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Gravity Inversion

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Gravity Inversion and Integration

Abstract

This chapter describes gravity inversion for various geophysical, geodetic and geodynamic applications. After introducing some basic geophysical concepts and formulas for gravity inversion, various isostatic models and their use in determining crustal depth by gravity is described at length and compared and combined with seismic models of crustal depth. The preferred isostatic model is based on Vening Meinesz-Moritz hypothesis with a global isostatic compensation of Bouguer gravity disturbances rather than Bouguer gravity anomalies. There are also applications of gravity for estimating tectonic stress in the mantle and viscosity in the mantle (based on post-glacial land uplift rate data in Fennoscandia). Temporal changes of the gravity field by many years of monthly repeated data from the satellite mission GRACE are used to demonstrate their power in determining large-scale Earth mass and geoid changes, such as positive geoid height rates in Laurentia and Fennoscandia related to glacial isostatic adjustments, and negative rates in Greenland and West Antarctica, as a result of mass losses due to ice-sheet melting. Also, the upper mantle viscosity in Fennoscandia is determined by these data.

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References

  • Abramowitz M, Stegun I (1964) Handbook of Mathematical functions. National Bureau of Standards, Washington, DC

    Google Scholar 

  • Airy GB (1855) On the computations of the effect of the attraction of the mountain masses as disturbing the apparent astronomical latitude of stations in geodetic surveys. Trans Roy Soc (London), Ser B 145

    Google Scholar 

  • Afonso JC, Fernàndez M, Ranalli G, Griffin WL, Connolly JAD (2008) Integrated geophysical-petrological modeling of the lithosphere and sublithospheric upper mantle: methodology and applications. Geochem Geophys Geosyst 9:Q05008

    Article  Google Scholar 

  • Ågren J, Svensson R (2007) Postglacial land uplift model and system definition for the new Swedish height system RH 2000. Reports in Geodesy and Geographical Information Systems, LMV-Rapport 2007:4. Lantmateriet, Gävle, Sweden

    Google Scholar 

  • Ågren J, Svensson R (2011) The height system RH 2000 and the land uplift model NKG2005LU. Mapp Image Sci 2011(3):4–12

    Google Scholar 

  • Allenby RJ, Sehnetzler CC (1983) United States crustal thickness. Tectonophysics 93(1983):13

    Article  Google Scholar 

  • Anderson DL (1989) Theory of the Earth. Blackwell Scientific Publications, Boston. http://resolver.caltech.edu/CaltechBOOK:1989.001

  • Artemieva IM, Mooney WD (2001) Thermal thickness and evolution of Precambrian lithosphere: a global study. J Geophys Res 106:16387–16414

    Google Scholar 

  • Artemieva IM (2006) Global 1° × 1° thermal model TC1 for the continental lithosphere: implications for lithosphere secular evolution. Tectonophysics 416:245–277

    Article  Google Scholar 

  • Artemieva IM, Thybo H, Kaban M (2006) Deep Europe today: Geophysical synthesis of the upper mantle structure and lithospheric processes over 3.5 By, in European Lithosphere Dynamics, Gee DG, Stephenson RA (eds). Geol Soc Mem, Lond 32:11–41

    Google Scholar 

  • Assumpção M, Bianchi MB, Julià J, Dias FL, França GS, Nascimento RM, Drouet S, Pavão CG, Albuquerque DF, Lopes AEV (2013) Crustal thickness map of Brazil: data compilation and main features. J S Am Earth Sci. doi:10.1016/j.jsames.2012.12.009. Accepted 18 Dec 2012

  • Bagherbandi M (2011) An isostatic Earth crustal thickness model and its applications. PhD thesis. Royal institute of technology, 207 p

    Google Scholar 

  • Bagherbandi M, Sjöberg LE (2013) Improving gravimetric-isostatic models of crustal depth by correcting for non-isostatic effects and using CRUST2.0. Earth Sci Rev 29–39. doi:10.1016/j.earscirev.2012.12.002

  • Bagherbandi M, Tenzer R, Sjöberg LE, Novak P (2013) Improved global crustal thickness modeling based on the VMM isostatic model and non-isostatic gravity correction. J Geodyn 66(2013):25–37. doi:10.1016/j.jog.2013.01.002

    Article  Google Scholar 

  • Bai Y, Williams S, Müller R, Liu Z, Hosseinpour M (2014) Mapping crustal thickness using marine gravity data: methods and uncertainties. Geophysics 79:G27–G36

    Article  Google Scholar 

  • Baranov A, Morelli A (2013) The Moho depth map of the Antarctica region. Tectonophysics 609:299–313. doi:10.1016/j.tecto.2012.12.023. 8 Dec 2013

  • Barzaghi R, Biagi L (2014) The collocation approach to Moho estimate. Ann Geophys 57(1):S0190. doi:10.4401/ag-6367

  • Bassin C, Laske G, Masters TG (2000) The current limits of resolution for surface wave tomography in North America. EOS Trans AGU 81:F897

    Google Scholar 

  • Becker TW, O’Connell RJ (2001) Lithospheric stresses caused by mantle convection: the role of plate rheology. Am Geophys Union, Fall Meeting 2001, abstract #T12C-0921

    Google Scholar 

  • Belyaevsky NA, Volkovsky IS (1980) Tectonic map of Northern Eurasia. In: Relief of the Moho Surface, Moscow

    Google Scholar 

  • Belyaevsky NA (1981) Structure of the earth crust from geologic-geophysical data. Nedra, Moscow (in Russian)

    Google Scholar 

  • Bendick R, Bilham R, Freymueller J, Larson K, Yin G (2000) Geodetic evidence for a low slip rate in the Altyn Tagh fault system. Nature 404(6773):69–72. doi:10.1038/35003555. PMID 10716442

