Геоид — разлика између измена

Садржај обрисан Садржај додат

Инлајн

Верзија на датум 13. фебруар 2023. у 10:13

Геоид је еквипотенцијална површ, на коју је, у свакој њеној тачки, правац силе теже управан. То је неправилна површ, која се поклапа са мирном површи воде у океанима. Појам речи геоид (према грчком - облик Земље) први пут је употребио Г. И. Листинг 1873. године.

Геоид, који се на океанима поклапа са нивоом воде, продужава се испод континената, тако да је у свакој његовој тачки сила теже усмерена по нормали на геоид (у ствари, нормална је на тангенту раван геоида у тачки посматрања). Положај геоида под континентима може се представити замишљеном мрежом канала просеченим кроз чврсту кору и спојеним са океанима, довољно уским, али у којима нема трења и утицаја капиларности. Тада би вода из океана, попунивши канале, достигла ниво који би одговарао површи геоида.

Првим приближењем облику Земље сматра се сфера, другим ротациони елипсоид, док стварни облик Земље најприближније описује геоид. Геоид се разликује од елипсоида око 100 m ^[1], што значи да су одступања геоида од стварног облика Земље истог реда као и код елипсоида. Прелазак са елипсоида на геоид на континентима не решава задатак следећег приближења.

Како је геоид неправилна фигура, он не може да се изрази аналитички. То значи да се геоид не може користити за решавање разних геодетских задатака. Без обзира на то, геоид има велики научни и практични значај. У односу на геоид одређују се апсолутне висине тачака физичке површи Земље, а пошто се геоид поклапа са мирном површи воде океана, висине над геоидом обично се називају надморске висине.

According to Gauss, who first described it, it is the "mathematical figure of the Earth", a smooth but irregular surface whose shape results from the uneven distribution of mass within and on the surface of Earth.^[2] It can be known only through extensive gravitational measurements and calculations. Despite being an important concept for almost 200 years in the history of geodesy and geophysics, it has been defined to high precision only since advances in satellite geodesy in the late 20th century.

All points on a geoid surface have the same geopotential (the sum of gravitational potential energy and centrifugal potential energy). The force of gravity acts everywhere perpendicular to the geoid, meaning that plumb lines point perpendicular and water levels parallel to the geoid if only gravity and rotational acceleration were at work. Earth's gravity acceleration is non-uniform over the geoid, which is only an equipotential surface, a sufficient condition for a ball to remain at rest instead of rolling over the geoid.^[3] The geoid undulation or geoidal height is the height of the geoid relative to a given reference ellipsoid.

Determination

Calculating the undulation is mathematically challenging.^[4]^[5] This is why many handheld GPS receivers have built-in undulation lookup tables^[6] to determine the height above sea level.

The precise geoid solution by Vaníček and co-workers improved on the Stokesian approach to geoid computation.^[7] Their solution enables millimetre-to-centimetre accuracy in geoid computation, an order-of-magnitude improvement from previous classical solutions.^[8]^[9]^[10]^[11]

Geoid undulations display uncertainties which can be estimated by using several methods, e.g. least-squares collocation (LSC), fuzzy logic, artificial neutral networks, radial basis functions (RBF), and geostatistical techniques. Geostatistical approach has been defined as the most improved technique in prediction of geoid undulation.^[12]

Temporal change

Recent satellite missions, such as the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) and GRACE, have enabled the study of time-variable geoid signals. The first products based on GOCE satellite data became available online in June 2010, through the European Space Agency (ESA)'s Earth observation user services tools.^[13]^[14] ESA launched the satellite in March 2009 on a mission to map Earth's gravity with unprecedented accuracy and spatial resolution. On 31 March 2011, the new geoid model was unveiled at the Fourth International GOCE User Workshop hosted at the Technical University of Munich, Germany.^[15] Studies using the time-variable geoid computed from GRACE data have provided information on global hydrologic cycles,^[16] mass balances of ice sheets,^[17] and postglacial rebound.^[18] From postglacial rebound measurements, time-variable GRACE data can be used to deduce the viscosity of Earth's mantle.^[19]

