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Gravity gradiometry is the study of variations ( ''anomalies'') in the
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 qu ...
field via measurements of the
spatial gradient A spatial gradient is a gradient whose components are spatial derivatives, i.e., rate of change of a given scalar physical quantity with respect to the position coordinates in physical space. Homogeneous regions have spatial gradient vector ...
of
gravitational acceleration In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag (physics), drag). This is the steady gain in speed caused exclusively by gravitational attraction. All bodi ...
. The gravity gradient tensor is a 3x3
tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space. Tensors may map between different objects such as vectors, scalars, and even other ...
; it is given in coordinates by the
Jacobian matrix In vector calculus, the Jacobian matrix (, ) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. If this matrix is square, that is, if the number of variables equals the number of component ...
of the acceleration vector (g= _x g_y g_zT), totaling 9 scalar quantities: : G=\nabla g = \begin \partial/\partial & \partial/\partial & \partial/\partial\\ \partial/\partial & \partial/\partial & \partial/\partial\\ \partial/\partial & \partial/\partial & \partial/\partial \end It has
dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coo ...
of square reciprocal time, in
units Unit may refer to: General measurement * Unit of measurement, a definite magnitude of a physical quantity, defined and adopted by convention or by law **International System of Units (SI), modern form of the metric system **English units, histo ...
of s−2 (or mm−1s−2). Gravity gradiometry is used by oil and mineral prospectors to measure the density of the subsurface, effectively by measuring the rate of change of gravitational acceleration due to underlying rock properties. From this information it is possible to build a picture of subsurface anomalies which can then be used to more accurately target oil, gas and mineral deposits. It is also used to image
water column The (oceanic) water column is a concept used in oceanography to describe the physical (temperature, salinity, light penetration) and chemical ( pH, dissolved oxygen, nutrient salts) characteristics of seawater at different depths for a defined ...
density, when locating submerged objects, or determining water depth (
bathymetry Bathymetry (; ) is the study of underwater depth of ocean floors ('' seabed topography''), river floors, or lake floors. In other words, bathymetry is the underwater equivalent to hypsometry or topography. The first recorded evidence of wate ...
). Physical scientists use
gravimeter Gravimetry is the measurement of the strength of a gravitational field. Gravimetry may be used when either the magnitude of a gravitational field or the properties of matter responsible for its creation are of interest. The study of gravity c ...
s to determine the exact size and shape of the earth and they contribute to the gravity compensations applied to inertial navigation systems.


Gravity gradient

Gravity measurements are a reflection of the earth's gravitational attraction, its
centripetal force Centripetal force (from Latin ''centrum'', "center" and ''petere'', "to seek") is the force that makes a body follow a curved trajectory, path. The direction of the centripetal force is always orthogonality, orthogonal to the motion of the bod ...
,
tidal acceleration Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite (e.g. the Moon) and the primary planet that it orbits (e.g. Earth). The acceleration causes a gradual recession of a satellite in a prograde orbit (satel ...
s due to the sun, moon, and planets, and other applied forces. Gravity gradiometers measure the spatial derivatives of the gravity vector. The most frequently used and intuitive component is the vertical gravity gradient, ''Gzz'', which represents the rate of change of vertical gravity (''gz'') with height (''z''). It can be deduced by differencing the value of gravity at two points separated by a small vertical distance, l, and dividing by this distance. :G_ = \approx The two gravity measurements are provided by accelerometers which are matched and aligned to a high level of accuracy.


Units

The unit of gravity gradient is the eotvos (abbreviated as E), which is equivalent to 10−9 s−2 (or 10−4 m Gal/m). A person walking past at a distance of 2 metres would provide a gravity gradient signal approximately one E. Mountains can give signals of several hundred Eotvos.


Gravity gradient tensor

Full tensor gradiometers measure the rate of change of the gravity vector in all three perpendicular directions giving rise to a gravity gradient tensor (Fig 1).


Comparison to gravity

Being the derivatives of gravity, the spectral power of gravity gradient signals is pushed to higher frequencies. This generally makes the gravity gradient anomaly more localised to the source than the gravity anomaly. The table (below) and graph (Fig 2) compare the ''gz'' and ''Gzz'' responses from a point source. Conversely, gravity measurements have more signal power at low frequency therefore making them more sensitive to regional signals and deeper sources.


Dynamic survey environments (airborne and marine)

The derivative measurement sacrifices the overall energy in the signal, but significantly reduces the noise due to motional disturbance. On a moving platform, the acceleration disturbance measured by the two accelerometers is the same so that when forming the difference, it cancels in the gravity gradient measurement. This is the principal reason for deploying gradiometers in airborne and marine surveys where the acceleration levels are orders of magnitude greater than the signals of interest. The signal to noise ratio benefits most at high frequency (above 0.01 Hz), where the airborne acceleration noise is largest.


