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59-409: Geodynamical phenomena, including crustal motion, tides , and polar motion , can be studied by designing global and national control networks , applying space geodesy and terrestrial geodetic techniques, and relying on datums and coordinate systems . Geodetic job titles include geodesist and geodetic surveyor . Geodesy began in pre-scientific antiquity , so the very word geodesy comes from

118-644: A geocentric coordinate frame. One such frame is WGS84 , as well as frames by the International Earth Rotation and Reference Systems Service ( IERS ). GNSS receivers have almost completely replaced terrestrial instruments for large-scale base network surveys. To monitor the Earth's rotation irregularities and plate tectonic motions and for planet-wide geodetic surveys, methods of very-long-baseline interferometry (VLBI) measuring distances to quasars , lunar laser ranging (LLR) measuring distances to prisms on

177-457: A map projection . It is impossible to map the curved surface of Earth onto a flat map surface without deformation. The compromise most often chosen — called a conformal projection — preserves angles and length ratios so that small circles get mapped as small circles and small squares as squares. An example of such a projection is UTM ( Universal Transverse Mercator ). Within the map plane, we have rectangular coordinates x and y . In this case,

236-462: A tide gauge . The geoid can, therefore, be considered a physical ("real") surface. The reference ellipsoid, however, has many possible instantiations and is not readily realizable, so it is an abstract surface. The third primary surface of geodetic interest — the topographic surface of Earth — is also realizable. The locations of points in 3D space most conveniently are described by three cartesian or rectangular coordinates, X , Y , and Z . Since

295-405: A "reference frame" for the same. The ISO term for a datum transformation again is a "coordinate transformation". General geopositioning , or simply positioning, is the determination of the location of points on Earth, by myriad techniques. Geodetic positioning employs geodetic methods to determine a set of precise geodetic coordinates of a point on land, at sea, or in space. It may be done within

354-566: A coordinate system ( point positioning or absolute positioning ) or relative to another point ( relative positioning ). One computes the position of a point in space from measurements linking terrestrial or extraterrestrial points of known location ("known points") with terrestrial ones of unknown location ("unknown points"). The computation may involve transformations between or among astronomical and terrestrial coordinate systems. Known points used in point positioning can be GNSS continuously operating reference stations or triangulation points of

413-420: A country, usually documented by national mapping agencies. Surveyors involved in real estate and insurance will use these to tie their local measurements. In geometrical geodesy, there are two main problems: The solutions to both problems in plane geometry reduce to simple trigonometry and are valid for small areas on Earth's surface; on a sphere, solutions become significantly more complex as, for example, in

472-418: A few kilometers depth, most of these kinds of observations become impractical. Geologists studying the geodynamics of the mantle and core must rely entirely on remote sensing, especially seismology, and experimentally recreating the conditions found in the Earth in high pressure high temperature experiments.(see also Adams–Williamson equation ). Because of the complexity of geological systems, computer modeling

531-420: A given initial condition over time or a statistical (quasi) steady-state of a given system. IUGG The International Union of Geodesy and Geophysics ( IUGG ; French : Union géodésique et géophysique internationale , UGGI ) is an international non-governmental organization dedicated to the scientific study of Earth and its space environment using geophysical and geodetic techniques. The IUGG

590-418: A higher-order network. Traditionally, geodesists built a hierarchy of networks to allow point positioning within a country. The highest in this hierarchy were triangulation networks, densified into the networks of traverses ( polygons ) into which local mapping and surveying measurements, usually collected using a measuring tape, a corner prism , and the red-and-white poles, are tied. Commonly used nowadays

649-408: A phenomenon closely monitored by geodesists. In geodetic applications like surveying and mapping , two general types of coordinate systems in the plane are in use: One can intuitively use rectangular coordinates in the plane for one's current location, in which case the x -axis will point to the local north. More formally, such coordinates can be obtained from 3D coordinates using the artifice of

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708-509: A physical (real-world) realization of a coordinate system used for describing point locations. This realization follows from choosing (therefore conventional) coordinate values for one or more datum points. In the case of height data, it suffices to choose one datum point — the reference benchmark, typically a tide gauge at the shore. Thus we have vertical datums, such as the NAVD 88 (North American Vertical Datum 1988), NAP ( Normaal Amsterdams Peil ),