  • Bentley CR, Wahr JM (1998) Satellite gravity and the mass balance of the Antarctic ice sheet. J Glaciol 44:207–213

    Article  Google Scholar 

  • Bercovici D (2010) Mantle convection. In: Gupta HK (ed) Encyclopedia of Solid Earth Geophysics. Springer 2011. 1539 Seiten

    Google Scholar 

  • Bergstrand S, Scherneck H-G, Milne GA, Johansson JM (2005) Upper mantle viscosity from continuous GPS baselines in Fennoscandia. J Geodyn 39:91–109. doi:10.1016/j.jog.2004.08.004

    Article  Google Scholar 

  • Bjerhammar A, Stocki S, Svensson L (1980) A geodetic determination of viscosity. Division of Geodesy. The Royal Institute of Technology, Stockholm, Sweden

    Google Scholar 

  • Bois P (1961) Indefinite integrals. Dover, New York

    Google Scholar 

  • Bott MHP (1971) The interior of the Earth. Edward Arnold Ltd., London

    Google Scholar 

  • Bouhifd MA, Andrault D, Fiquet G, Richet P (1996) Thermal expansion of forsterite up to the melting point. Geophys Res Lett 23:1143–1146. doi:10.1029/96GL01118

    Article  Google Scholar 

  • Bowin C (1994) The geoid and deep earth mass anomaly structure. In Vanicke P, Christou N T (Eds.): Gravity and its geophysical interpretation, CRC Press, Inc, Chap. 10

    Google Scholar 

  • Bungum H, Pirhonen SE, Husebye ES (1980) Crustal thicknesses in Fennoscandia. Geophys J Int 63(3):759–774. doi:10.1111/j.1365-246X.1980.tb02650.x

    Article  Google Scholar 

  • Bürgmann R, Rosen PA, Fielding EJ (2000) Synthetic aperture radar interferometry to measure Earth’s surface topography and its deformation. Annu Rev Earth Planet Sci 28:169–209

    Article  Google Scholar 

  • Čadak O, Martinec Z (1991) Spherical harmonic expansion of the earth’s crustal thickness up to degree and order 30. Studia Geoph Et Geod 35:151–165

    Article  Google Scholar 

  • Cathles LM (1971) The viscosity of the Earth’s mantle. PhD thesis, Princeton University

    Google Scholar 

  • Cathles LM (1975) The viscosity of the Earth’s mantle. Princeton University Press, Princeton

    Google Scholar 

  • Chappell AR, Kusznir NJ (2008) Three-dimensional gravity inversion for Moho depth at rifted continental margins incorporating a lithosphere thermal gravity anomaly correction. Geophys J Int 174:1–13

    Article  Google Scholar 

  • Cheng MK, Tapley BD (2004) Variations in the Earth’s oblateness during the past 28 years. J Geophys Res Solid Earth 109(B09402):9. doi:10.1029/2004jb003028

    Google Scholar 

  • Christensen NI (1982) Seismic velocities. In: Carmichael RS (ed) Handbook of physical properties of rocks, vol 2, pp 1–228. CRC Press, Boca Raton, FL

    Google Scholar 

  • Chulick GS, Detweiler S, Mooney WD (2013) Seismic structure of the crust and uppermost mantle of South America and surrounding oceanic basins. J S Am Earth Sci 42:260–276

    Google Scholar 

  • Cordani UG, Sato K (1999) Crustal evolution of the South America Platform based on Nd isotopic systematics of igneous rocks. Episodes 22:167–173

    Google Scholar 

  • Cooper M (2007) Structural style and hydrocarbon prospectivity in fold and thrust belts: a global review. In: Ries AC, Butler RW, Graham RH (eds) Deformation of the continental crust: the legacy of Mike Coward (PDF). Special Publications 272. Geological Society, London, pp 447–472. ISBN 978-1-86239-215-1. Retrieved 2 July 2011

    Google Scholar 

  • Davies GF (1999) Dynamic earth plates. Cambridge University Press, Plumes and Mantle Convection, p 458

    Book  Google Scholar 

  • De Geer G (1888) Om Skandinaviens nivåförändringar under Quartärperioden. Geol Fören Stockh Förh 10:366–379

    Article  Google Scholar 

  • Devoti R, Pietrantonio G, Riguzzi F (2014) GNSS networks for geodynamics in Italy. Física de la tierra, no 26, pp 11–24. ISSN 0214-4557

    Google Scholar 

  • Divins DL (2003) Total sediment thickness of the World’s oceans & marginal seas. Boulder, Colo

    Google Scholar 

  • Dobrin MB (1976) Introduction to geophysical prospecting (3d ed). McGraw-Hill, New York, 630 p

    Google Scholar 

  • Dorman LM, Lewis TR (1970) Experimental Isostasy: 2. An isostatic model for the U.S.A. derived from gravity and topographic data. J Geophys Res 75, p 3367

    Google Scholar 

  • Dziewonski AM, Anderson DL (1981) Preliminary reference Earth model. Phys Earth Planet Inter 25:297–356

    Article  Google Scholar 

  • Ebbing J, England RW, Korja T, Lauritsen T, Olesen O, Stratford W, Weidle C (2012) Structure of the Scandes lithosphere from surface to depth. Tectonophysics 536–537:1–24. 16 Apr 2012

    Google Scholar 

  • Eken T, Shomali ZH, Roberts R, Hieronymus CF, Bodvarsson R (2008) S and P velocity heterogeneities within the upper mantle below the Baltic Shield. Tectonophysics 462:109–124. doi:10.1016/j.tecto.2008.02.015

    Article  Google Scholar 

  • Ekman M (1991) Course and origin of the Fennoscandian uplift: the case for two separate mechanisms. Terra Nova 3:408–413

    Article  Google Scholar 

  • Ekman M, Mäkinen J (1996) Recent postglacial rebound, gravity change and mantle flow in Fennoscandia. Geophys J Int 126(1):229–234. doi:10.1111/j.1365-246X.1996.tb05281.x

