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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.


Units of measurement

Gravity is usually measured in units of
acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by t ...
. In the SI system of units, the standard unit of acceleration is 1
metre per second squared The metre per second squared is the unit of acceleration in the International System of Units (SI). As a derived unit, it is composed from the SI base units of length, the metre, and time, the second. Its symbol is written in several forms as m/ ...
(abbreviated as m/s2). Other units include the cgs gal (sometimes known as a ''galileo'', in either case with symbol Gal), which equals 1
centimetre 330px, Different lengths as in respect to the Electromagnetic spectrum, measured by the Metre and its deriveds scales. The Microwave are in-between 1 meter to 1 millimeter. A centimetre (international spelling) or centimeter (American spellin ...
per second squared, and the '' g'' (''g''n), equal to 9.80665 m/s2. The value of the ''g''n is defined approximately equal to the acceleration due to gravity at the Earth's surface (although the value of ''g'' varies by location).


Gravimeters

An instrument used to measure gravity is known as a gravimeter. For a small body,
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
predicts gravitational effects indistinguishable from the effects of
acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by t ...
by the equivalence principle. Thus, gravimeters can be regarded as special-purpose
accelerometer An accelerometer is a tool that measures proper acceleration. Proper acceleration is the acceleration (the rate of change of velocity) of a body in its own instantaneous rest frame; this is different from coordinate acceleration, which is acc ...
s. Many
weighing scale A scale or balance is a device used to measure weight or mass. These are also known as mass scales, weight scales, mass balances, and weight balances. The traditional scale consists of two plates or bowls suspended at equal distances from a ...
s may be regarded as simple gravimeters. In one common form, a spring is used to counteract the force of gravity pulling on an object. The change in length of the spring may be calibrated to the force required to balance the gravitational pull. The resulting measurement may be made in units of force (such as the newton), but is more commonly made in units of gals or cm/s2. Researchers use more sophisticated gravimeters when precise measurements are needed. When measuring the Earth's gravitational field, measurements are made to the precision of microgals to find density variations in the rocks making up the Earth. Several types of gravimeters exist for making these measurements, including some that are essentially refined versions of the spring scale described above. These measurements are used to define gravity anomalies. Besides
precision Precision, precise or precisely may refer to: Science, and technology, and mathematics Mathematics and computing (general) * Accuracy and precision, measurement deviation from true value and its scatter * Significant figures, the number of digit ...
,
stability Stability may refer to: Mathematics *Stability theory, the study of the stability of solutions to differential equations and dynamical systems ** Asymptotic stability ** Linear stability ** Lyapunov stability ** Orbital stability ** Structural sta ...
is also an important property of a gravimeter, as it allows the monitoring of gravity ''changes''. These changes can be the result of mass displacements inside the Earth, or of vertical movements of the Earth's crust on which measurements are being made: remember that gravity decreases 0.03 mGal for every metre of
height Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is). For example, "The height of that building is 50 m" or "The height of an airplane in-flight is ab ...
. The study of gravity changes belongs to
geodynamics Geodynamics is a subfield of geophysics dealing with dynamics of the Earth. It applies physics, chemistry and mathematics to the understanding of how mantle convection leads to plate tectonics and geologic phenomena such as seafloor spreading, mo ...
. The majority of modern gravimeters use specially-designed metal or
quartz Quartz is a hard, crystalline mineral composed of silica ( silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical ...
zero-length springs to support the test mass. Zero-length springs do not follow
Hooke's law In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring by some distance () scales linearly with respect to that distance—that is, where is a constant factor characteristic of ...
; instead they have a force proportional to their length. The special property of these springs is that the natural resonant period of
oscillation Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
of the spring–mass system can be made very long – approaching a thousand seconds. This detunes the test mass from most local vibration and mechanical
noise Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference aris ...
, increasing the sensitivity and utility of the gravimeter. Quartz and metal springs are chosen for different reasons; quartz springs are less affected by magnetic and electric fields while metal springs have a much lower drift (elongation) with time. The test mass is sealed in an air-tight container so that tiny changes of barometric pressure from blowing wind and other weather do not change the buoyancy of the test mass in air. Spring gravimeters are, in practice, relative instruments which measure the difference in gravity between different locations. A relative instrument also requires calibration by comparing instrument readings taken at locations with known complete or absolute values of gravity. Absolute gravimeters provide such measurements by determining the gravitational acceleration of a test mass in vacuum. A test mass is allowed to fall freely inside a vacuum chamber and its position is measured with a laser interferometer and timed with an atomic clock. The laser wavelength is known to ±0.025 ppb and the clock is stable to ±0.03 ppb as well. Great care must be taken to minimize the effects of perturbing forces such as residual air resistance (even in vacuum), vibration, and magnetic forces. Such instruments are capable of an accuracy of about two parts per billion or 0.002 mGal and reference their measurement to atomic standards of length and
time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, ...
. Their primary use is for calibrating relative instruments, monitoring crustal deformation, and in geophysical studies requiring high accuracy and stability. However, absolute instruments are somewhat larger and significantly more expensive than relative spring gravimeters, and are thus relatively rare. Gravimeters have been designed to mount in vehicles, including aircraft (note the field of aerogravity), ships and submarines. These special gravimeters isolate acceleration from the movement of the vehicle and subtract it from measurements. The acceleration of the vehicles is often hundreds or thousands of times stronger than the changes being measured. A gravimeter (the ''Lunar Surface Gravimeter'') deployed on the surface of the moon during the Apollo 17 mission did not work due to a design error. KoA second device (the ''Traverse Gravimeter Experiment'') functioned as anticipated.