Референце

^ Старчевић М. 1991. Гравиметријске методе истраживања. Београд: Наука
^ Gauß, C.F. (1828). Bestimmung des Breitenunterschiedes zwischen den Sternwarten von Göttingen und Altona durch Beobachtungen am Ramsdenschen Zenithsector (на језику: немачки). Vandenhoeck und Ruprecht. стр. 73. Приступљено 2021-07-06.
^ Geodesy: The Concepts. Petr Vanicek and E.J. Krakiwsky. Amsterdam: Elsevier. 1982 (first ed.): ISBN 0-444-86149-1, ISBN 978-0-444-86149-8. 1986 (third ed.): ISBN 0-444-87777-0, ISBN 978-0-444-87777-2. ASIN 0444877770.
^ Sideris, Michael G. (2011). „Geoid Determination, Theory and Principles”. Encyclopedia of Solid Earth Geophysics. Encyclopedia of Earth Sciences Series. стр. 356—362. ISBN 978-90-481-8701-0. S2CID 241396148. doi:10.1007/978-90-481-8702-7_154.
^ Sideris, Michael G. (2011). „Geoid, Computational Method”. Encyclopedia of Solid Earth Geophysics. Encyclopedia of Earth Sciences Series. стр. 366—371. ISBN 978-90-481-8701-0. doi:10.1007/978-90-481-8702-7_225.
^ Wormley, Sam. „GPS Orthometric Height”. edu-observatory.org. Архивирано из оригинала 20. 6. 2016. г. Приступљено 15. 6. 2016.
^ „UNB Precise Geoid Determination Package”. Приступљено 2. 10. 2007.
^ Vaníček, P.; Kleusberg, A. (1987). „The Canadian geoid-Stokesian approach”. Manuscripta Geodaetica. 12 (2): 86—98.
^ Vaníček, P.; Martinec, Z. (1994). „Compilation of a precise regional geoid” (PDF). Manuscripta Geodaetica. 19: 119—128.
^ P., Vaníček; A., Kleusberg; Z., Martinec; W., Sun; P., Ong; M., Najafi; P., Vajda; L., Harrie; P., Tomasek; B., ter Horst. Compilation of a Precise Regional Geoid (PDF) (Извештај). Department of Geodesy and Geomatics Engineering, University of New Brunswick. 184. Приступљено 22. 12. 2016.
^ Kopeikin, Sergei; Efroimsky, Michael; Kaplan, George (2009). Relativistic celestial mechanics of the solar system. Weinheim: Wiley-VCH. стр. 704. ISBN 9783527408566.
^ Chicaiza, E.G.; Leiva, C.A.; Arranz, J.J.; Buenańo, X.E. (2017-06-14). „Spatial uncertainty of a geoid undulation model in Guayaquil, Ecuador”. Open Geosciences. 9 (1): 255—265. Bibcode:2017OGeo....9...21C. ISSN 2391-5447. doi:10.1515/geo-2017-0021 .
^ „ESA makes first GOCE dataset available”. GOCE. European Space Agency. 9. 6. 2010. Приступљено 22. 12. 2016.
^ „GOCE giving new insights into Earth's gravity”. GOCE. European Space Agency. 29. 6. 2010. Архивирано из оригинала 2. 7. 2010. г. Приступљено 22. 12. 2016.
^ „Earth's gravity revealed in unprecedented detail”. GOCE. European Space Agency. 31. 3. 2011. Приступљено 22. 12. 2016.
^ Schmidt, R.; Schwintzer, P.; Flechtner, F.; Reigber, C.; Guntner, A.; Doll, P.; Ramillien, G.; Cazenave, A.; et al. (2006). „GRACE observations of changes in continental water storage”. Global and Planetary Change. 50 (1–2): 112—126. Bibcode:2006GPC....50..112S. doi:10.1016/j.gloplacha.2004.11.018.
^ Ramillien, G.; Lombard, A.; Cazenave, A.; Ivins, E.; Llubes, M.; Remy, F.; Biancale, R. (2006). „Interannual variations of the mass balance of the Antarctica and Greenland ice sheets from GRACE”. Global and Planetary Change. 53 (3): 198. Bibcode:2006GPC....53..198R. doi:10.1016/j.gloplacha.2006.06.003.
^ Vanderwal, W.; Wu, P.; Sideris, M.; Shum, C. (2008). „Use of GRACE determined secular gravity rates for glacial isostatic adjustment studies in North-America”. Journal of Geodynamics. 46 (3–5): 144. Bibcode:2008JGeo...46..144V. doi:10.1016/j.jog.2008.03.007.
^ Paulson, Archie; Zhong, Shijie; Wahr, John (2007). „Inference of mantle viscosity from GRACE and relative sea level data”. Geophysical Journal International. 171 (2): 497. Bibcode:2007GeoJI.171..497P. doi:10.1111/j.1365-246X.2007.03556.x .