  • Farrell WE (1972) Deformation of the Earth by surface loading. Rev Geophys 10:761–797

    Article  Google Scholar 

  • Fjeldskaar W, Cathles L (1991) The present rate of uplift of Fennoscandia implies a low-viscosity asthenosphere. Terra Nova 3:393–400

    Article  Google Scholar 

  • Forte AM, Mitrovica JX (1996) New inferences of mantle viscosity from joint inversion of long-wavelength mantle convection and post-glacial rebound data. Geophys Res Lett 23(10):1147–1150

    Article  Google Scholar 

  • Fraeijs de Veubeke BM (1979) A course in elasticity. Springer, New York

    Book  Google Scholar 

  • Gerhard Franz, Lucassen Friedrich, Kramer Wolfgang, Trumbull Robert B, Romer Rolf L, Wilke Hans-Gerhard, Viramonte José G, Becchio Raúl, Siebel Wolfgang (2006) The Andes, crustal evolution at the Central Andean continental margin: a geochemical record of crustal growth, recycling and destruction. Front Earth Sci 2006:45–64

    Google Scholar 

  • Gorbatchev R (2004) The Transscandinavian IGNEOUS belt—introduction and background. In: Högdahl K, Andersson U, Eklund O (eds) The Transscandinavian Igneous Belt (TIB) in Sweden: a review of its character and evolution. Geological survey of Finland, Special Paper vol 37. Geological Survey of Finland, pp 9–15

    Google Scholar 

  • Goiginger H, Rieser D, Mayer-Guerr T, Pail R, Schuh W-D, Jäggi A, Maier A (2011) GOCO consortium, the combined satellite-only global gravity field model GOCO02S. European Geosciences Union General Assembly 2011, Wien, 04.04.2011

    Google Scholar 

  • Grad M, Tiira T, ESC Working Group (2009) The Moho depth map of the European plate. Geophys J Int 176:279–292. doi:10.1111/j.1365-246X.2008.03919.x

  • Gradmann S, Ebbing J, Fullea J (2013) Integrated geophysical modelling of a lateral transition zone in the lithospheric mantle under Norway and Sweden. Geophys J Int 194:1358–1373

    Article  Google Scholar 

  • Goslin J, Beuzart P, Frauchetau J, Le Piehon X (1972) Thickening of the oceanic layer in the Pacific Ocean. Mar Geophys Res 1:418

    Article  Google Scholar 

  • Haas R, Scherneck H-G, Gueguen E, Nothnagel A, Campbell J (2002) Large-scale strain-rates in Europe derived from observations in the European geodetic VLBI network. European Geosciences Union 2002 (EGU) Stephan Mueller Special Publication Series, vol 2, pp 139–152

    Google Scholar 

  • Hackney RI, Featherstone WE (2003) Geodetic versus geophysical perspectives of the ‘gravity anomaly’. Geophys J Int 154(35–43):2003

    Google Scholar 

  • Han S-C, Shum CK, Jekeli C, Kuo C-Y, Wilson C, Seo K-W (2005) Non-isotropic filtering of GRACE temporal gravity for geophysical signal enhancement. Geophys J Int 163:18–25. doi:10.1111/j.1365-246X.2005.02756

    Article  Google Scholar 

  • Hanssen RF (2001) Radar interferometry: data interpretation and error analysis. Kluwer Academic, ISBN 9780792369455.

    Google Scholar 

  • Haskell NA (1935) The motion of a fluid under a surface load, 1. Physics 6(265–269):1935

    Google Scholar 

  • Heidbach O, Tingay M, Barth A, Reinecker J, Kurfeß D, Müller B (2008) The world stress map database release 2008. doi:10.1594/GFZ.WSM.Rel2008

  • Heiskanen WA, Vening Meinesz FA (1958) The Earth and its gravity field. McGraw-Hill Book Company, Inc, New York

    Google Scholar 

  • Heiskanen WA, Moritz H (1967) Physical geodesy. W.H. Freeman, New York

    Google Scholar 

  • Henkel H, Eriksson L (1987) Regional aeromagnetic and gravity studies in Scandinavia. Precambrian Res 35:169–180

    Article  Google Scholar 

  • Hinze WJ, Aiken C, Brozena J, Coakley B, Dater D, Flanagan G, Forsberg R, Hildenbrand T, Keller GR, Kellogg J (2005) New standards for reducing gravity data: The North American gravity database. Geophysics 70(4):J25–J32

    Article  Google Scholar 

  • Holmes A (1931) Radioactivity and earth movements. Geol Soc Glasgow Trans 18(559–606):1931

    Google Scholar 

  • Horemuz M (2010) Deformation measurements and analysis. Lecture notes. Royal Institute of Technology, Stockholm, School of Architecture and Built Environment, Division of Geodesy and Geoinformatics, Stockholm, October 2010

    Google Scholar 

  • Hotine M (1969) Mathematical geodesy, ESSA monograph 2. Department of Commerce, Washington

    Google Scholar 

  • Ilk KH (1983) Ein eitrag zur Dynamik ausgedehnter Körper-Gravitationswechselwirkung. Deutsche Geodätische Kommission, Reihe C, Heft Nr. 288, München

    Google Scholar 

  • Jacob T, Wahr J, Gross R, Swenson S, Geruo A (2012) Estimating geoid height change in North America: Past, present and future. J Geodesy 86:337–358. doi:10.1007/s00190-011-0522-7

    Article  Google Scholar 

  • Kaban MK, Schwintzer P, Artemieva IM, Mooney WD (2003) Density of the continental roots: compositional and thermal contributions. Earth Planet Sci Lett 209:53–69