Further information

A gravimeter is an instrument used to measure
gravitational acceleration In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag). This is the steady gain in speed caused exclusively by the force of gravitational attraction. All bodi ...
. Every mass has an associated gravitational potential. The gradient of this potential is a force. A gravimeter measures this gravitational force. The first gravimeters were vertical
accelerometer An accelerometer is a tool that measures proper acceleration. Proper acceleration is the acceleration (the rate of change of velocity) of a body in its own instantaneous rest frame; this is different from coordinate acceleration, which is acc ...
s, specialized for measuring the constant downward acceleration of gravity on the earth's surface. The earth's vertical gravity varies from place to place over the surface of the Earth by about ±0.5%. It varies by about (nanometers per second squared) at any location because of the changing positions of the sun and moon relative to the earth. The change from calling a device an "accelerometer" to calling it a "gravimeter" occurs at approximately the point where it has to make corrections for earth tides. Though similar in design to other accelerometers, gravimeters are typically designed to be much more sensitive. Their first uses were to measure the changes in gravity from the varying densities and distribution of masses inside the earth, from temporal "
tidal Tidal is the adjectival form of tide. Tidal may also refer to: * ''Tidal'' (album), a 1996 album by Fiona Apple * Tidal (king), a king involved in the Battle of the Vale of Siddim * TidalCycles, a live coding environment for music * Tidal (servic ...
" variations in the shape and distribution of mass in the oceans, atmosphere and earth. Gravimeters can detect
vibration Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin ''vibrationem'' ("shaking, brandishing"). The oscillations may be periodic, such as the motion of a pendulum—or random, su ...
s and gravity changes from human activities. Depending on the interests of the researcher or operator, this might be counteracted by integral vibration isolation and
signal processing Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, ...
. The resolution of gravimeters can be increased by averaging samples over longer periods. Fundamental characteristics of gravimeters are the accuracy of a single measurement (a single "sample"), and the sampling rate (samples per second). :\text = for example: :\text = Gravimeters display their measurements in units of gals (cm/s2), nanometers per second squared, and parts per million, parts per billion, or parts per trillion of the average vertical acceleration with respect to the earth. Some newer units are pm/s2 (picometers per second squared), fm/s2 (femto), am/s2 (atto) for very sensitive instruments. Gravimeters are used for petroleum and mineral
prospecting Prospecting is the first stage of the geological analysis (followed by exploration) of a territory. It is the search for minerals, fossils, precious metals, or mineral specimens. It is also known as fossicking. Traditionally prospecting rel ...
,
seismology Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...
, geodesy,
geophysical survey Geophysical survey is the systematic collection of geophysical data for spatial studies. Detection and analysis of the geophysical signals forms the core of Geophysical signal processing. The magnetic and gravitational fields emanating from the E ...
s and other
geophysical 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'' some ...
research, and for metrology. Their fundamental purpose is to map the gravity field in space and time. Most current work is earth-based, with a few satellites around earth, but gravimeters are also applicable to the moon, sun, planets, asteroids, stars, galaxies and other bodies. Gravitational wave experiments monitor the changes with time in the gravitational potential itself, rather than the gradient of the potential which the gravimeter is tracking. This distinction is somewhat arbitrary. The subsystems of the gravitational radiation experiments are very sensitive to changes in the gradient of the potential. The local gravity signals on earth that interfere with gravitational wave experiments are disparagingly referred to as "Newtonian noise", since Newtonian gravity calculations are sufficient to characterize many of the local (earth-based) signals. The term ''absolute gravimeter'' has most often been used to label gravimeters which report the local vertical acceleration due to the earth. ''Relative gravimeter'' usually refer to differential comparisons of gravity from one place to another. They are designed to subtract the average vertical gravity automatically. They can be calibrated at a location where the gravity is known accurately, and then transported to the location where the gravity is to be measured. Or they can calibrated in absolute units at their operating location. There are many methods for displaying acceleration fields, also called ''gravity fields''. This includes traditional 2D maps, but increasingly 3D video. Since gravity and acceleration are the same, "acceleration field" might be preferable, since "gravity" is an oft misused prefix.