Литература

Старчевић М. 1991. Гравиметријске методе истраживања. Београд: Наука
Старчевић М., Ђорђевић А. 1998. Основе геофизике 2. Београд: Универзитет у Београду
H. Moritz (2011). „A contemporary perspective of geoid structure”. Journal of Geodetic Science. Versita. 1 (March): 82—87. Bibcode:2011JGeoS...1...82M. doi:10.2478/v10156-010-0010-7 .
„CHAPTER V PHYSICAL GEODESY”. ngs.noaa.gov. NOAA. Приступљено 15. 6. 2016.
Alexander, J. C. (1985). „The Numerics of Computing Geodetic Ellipsoids”. SIAM Review. 27 (2): 241—247. Bibcode:1985SIAMR..27..241A. doi:10.1137/1027056.
Heine, George (септембар 2013). „Euler and the Flattening of the Earth”. Math Horizons. 21 (1): 25—29. S2CID 126412032. doi:10.4169/mathhorizons.21.1.25.
Choi, Charles Q. (12. 4. 2007). „Strange but True: Earth Is Not Round”. Scientific American (на језику: енглески). Приступљено 4. 5. 2021.
Torge, W (2001) Geodesy (3rd edition), published by de Gruyter, ISBN 3-11-017072-8
Snyder, John P. (1993). Flattening the Earth: Two Thousand Years of Map Projections. University of Chicago Press. стр. 82. ISBN 0-226-76747-7.
P. K. Seidelmann (Chair), et al. (2005), “Report Of The IAU/IAG Working Group On Cartographic Coordinates And Rotational Elements: 2003,” Celestial Mechanics and Dynamical Astronomy, 91, pp. 203–215.
OpenGIS Implementation Specification for Geographic information - Simple feature access - Part 1: Common architecture, Annex B.4. 2005-11-30
Wang, Yan Ming (2016). „Geodetic Boundary Value Problems”. Encyclopedia of Geodesy. Cham: Springer International Publishing. стр. 1—8. ISBN 978-3-319-02370-0. doi:10.1007/978-3-319-02370-0_42-1.
B. Hofmann-Wellenhof and H. Moritz, Physical Geodesy, Springer-Verlag Wien, 2005. (This text is an updated edition of the 1967 classic by W.A. Heiskanen and H. Moritz).
Jackson, Julia A., ур. (1997). „gravity anomaly”. Glossary of geology. (Fourth изд.). Alexandria, Virginia: American Geological Institute. ISBN 0922152349.
Lowrie, William (2007). „2”. Fundamentals of geophysics (2nd изд.). Cambridge: Cambridge University Press. ISBN 978-1-60119-744-3.
Allaby, Michael (2013). „gravity anomaly”. A dictionary of geology and earth sciences (Fourth изд.). Oxford: Oxford University Press. ISBN 9780199653065.
Kearey, P.; Klepeis, K.A.; Vine, F.J. (2009). Global tectonics. (3rd изд.). Oxford: Wiley-Blackwell. ISBN 9781405107778.
Werner, Dietrich; Kissling, Eduard (август 1985). „Gravity anomalies and dynamics of the Swiss Alps”. Tectonophysics. 117 (1–2): 97—108. doi:10.1016/0040-1951(85)90239-2.
Monroe, James S.; Wicander, Reed (1992). Physical geology : exploring the Earth. St. Paul: West Pub. Co. ISBN 0314921958.
Burov, E. V.; Kogan, M. G.; Lyon-Caen, Hélène; Molnar, Peter (1. 1. 1990). „Gravity anomalies, the deep structure, and dynamic processes beneath the Tien Shan”. Earth and Planetary Science Letters. 96 (3): 367—383. doi:10.1016/0012-821X(90)90013-N.
Detrick, Robert S.; Crough, S. Thomas (1978). „Island subsidence, hot spots, and lithospheric thinning”. Journal of Geophysical Research. 83 (B3): 1236. doi:10.1029/JB083iB03p01236.
Herman, G.C.; Dooley, J.H.; Monteverde, D.H. (2013). „Structure of the CAMP bodies and positive Bouger gravity anomalies of the New York Recess”. Igneous processes during the assembly and breakup of Pangaea: Northern New Jersey and New York City: 30th Annual Meeting of the Geological Association of New Jersey (PDF). New York: College of Staten Island. стр. 103—142. Приступљено 29. 1. 2022.

Спољашње везе

Main NGA (was NIMA) page on Earth gravity models Архивирано 20 јун 2006 на сајту Wayback Machine
International Geoid Service (IGeS) Архивирано 5 април 2014 на сајту Wayback Machine
EGM96 NASA GSFC Earth gravity model
Earth Gravitational Model 2008 (EGM2008, Released in July 2008) Архивирано 8 мај 2010 на сајту Wayback Machine
NOAA Geoid webpage
International Centre for Global Earth Models (ICGEM)
Kiamehr's Geoid Home Page Архивирано 20 јул 2019 на сајту Wayback Machine
Geoid tutorial from Li and Gotze (964KB pdf file)
Geoid tutorial at GRACE website
Precise Geoid Determination Based on the Least-Squares Modification of Stokes’ Formula (PhD Thesis PDF)

[1] Старчевић М. 1991. Гравиметријске методе истраживања. Београд: Наука

[Gauß1828-2] Gauß, C.F. (1828). Bestimmung des Breitenunterschiedes zwischen den Sternwarten von Göttingen und Altona durch Beobachtungen am Ramsdenschen Zenithsector (на језику: немачки). Vandenhoeck und Ruprecht. стр. 73. Приступљено 2021-07-06.

[BookGeodesyConcepts-3] Geodesy: The Concepts. Petr Vanicek and E.J. Krakiwsky. Amsterdam: Elsevier. 1982 (first ed.): ISBN 0-444-86149-1, ISBN 978-0-444-86149-8. 1986 (third ed.): ISBN 0-444-87777-0, ISBN 978-0-444-87777-2. ASIN 0444877770.

