Encyclopedia of Geodesy

Living Edition
| Editors: Erik Grafarend

Gravity Forward Modeling

  • Christian HirtEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-02370-0_106-1

Definition

Gravity forward modeling. Computation of the gravity field of some given mass distribution

Introduction

Gravity forward modeling (GFM) denotes the computation of the gravitational field generated by some source mass distribution . The foundation of GFM is Newton’s law of universal gravitation (1687) which states that the attraction force F between two bodies is proportional to the product of their masses m, M and inversely proportional to the square of their distance r:
$$ F=G\frac{mM}{r^2} $$

Keywords

Gravity Field Gravitational Potential Gravity Effect Mass Model Bouguer Gravity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

References and Reading

  1. Asgharzadeh, M. F., von Frese, R. B., Kim, H. R., Leftwich, T. E., and Kim, J. W., 2007. Spherical prism gravity effects by Gauss-Legendre quadrature integration. Geophysical Journal International, 169, 1–11.CrossRefGoogle Scholar
  2. Bagherbandi, M., and Sjöberg, L. E., 2012. A synthetic Earth gravity model based on a topographic-isostatic model. Studia Geophysica et Geodetica, 56, 935–955.CrossRefGoogle Scholar
  3. Balmino, G., Vales, N., Bonvalot, S., and Briais, A., 2012. Spherical harmonic modelling to ultra-high degree of Bouguer and isostatic anomalies. Journal of Geodesy, 86, 499–520.CrossRefGoogle Scholar
  4. Baran, I., Kuhn, M., Claessens, S. J., Featherstone, W. E., Holmes, S. A., and Vaníček, P., 2006. A synthetic Earth Gravity Model designed specifically for testing regional gravimetric geoid determination algorithms. Journal of Geodesy, 80, 1–16.CrossRefGoogle Scholar
  5. Blakeley, R. J., 1996. Potential Theory in Gravity and Magnetic Applications. Cambridge: Cambridge University Press.Google Scholar
  6. Claessens, S. J., and Hirt, C., 2013. Ellipsoidal topographic potential – new solutions for spectral forward gravity modelling of topography with respect to a reference ellipsoid. Journal of Geophysical Research – Solid Earth, 118, 5991–6002.CrossRefGoogle Scholar
  7. D’Urso, M. G., 2014. Analytical computation of gravity effects for polyhedral bodies. Journal of Geodesy, 88, 13–29.CrossRefGoogle Scholar
  8. Ebbing, J., Braitenberg, C., and Götze, H.-J., 2001. Forward and inverse modelling of gravity revealing insight into crustal structures of the Eastern Alps. Tectonophysics, 337, 191–208.CrossRefGoogle Scholar
  9. Eshagh, M., 2009. Comparison of two approaches for considering laterally varying density in topographic effect on satellite gravity gradiometric data. Acta Geophysica, 58, 661–686.Google Scholar
  10. Forsberg, R., 1984. A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modelling. Report 355, Department of Geodetic Science and Surveying, Ohio State University, Columbus, OH.Google Scholar
  11. Forsberg, R., and Tscherning, C. C., 1981. The use of height data in gravity field approximation by collocation. Journal of Geophysical Research, 86(B9), 7843–7854.CrossRefGoogle Scholar
  12. Göttl, F., and Rummel, R., 2009. A geodetic view on isostatic models. Pure and Applied Geophysics, 166, 1247–1260.CrossRefGoogle Scholar
  13. Grombein, T., Seitz, K., and Heck, B., 2013. Optimized formulas for the gravitational field of a tesseroid. Journal of Geodesy, 87, 645–660.CrossRefGoogle Scholar
  14. Grombein, T., Luo, X., Seitz, K., and Heck, B., 2014. A wavelet-based assessment of topographic-isostatic reductions for GOCE gravity gradients. Surveys in Geophysics, 35, 959–982.CrossRefGoogle Scholar