Commercial absolute gravimeters

Gravimeters for measuring the earth's gravity as precisely as possible are getting smaller and more portable. A common type measures the acceleration of small masses free falling in a
vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or " void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often di ...
, when the accelerometer is firmly attached to the ground. The mass includes a
retroreflector A retroreflector (sometimes called a retroflector or cataphote) is a device or surface that reflection (physics), reflects radiation (usually light) back to its source with minimum scattering. This works at a wide range of angle of incidence (opt ...
and terminates one arm of a
Michelson interferometer The Michelson interferometer is a common configuration for optical interferometry and was invented by the 19/20th-century American physicist Albert Abraham Michelson. Using a beam splitter, a light source is split into two arms. Each of those ...
. By counting and timing the interference fringes, the acceleration of the mass can be measured. A more recent development is a "rise and fall" version that tosses the mass upward and measures both upward and downward motion. This allows cancellation of some
measurement error Observational error (or measurement error) is the difference between a measured value of a quantity and its true value.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. In statistics, an error is not necessarily a "mistake ...
s; however, "rise and fall" gravimeters are not yet in common use. Absolute gravimeters are used in the calibration of relative gravimeters, surveying for gravity anomalies (voids), and for establishing the vertical control network. Atom interferometric and atomic fountain methods are used for precise measurement of the earth's gravity, and atomic clocks and purpose-built instruments can use time dilation (also called general relativistic) measurements to track changes in the gravitational potential and gravitational acceleration on the earth. The term "absolute" does not convey the instrument's stability, sensitivity, accuracy, ease of use, and bandwidth. So it and "relative" should not be used when more specific characteristics can be given.