[4] Sideris, Michael G. (2011). „Geoid Determination, Theory and Principles”. Encyclopedia of Solid Earth Geophysics. Encyclopedia of Earth Sciences Series. стр. 356—362. ISBN 978-90-481-8701-0. S2CID 241396148. doi:10.1007/978-90-481-8702-7_154.

[5] Sideris, Michael G. (2011). „Geoid, Computational Method”. Encyclopedia of Solid Earth Geophysics. Encyclopedia of Earth Sciences Series. стр. 366—371. ISBN 978-90-481-8701-0. doi:10.1007/978-90-481-8702-7_225.

[6] Wormley, Sam. „GPS Orthometric Height”. edu-observatory.org. Архивирано из оригинала 20. 6. 2016. г. Приступљено 15. 6. 2016.

[7] „UNB Precise Geoid Determination Package”. Приступљено 2. 10. 2007.

[8] Vaníček, P.; Kleusberg, A. (1987). „The Canadian geoid-Stokesian approach”. Manuscripta Geodaetica. 12 (2): 86—98.

[9] Vaníček, P.; Martinec, Z. (1994). „Compilation of a precise regional geoid” (PDF). Manuscripta Geodaetica. 19: 119—128.

[10] P., Vaníček; A., Kleusberg; Z., Martinec; W., Sun; P., Ong; M., Najafi; P., Vajda; L., Harrie; P., Tomasek; B., ter Horst. Compilation of a Precise Regional Geoid (PDF) (Извештај). Department of Geodesy and Geomatics Engineering, University of New Brunswick. 184. Приступљено 22. 12. 2016.

[11] Kopeikin, Sergei; Efroimsky, Michael; Kaplan, George (2009). Relativistic celestial mechanics of the solar system. Weinheim: Wiley-VCH. стр. 704. ISBN 9783527408566.

[12] Chicaiza, E.G.; Leiva, C.A.; Arranz, J.J.; Buenańo, X.E. (2017-06-14). „Spatial uncertainty of a geoid undulation model in Guayaquil, Ecuador”. Open Geosciences. 9 (1): 255—265. Bibcode:2017OGeo....9...21C. ISSN 2391-5447. doi:10.1515/geo-2017-0021 .

[13] „ESA makes first GOCE dataset available”. GOCE. European Space Agency. 9. 6. 2010. Приступљено 22. 12. 2016.

[14] „GOCE giving new insights into Earth's gravity”. GOCE. European Space Agency. 29. 6. 2010. Архивирано из оригинала 2. 7. 2010. г. Приступљено 22. 12. 2016.

[15] „Earth's gravity revealed in unprecedented detail”. GOCE. European Space Agency. 31. 3. 2011. Приступљено 22. 12. 2016.

[16] Schmidt, R.; Schwintzer, P.; Flechtner, F.; Reigber, C.; Guntner, A.; Doll, P.; Ramillien, G.; Cazenave, A.; et al. (2006). „GRACE observations of changes in continental water storage”. Global and Planetary Change. 50 (1–2): 112—126. Bibcode:2006GPC....50..112S. doi:10.1016/j.gloplacha.2004.11.018.

[17] Ramillien, G.; Lombard, A.; Cazenave, A.; Ivins, E.; Llubes, M.; Remy, F.; Biancale, R. (2006). „Interannual variations of the mass balance of the Antarctica and Greenland ice sheets from GRACE”. Global and Planetary Change. 53 (3): 198. Bibcode:2006GPC....53..198R. doi:10.1016/j.gloplacha.2006.06.003.

[18] Vanderwal, W.; Wu, P.; Sideris, M.; Shum, C. (2008). „Use of GRACE determined secular gravity rates for glacial isostatic adjustment studies in North-America”. Journal of Geodynamics. 46 (3–5): 144. Bibcode:2008JGeo...46..144V. doi:10.1016/j.jog.2008.03.007.

[19] Paulson, Archie; Zhong, Shijie; Wahr, John (2007). „Inference of mantle viscosity from GRACE and relative sea level data”. Geophysical Journal International. 171 (2): 497. Bibcode:2007GeoJI.171..497P. doi:10.1111/j.1365-246X.2007.03556.x .

