The vertical deflections (deflections of the plumb line, astro-geodetic deflections) are important parameters of the local gravity field. A plumb-bob or a plummet is a weight with a pointed tip on the bottom that is suspended from a string and used as a vertical reference line A gravitational field is a model used within Physics to explain how gravity exists in the universe They are widely used in geodesy, for surveying networks and for geophysical purposes. Geodesy (dʒiːˈɒdɪsi also called geodetics, a branch of Earth sciences, is the scientific discipline that deals Surveying is the technique and science of accurately determining the terrestrial or three-dimensional space Position of points and the distances and angles between

The vertical deflection (abbrev. VD or ξ,η) is the local difference between the true zenith (plumb line) and its theoretical vertical direction on a global ellipsoid. In broad terms the zenith is the direction pointing directly above a particular location ( Perpendicular, Orthogonal) In Astronomy, Geography, Geometry and related sciences and contexts a direction passing by a given point is said to be vertical if An ellipsoid is a type of quadric surface that is a higher dimensional analogue of an Ellipse. VDs are caused by mountains and by geological irregularities of the subsurface, and amount to 10" (flat areas) or 20-50" (alpine terrain). A mountain is a Landform that extends above the surrounding Terrain in a limited area with a peak Geology (from Greek γη gê, "earth" and λόγος Logos, "speech" lit Terrain, or relief, is the third or vertical dimension of land surface. At the axis of valleys the values are rather small, whereas the maxima occur at steep mountain slopes. In Geology, a valley (also called a vale, dale, glen or strath and near or in Appalachia, a draw) is Slope is used to describe the steepness incline gradient or grade of a straight line.

The deflection of the vertical is a difference vector and therefore has two components: a north-south component ξ and an east-west component η. The value of ξ is the difference of geographic and ellipsoidal latitude; the latter is usually calculated by geodetic network coordinates. Latitude, usually denoted symbolically by the Greek letter phi ( Φ) gives the location of a place on Earth (or other planetary body north or south of the In Mathematics and its applications a coordinate system is a system for assigning an n - Tuple of Numbers or scalars to each point The value of η corresponds to the difference of the adequate longitudes. Longitude (ˈlɒndʒɪˌtjuːd or ˈlɒŋgɪˌtjuːd symbolized by the Greek character Lambda (λ is the east-west Geographic coordinate measurement

Earth's ellipsoid, geoid, and two types of vertical deflection

Determination of vertical deflections

The deflections are connected with the local and regional undulations of the geoid — and also with gravity anomalies — for they are functionals of the gravity field and its inhomogeneities. The geoid is that Equipotential surface which would coincide exactly with the mean ocean surface of the Earth if the oceans were in equilibrium at rest and extended through A gravity anomaly is the difference between the observed Gravity and a value predicted from a model A gravitational field is a model used within Physics to explain how gravity exists in the universe

VDs are usually determined astronomically. The true zenith is observed astronomically with respect to the stars, and the ellipsoidal zenith (theoretical vertical) by geodetic network computation, which always takes place on a reference ellipsoid. A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth In Geodesy, a reference ellipsoid is a mathematically-defined surface that approximates the Geoid, the truer Figure of the Earth, or other planetary body Additionally, the very local variations of the VD can be computed from gravimetric survey data and by means of digital terrain models (DTM), using a theory originally developed by Vening-Meinesz. A digital elevation model ( DEM) is a Digital representation of ground Surface Topography or Terrain.

VDs are used in astro-geodetic levelling, a geoid determination technique. As a vertical deflection describes the difference between the geoidal and ellipsoidal normals, it represents the horizontal gradient of the undulations of the geoid, i. In Vector calculus, the gradient of a Scalar field is a Vector field which points in the direction of the greatest rate of increase of the scalar e. the separation between geoid and reference ellipsoid. Given a starting value for the geoid undulation at one point, determining geoid undulations for an area becomes a matter for simple integration.