    Article  Google Scholar 

  • Kaban MK, Schwintzer P, Reigber Ch (2004) A new isostatic model of the lithosphere and gravity field. J Geodesy 78:368–385

    Article  Google Scholar 

  • Kaban MK, Tesauro M, Cloetingh S (2010) An integrated gravity model for Europe’s crust and upper mantle. Earth Planet Sci Lett 296(3–4):195–209. ISSN 0012-821X, doi:10.1016/j.epsl.2010.04.041 (1 Aug 2010)

  • Kaufmann G, Lambeck K (2000) Mantle dynamics, postglacial rebound and the radial viscosity profile. Phys Earth Planet Inter 121:301–324

    Article  Google Scholar 

  • Kaufmann G, Wu P, Guoying L (2000) Glacial isostatic adjustment in Fennoscandia for a laterally homogeneous earth. Geophys J Int 143:262–273

    Article  Google Scholar 

  • Kennett BLN, Engdahl ER (1991) Travel times for global earthquake location and phase identification. Geophys J Int 105:429–465

    Article  Google Scholar 

  • Kierulf HP, Steffen H, Simpson MJR, Lidberg M, Wu P, Wang H (2014) A GPS velocity field for Fennoscandia and a consistent comparison to glacial isostatic adjustment models. J Geophys Res Solid Earth 119(8):6613–6629

    Article  Google Scholar 

  • King Scott D (1995) Models of mantle viscosity. Sciences, West Lafayette, IN 47907-1397. Mineral Physics and Crystallography A Handbook of Physical Constants. AGU Reference Shelf 2

    Google Scholar 

  • Klees R, Revtova EA, Gunter BC, Ditmar P, Oudman E, Winsemius HC, Savenije HHG (2008) The design of an optimal filter for monthly GRACE gravity models. Geophys J Int 175:417–432. doi:10.1111/j.1365-246X.2008.03922.x

    Article  Google Scholar 

  • Kolstrup ML, Pascal C, Maupin V (2012) What compensates the topography of southern Norway? Insights from thermo-isostatic modelling. J Geodynamics 61:105–119

    Article  Google Scholar 

  • Korja A (1995). Structure of the Svecofennian crust growth and destruction of the Svecofennian Orogen (Dissertation). Institute of Seismology, University of Helsinki, Report S-31, 36 pp

    Google Scholar 

  • Korja A, Korja T, Luosto U, Heikkinen P (1993) Seismic and geoelectric evidence for collisional and extensional events in the Fennoscandian shield—implications for precambrian crustal evolution. In: Green AG, Kröner A, Götze J-J, Pavlenkova N (eds) Plate Tectonic signatures in the continental lithosphere. Tectonophysics, vol 219, pp 129–152

    Google Scholar 

  • Kroll H, Kirfel A, Heinemann R, Barbier B (2012) Volume thermal expansion and related thermophysical parameters in the Mg, Fe olivine solid-solution series. Eur J Miner 24:935–956

    Article  Google Scholar 

  • Kusche J (2007) Approximate decorrelation and non-isotropic smoothing of time-variable GRACE-type gravity field models. J Geodesy 81(11):733–749

    Google Scholar 

  • Kusche J, Schmidt R, Petrovic S, Rietbroek R (2009) Decorrelated GRACE time-variable gravity solutions by GFZ, and their validation using a hydrological model. J Geodesy. doi:10.1007/s00190-009-0308-3

  • Lambeck K, Johnston P, Smither C, Nakada M (1996) Glacial rebound of the British Isles. III. Constraints on mantle viscosity. Geophys J Int 125:340–354

    Article  Google Scholar 

  • Lambeck K, Smither C, Johnston P (1998) Sea-level change, glacial rebound and mantle viscosity for northern Europe. Geophys J Int 134:102–144

    Article  Google Scholar 

  • Laske G, Masters G, Reif C (2000) A new global crustal model at 2×2 degrees (CRUST2.0). (http://igppweb.ucsd.edu/~gabi/rem.dir/crust/crust2.html)

  • Laske G, Masters G, Ma Z, Pasyanos M (2013) Update on CRUST1.0—A 1-degree global model of Earth’s crust. Geophys Res Abstracts, vol 15, Abstract EGU2013-2658

    Google Scholar 

  • Lemoine JM, Bruinsma S, Loyer S, Biancale R, Marty J-C, Perosanz F, Balmino G (2007) Temporal gravity field models inferred from GRACE data. Adv Space Res 39(1620–1629):2007

    Google Scholar 

  • Le Pichon X (1968) Sea-floor spreading and continental drift. J Geophys Res 73:3661–3697

    Article  Google Scholar 

  • Li X, Götze H-J (2001) Tutorial: ellipsoid, geoid, gravity, geodesy, and geophysics. Geophysics 66:1660–1668 (with the Erratum in 67, 997)

    Google Scholar 

  • Lidberg M, Johansson JM, Scherneck H-G, Davis JL (2007) An improved and extended GPS derived velocity field for the glacial isostatic adjustment in Fennoscandia. J Geodesy 81(3):213–230. doi:10.1007/s00190-006-0102-4

  • Lidberg M, Johansson JM, Scherneck H-G, Milne GA (2010) Recent results based on continuous GPS observations of the GIA process in Fennoscandia from BIFROST. J Geodyn 50:8–18. doi:10.1016/j.jog.2009.11.010

    Article  Google Scholar 

  • Lloyd S, van der Lee S, França GS, Assumpção M, Feng M (2010) Moho map of South America from receiver functions and surface waves. J Geophys Res 115:B11315. doi:10.1029/2009JB006829

    Article  Google Scholar 

  • Liu HS (1977) Convection pattern and stress system under the African plate. Phys Earth Planet Int 15:60–68

    Google Scholar 

  • Lowrie W (2007) Fundamentals of geophysics. Cambridge University Press. The Edinburgh Building, Cambridge CB2 8RU, UK. ISBN-13 978-0-511-35447-2