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

@@ Ред 1: / Ред 1: @@
 [[Датотека:Gravity anomalies on Earth.jpg|250п|десно|мини|Тродимензиони модел геоида]]
 '''Геоид''' је [[еквипотенцијална површ]], на коју је, у свакој њеној тачки, правац [[гравитација|силе теже]] управан. То је неправилна површ, која се поклапа са мирном површи [[вода|воде]] у [[океан]]има. Појам речи геоид (према [[грчки језик|грчком]] - облик [[Земља|Земље]]) први пут је употребио Г. И. Листинг 1873. године.
@@ Ред 7: / Ред 8: @@
 Како је геоид неправилна фигура, он не може да се изрази аналитички. То значи да се геоид не може користити за решавање разних [[геодезија|геодетских]] задатака. Без обзира на то, геоид има велики научни и практични значај. У односу на геоид одређују се [[апсолутна висина|апсолутне висине]] тачака физичке површи Земље, а пошто се геоид поклапа са мирном површи воде океана, висине над геоидом обично се називају [[апсолутна висина|надморске висине]].
+{{rut}}
+According to [[Carl Friedrich Gauss|Gauss]], who first described it, it is the "mathematical [[figure of the Earth]]", a smooth but irregular [[surface]] whose shape results from the uneven distribution of mass within and on the surface of Earth.<ref name="Gauß1828">{{cite book | last=Gauß | first=C.F. | title=Bestimmung des Breitenunterschiedes zwischen den Sternwarten von Göttingen und Altona durch Beobachtungen am Ramsdenschen Zenithsector | publisher=Vandenhoeck und Ruprecht | year=1828 | url=https://books.google.com/books?id=tIg_AAAAcAAJ&pg=PA73 | language=de | access-date=2021-07-06 | page=73}}</ref> It can be known only through extensive gravitational measurements and calculations. Despite being an important concept for almost 200 years in the history of [[geodesy]] and [[geophysics]], it has been defined to high precision only since advances in [[satellite geodesy]] in the late 20th century.
+All points on a geoid surface have the same [[geopotential]] (the sum of [[gravitational energy|gravitational potential energy]] and [[centrifugal force|centrifugal]] potential energy). The [[force of gravity]] acts everywhere perpendicular to the geoid, meaning that [[plumb bob|plumb lines]] point perpendicular and [[spirit level|water level]]s parallel to the geoid if only gravity and rotational acceleration were at work.
+Earth's gravity acceleration is non-uniform over the geoid, which is only an [[equipotential surface]], a sufficient condition for a ball to remain at rest instead of rolling over the geoid.<ref name="BookGeodesyConcepts">''Geodesy: The Concepts.''  Petr Vanicek and E.J. Krakiwsky.  Amsterdam: Elsevier.  1982 (first ed.): {{ISBN|0-444-86149-1}}, {{ISBN|978-0-444-86149-8}}.  1986 (third ed.): {{ISBN|0-444-87777-0}}, {{ISBN|978-0-444-87777-2}}.  {{ASIN|0444877770}}.</ref>
+The '''geoid undulation''' or '''geoidal height''' is the height of the geoid relative to a given [[reference ellipsoid]].
+[[File:Geoid undulation 10k scale.jpg|thumb|Geoid undulation in [[pseudocolor]], [[shaded relief]] and [[vertical exaggeration]] (10000 vertical scaling factor).]]
+[[File:Geoid undulation to scale.jpg|thumb|Geoid undulation in pseudocolor, without vertical exaggeration.]]
+==Determination==
+Calculating the undulation is mathematically challenging.<ref>{{Cite book | doi=10.1007/978-90-481-8702-7_154| chapter=Geoid Determination, Theory and Principles| title=Encyclopedia of Solid Earth Geophysics| pages=356–362| series=Encyclopedia of Earth Sciences Series| year=2011| last1=Sideris| first1=Michael G.| isbn=978-90-481-8701-0| s2cid=241396148}}</ref><ref>{{Cite book |doi = 10.1007/978-90-481-8702-7_225|chapter = Geoid, Computational Method|title = Encyclopedia of Solid Earth Geophysics|pages = 366–371|series = Encyclopedia of Earth Sciences Series|year = 2011|last1 = Sideris|first1 = Michael G.|isbn = 978-90-481-8701-0}}</ref>
+This is why many handheld GPS receivers have built-in undulation [[lookup table]]s<ref>{{cite web|last1=Wormley|first1=Sam|title=GPS Orthometric Height|url=http://www.edu-observatory.org/gps/height.html|website=edu-observatory.org|access-date=15 June 2016|url-status=dead|archive-url=https://web.archive.org/web/20160620102914/http://www.edu-observatory.org/gps/height.html|archive-date=20 June 2016}}</ref> to determine the height above sea level.