In practice, the deflections are observed at special points with spacings of 20 or 50 kilometers. The densification is done by a combination of DTM models and areal gravimetry. Gravimetry is the measurement of a gravitational field Gravimetry may be used when either the magnitude of gravitational field or the properties of matter responsible Precise VD observations have accuracies of ± 0. 2" (on high mountains ± 0. 5"), calculated values of about 1–2".

The maximal VD of Central Europe seems to be a point near of the Großglockner (3798 m), the highest peak of the Austrian Alps. Central Europe is the Region lying between the variously and vaguely defined areas of Eastern and The Grossglockner (Veliki Klek Großglockner also Glockner) is at 3798  m Above sea level, Austria 's highest Mountain Austria (Österreich ( officially the Republic of Austria (Republik Österreich The approx. values are ξ = +50" and η = -30". In the Himalaya region, very asymmetric peaks may have VDs up to 100" (0. 03°). In the rather flat area between Vienna and Hungary the values are less than 15", but scatter by ± 10" for irregular rock densities in the subsurface. Vienna ( in Wien; see also other names) is the Capital of Austria, and is also one of the nine States of Austria. Hungary (Magyarország 'mɔɟɔrorsaːg) officially in English the Republic of Hungary ( Magyar Köztársaság, literally Magyar (Hungarian Republic

Application of deflection data

Vertical deflections are principally used in a threefold matter:

1. For precise calculation of survey networks. The geodetic theodolites and levelling instruments are oriented with respect to the true vertical, but its deflection exceeds the geodetic measuring accuracy by a factor of 5 to 50. A theodolite ( is an instrument for measuring both horizontal and vertical Angles as used in Triangulation networks In the Physical sciences Quality assurance, and Engineering, Measurement is the activity of obtaining and comparing physical quantities In Astronomy, Geography, Geometry and related sciences and contexts a direction passing by a given point is said to be vertical if Therefore the data have to be corrected exactly with respect to the global ellipsoid. Without these reductions, the surveys may be distorted by some centimeters or even decimeters per km. A distortion is the alteration of the original shape (or other characteristic of an object image sound waveform or other form of information or representation
2. For the geoid determination (mean sea level) and for exact transformation of elevations. The elevation of a Geographic location is its height above a fixed reference point often the mean sea level. The global geoidal undulations amount to 50-100 m, and their regional values to 10-50 m. The article is about the geographic sense of the term For other uses including Regions and Regional, see Region (disambiguation. They are adequate to the integrals of VD components ξ,η and therefore can be calculated with cm accuracy over distances of many kilometers. The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space
3. For GPS surveys. Basic concept of GPS operation A GPS receiver calculates its position by carefully timing the signals sent by the constellation of GPS Satellites high above the Earth The satellites measurements refer to a pure geometrical system (usually the WGS84 ellipsoid), whereas the terrestrial heights refer to the geoid. This article is about artificial satellites For natural satellites also known as moons see Natural satellite. Geometry ( Greek γεωμετρία; geo = earth metria = measure is a part of Mathematics concerned with questions of size shape and relative position The World Geodetic System defines a reference frame for the earth for use in Geodesy and Navigation. We need accurate geoid data to combine the different types of measurements.
4. For geophysics. Geophysics, a major discipline of Earth sciences, is the study of the Earth by quantitative physical methods especially by seismic, electromagnetic Because VD deflection data are affected by the physical structure of the Earth's crust and mantle, geodesists are engaged in models to improve our knowledge of the earth's interior. In Geology, a crust is the outermost solid shell of a planet or moon Geodesy (dʒiːˈɒdɪsi also called geodetics, a branch of Earth sciences, is the scientific discipline that deals Scientific modelling is the process of generating abstract, conceptual, Graphical and or mathematical models. Additionally and similar to applied geophysics, the VD data can support the future exploration of raw materials, oil, gas or ores. Petroleum ( L petroleum, from Greek πετρέλαιον, lit An ore is a volume of rock containing components or Minerals in a mode of occurrence that renders it valuable for mining

See also

• Vertical direction
• Zenith
• Gravity anomaly