    Google Scholar 

  • Luosto U (1997) Structure of the Earth’s crust in Fennoscandia as revealed from refraction and wide-angle reflection studies. Geophysica 33(1):3–16

    Google Scholar 

  • Makhloof A (2007) The use of topographic-isostatic mass information in geodetic applications, Doctoral dissertation. Department of Theoretical and Physical Geodesy, Bonn, Germany

    Google Scholar 

  • Massonnet D, Feigl KL (1998) Radar interferometry and its application to changes in the earth’s surface. Rev Geophys 36(4):441–500. doi:10.1029/97RG03139

  • Mayer-Guerr T, Rieser D, Höck E, Brockmann JM, Schuh, W-D, Krasbutter I, Kusche J, Maier A, Krauss S, Hausleitner W, Baur O, Jäggi A, Meyer U, Prange L, Pail R, Fecher T, Gruber T (2012) The new combined satellite only model GOCO03s. Abstract, GGHS2012, Venice

    Google Scholar 

  • Martinec Z (1994) The minimum depth of compensation of topographic masses. Geophys J Int 117:545–554

    Article  Google Scholar 

  • Maupin V, Agostini A, Artemieva I, Balling N, Beekman F, Ebbing J, England RW, Frassett A, Gradmann S, Jacobsen BH, Köhler A, Kvarven T, Medhus AB, Mjelde R, Ritter J, Sokoutis D, Stratford W, Thybo H, Wawerzinek B, Weidle C (2013) The deep structure of the Scandes and its relation to tectonic history and present-day topography. Tectonophysics. doi:10.1016/j.tecto.2013.03.010

  • McConnell RK (1965) Isostatic adjustment in a layered earth. J Geophys Res 70:5171

    Article  Google Scholar 

  • McKenzie DP, Parker RL (1967) The North Pacific: an example of tectonics on a sphere. Nature 216:1276–1280

    Article  Google Scholar 

  • McKenzie D (1978) Some remarks on the development of sedimentary basins. Earth Planet Sci Lett 40:25–32

    Article  Google Scholar 

  • Medhus AB, Balling N, Jacobsen BH, Weidle C, England RW, Kind R, Thybo H, Voss P (2012) Upper-mantle structure beneath the Southern Scandes Mountains and the Northern Tornquist Zone revealed by P-wave travel time tomography. Geophys J Int 189(3):1315–1334

    Article  Google Scholar 

  • Meissner R (1973) The Moho as a transition zone. Geophys Surv 1(195–216):1973

    Google Scholar 

  • Meissner R, Wever Th, Fluh ER (1987) The Moho in Europe—implications for crustal development. Ann Geophys 5B(4):357

    Google Scholar 

  • McKenzie D, Jackson J, Priestley K (2005) Thermal structure of oceanic and continental lithosphere. Earth Planet Sci Lett 233:337–349

    Article  Google Scholar 

  • Milne GA, Davis JL, Mitrivica JX, Scherneck H-G, Johansson JM, Vermeer M, Koivula H (2001) Space geodetic constraints on glacial isostatic adjustment in Fennoscandia. Science 291:2381–2385

    Article  Google Scholar 

  • Mishra DC, Ravi Kumar M (2012) Long and short wavelengths of Indian Ocean geoid and gravity lows: mid-to-upper mantle sources, rapid drift and seismicity of Kachchh and Shillong plateau, India. J Asian Earth Sci 60:212–224. 22 Oct 2012

    Google Scholar 

  • Moritz H (1990) The figure of the Earth. Wichmann H, Karlsruhe

    Google Scholar 

  • Moritz H (2000) Geodetic reference system 1980. J Geod 74(1):128–162. doi:10.1007/S001900050278

    Article  Google Scholar 

  • Mooney WD, Laske G, Masters TG (1998) CRUST 5.1: a global crustal model at 5 × 5 deg. J Geophys Res 103:727–747

    Article  Google Scholar 

  • Moore P, Zhang Q, Alothman A (2005) Annual and semiannual variations of the Earth’s gravitational field from satellite laser ranging and CHAMP. J Geophys Res 110:2005. doi:10.1029/2004JB003448

    Google Scholar 

  • Müller RD, Sdrolias M, Gaina C, Roest WR (2008) Age, spreading rates, and spreading asymmetry of the world’s ocean crust. Geochem Geophys Geosyst 9:Q04006

    Article  Google Scholar 

  • Nansen F (1928) The Earth’s crust, its surface forms and isostatic adjustment, Norske Videnskaps-Akad. Oslo, I. Mat.-Naturv. Kl., Vol, Avhandl, p 12

    Google Scholar 

  • Nicolls RJ, Cazenave A (2010) Sea-level rise and its impact on coastal zones. Science 328:1517–1520

    Article  Google Scholar 

  • Nieuwland DA (ed) (2003) New insights into structural interpretation and modelling, p 101. Geological Society, London, Special Publications, vol 212, pp 101–116. 0305-8719/03/$15 © The Geological Society of London 2003

    Google Scholar 

  • Niskanen E (1949) On the elastic resistance of the earth’s crust. Ann Acad Sci Fenn, AIII 21:1–23

    Google Scholar 

  • Noomen R, Springer TA, Ambrosius BAC, Herzberger K, Kuijper DC, Mets G-J, Overgaauw B, Wakker KF (1996) Crustal deformations in the Mediterranean area computed from SLR and GPS observations. J Geodyn 21:73–96

    Article  Google Scholar 

  • Oldenburg DW (1974) The inversion and interpretation of gravity anomalies. Geophysics 39:526–536

    Article  Google Scholar 

  • Ortlieb L, Ruegg JC, Angelier J, Colletta B, Kasser M, Lesage P (1989) Geodetic and tectonic analyses along an active plate boundary: the central Gulf of California. Tectonics 8(3):429–441. doi:10.1029/TC008i003p00429

