular to the plate, towards it, with magnitude 2πG times the mass per unit area, where G = 6.67 × 10−11 N m² kg−2, hence we have 4.191 × 10−10 N m² kg−2 times the mass per unit area.
Using 1 Gal
= 0.01 m/s² we get 4.191 × 10−5 mGal m² kg−1 times the mass per unit area.
For mean rock
density
(2.67 g/cm³) this gives 0.1119 mGal/m.
This is independent of the distance to the plate. (This can be proven most simply with Gauss's law for gravity, but can also be proven directly with Newton's law of gravity
.)
with the density depending on one Cartesian coordinate z only, gravity for any z is 2πG times the difference in mass per unit area on either side of this z value.
In particular, a combination of two equal parallel infinite plates does not produce any gravity inside.
Geodesy
Geodesy , also named geodetics, a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth, including its gravitational field, in a three-dimensional time-varying space. Geodesists also study geodynamical phenomena such as crustal...
and geophysics
Geophysics
Geophysics is the physics of the Earth and its environment in space; also the study of the Earth using quantitative physical methods. The term geophysics sometimes refers only to the geological applications: Earth's shape; its gravitational and magnetic fields; its internal structure and...
, the Bouguer anomaly (named after Pierre Bouguer
Pierre Bouguer
Pierre Bouguer was a French mathematician, geophysicist, geodesist, and astronomer. He is also known as "the father of naval architecture"....
) is a gravity anomaly
Gravity anomaly
A gravity anomaly is the difference between the observed acceleration of Earth's gravity and a value predicted from a model.-Geodesy and geophysics:...
, corrected for the height at which it is measured and the attraction of terrain. The height correction alone gives a free-air anomaly
Free-air 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 correct for the elevation at which a measurement is made...
.
Bouguer reduction
The correction for terrain is called the Bouguer reduction. Where the effects of terrain are removed precisely, we speak of a refined or complete Bouguer reduction. Where the terrain is approximated by a flat plate of thickness, the height of the gravity measurement location above sea level, we speak of a simple or incomplete Bouguer reduction. The difference between the two, the differential gravitational effect of the unevenness of the terrain, is called the terrain effect. It is always negative.The equation for the simple Bouguer reduction is
where
is the density of the material, is the constant of gravitation and is the thickness of the plate.Bouguer plate
A Bouguer plate is an infinite, flat plate, used as a model in gravity and gravity anomalyGravity anomaly
A gravity anomaly is the difference between the observed acceleration of Earth's gravity and a value predicted from a model.-Geodesy and geophysics:...
computations.
Gravity outside the plate is perpendicular to the plate, towards it, with magnitude 2πG times the mass per unit area, where G = 6.67 × 10−11 N m² kg−2, hence we have 4.191 × 10−10 N m² kg−2 times the mass per unit area.
Using 1 Gal
Gal (unit)
The gal, sometimes called galileo, is a unit of acceleration used extensively in the science of gravimetry. The gal is defined as 1 centimeter per second squared ....
= 0.01 m/s² we get 4.191 × 10−5 mGal m² kg−1 times the mass per unit area.
For mean rock
Rock (geology)
In geology, rock or stone is a naturally occurring solid aggregate of minerals and/or mineraloids.The Earth's outer solid layer, the lithosphere, is made of rock. In general rocks are of three types, namely, igneous, sedimentary, and metamorphic...
density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
(2.67 g/cm³) this gives 0.1119 mGal/m.
This is independent of the distance to the plate. (This can be proven most simply with Gauss's law for gravity, but can also be proven directly with Newton's law of gravity
Newton's law of universal gravitation
Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them...
.)
Bouguer gradient
On Earth the effect on gravity of elevation is 0.3086 mGal/m decrease when going up, minus the gravity of the Bouguer plate, giving the Bouguer gradient of 0.1967 mGal/m.General
More generally, for a mass distributionMass distribution
Mass distribution is a term used in physics and mechanics and describes 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:...
with the density depending on one Cartesian coordinate z only, gravity for any z is 2πG times the difference in mass per unit area on either side of this z value.
In particular, a combination of two equal parallel infinite plates does not produce any gravity inside.
See also
- Earth's gravityEarth's gravityThe gravity of Earth, denoted g, refers to the acceleration that the Earth imparts to objects on or near its surface. In SI units this acceleration is measured in metres per second per second or equivalently in newtons per kilogram...
- Gravity anomalyGravity anomalyA gravity anomaly is the difference between the observed acceleration of Earth's gravity and a value predicted from a model.-Geodesy and geophysics:...
- Physical geodesyPhysical geodesyPhysical geodesy is the study of the physical properties of the gravity field of the Earth, the geopotential, with a view to their application in geodesy.-Measurement procedure:...
- Vertical deflectionVertical deflectionThe vertical deflection at a point on the earth is a measure of how far the direction of the local gravity field has been shifted by local anomalies such as nearby mountains....
- divergence theoremDivergence theoremIn vector calculus, the divergence theorem, also known as Gauss' theorem , Ostrogradsky's theorem , or Gauss–Ostrogradsky theorem is a result that relates the flow of a vector field through a surface to the behavior of the vector field inside the surface.More precisely, the divergence theorem...
- potential theoryPotential theoryIn mathematics and mathematical physics, potential theory may be defined as the study of harmonic functions.- Definition and comments :The term "potential theory" was coined in 19th-century physics, when it was realized that the fundamental forces of nature could be modeled using potentials which...
- Gauss's law for gravity
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 [United States Geological Survey].
- Bouguer anomaly map of Grahamland F.J. Davy (et al.), British Antarctic Survey, BAS Bulletins 1963-1988
- Bouguer anomaly map depicting south-eastern UruguayUruguayUruguay ,officially the Oriental Republic of Uruguay,sometimes the Eastern Republic of Uruguay; ) is a country in the southeastern part of South America. It is home to some 3.5 million people, of whom 1.8 million live in the capital Montevideo and its metropolitan area...
's Merín Lagoon anomaly (amplitude greater than +100 mGalGal (unit)The gal, sometimes called galileo, is a unit of acceleration used extensively in the science of gravimetry. The gal is defined as 1 centimeter per second squared ....
), and detail of site. - List of Magnetic and Gravity Maps by State by the [United States Geological Survey].