+The precise geoid solution by [[Petr Vaníček|Vaníček]] and co-workers improved on the [[George Gabriel Stokes|Stokesian]] approach to geoid computation.<ref>{{cite web|url=http://www2.unb.ca/gge/Research/GRL/GeodesyGroup/SHGeo.html |title=UNB Precise Geoid Determination Package |access-date=2 October 2007 }}</ref> Their solution enables millimetre-to-centimetre [[accuracy]] in geoid [[computation]], an [[order of magnitude|order-of-magnitude]] improvement from previous classical solutions.<ref>{{cite journal |last=Vaníček |first=P. |author2=Kleusberg, A. |date=1987 |title=The Canadian geoid-Stokesian approach |journal=Manuscripta Geodaetica |volume=12 |issue=2 |pages=86–98 }}</ref><ref>{{cite journal |last=Vaníček |first=P. |author2=Martinec, Z. |date=1994 |title=Compilation of a precise regional geoid |journal=Manuscripta Geodaetica |volume=19 |pages=119–128 |url=http://gge.unb.ca/Personnel/Vanicek/StokesHelmert.pdf }}</ref><ref>{{cite report|last1=P.|first1=Vaníček|last2=A.|first2=Kleusberg|last3=Z.|first3=Martinec|last4=W.|first4=Sun|last5=P.|first5=Ong|last6=M.|first6=Najafi|last7=P.|first7=Vajda|last8=L.|first8=Harrie|last9=P.|first9=Tomasek|last10=B.|first10=ter Horst|title=Compilation of a Precise Regional Geoid|publisher=Department of Geodesy and Geomatics Engineering, University of New Brunswick |docket=184|url=http://gge.unb.ca/Personnel/Vanicek/GeoidReport950327.pdf|access-date=22 December 2016}}</ref><ref>{{cite book|last1=Kopeikin|first1=Sergei|last2=Efroimsky|first2=Michael|last3=Kaplan|first3=George|title=Relativistic celestial mechanics of the solar system|url=https://archive.org/details/relativisticcele00kope|url-access=limited|date=2009|publisher=[[Wiley-VCH]]|location=Weinheim|isbn=9783527408566|page=[https://archive.org/details/relativisticcele00kope/page/n735 704]}}</ref>
+Geoid undulations display uncertainties which can be estimated by using several methods, e.g. [[Least squares|least-squares]] collocation (LSC), [[fuzzy logic]], [[Artificial neural network|artificial neutral networks]], [[radial basis function]]s (RBF), and [[Geostatistics|geostatistical]] techniques. Geostatistical approach has been defined as the most improved technique in prediction of geoid undulation.<ref>{{Cite journal|last1=Chicaiza|first1=E.G.|last2=Leiva|first2=C.A.|last3=Arranz|first3=J.J.|last4=Buenańo|first4=X.E.|date=2017-06-14|title=Spatial uncertainty of a geoid undulation model in Guayaquil, Ecuador|journal=Open Geosciences|volume=9|issue=1|pages=255–265|doi=10.1515/geo-2017-0021|issn=2391-5447|bibcode=2017OGeo....9...21C|doi-access=free}}</ref>
+==Temporal change==
+Recent satellite missions, such as the [[Gravity Field and Steady-State Ocean Circulation Explorer]] (GOCE) and
+[[GRACE (satellite)|GRACE]], have enabled the study of time-variable geoid signals. The first products based on GOCE satellite data became available online in June 2010, through the European Space Agency (ESA)'s Earth observation user services tools.<ref>{{cite web|url=http://www.esa.int/SPECIALS/GOCE/SEMB1EPK2AG_1.html|title=ESA makes first GOCE dataset available|date=9 June 2010|work=GOCE|publisher=[[European Space Agency]]|access-date=22 December 2016}}</ref><ref>{{cite web|url=http://www.esa.int/SPECIALS/GOCE/SEMY0FOZVAG_0.html|title=GOCE giving new insights into Earth's gravity|date=29 June 2010|work=GOCE|publisher=European Space Agency|access-date=22 December 2016|archive-date=2 July 2010|archive-url=https://web.archive.org/web/20100702013747/http://www.esa.int/SPECIALS/GOCE/SEMY0FOZVAG_0.html|url-status=dead}}</ref> ESA launched the satellite in March 2009 on a mission to map Earth's gravity with unprecedented accuracy and spatial resolution. On 31 March 2011, the new geoid model was unveiled at the Fourth International GOCE User Workshop hosted at the [[Technical University of Munich]], Germany.<ref>{{cite web|url=http://www.esa.int/esaCP/SEM1AK6UPLG_index_0.html|title=Earth's gravity revealed in unprecedented detail|date=31 March 2011|work=GOCE|publisher=European Space Agency|access-date=22 December 2016}}</ref> Studies using the time-variable geoid computed from GRACE data have provided information on global hydrologic cycles,<ref>{{cite journal|last1=Schmidt|first1=R.|last2=Schwintzer|first2=P.|last3=Flechtner|first3=F.|last4=Reigber|first4=C.|last5=Guntner|first5=A.|last6=Doll|first6=P.|last7=Ramillien|first7=G.|last8=Cazenave|first8=A.