    Article  Google Scholar 

  • Pavlis N, Factor K, Holmes SA (2007) Terrain-Related Gravimetric Quantities Computed for the Next EGM. Presented at the 1st international symposium of the international gravity service 2006, August 28–September 1, Istanbul, Turkey

    Google Scholar 

  • Pavlis N, Holmes SA, Kenyon SC, Factor JK (2008) An Earth gravitational model to degree 2160: EGM08. Presented at the 2008 general assembly of the European Geosciences Union, Vienna, Austria, 13–18 Apr 2008

    Google Scholar 

  • Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the Earth gravitational model 2008 (EGM2008). J Geophys Res 117:B04406

    Article  Google Scholar 

  • Parsons B, Richter FM (1980) A relation between the driving force and geoid anomaly associated with mid-ocean ridges. Earth Planet Sci Lett 51:445–450. doi:10.1016/0012-821X(80)90223-X

    Article  Google Scholar 

  • Parker RL (1972) The rapid calculation of potential anomalies. Geophys J R Astr Soc 31:447–455

    Article  Google Scholar 

  • Peltier WR (1974) The impulse response of a Maxwell Earth. Rev Geophys Space Phys 12:649–669

    Article  Google Scholar 

  • Peltier WR, Andrews JT (1976) Glacial isostatic adjustment I. The forward Problem. Geophys J R Astron Soc 46:605–646

    Article  Google Scholar 

  • Peltier WR (2004) Global glacial isostasy and the surface of the ice-age Earth: the ICE-5G(VM2) model and GRACE. Annu Rev Earth Planet Sci 32:111–149. doi:10.1146/annurev.earth.32.082503.144359

  • Peltier WR (2007) Mantle dynamics and the D-double prime layer implications of the post-perovskite phase. In: Hirose K, Brodholt J, Lay T, Yuen D (eds) Post-perovskite: the last mantle phase transition, vol 174. AGU Geophysical Monograph, American Geophysics Union, pp 217–227

    Chapter  Google Scholar 

  • Petrovskaya MS, Vershkov AN (2006) Non-singular expressions for the gravity gradients in the local north-oriented and orbital reference frames. J Geod 80:117–127

    Article  Google Scholar 

  • Pick M (1994) The geoid and tectonic forces. In: Vanicek P, Christou N (eds) Geoid and its geophysical interpretations. CRC Press 386 p

    Google Scholar 

  • Pratt JH (1855) On the attraction of the Himalaya Mountains and of the elevated regions beyond upon the plumb-line in India. Trans Roy Soc (London), ser B, 145

    Google Scholar 

  • Prutkin I, Saleh M (2009) Gravity and magnetic data inversion for 3D topography of the Moho discontinuity in the northern Red Sea area, Egypt. J Geodyn 47(5):237–245

    Google Scholar 

  • Reguzzoni M, Sampietro D (2012) Moho estimation using GOCE data: a numerical simulation. In: Kenyon SC, Pacino MC, Marti U (eds) International Association of Geodesy symposia, Geodesy for planet Earth, vol 136, pp 205–214

    Google Scholar 

  • Reguzzoni M, Sampietro D, Sansò F (2013) Global Moho from the combination of the CRUST2.0 model and GOCE data. Geophys J Int 195(1):222–237. doi:10.1093/gji/ggt247

    Article  Google Scholar 

  • Richter FJ, Parsons B (1975) On the interaction of two scales of convection in the mantle. J Geophys Res, Dawson, J.B., 1970. The structural setting of African kimber 80(17):2529

    Google Scholar 

  • Riguzzi F, Crespi M, Devoti R, Doglioni C, Pietrantonio G, Pisani AR (2013) Strain rate relaxation of normal and thrust faults in Italy. Geophys J Int (2013) 195:815–820. doi:10.1093/gji/ggt304

  • Rummel R, Rapp RH, Sünkel H, Tscherning CC (1988) Comparisons of global topographic isostatic models to the Earth’s observed gravity field. Report No. 388, Department of Geodetic Science and Surveying, Ohio State University, Columbus

    Google Scholar 

  • Runcorn S (1962a) Towards a theory of continental drift. Nature 193:311–314

    Google Scholar 

  • Runcorn S (1962b) Convection currents in the Earth’s mantle. Nature 195:1248–1249

    Google Scholar 

  • Runcorn S (1967) Flow in the mantle inferred from the low degree harmonics of the geopotential. Geophys J Int 14(1–4):375–384. doi:10.1111/j.1365-246X.1967.tb06253.x

  • Sampietro D (2009) An inverse gravimetric problem with GOCE data, presented in geodesy for planet earth IAG scientific assembly 2009, August 31–Sptember 4, 2009 Buenos Aires, Argentina

    Google Scholar 

  • Sampietro D, Reguzzoni M, Braitenberg C (2013) The GOCE estimated Moho beneath the Tibetan Plateau and Himalaya. In: Rizos C, Willis P (eds) International Association of Geodesy Symposia, Earth on the edge: science for a sustainable planet, Proceedings of the IAG General assembly, 28 June–2 July 2011, Melbourne, Australia, 139, Springer, Berlin

    Google Scholar 

  • Sasgen I, Detlef W, Zdenˇek M, Volker K, Jan H (2005) Geodetic signatures of glacial changes in Antarctica: rates of geoid-height change and radial displacement due to present and past ice-mass variations, GFZ, Scientific Technical Report STR05/01

    Google Scholar 

  • Sauramo M (1958) Die Geschichte der Ostsee. Ann Acad Sci Fenn, AIII 51:1–522

    Google Scholar 

  • Seton M, Müller RD, Zahirovic S, Gaina C, Torsvik T, Shephard G, Talsma A, Gurnis M, Turner M, Maus S, Chandler M (2012) Global continental and ocean basin reconstructions since 200  Ma. Earth Sci Rev 113:212–270

    Article  Google Scholar 

  • Scherneck H-G, Lidberg M, Haas R, Johansson JM, Milne GA (2010) Fennoscandian strain rates from BIFROST GPS: a gravitating, thick-plate approach. J Geodyn 50(1):19–26

    Article  Google Scholar 

  • Schowalter WR (1978) Mechanics of non-newtonian fluids pergamon. ISBN 0-08-021778-8

    Google Scholar 

  • Sjöberg LE (1975) On the discrete boundary value problem of physical geodesy with harmonic reduction to an internal sphere. Royal Institute of Technology, Division of Geodesy, Stockholm. (Ph.D. Thesis.)