Applications

Gravity gradiometry has predominately been used to image subsurface geology to aid hydrocarbon and mineral exploration. Over 2.5 million line km has now been surveyed using the technique. The surveys highlight gravity anomalies that can be related to geological features such as Salt diapirs, Fault systems,
Reef A reef is a ridge or shoal of rock, coral, or similar relatively stable material lying beneath the surface of a natural body of water. Many reefs result from natural, abiotic component, abiotic (non-living) processes such as deposition (geol ...
structures,
Kimberlite Kimberlite is an igneous rock and a rare variant of peridotite. It is most commonly known as the main host matrix for diamonds. It is named after the town of Kimberley, Northern Cape, Kimberley in South Africa, where the discovery of an 83.5-Car ...
pipes, etc. Other applications include tunnel and bunker detection and the recent
GOCE The Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) was the first of European Space Agency, ESA's Living Planet Programme satellite, heavy satellites intended to map in unprecedented detail the Earth's gravity field. The spacecr ...
mission that aims to improve the knowledge of ocean circulation.


Gravity gradiometers


Lockheed Martin gravity gradiometers

During the 1970s, as an executive in the US Dept. of Defense, John Brett initiated the development of the gravity gradiometer to support the Trident 2 system. A committee was commissioned to seek commercial applications for the Full Tensor Gradient (FTG) system that was developed by Bell Aerospace (later acquired by
Lockheed Martin The Lockheed Martin Corporation is an American Arms industry, defense and aerospace manufacturer with worldwide interests. It was formed by the merger of Lockheed Corporation with Martin Marietta on March 15, 1995. It is headquartered in North ...
) and was being deployed on US Navy Trident submarines designed to aid covert navigation. As the Cold War came to a close, the US Navy released the classified technology and opened the door for full commercialization of the technology. The existence of the gravity gradiometer was famously exposed in the film ''The Hunt for Red October'' released in 1990. There are two types of Lockheed Martin gravity gradiometers currently in operation: the 3D Full Tensor Gravity Gradiometer (FTG; deployed in either a fixed wing aircraft or a ship) and the FALCON gradiometer (a partial tensor system with 8 accelerometers and deployed in a fixed wing aircraft or a helicopter). The 3D FTG system contains three gravity gradiometry instruments (GGIs), each consisting of two opposing pairs of accelerometers arranged on a spinning disc with measurement direction in the spin direction.


Other gravity gradiometers

;Electrostatic gravity gradiometer: This is the gravity gradiometer deployed on the European Space Agency's
GOCE The Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) was the first of European Space Agency, ESA's Living Planet Programme satellite, heavy satellites intended to map in unprecedented detail the Earth's gravity field. The spacecr ...
mission. It is a three-axis diagonal gradiometer based on three pairs of electrostatic servo-controlled accelerometers. ;ARKeX Exploration gravity gradiometer: An evolution of technology originally developed for European Space Agency, the Exploration Gravity Gradiometer (EGG), developed by ARKeX (a corporation that is now defunct), uses two key principles of
superconductivity Superconductivity is a set of physical properties observed in superconductors: materials where Electrical resistance and conductance, electrical resistance vanishes and Magnetic field, magnetic fields are expelled from the material. Unlike an ord ...
to deliver its performance: the
Meissner effect In condensed-matter physics, the Meissner effect (or Meißner–Ochsenfeld effect) is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state when it is cooled below the critical temperature. Th ...
, which provides levitation of the EGG proof masses and flux quantization, which gives the EGG its inherent stability. The EGG has been specifically designed for high dynamic survey environments. ;Ribbon sensor gradiometer: The Gravitec gravity gradiometer sensor consists of a single sensing element (a ribbon) that responds to gravity gradient forces. It is designed for borehole applications. ;UWA gravity gradiometer: The University of Western Australia (aka VK-1) Gravity Gradiometer is a superconducting instrument which uses an orthogonal quadrupole responder (OQR) design based on pairs of micro-flexure supported balance beams. ;Gedex gravity gradiometer: The Gedex gravity gradiometer (AKA High-Definition Airborne Gravity Gradiometer, HD-AGG) is also a superconducting OQR-type gravity gradiometer, based on technology developed at the University of Maryland. ;iCORUS gravity gradiometer: The iCORUS gravity gradiometer is a strapdown airborne gravity gradiometer, based on technology developed at iMAR Navigation in Germany. ;Quantum Technology gravity gradiometers: Quantum Technology gravity gradiometers based on
atom interferometry An atom interferometer uses the wave-like nature of atoms in order to produce interference. In atom interferometers, the roles of matter and light are reversed compared to the laser based interferometers, i.e. the beam splitter and mirrors are lase ...
are currently under development by a number of universities world wide and are beginning to be used in practical applications.


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 ...
* * * * *


References


External links


Advances and Challenges in the Development and Deployment of Gravity Gradiometer Systems


{{DEFAULTSORT:Gravity Gradiometry Geophysical survey Geodesy Geological techniques Gravimetry