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Gravity Modeling, Theory and Computation

  • Living reference work entry
  • First Online:
Encyclopedia of Solid Earth Geophysics

Part of the book series: Encyclopedia of Earth Sciences Series ((EESS))

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Definition

Gravity modeling :

Explaining the variations of the external gravity field of a body in terms of its internal density variations. Applications range from oil prospecting to the deep structure of the Earth.

Inverse problem :

In Gravity modeling, the forward problem is to compute the external gravity field of a body knowing its internal density distribution. The inverse problem is the opposite, and is much more difficult to solve for.

The Gravity Modeling from a Theoretical Point of View

Gravity is an elusive quantity to deal with, but a powerful one. This is mainly because unlike electromagnetic forces, gravity cannot be shielded as there are no negative masses. We refer to LaFehr (1980) and Milsom (1996) for an introduction to the gravimetric techniques (see also “Gravity Method, Principles”), and Zidarov (1990) for the subtleties of gravimetric inversion. Good monographs are available on the theory and computational aspects of gravity modeling. The one from Blakely (1996)...

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Bibliography

  • Abadi M, Agarwal A, Barham P, Brevdo E, Chen Z, Citro C, Corrado GS, Davis A, Dean J, Devin M, Ghemawat S, Goodfellow I, Harp A, Irving G, Isard M, Jozefowicz R, Jia Y, Kaiser L, Kudlur M, Levenberg J, Mané D, Schuster M, Monga R, Moore S, Murray D, Olah C, Shlens J, Steiner B, Sutskever I, Talwar K, Tucker P, Vanhoucke V, Vasudevan V, Viégas F, Vinyals O, Warden P, Wattenberg M, Wicke M, Yu Y, Zheng X (2015) TensorFlow: large-scale machine learning on heterogeneous systems. Software available from tensorflow.org

  • Akimova E, Misilov V, Sultanov M (2018) Solving the structural inverse gravimetry problem in the case of multilayered medium using GPU. In: Proceedings of the Ural-PDC 2018 workshop on parallel, distributed, and cloud computing for young scientists, Yekaterinburg

    Google Scholar 

  • Backus GE, Gilbert JF (1968) The resolving power of gross earth data. Geophys J R Astron Soc 16:169–205

    Google Scholar 

  • Ballani L, Engelis J, Grafarend G (1993) Global base functions for the mass density in the interior of a massive body (Earth). Manuscr Geodaet 18(2):99–114

    Google Scholar 

  • Barriot J-P, Kofman W, Herique A, Leblanc S, Portal A (1999) A two dimensional simulation of the CONSERT experiment (radio tomography of comet Wirtanen). Adv Space Res 24(9):1127–1138

    Google Scholar 

  • Blakely RJ (1996) Potential theory in gravity and magnetic applications. Cambridge University Press, Cambridge. ISBN 0-521-57547-8

    Google Scholar 

  • Branham RL Jr (1990) Scientific data analysis: an introduction to overdetermined systems. Springer, New York. ISBN 0-387-97201-3

    Google Scholar 

  • Campbell SL, Meyer CD Jr (1979) Generalized inverses of linear transformations, Surveys and reference works in mathematics, vol 4. Pitman, Boston. ISBN 0-273-08422-4

    Google Scholar 

  • Chao BF (2005) On inversion for mass distribution from global (time-variable) gravity field. J Geodyn 39(3):223–230

    Google Scholar 

  • Chui CK (1992) An introduction to wavelets. Academic, San Diego

    Google Scholar 

  • Cordell L, Henderson RG (1968) Iterative three-dimensional solution of gravity anomaly data using a digital computer. Geophysics 33:596–601

    Google Scholar 

  • Cuer M, Bayer R (1980) Fortran routines for linear inverse problems. Geophysics 45:1706–1719

    Google Scholar 

  • Davidson-Pilon C (2016) Bayesian methods for hackers: probabilistic programming and Bayesian inference. Addison-Wesley, New York. ISBN-13 978-0133902839

    Google Scholar 

  • Dean WC (1958) Frequency analysis for gravity and magnetic interpretation. Geophysics 23:97–127