    Google Scholar 

  • Sjöberg LE (1983) Land uplift and its implications on the geoid in Fennoscandia. Tectonophysics 97:97–101

    Article  Google Scholar 

  • Sjöberg LE, Nord T, Fan H (1991) The Fennoscandian geoid bulge and its correlation with land uplift and Moho depth. In: Schultz BE, Anderson A, Froidevaux G, Park M (eds) Gravimetry and space techniques applied to geodynamics and ocean dynamics. AGU geophysical monograph series, vol 82, pp 133–142

    Google Scholar 

  • Sjöberg LE (1994) The total terrain effect in the modified Stokes’ formula. In: Sünkel H, Marson I (eds) Gravity and geoid, IAG symposia, vol 113, Springer, pp 616–623

    Google Scholar 

  • Sjöberg LE, Fan H, Nord T (1994) Further studies on the Fennoscandian gravity field versus the Moho depth and land uplift. Bull. Geodesique 69:32–42

    Article  Google Scholar 

  • Sjöberg LE (1997) The total terrain effect in gravimetric geoid determinations. Bolletino di Geodesia e Scienze Affini, LVI, pp 209–222

    Google Scholar 

  • Sjöberg LE (1998a) The exterior Airy/Heiskanen topographic-isostatic gravity potential anomaly and the effect of analytical continuation in Stokes’ formula. J Geodesy 72:654–662

    Article  Google Scholar 

  • Sjöberg LE (1998b) On the Pratt and Airy models of isostatic geoid undulations. J Geodyn 26(1):137–147

    Article  Google Scholar 

  • Sjöberg LE (2000) Topographic effects by the Stokes-Helmert method of geoid and quasigeoid determinations. J. of Geodesy 74(2):255–268

    Article  Google Scholar 

  • Sjöberg LE (2007) Topographic bias by analytical continuation in physical geodesy. J Geod 81:345–350

    Article  Google Scholar 

  • Sjöberg LE (2009) Solving Vening Meinesz-Moritz inverse problem in Isostasy. Geophys J Int 179(3):1527–1536. doi:10.1111/j.1365-246X.2009.04397.x

    Article  Google Scholar 

  • Sjöberg LE, Bagherbandi M (2011) A method of estimating the moho density contrast with a tentative application by EGM08 and CRUST2.0. Acta Geophysica 58:1–24. doi:10.2478/s11600-011-0003-7

  • Sjöberg LE (2013) On the isostatic gravity anomaly and disturbance and their applications to Vening Meinesz-Moritz inverse problem of isostasy. Geophys J Int 193:1277–1282

    Article  Google Scholar 

  • Sjöberg LE, Bagherbandi M (2013) A study on the Fennoscandian post-glacial rebound as observed by present-day uplift rates and gravity field model GOCO02S. Acta Geod Geophys 48:317–331. doi:10.1007/s40328-013-0025-5

  • Sjöberg LE, Bagherbandi M, Tenzer R (2015) On gravity inversion by no-topography and rigorous isostatic gravity anomalies. Pure Appl Geophys 172(10):2669–2680. doi:10.1007/s00024-015-1032-y

  • Shin YH, Shum CK, Braitenberg C, Lee SM, Xu H, Choi KS, Baek JH, Park JU (2009) Three-dimensional fold structure of the Tibetan Moho from GRACE gravity data. Geophys Res Lett 36(1)

    Google Scholar 

  • Skinner BJ, Porter SC (1995) The blue planet. An introduction to earth system science, xxiii + 493 + lii pp. Wiley, New York. Price £47.95 (hard covers). ISBN 0 471 54021 8

    Google Scholar 

  • Spada G, Barletta VR, Klemann V, Riva REM, Martinec Z, Gasperini P, Lund B, Wolf D, Vermeersen LLA, King MA (2011) Benchmark study for glacial isostatic adjustment codes. Geophys J Int 185:106–132

    Google Scholar 

  • Steffen H, Wu P, Wang H (2010) Determination of the Earth’s structure in Fennoscandia from GRACE and implications for the optimal post-processing of GRACE data. Geophys J Int 182:1295–1310

    Article  Google Scholar 

  • Steffen H, Wu P, Wang H (2012) Optimal locations for absolute gravity measurements and sensitivity of GRACE observations for constraining glacial isostatic adjustment on the northern hemisphere. Geophys J Int 190(1483–1494):2012. doi:10.1111/j.1365-246X.2012.05563.x

    Google Scholar 

  • Sun W, Sjöberg LE (1999) Gravitational potential changes of a spherically symmetric earth model caused by a surface load. Geophys J Int 137:449–468

    Article  Google Scholar 

  • Swenson S, Wahr J (2006) Post-processing removal of correlated errors in GRACE data. Geophys Res Lett 33:L08402. doi:10.1029/2005GL025285

    Google Scholar 

  • Swenson S, Chambers D, Wahr J (2008) Estimating geocentre variations from a combination of GRACE and ocean model output. J Geophys Res Solid Earth 113(B08410):12. doi:10.1029/2007jb005338