767-426: A positive feedback between the accumulation or propagation of defects especially those produced by strain in areas of high strain, and the localization of strain along these dislocations and fractures. In other words, any fracture, however small, tends to focus strain at its leading edge, which causes the fracture to extend. In general, the mode of deformation is controlled not only by the amount of stress, but also by

826-481: A series expansion — see, for example, Vincenty's formulae . As defined in geodesy (and also astronomy ), some basic observational concepts like angles and coordinates include (most commonly from the viewpoint of a local observer): The reference surface (level) used to determine height differences and height reference systems is known as mean sea level . The traditional spirit level directly produces such (for practical purposes most useful) heights above sea level ;

885-543: A single global, geocentric reference frame that serves as the "zero-order" (global) reference to which national measurements are attached. Real-time kinematic positioning (RTK GPS) is employed frequently in survey mapping. In that measurement technique, unknown points can get quickly tied into nearby terrestrial known points. One purpose of point positioning is the provision of known points for mapping measurements, also known as (horizontal and vertical) control. There can be thousands of those geodetically determined points in

944-657: A variety of mechanisms: Geodynamics is the discipline that studies deformations and motions of Earth's crust and its solidity as a whole. Often the study of Earth's irregular rotation is included in the above definition. Geodynamical studies require terrestrial reference frames realized by the stations belonging to the Global Geodetic Observing System (GGOS). Techniques for studying geodynamic phenomena on global scales include: [REDACTED] Geodesy at Wikibooks [REDACTED] Media related to Geodesy at Wikimedia Commons Geodynamics Geodynamics

1003-454: Is approximately the same as the direction of the plumbline, i.e., local gravity, which is also the normal to the geoid surface. For this reason, astronomical position determination – measuring the direction of the plumbline by astronomical means – works reasonably well when one also uses an ellipsoidal model of the figure of the Earth. One geographical mile, defined as one minute of arc on the equator, equals 1,855.32571922 m. One nautical mile

1062-466: Is GPS, except for specialized measurements (e.g., in underground or high-precision engineering). The higher-order networks are measured with static GPS , using differential measurement to determine vectors between terrestrial points. These vectors then get adjusted in a traditional network fashion. A global polyhedron of permanently operating GPS stations under the auspices of the IERS is the basis for defining

1121-824: Is a member of the International Science Council (ISC), which is composed of international scholarly and scientific institutions and national academies of sciences . The IUGG was established in Brussels, Belgium in 1919. IUGG's objectives are the promotion and coordination of studies related to Earth's physical, chemical and mathematical representation. This includes geometrical shape, internal structure, gravity and magnetic fields, seismicity , volcanism , hydrologic cycle , glaciers, oceans, atmosphere, ionosphere , and magnetosphere of Earth. It also includes solar, lunar and planetary studies. Some areas within its scope are environmental preservation , reduction of

1180-473: 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 , mountain building , volcanoes , earthquakes , faulting . It also attempts to probe the internal activity by measuring magnetic fields , gravity, and seismic waves , as well as

1239-517: Is cooled at the surface can become less buoyant than the rock below it. Eventually this can lead to a Rayleigh-Taylor instability (Figure 2), or interpenetration of rock on different sides of the buoyancy contrast. Negative thermal buoyancy of the oceanic plates is the primary cause of subduction and plate tectonics, while positive thermal buoyancy may lead to mantle plumes, which could explain intraplate volcanism. The relative importance of heat production vs. heat loss for buoyant convection throughout

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1298-484: Is in hydrostatic equilibrium to a good approximation. The pressure on rock depends only on the weight of the rock above, and this depends on gravity and the density of the rock. In a body like the Moon , the density is almost constant, so a pressure profile is readily calculated. In the Earth, the compression of rocks with depth is significant, and an equation of state is needed to calculate changes in density of rock even when it

1357-538: Is indirect and depends on the internal density distribution or, in simplest terms, the degree of central concentration of mass. The 1980 Geodetic Reference System ( GRS 80 ), adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics ( IUGG ), posited a 6,378,137 m semi-major axis and a 1:298.257 flattening. GRS 80 essentially constitutes the basis for geodetic positioning by

1416-402: Is of uniform composition. Elastic deformation is always reversible, which means that if the stress field associated with elastic deformation is removed, the material will return to its previous state. Materials only behave elastically when the relative arrangement along the axis being considered of material components (e.g. atoms or crystals) remains unchanged. This means that the magnitude of