    Google Scholar 

  • Dimri V (1992) Deconvolution and inverse theory: application to geophysical problems, methods in geochemistry and geophysics. Elsevier, Amsterdam. ISBN 0-444-89493-4

    Google Scholar 

  • Dubois J, Diament M (2005) Géophysique – Cours et exercices corrigés, 3ème édition. Dunod, Paris. ISBN 9782100491858

    Google Scholar 

  • Goodacre AK (2006) Estimation of the minimum density contrast of a homogeneous body as an aid to the interpretation of gravity anomalies. Geophys Prospect 28(3):408–414

    Google Scholar 

  • Hadamard J (1902) Sur les problèmes aux derivées partielles et leur signification physique. Princeton Univ Bull 13:49–52

    Google Scholar 

  • Hildebrand AR, Penfield GT, Glen T, Kring DA, Pilkington M, Zanoguera AC, Jacobsen SB, Boynton WV (1991) Chicxulub Crater: a possible cretaceous/tertiary boundary impact crater on the Yucatan Peninsula, Mexico. Geology 19(9):867–871

    Google Scholar 

  • Holland JH (1975) Adaptation in natural and artificial systems. Michigan University Press, Ann Arbor

    Google Scholar 

  • Izquierdo K, Lekić V, Montési LGJ (2020) A Bayesian approach to infer interior mass anomalies from the gravity data of celestial bodies. Geophys J Int 220(3):1687–1699. https://doi.org/10.1093/gji/ggz544

    Article  Google Scholar 

  • LaFehr TR (1980) Gravity method. Geophysics 45(11):1634–1639. ISSN 0016-8033

    Google Scholar 

  • LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521:436–444. https://doi.org/10.1038/nature14539

    Article  Google Scholar 

  • Levassor F, Foudil Bey N, Caumon G (2009) Kohonen’s neural networks: application to determine geological models from gravimetric datasets. In: Proceedings of 29th Gocad meeting, Nancy

    Google Scholar 

  • Levenberg K (1944) A method for the solution of certain problems in least squares. Q Appl Math 2:164–168

    Google Scholar 

  • Levy AV, Montalvo A (1985) The tunneling algorithm for the global minimization of functions. SIAM J Sci Stat Comput 6(1):15–29

    Google Scholar 

  • Marquardt D (1963) An algorithm for least-squares estimation of nonlinear parameters. SIAM J Appl Math 11:431–441

    Google Scholar 

  • Menke W (1989) Geophysical data analysis: discrete inverse theory, International geophysics series, vol 45. Academic, San Diego. ISBN 0-12-490921-3

    Google Scholar 

  • Milsom J (1996) Field geophysics. Wiley, Chichester. ISBN 0-471-96634-7

    Google Scholar 

  • Monteiro Santos FA (2010) Inversion of self-potential of idealized bodies anomalies using particle swarm optimization. Comput Geosci 36(9):1185–1190

    Google Scholar 

  • Moritz H (1989) A set of continuous density distributions within a sphere compatible with a given external gravitational potential. Gerlands Beitr Geophysik 98:185–192

    Google Scholar 

  • Parker RL (1975) The theory of ideal bodies for gravity interpretation. Geophys J R Astron Soc 42:315–334

    Google Scholar 

  • Sabatier PC (2000) Past and future of inverse problems. J Math Phys 41(6):4082–4124

    Google Scholar 

  • Shimelevich MI, Obornev EA, Obornev IE, Rodionov EA, Lyakhovets DA (2019) Formalized inversion of geophysical data using neural network technologies with application to the tasks of geoelectrics and gravimetry. In: Proceedings of the 15th conference in engineering and mining geophysics, Apr 2019, vol 2019. European Association of Geoscientists & Engineers, pp 1–5. https://doi.org/10.3997/2214-4609.201901717

  • Strykowski G (1998) Some technical details concerning a new method of gravimetric-seismic inversion. In: Proceedings of the XXIII General Assembly of the European Geophysical Society, Nice. Physics and chemistry of the earth, vol 24. pp 207–214