    Google Scholar 

  • Swieczak M, Kozlovskaya E, Majdanski M, Grad M (2009) Interpretation of geoid anomalies in the contact zone between the East European Craton and the Paleozoic platform—II: modeling of density in the lithospheric mantle. Geophys J Int 177:334–346

    Article  Google Scholar 

  • Sünkel H (1985) An isostatic earth model. In: The department of geodetic science and surveying report no. 367. The Ohio State University, Columbus

    Google Scholar 

  • Talebian M, Jackson J (2004) A reappraisal of earthquake focal mechanisms and active shortening in the Zagros mountains of Iran (PDF). Geophys J Int (Royal Astronomical Society) 156(3):506–526. Bibcode:2004GeoJI.156..506T. doi:10.1111/j.1365-246X.2004.02092.x. Retrieved 2 July 2011

  • Tenzer R, Novák P, Vajda P, Gladkikh V, Hamayun (2012) Spectral harmonic analysis and synthesis of Earth’s crust gravity field. Comp Geosci 16(1):193–207

    Google Scholar 

  • Tenzer R, Hamayun VP (2009) A global correlation of the step-wise consolidated crust-stripped gravity field quantities with the topography, bathymetry, and the CRUST2.0 Moho boundary. Contributions Geophys Geodesy 39(2)133–147

    Google Scholar 

  • Tenzer R, Bagherbandi M (2012) Reformulation of the Vening–Meinesz Moritz inverse problem of isostasy for isostatic gravity disturbances. Int J Geosci 2012(3):918–929. doi:10.4236/ijg.2012.325094

    Article  Google Scholar 

  • Tenzer R, Wenjin C, Tsoulis D, Bagherbandi M, Sjöberg LE, Novák P (2014) Analysis of the refined CRUST1.0 crustal model and its gravity field. Surveys in Geophysics 36:139–165. doi:10.1007/s10712-12-014-9299-6

  • Tesauro M, Kaban MK, Cloetingh S (2008) EuCRUST-07: a new reference model for the European crust. Geoph Res Let 35. doi:10.1029/2007GL032244

  • Turcotte D, Schubert G (2002) Geodynamics, 2nd ed., Cambridge University Press

    Google Scholar 

  • Vajda P, Vaníček P, Novak P, Tenzer R, Ellmann A (2007) Secondary indirect effects in gravity anomaly data inversion or interpretation. J Geophys Res 112(B06411)

    Google Scholar 

  • Vening Meinesz FA (1931) Une nouvelle methode pour la reduction isostatique regionale del’intensite de la pesanteur. Bull Geod 29:33–51

    Article  Google Scholar 

  • Walcott RI (1980) Rheological models and observational data of glacio-isostatic rebound. In: Mörner N-A (ed) Earth rheology, isostasy and eustasy. Wiley, Chichester

    Google Scholar 

  • Wallace K, Yin G, Bilham R (2004) Inescapable slow slip on the Altyn Tagh fault. Geophys Res Lett 31(9):1–4. Bibcode: 2004GeoRL. 3109613W. doi:10.1029/2004GL019724

  • Wahr J, Molenaar M, Bryan F (1998) Time variability of the Earth’s gravity field: hydrological and oceanic effects and their possible detection using GRACE. J Geophys Res 103, 30205–30229

    Google Scholar 

  • Watts AB (2001) Isostasy and flexure of the lithosphere. Cambridge University Press, Cambridge

    Google Scholar 

  • Wegener A (1912) Die Entstehung der Kontinente. Sid. 185–195(253–256):305–309

    Google Scholar 

  • Wegener A (1924) The origin of continents and oceans. Methuen and Co., Ltd, p 1924

    Google Scholar 

  • Wild F, Heck B (2004a) A comparison of different isostatic models applied to satellite gravity gradiometry, Gravity, Geoid and Space Missions GGSM 2004 IAG International Symposium Porto, Portugal August 30–September 3

    Google Scholar 

  • Wild F, Heck B (2004b) Effects of topographic and isostatic masses in satellite gravity gradiometry. In: Proceedings of the second international GOCE user workshop GOCE. The Geoid and Oceanography, ESA-ESRIN, Frascati/Italy, 8–10 Mar 2004 (ESA SP–569, June 2004), CDROM

    Google Scholar 

  • Wouters B, Schrama EJO (2007) Improved accuracy of GRACE gravity solutions through empirical orthogonal function filtering of spherical harmonics. Geophys Res Lett 34:L23711. doi:10.1029/2007GL032098

    Article  Google Scholar 

  • Wu P, Steffen H, Wang HS (2010) Optimal locations for GPS measurements in North America and northern Europe for constraining Glacial Isostatic Adjustment. Geophys J Int 181(653–664):2010. doi:10.1111/j.1365-246X.2010.04545.x

    Google Scholar 

  • Zhang P-Z, Molnar P, Xu X (2007) Late quaternary and present-day rates of slip along the Altyn Tagh fault, northern margin of the Tibetan Plateau. Tectonics 27 (TC5010): 1–24. Bibcode:2007Tecto..26.5010Z. doi:10.1029/2006TC002014

  • Zhao S, Lambeck K, Lidberg M (2012) Lithosphere thickness and mantle viscosity inverted from GPS-derived deformation rates in Fennoscandia. Geophys J Int 190:278–292

    Article  Google Scholar 

  • Zhong S, McNamara A, Tan E, Moresi L, Gurnis M (2008) A benchmark study on mantle convection in a 3-D spherical shell using CitcomS. Geochem Geophys Geosyst 9(10). doi:10.1029/2008GC002048. http://maps.unomaha.edu/Maher/plate/week13/mechanisms.html

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Sjöberg, L.E., Bagherbandi, M. (2017). Gravity Inversion. In: Gravity Inversion and Integration. Springer, Cham. https://doi.org/10.1007/978-3-319-50298-4_8

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