1475-578: Is off by 200 ppm in the current definitions). This situation means that one kilometre roughly equals (1/40,000) * 360 * 60 meridional minutes of arc, or 0.54 nautical miles. (This is not exactly so as the two units had been defined on different bases, so the international nautical mile is 1,852 m exactly, which corresponds to rounding the quotient from 1,000/0.54 m to four digits). Various techniques are used in geodesy to study temporally changing surfaces, bodies of mass, physical fields, and dynamical systems. Points on Earth's surface change their location due to

1534-457: Is one minute of astronomical latitude. The radius of curvature of the ellipsoid varies with latitude, being the longest at the pole and the shortest at the equator same as with the nautical mile. A metre was originally defined as the 10-millionth part of the length from the equator to the North Pole along the meridian through Paris (the target was not quite reached in actual implementation, as it

1593-448: Is the geoid , an equigeopotential surface approximating the mean sea level as described above. For normal heights, the reference surface is the so-called quasi-geoid , which has a few-metre separation from the geoid due to the density assumption in its continuation under the continental masses. One can relate these heights through the geoid undulation concept to ellipsoidal heights (also known as geodetic heights ), representing

1652-414: Is used to test theoretical predictions about geodynamics using data from these sources. There are two main ways of geodynamic numerical modeling. Basic fluid dynamics modelling can further be subdivided into instantaneous studies, which aim to reproduce the instantaneous flow in a system due to a given buoyancy distribution, and time-dependent studies, which either aim to reproduce a possible evolution of

1711-578: Is why shear mode elastic deformation (S-Waves) will not propagate through melts. The main motive force behind stress in the Earth is provided by thermal energy from radioisotope decay, friction, and residual heat. Cooling at the surface and heat production within the Earth create a metastable thermal gradient from the hot core to the relatively cool lithosphere. This thermal energy is converted into mechanical energy by thermal expansion. Deeper and hotter rocks often have higher thermal expansion and lower density relative to overlying rocks. Conversely, rock that

1770-491: The Ancient Greek word γεωδαισία or geodaisia (literally, "division of Earth"). Early ideas about the figure of the Earth held the Earth to be flat and the heavens a physical dome spanning over it. Two early arguments for a spherical Earth were that lunar eclipses appear to an observer as circular shadows and that Polaris appears lower and lower in the sky to a traveler headed South. In English , geodesy refers to

1829-545: The Global Positioning System (GPS) and is thus also in widespread use outside the geodetic community. Numerous systems used for mapping and charting are becoming obsolete as countries increasingly move to global, geocentric reference systems utilizing the GRS 80 reference ellipsoid. The geoid is a "realizable" surface, meaning it can be consistently located on Earth by suitable simple measurements from physical objects like

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1888-447: The collision of plates , as well as of volcanism , resisted by Earth's gravitational field. This applies to the solid surface, the liquid surface ( dynamic sea surface topography ), and Earth's atmosphere . For this reason, the study of Earth's gravitational field is called physical geodesy . The geoid essentially is the figure of Earth abstracted from its topographical features. It is an idealized equilibrium surface of seawater ,

1947-456: The mean sea level surface in the absence of currents and air pressure variations, and continued under the continental masses. Unlike a reference ellipsoid , the geoid is irregular and too complicated to serve as the computational surface for solving geometrical problems like point positioning. The geometrical separation between the geoid and a reference ellipsoid is called geoidal undulation , and it varies globally between ±110 m based on

2006-418: The mineralogy of rocks and their isotopic composition . Methods of geodynamics are also applied to exploration of other planets. Geodynamics is generally concerned with processes that move materials throughout the Earth. In the Earth's interior , movement happens when rocks melt or deform and flow in response to a stress field . This deformation may be brittle , elastic , or plastic , depending on

2065-489: The science of measuring and representing geospatial information , while geomatics encompasses practical applications of geodesy on local and regional scales, including surveying . In German , geodesy can refer to either higher geodesy ( höhere Geodäsie or Erdmessung , literally "geomensuration") — concerned with measuring Earth on the global scale, or engineering geodesy ( Ingenieurgeodäsie ) that includes surveying — measuring parts or regions of Earth. For