|author8-link=Anny Cazenave|last9=Petrovic|first9=S.| display-authors = 8|title=GRACE observations of changes in continental water storage|journal=Global and Planetary Change|volume=50|issue=1–2|pages=112–126|date=2006|doi=10.1016/j.gloplacha.2004.11.018|bibcode = 2006GPC....50..112S }}</ref> mass balances of [[ice sheet]]s,<ref>{{cite journal|last1=Ramillien|first1=G.|last2=Lombard|first2=A.|last3=Cazenave|first3=A.|author3-link=Anny Cazenave|last4=Ivins|first4=E.|last5=Llubes|first5=M.|last6=Remy|first6=F.|last7=Biancale|first7=R.|title=Interannual variations of the mass balance of the Antarctica and Greenland ice sheets from GRACE|journal=Global and Planetary Change|volume=53|pages=198|date=2006|doi=10.1016/j.gloplacha.2006.06.003|bibcode = 2006GPC....53..198R|issue=3 }}</ref> and [[postglacial rebound]].<ref>{{cite journal|last1=Vanderwal|first1=W.|last2=Wu|first2=P.|last3=Sideris|first3=M.|last4=Shum|first4=C.|title=Use of GRACE determined secular gravity rates for glacial isostatic adjustment studies in North-America|journal=Journal of Geodynamics|volume=46|pages=144|date=2008|doi=10.1016/j.jog.2008.03.007|bibcode = 2008JGeo...46..144V|issue=3–5 }}</ref> From postglacial rebound measurements, time-variable GRACE data can be used to deduce the [[viscosity]] of [[Earth's mantle]].<ref>{{cite journal|last1=Paulson|first1=Archie|last2=Zhong|first2=Shijie|last3=Wahr|first3=John|title=Inference of mantle viscosity from GRACE and relative sea level data|journal=[[Geophysical Journal International]]|volume=171|pages=497|date=2007|doi=10.1111/j.1365-246X.2007.03556.x|bibcode = 2007GeoJI.171..497P|issue=2 |doi-access=free}}</ref>
+== Референце ==
+{{reflist|}}
 == Литература ==
+{{Refbegin|30em}}
 * Старчевић М. 1991. ''Гравиметријске методе истраживања''. Београд: Наука
 * Старчевић М., Ђорђевић А. 1998. ''Основе геофизике 2''. Београд: Универзитет у Београду
+* {{Cite journal |author=H. Moritz |date=2011 |title=A contemporary perspective of geoid structure |journal=Journal of Geodetic Science |volume=1 |issue=March |pages=82–87 |publisher=Versita |doi=10.2478/v10156-010-0010-7 |bibcode = 2011JGeoS...1...82M |doi-access=free }}
+* {{cite web|title=CHAPTER V PHYSICAL GEODESY|url=http://www.ngs.noaa.gov/PUBS_LIB/Geodesy4Layman/TR80003C.HTM|website=ngs.noaa.gov|publisher=NOAA|access-date=15 June 2016}}
+* {{Cite journal | last1 = Alexander | first1 = J. C. | title = The Numerics of Computing Geodetic Ellipsoids | doi = 10.1137/1027056 | journal = SIAM Review | volume = 27 | issue = 2 | pages = 241–247 | year = 1985 | bibcode = 1985SIAMR..27..241A }}
+* {{cite journal |last1=Heine |first1=George |title=Euler and the Flattening of the Earth |journal=Math Horizons |date=September 2013 |volume=21 |issue=1 |pages=25–29 |doi=10.4169/mathhorizons.21.1.25|s2cid=126412032 }}
+* {{cite news |last1=Choi |first1=Charles Q. |title=Strange but True: Earth Is Not Round |url=https://www.scientificamerican.com/article/earth-is-not-round/ |access-date=4 May 2021 |work=Scientific American |date=12 April 2007 |language=en}}
+* Torge, W (2001) Geodesy (3rd edition), published by de Gruyter, {{ISBN|3-11-017072-8}}
+* {{cite book | author=Snyder, John P. |title=Flattening the Earth: Two Thousand Years of Map Projections | publisher =University of Chicago Press|year=1993|isbn=0-226-76747-7 | page=82}}
+* P. K. Seidelmann (Chair), et al. (2005), “Report Of The IAU/IAG Working Group On Cartographic Coordinates And Rotational Elements: 2003,” ''Celestial Mechanics and Dynamical Astronomy'', 91, pp.&nbsp;203–215.
+* ''OpenGIS Implementation Specification for Geographic information - Simple feature access - Part 1: Common architecture'', Annex B.4. 2005-11-30
+* {{cite book | last=Wang | first=Yan Ming | title=Encyclopedia of Geodesy | chapter=Geodetic Boundary Value Problems | publisher=Springer International Publishing | publication-place=Cham | year=2016 | isbn=978-3-319-02370-0 | doi=10.1007/978-3-319-02370-0_42-1 | pages=1–8}}
+* B. Hofmann-Wellenhof and H. Moritz, '''Physical Geodesy,''' Springer-Verlag Wien, 2005. (This text is an updated edition of the 1967 classic by W.A. Heiskanen and H. Moritz).
+* {{cite book |editor1-last=Jackson |editor1-first=Julia A. |title=Glossary of geology. |date=1997 |publisher=American Geological Institute |location=Alexandria, Virginia |isbn=0922152349 |edition=Fourth |chapter=gravity anomaly}}