    Google Scholar 

  • Talwani M, Worzel JL, Landisman M (1959) Rapid gravity computations for two-dimensional bodies with application to the Mendocino submarine fracture zone. J Geophys Res 64:49–61

    Google Scholar 

  • Tarantola A (2005) Inverse problem theory and methods for model parameter estimation. SIAM, Philadelphia. ISBN 978-0-898715-72-9

    Google Scholar 

  • Tarantola A, Valette B (1982) Generalized nonlinear inverse problems solved using the least squares criterion. Rev Geophys Space Phys 20(2):219–232

    Google Scholar 

  • Tikhonov A, Arsenine V (1976) Méthodes de Résolution des Problèmes Mal Posés. Editions Mir, Moscou

    Google Scholar 

  • Troyan VN, Hayakawa M (2002) Inverse geophysical problems. Terrapub Editor, Tokyo. ISBN 4-88704-131-4

    Google Scholar 

  • Tsoulis D, Petrovi S (2001) Short Note On the singularities of the gravity field of a homogeneous polyhedral body. Geophysics 66(2):535–539

    Google Scholar 

  • Valentine AP, Sambridge M (2020a) Gaussian process models – I. A framework for probabilistic continuous inverse theory. Geophys J Int 220(3):1632–1647. https://doi.org/10.1093/gji/ggz520

    Article  Google Scholar 

  • Valentine AP, Sambridge M (2020b) Gaussian process models – II. Lessons for discrete inversion. Geophys J Int 220(3):1648–1656. https://doi.org/10.1093/gji/ggz521

    Article  Google Scholar 

  • Vanicek P, Kleusberg A (1985) What an external gravitational potential can really tell us about mass distribution. B Geofis Teor Appl XXCII(108):243–250

    Google Scholar 

  • Volker M (2005) Regularized wavelet-based multiresolution recovery of the harmonic mass density distribution from data of the Earth’s gravitational field at satellite height. Inverse Probl 21:997–1025. https://doi.org/10.1088/0266-5611/21/3/013

    Article  Google Scholar 

  • Widrow B, Lehr M (1990) 30 years of adaptive neural networks: perceptron, Madaline, and backpropagation. Proc IEEE 78(9):1415–1442

    Google Scholar 

  • Wu S-Y, Wang Y-J, Li L, Hu J-S, Feng G-Z, Yan H-J (2007) The application of support vector machine in the joint inversion of gravimetric and seismic data. Prog Geophys 22(5):1611–1616

    Google Scholar 

  • Zhdanov MS (1988) Integral transform in geophysics. Springer, Berlin. ISBN 3-540-17759-0

    Google Scholar 

  • Zidarov D (1990) Inverse gravimetric problems in geoprospecting and geodesy. Elsevier, Amsterdam. ISBN 0-444-98777-0

    Google Scholar 

  • Zuber MT, Solomon SC, Phillips RJ, Smith DE, Tyler GL, Aharonson O, Balmino G, Banerdt WB, Head JW, Johnson CL, Lemoine FG, McGovern PJ, Neumann GA, Rowlands DD, Zhong S (2000) Internal structure and early thermal evolution of mars from mars global surveyor topography and gravity. Science 287(5459):1788–1793

    Google Scholar 

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Authors and Affiliations

  1. Observatoire Géodésique de Tahiti, University of French Polynesia, Faaa-Tahiti, French Polynesia

    Jean-Pierre Barriot & Lydie Sichoix

Authors
  1. Jean-Pierre Barriot
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  2. Lydie Sichoix
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Correspondence to Jean-Pierre Barriot .

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Editors and Affiliations

  1. Seismology, National Geophysical Research Insti, Hyderabad, India

    Harsh K. Gupta

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Barriot, JP., Sichoix, L. (2020). Gravity Modeling, Theory and Computation. In: Gupta, H.K. (eds) Encyclopedia of Solid Earth Geophysics. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-030-10475-7_233-1

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  • DOI: https://doi.org/10.1007/978-3-030-10475-7_233-1

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