2124-702: The tachymeter determines, electronically or electro-optically , the distance to a target and is highly automated or even robotic in operations. Widely used for the same purpose is the method of free station position. Commonly for local detail surveys, tachymeters are employed, although the old-fashioned rectangular technique using an angle prism and steel tape is still an inexpensive alternative. As mentioned, also there are quick and relatively accurate real-time kinematic (RTK) GPS techniques. Data collected are tagged and recorded digitally for entry into Geographic Information System (GIS) databases. Geodetic GNSS (most commonly GPS ) receivers directly produce 3D coordinates in

2183-404: The thermodynamic state of the rock and composition. The most important thermodynamic variables in this case are temperature and pressure. Both of these increase with depth, so to a first approximation the mode of deformation can be understood in terms of depth. Within the upper lithosphere, brittle deformation is common because under low pressure rocks have relatively low brittle strength, while at

2242-528: The GRS 80 ellipsoid. A reference ellipsoid, customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorial radius) a and flattening f . The quantity f = ⁠ a − b / a ⁠ , where b is the semi-minor axis (polar radius), is purely geometrical. The mechanical ellipticity of Earth (dynamical flattening, symbol J 2 ) can be determined to high precision by observation of satellite orbit perturbations . Its relationship with geometrical flattening

2301-611: The Kronstadt datum, the Trieste datum, and numerous others. In both mathematics and geodesy, a coordinate system is a "coordinate system" per ISO terminology, whereas the International Earth Rotation and Reference Systems Service (IERS) uses the term "reference system" for the same. When coordinates are realized by choosing datum points and fixing a geodetic datum, ISO speaks of a "coordinate reference system", whereas IERS uses

2360-580: The Moon, and satellite laser ranging (SLR) measuring distances to prisms on artificial satellites , are employed. Gravity is measured using gravimeters , of which there are two kinds. First are absolute gravimeter s, based on measuring the acceleration of free fall (e.g., of a reflecting prism in a vacuum tube ). They are used to establish vertical geospatial control or in the field. Second, relative gravimeter s are spring-based and more common. They are used in gravity surveys over large areas — to establish

2419-449: The advent of satellite positioning, such coordinate systems are typically geocentric , with the Z-axis aligned to Earth's (conventional or instantaneous) rotation axis. Before the era of satellite geodesy , the coordinate systems associated with a geodetic datum attempted to be geocentric , but with the origin differing from the geocenter by hundreds of meters due to regional deviations in

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2478-423: The average response to average stress. Experts in geodynamics commonly use data from geodetic GPS , InSAR , and seismology , along with numerical models , to study the evolution of the Earth's lithosphere , mantle and core . Work performed by geodynamicists may include: Rocks and other geological materials experience strain according to three distinct modes, elastic, plastic, and brittle depending on

2537-429: The direction of the plumbline (vertical). These regional geodetic datums, such as ED 50 (European Datum 1950) or NAD 27 (North American Datum 1927), have ellipsoids associated with them that are regional "best fits" to the geoids within their areas of validity, minimizing the deflections of the vertical over these areas. It is only because GPS satellites orbit about the geocenter that this point becomes naturally

2596-443: The distribution of strain and strain associated features. Whichever mode of deformation ultimately occurs is the result of a competition between processes that tend to localize strain, such as fracture propagation, and relaxational processes, such as annealing, that tend to delocalize strain. Structural geologists study the results of deformation, using observations of rock, especially the mode and geometry of deformation to reconstruct

2655-471: The figure of the geoid over these areas. The most accurate relative gravimeters are called superconducting gravimeter s, which are sensitive to one-thousandth of one-billionth of Earth-surface gravity. Twenty-some superconducting gravimeters are used worldwide in studying Earth's tides , rotation , interior, oceanic and atmospheric loading, as well as in verifying the Newtonian constant of gravitation . In

2714-401: The future, gravity and altitude might become measurable using the special-relativistic concept of time dilation as gauged by optical clocks . Geographical latitude and longitude are stated in the units degree, minute of arc, and second of arc. They are angles , not metric measures, and describe the direction of the local normal to the reference ellipsoid of revolution. This direction

2773-430: The height of a point above the reference ellipsoid . Satellite positioning receivers typically provide ellipsoidal heights unless fitted with special conversion software based on a model of the geoid. Because coordinates and heights of geodetic points always get obtained within a system that itself was constructed based on real-world observations, geodesists introduced the concept of a "geodetic datum" (plural datums ):