Relative gravimeters

The most common gravimeters are spring-based. They are used in gravity surveys over large areas for establishing the figure of the
geoid The geoid () is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended ...
over those areas. They are basically a weight on a spring, and by measuring the amount by which the weight stretches the spring, local gravity can be measured. However, the strength of the spring must be
calibrate In measurement technology and metrology, calibration is the comparison of measurement values delivered by a device under test with those of a calibration standard of known accuracy. Such a standard could be another measurement device of known ...
d by placing the instrument in a location with a known gravitational acceleration. The current standard for sensitive gravimeters are the ''superconducting gravimeters'', which operate by suspending a superconducting niobium sphere in an extremely stable magnetic field; the current required to generate the magnetic field that suspends the niobium sphere is proportional to the strength of the Earth's gravitational acceleration. The
superconducting Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
gravimeter achieves sensitivities of (one nanogal), approximately one trillionth (10) of the Earth surface gravity. In a demonstration of the sensitivity of the superconducting gravimeter, Virtanen (2006), describes how an instrument at Metsähovi, Finland, detected the gradual increase in surface gravity as workmen cleared snow from its laboratory roof. The largest component of the signal recorded by a superconducting gravimeter is the tidal gravity of the sun and moon acting at the station. This is roughly (nanometers per second squared) at most locations. "SGs", as they are called, can detect and characterize
earth tides Earth tide (also known as solid Earth tide, crustal tide, body tide, bodily tide or land tide) is the displacement of the solid earth's surface caused by the gravity of the Moon and Sun. Its main component has meter-level amplitude at periods of a ...
, changes in the density of the atmosphere, the effect of changes in the shape of the surface of the ocean, the effect of the atmosphere's pressure on the earth, changes in the rate of rotation of the earth, oscillations of the earth's core, distant and nearby seismic events, and more. Many broadband, three axis, seismometers in common use are sensitive enough to track the sun and moon. When operated to report acceleration, they are useful gravimeters. Because they have three axes, it is possible to solve for their position and orientation, by either tracking the arrival time and pattern of seismic waves from earthquakes, or by referencing them to the sun and moon tidal gravity. Recently, the SGs, and broadband three axis seismometers operated in gravimeter mode, have begun to detect and characterize the small gravity signals from earthquakes. These signals arrive at the gravimeter at the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
, so have the potential to improve earthquake early warning methods. There is some activity to design purpose-built gravimeters of sufficient sensitivity and bandwidth to detect these prompt gravity signals from earthquakes. Not just the magnitude 7+ events, but also the smaller, much more frequent, events. Newer MEMS gravimeters, atom gravimeters – MEMS gravimeters offer the potential for low cost arrays of sensors. MEMS gravimeters are currently variations on spring type accelerometers where the motions of a tiny cantilever or mass are tracked to report acceleration. Much of the research is focussed on different methods of detecting the position and movements of these small masses. In Atom gravimeters, the mass is a collection of atoms. For a given restoring force, the central frequency of the instrument is often given by : \omega = 2\pi \times \text = \sqrt (in radians per second) The term for the "force constant" changes if the restoring force is electrostatic, magnetostatic, electromagnetic, optical, microwave, acoustic, or any of dozens of different ways to keep the mass stationary. The "force constant" is just the coefficient of the displacement term in the equation of motion: : :''m'' mass, ''a'' acceleration, ''b'' viscosity, ''v'' velocity, ''k'' force constant, ''x'' displacement :''F'' external force as a function of location/position and time. ''F'' is the force being measured, and is the acceleration. : + higher derivatives of the restoring force Precise GPS stations can be operated as gravimeters since they are increasingly measuring three axis positions over time, which, when differentiated twice, give an acceleration signal. The satellite borne gravimeters
GOCE ''Goce'' is an opera composed by Kiril Makedonski (1925–1984), written by Venko Markovski and dedicated to Gotse Delchev. The work was commissioned to be the very first opera performed by the Macedonian National Opera Company. It premiered o ...
,
GRACE Grace may refer to: Places United States * Grace, Idaho, a city * Grace (CTA station), Chicago Transit Authority's Howard Line, Illinois * Little Goose Creek (Kentucky), location of Grace post office * Grace, Carroll County, Missouri, an uninco ...
, are mostly operating in gravity gradiometer mode. They yield detailed information about the earth's time varying gravity field The spherical harmonic gravitational potential models are slowly improving in both spatial and temporal resolution. Taking the gradient of the potentials gives estimate of local acceleration which are what is measured by the gravimeter arrays. The superconducting gravimeter network has been used to
ground truth Ground truth is information that is known to be real or true, provided by direct observation and measurement (i.e. empirical evidence) as opposed to information provided by inference. Etymology The ''Oxford English Dictionary'' (s.v. "ground t ...
the satellite potentials. This should eventually improve both the satellite and earth-based methods and intercomparisons. Transportable relative gravimeters also exist; they employ an extremely stable inertial platform to compensate for the masking effects of motion and vibration, a difficult engineering feat. The first transportable relative gravimeters were, reportedly, a secret military technology developed in the 1950–1960s as a navigational aid for
nuclear submarine A nuclear submarine is a submarine powered by a nuclear reactor, but not necessarily nuclear-armed. Nuclear submarines have considerable performance advantages over "conventional" (typically diesel-electric) submarines. Nuclear propulsion, ...
s. Subsequently in the 1980s, transportable relative gravimeters were
reverse engineered Reverse engineering (also known as backwards engineering or back engineering) is a process or method through which one attempts to understand through deductive reasoning how a previously made device, process, system, or piece of software accompli ...
by the civilian sector for use on ship, then in air and finally satellite borne gravity surveys.