  15. Gruber, C., Novák, P., Flechtner, F., and Barthelmes, F., 2013. Derivation of the topographic potential from global DEM models. In International Association of Geodesy Symposia Series. Berlin/Heidelberg: Springer, Vol. 139, pp. 535–542.Google Scholar
  16. Heck, B., and Seitz, K., 2007. A comparison of the tesseroid, prism and point-mass approaches for mass reductions in gravity field modelling. Journal of Geodesy, 81, 121–136.CrossRefGoogle Scholar
  17. Hirt, C., 2010. Prediction of vertical deflections from high-degree spherical harmonic synthesis and residual terrain model data. Journal of Geodesy, 84, 179–190.CrossRefGoogle Scholar
  18. Hirt, C., and Kuhn, M., 2014. A band-limited topographic mass distribution generates a full-spectrum gravity field – gravity forward modelling in the spectral and spatial domain revisited. Journal of Geophysical Research – Solid Earth, 119, 3646–3661.CrossRefGoogle Scholar
  19. Hirt, C., Kuhn, M., Featherstone, W., and Göttl, F., 2012. Topographic/isostatic evaluation of new-generation GOCE gravity field models. Journal of Geophysical Research – Solid Earth, 117, B05407.Google Scholar
  20. Hirt, C., Claessens, S. J., Fecher, T., Kuhn, M., Pail, R., and Rexer, M., 2013. New ultra-high resolution picture of Earth’s gravity field. Geophysical Research Letters, 40, 4279–4283.CrossRefGoogle Scholar
  21. Jacoby, W., and Smilde, P. L., 2009. Gravity Interpretation. New York: Springer.Google Scholar
  22. Jekeli, C., and Serpas, J. G., 2003. Review and numerical assessment of the direct topographical reduction in geoid determination. Journal of Geodesy, 77, 226–239.CrossRefGoogle Scholar
  23. Kuhn, M., and Seitz, K., 2005. Comparison of Newton’s integral in the space and frequency domains. In International Association of Geodesy Symposia Series. Berlin/Heidelberg: Springer, Vol. 128, pp. 386–391.Google Scholar
  24. Kuhn, M., Featherstone, W. E., and Kirby, J. F., 2009. Complete spherical Bouguer gravity anomalies over Australia. Australian Journal of Earth Sciences, 56, 213–223.CrossRefGoogle Scholar
  25. Makhloof, A. A., and Ilk, K.-H., 2008. Effects of topographic–isostatic masses on gravitational functionals at the Earth’s surface and at airborne and satellite altitudes. Journal of Geodesy, 82, 93–111.CrossRefGoogle Scholar
  26. Mohr, P. J., Taylor, B. N., and Newell, D. B., 2012. CODATA recommended values of the fundamental physical constants: 2010. Reviews of Modern Physics, 84, 1527–1605 [Values available from http://physics.nist.gov/constants. Last accessed September 9, 2014].CrossRefGoogle Scholar
  27. Nagy, D., Papp, G., and Benedek, J., 2000. The gravitational potential and its derivatives for the prism. Journal of Geodesy, 74, 552–560, Erratum in Journal of Geodesy, 76, 475.CrossRefGoogle Scholar
  28. Nahavandchi, H., and Sjöberg, L. E., 1998. Terrain correction to power H3 in gravimetric geoid determination. Journal of Geodesy, 72, 124–135.CrossRefGoogle Scholar
  29. Neumann, G. A., et al., 2004. Crustal structure of Mars from gravity and topography. Journal of Geophysical Research, Planets, 109(E8), 1–18.Google Scholar
  30. Novák, P., 2010. Direct modelling of the gravitational field using harmonic series. Acta Geodynamics et Geomaterialia, 7, 35–47.Google Scholar
  31. Oldenburg, D. W., 1974. The inversion and interpretation of gravity anomalies. Geophysics, 39, 526–536.CrossRefGoogle Scholar