2832-405: The inverse problem, the azimuths differ going between the two end points along the arc of the connecting great circle . The general solution is called the geodesic for the surface considered, and the differential equations for the geodesic are solvable numerically. On the ellipsoid of revolution, geodesics are expressible in terms of elliptic integrals, which are usually evaluated in terms of

2891-409: The longest time, geodesy was the science of measuring and understanding Earth's geometric shape, orientation in space, and gravitational field; however, geodetic science and operations are applied to other astronomical bodies in our Solar System also. To a large extent, Earth's shape is the result of rotation , which causes its equatorial bulge , and the competition of geological processes such as

2950-462: The magnitude of the stress and the material's physical properties, especially the stress relaxation time scale . Rocks are structurally and compositionally heterogeneous and are subjected to variable stresses, so it is common to see different types of deformation in close spatial and temporal proximity. When working with geological timescales and lengths, it is convenient to use the continuous medium approximation and equilibrium stress fields to consider

3009-787: The material microstates (figure 1) are unbound, which means that a large fraction of the chemical bonds are in the process of being broken and reformed. During ductile deformation, this process of atomic rearrangement redistributes stress and strain towards equilibrium faster than they can accumulate. Examples include bending of the lithosphere under volcanic islands or sedimentary basins , and bending at oceanic trenches . Ductile deformation happens when transport processes such as diffusion and advection that rely on chemical bonds to be broken and reformed redistribute strain about as fast as it accumulates. When strain localizes faster than these relaxation processes can redistribute it, brittle deformation occurs. The mechanism for brittle deformation involves

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3068-496: The more economical use of GPS instruments for height determination requires precise knowledge of the figure of the geoid , as GPS only gives heights above the GRS80 reference ellipsoid. As geoid determination improves, one may expect that the use of GPS in height determination shall increase, too. The theodolite is an instrument used to measure horizontal and vertical (relative to the local vertical) angles to target points. In addition,

3127-741: The north direction used for reference is the map north, not the local north. The difference between the two is called meridian convergence . It is easy enough to "translate" between polar and rectangular coordinates in the plane: let, as above, direction and distance be α and s respectively, then we have The reverse transformation is given by: In geodesy, point or terrain heights are " above sea level " as an irregular, physically defined surface. Height systems in use are: Each system has its advantages and disadvantages. Both orthometric and normal heights are expressed in metres above sea level, whereas geopotential numbers are measures of potential energy (unit: m s) and not metric. The reference surface

3186-517: The origin of a coordinate system defined by satellite geodetic means, as the satellite positions in space themselves get computed within such a system. Geocentric coordinate systems used in geodesy can be divided naturally into two classes: The coordinate transformation between these two systems to good approximation is described by (apparent) sidereal time , which accounts for variations in Earth's axial rotation ( length-of-day variations). A more accurate description also accounts for polar motion as

3245-399: The properties of the material and the magnitude of the stress field. Stress is defined as the average force per unit area exerted on each part of the rock. Pressure is the part of stress that changes the volume of a solid; shear stress changes the shape. If there is no shear, the fluid is in hydrostatic equilibrium . Since, over long periods, rocks readily deform under pressure, the Earth

3304-420: The same time low temperature reduces the likelihood of ductile flow. After the brittle-ductile transition zone, ductile deformation becomes dominant. Elastic deformation happens when the time scale of stress is shorter than the relaxation time for the material. Seismic waves are a common example of this type of deformation. At temperatures high enough to melt rocks, the ductile shear strength approaches zero, which

3363-407: The stress cannot exceed the yield strength of a material, and the time scale of the stress cannot approach the relaxation time of the material. If stress exceeds the yield strength of a material, bonds begin to break (and reform), which can lead to ductile or brittle deformation. Ductile or plastic deformation happens when the temperature of a system is high enough so that a significant fraction of

3422-455: The stress field that affected the rock over time. Structural geology is an important complement to geodynamics because it provides the most direct source of data about the movements of the Earth. Different modes of deformation result in distinct geological structures, e.g. brittle fracture in rocks or ductile folding. The physical characteristics of rocks that control the rate and mode of strain, such as yield strength or viscosity , depend on

3481-466: The whole Earth remains uncertain and understanding the details of buoyant convection is a key focus of geodynamics. Geodynamics is a broad field which combines observations from many different types of geological study into a broad picture of the dynamics of Earth. Close to the surface of the Earth, data includes field observations, geodesy, radiometric dating , petrology , mineralogy, drilling boreholes and remote sensing techniques. However, beyond

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