+* {{cite book |last1=Lowrie |first1=William |title=Fundamentals of geophysics |date=2007 |publisher=Cambridge University Press |location=Cambridge |isbn=978-1-60119-744-3 |edition=2nd |chapter=2}}
+* {{cite book |last1=Allaby |first1=Michael |title=A dictionary of geology and earth sciences |date=2013 |publisher=Oxford University Press |location=Oxford |isbn=9780199653065 |edition=Fourth|chapter=gravity anomaly}}
+* {{cite book |last1=Kearey |first1=P. |last2=Klepeis |first2=K.A. |last3=Vine |first3=F.J. |title=Global tectonics. |date=2009 |publisher=Wiley-Blackwell |location=Oxford |isbn=9781405107778 |edition=3rd }}
+* {{cite journal |last1=Werner |first1=Dietrich |last2=Kissling |first2=Eduard |title=Gravity anomalies and dynamics of the Swiss Alps |journal=Tectonophysics |date=August 1985 |volume=117 |issue=1–2 |pages=97–108 |doi=10.1016/0040-1951(85)90239-2}}
+* {{cite book |last1=Monroe |first1=James S. |last2=Wicander |first2=Reed |title=Physical geology : exploring the Earth |date=1992 |publisher=West Pub. Co |location=St. Paul |isbn=0314921958 |page= }}
+* {{cite journal |last1=Burov |first1=E. V. |last2=Kogan |first2=M. G. |last3=Lyon-Caen |first3=Hélène |last4=Molnar |first4=Peter |title=Gravity anomalies, the deep structure, and dynamic processes beneath the Tien Shan |journal=Earth and Planetary Science Letters |date=1 January 1990 |volume=96 |issue=3 |pages=367–383 |doi=10.1016/0012-821X(90)90013-N }}
+* {{cite journal |last1=Detrick |first1=Robert S. |last2=Crough |first2=S. Thomas |title=Island subsidence, hot spots, and lithospheric thinning |journal=Journal of Geophysical Research |date=1978 |volume=83 |issue=B3 |pages=1236 |doi=10.1029/JB083iB03p01236 }}
+* {{cite book |last1=Herman |first1=G.C. |last2=Dooley |first2=J.H. |last3=Monteverde |first3=D.H. |year=2013 |chapter=Structure of the CAMP bodies and positive Bouger gravity anomalies of the New York Recess |title=Igneous processes during the assembly and breakup of Pangaea: Northern New Jersey and New York City: 30th Annual Meeting of the Geological Association of New Jersey |publisher=College of Staten Island |location=New York |pages=103–142 |url=https://www.researchgate.net/profile/Gregory-Herman-2/publication/270216459_Structure_of_the_CAMP_bodies_and_positive_Bouger_gravity_anomalies_of_the_New_York_Recess/links/55ba343408ae092e965da18d/Structure-of-the-CAMP-bodies-and-positive-Bouger-gravity-anomalies-of-the-New-York-Recess.pdf |access-date=29 January 2022}}
+{{Refend}}
+== Спољашње везе ==
-== Референце ==
+{{Commons category|Geoid}}
-{{reflist}}
+* [http://earth-info.nga.mil/GandG/wgs84/index.html Main NGA (was NIMA) page on Earth gravity models] {{Webarchive|url=https://web.archive.org/web/20060620100502/http://earth-info.nga.mil/GandG/wgs84/index.html |date=20 June 2006 }}
+* [http://www.iges.polimi.it International Geoid Service (IGeS)] {{Webarchive|url=https://web.archive.org/web/20140405092909/http://www.iges.polimi.it/ |date=5 April 2014 }}
+* [http://cddis.gsfc.nasa.gov/926/egm96/egm96.html EGM96 NASA GSFC Earth gravity model]
+* [http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008/index.html Earth Gravitational Model 2008 (EGM2008, Released in July 2008)] {{Webarchive|url=https://web.archive.org/web/20100508002312/http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008/index.html |date=8 May 2010 }}
+* [http://www.ngs.noaa.gov/GEOID/ NOAA Geoid webpage]
+* [http://icgem.gfz-potsdam.de/home International Centre for Global Earth Models (ICGEM)]
+* [http://www.kiamehr.ir/geoid.htm Kiamehr's Geoid Home Page] {{Webarchive|url=https://web.archive.org/web/20190720100135/http://www.kiamehr.ir/geoid.htm |date=20 July 2019 }}
+* [https://web.archive.org/web/20110113002553/http://www.fugro-gravmag.com/resources/Technical%20Papers/Li_Goetze_Geophysics_2001.pdf Geoid tutorial from Li and Gotze] (964KB pdf file)
+* [https://web.archive.org/web/20160304084208/http://www.csr.utexas.edu/grace/gravity/gravity_definition.html Geoid tutorial at GRACE website]
+* [https://web.archive.org/web/20081001095040/http://www.infra.kth.se/geo/geollab.htm Precise Geoid Determination Based on the Least-Squares Modification of Stokes’ Formula] (PhD Thesis PDF)
 {{нормативна контрола}}

Нормативна контрола
Државне	Немачка Летонија
Остале	Енциклопедија савремене Украјине Енциклопедија Британика