  32. Papp, G., 1996. Gravity field approximation based on volume element model of the density distribution. Acta Geodaetica et Geophysica Hungarica, 91, 339–358.Google Scholar
  33. Pavlis, N. K., Factor, J. K., and Holmes, S. A., 2007. Terrain-related gravimetric quantities computed for the next EGM. In Proceedings of the 1st International Symposium of the International Gravity Field Service. Istanbul, Turkey: Harita Dergisi, pp. 318–323.Google Scholar
  34. Rummel, R., Rapp, R.H., Sünkel, H., and Tscherning, C.C., 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, OH.Google Scholar
  35. Smith, D. A., 2000. The gravitational attraction of any polygonally shaped vertical prism with inclined top and bottom faces. Journal of Geodesy, 74, 414–420.CrossRefGoogle Scholar
  36. Strang van Hees, G.L. 2000. Some elementary relations between mass distributions inside the Earth and the geoid and gravity field. Journal of Geodynamics, 29, 111–123.CrossRefGoogle Scholar
  37. Tenzer, R., 2005. Spectral domain of Newton’s integral. Bollettino di Geodesia e Scienze Affini, 2, 61–73.Google Scholar
  38. Tenzer, R., Novák, P., and Gladkikh, V., 2011. On the accuracy of the bathymetry-generated gravitational field quantities for a depth-dependent seawater density distribution. Studia Geophysica et Geodaetica, 55, 609–626.CrossRefGoogle Scholar
  39. Tenzer, R., Gladkikh, V., Novák, P., and Vajda, P., 2012. Spatial and spectral analysis of refined gravity data for modelling the crust–mantle interface and mantle-lithosphere structure. Surveys in Geophysics, 33, 817–839.CrossRefGoogle Scholar
  40. Tocho, C., Vergos, G. S., and Sideris, M. G., 2012. Investigation of topographic reductions for marine geoid determination in the presence of an ultra-high resolution reference geopotential model. In International Association of Geodesy Symposia Series. Berlin/New York: Springer, Vol. 136, pp. 419–426.Google Scholar
  41. Tsoulis, D., 2013. Geodetic use of global digital terrain and crustal databases in gravity field modeling and interpretation. Journal of Geodetic Science, 1, 1–6.CrossRefGoogle Scholar
  42. Tsoulis, D., Novák, P., and Kadlec, M., 2009. Evaluation of precise terrain effects using high-resolution digital elevation, models. Journal of Geophysical Research, 114, B02404.CrossRefGoogle Scholar
  43. Tziavos, I. N., and Sideris, M. G., 2013. Topographic reductions in gravity and geoid modeling. In Lecture Notes in Earth System Sciences. Berlin/Heidelberg: Springer, Vol. 110, pp. 337–400.Google Scholar
  44. Tziavos, I. N., Vergos, G. S., and Grigoriadis, V. N., 2010. Investigation of topographic reductions and aliasing effects to gravity and the geoid over Greece based on various digital terrain models. Surveys in Geophysics, 31, 23–67.CrossRefGoogle Scholar
  45. Wang, Y. M., and Yang, X., 2013. On the spherical and spheroidal harmonic expansion of the gravitational potential of the topographic masses. Journal of Geodesy, 87, 909–921.CrossRefGoogle Scholar
  46. Wieczorek, M. A., 2007. Gravity and topography of the terrestrial planets. In Treatise on Geophysics. Oxford, UK: Elsevier-Pergamon, Vol. 10, pp. 165–206.CrossRefGoogle Scholar
  47. Wild-Pfeiffer, F., 2008. A comparison of different mass elements for use in gravity gradiometry. Journal of Geodesy, 82, 637–653.CrossRefGoogle Scholar
  48. Zuber, M. T., et al., 2013. Gravity field of the Moon from the Gravity Recovery and Interior Laboratory (GRAIL) mission. Science, 339, 668–671.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Spatial SciencesCurtin UniversityPerthAustralia
  2. 2.Institute for Advanced StudyTU MunichMunichGermany