Microgravimetry

Microgravimetry is an important branch developed on the foundation of classical gravimetry. Microgravity investigations are carried out in order to solve various problems of engineering geology, mainly location of voids and their monitoring. Very detailed measurements of high accuracy can indicate voids of any origin, provided the size and depth are large enough to produce gravity effect stronger than is the level of confidence of relevant gravity signal.


History

The modern gravimeter was developed by Lucien LaCoste and Arnold Romberg in 1936. They also invented most subsequent refinements, including the ship-mounted gravimeter, in 1965, temperature-resistant instruments for deep boreholes, and lightweight hand-carried instruments. Most of their designs remain in use with refinements in data collection and data processing.


Satellite gravimetry

Currently, the static and time-variable Earth's gravity field parameters are being determined using modern satellite missions, such as
GOCE ''Goce'' is an opera composed by Kiril Makedonski (1925–1984), written by Venko Markovski and dedicated to Gotse Delchev. The work was commissioned to be the very first opera performed by the Macedonian National Opera Company. It premiered o ...
, CHAMP,
Swarm Swarm behaviour, or swarming, is a collective behaviour exhibited by entities, particularly animals, of similar size which aggregate together, perhaps milling about the same spot or perhaps moving ''en masse'' or migrating in some direction. ...
,
GRACE and GRACE-FO The Gravity Recovery and Climate Experiment (GRACE) was a joint mission of NASA and the German Aerospace Center (DLR). Twin satellites took detailed measurements of Earth's gravity field anomalies from its launch in March 2002 to the end of it ...
. The lowest-degree parameters, including the Earth's oblateness and geocenter motion are best determined from Satellite laser ranging. Large-scale gravity anomalies can be detected from space, as a by-product of satellite gravity missions, e.g.,
GOCE ''Goce'' is an opera composed by Kiril Makedonski (1925–1984), written by Venko Markovski and dedicated to Gotse Delchev. The work was commissioned to be the very first opera performed by the Macedonian National Opera Company. It premiered o ...
. These satellite missions aim at the recovery of a detailed gravity field model of the Earth, typically presented in the form of a spherical-harmonic expansion of the Earth's gravitational potential, but alternative presentations, such as maps of
geoid The geoid () is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended ...
undulations or gravity anomalies, are also produced. The Gravity Recovery and Climate Experiment (GRACE) consists of two satellites that can detect gravitational changes across the Earth. Also these changes can be presented as gravity anomaly temporal variations. The
Gravity Recovery and Interior Laboratory The Gravity Recovery and Interior Laboratory (GRAIL) was an American lunar science mission in NASA's Discovery Program which used high-quality gravitational field mapping of the Moon to determine its interior structure. The two small spacecraf ...
(GRAIL) also consisted of two spacecraft orbiting the Moon, which orbited for three years before their deorbit in 2015.


See also

* Felix Andries Vening Meinesz *
Geophysical survey Geophysical survey is the systematic collection of geophysical data for spatial studies. Detection and analysis of the geophysical signals forms the core of Geophysical signal processing. The magnetic and gravitational fields emanating from the E ...
*
Gravity Field and Steady-State Ocean Circulation Explorer The Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) was the first of ESA's Living Planet Programme satellites intended to map in unprecedented detail the Earth's gravity field. The spacecraft's primary instrumentation was a hi ...
(GOCE) A modern satellite-borne
gradiometer A gradiometer measures the gradient (numerical rate of change) of a physical quantity, such as a magnetic field or gravity. Types of gradiometer There are at least two types of gradiometer to measure magnetic fields: # ''Axial gradiometer''. T ...
containing pairs of gravimeters (accelerometers), launched March 2009 * Gravity of Earth *
Gravity gradiometry Gravity gradiometry is the study and measurement of variations ( anomalies) in the Earth's gravity field. The gravity gradient tensor is the spatial rate of change of gravitational acceleration; as acceleration is a vector quantity, with magnitu ...
*
GRACE and GRACE-FO The Gravity Recovery and Climate Experiment (GRACE) was a joint mission of NASA and the German Aerospace Center (DLR). Twin satellites took detailed measurements of Earth's gravity field anomalies from its launch in March 2002 to the end of it ...
, spacecraft launched March 2002 * Physical geodesy


References

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