Skip to main content
SpringerLink
Log in

Gravity Forward Modeling

  • Living reference work entry
  • First Online:
Encyclopedia of Geodesy

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:

$$ F=G\frac{mM}{r^2} $$
(1)

where G = 6.67384 × 10−11 m3 kg−1 s−2 is the universal gravitational constant (Mohr et al., 2012). In most practical applications of GFM, unit mass is assumed in the computation point, and the second body’s mass M is considered the source of the gravitational field (Blakeley, 1996). The visible topography, given in the form of digital terrain models (DTMs), is the most frequently used mass distribution in GFM; other distributions may include, but are not...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References and Reading

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Blakeley, R. J., 1996. Potential Theory in Gravity and Magnetic Applications. Cambridge: Cambridge University Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • D’Urso, M. G., 2014. Analytical computation of gravity effects for polyhedral bodies. Journal of Geodesy, 88, 13–29.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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.

    Article  Google Scholar 

  • Göttl, F., and Rummel, R., 2009. A geodetic view on isostatic models. Pure and Applied Geophysics, 166, 1247–1260.

    Article  Google Scholar 

  • Grombein, T., Seitz, K., and Heck, B., 2013. Optimized formulas for the gravitational field of a tesseroid. Journal of Geodesy, 87, 645–660.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • Hirt, C., 2010. Prediction of vertical deflections from high-degree spherical harmonic synthesis and residual terrain model data. Journal of Geodesy, 84, 179–190.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • Jacoby, W., and Smilde, P. L., 2009. Gravity Interpretation. New York: Springer.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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].

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Nahavandchi, H., and Sjöberg, L. E., 1998. Terrain correction to power H3 in gravimetric geoid determination. Journal of Geodesy, 72, 124–135.

    Article  Google Scholar 

  • 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 

  • Novák, P., 2010. Direct modelling of the gravitational field using harmonic series. Acta Geodynamics et Geomaterialia, 7, 35–47.

    Google Scholar 

  • Oldenburg, D. W., 1974. The inversion and interpretation of gravity anomalies. Geophysics, 39, 526–536.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Tenzer, R., 2005. Spectral domain of Newton’s integral. Bollettino di Geodesia e Scienze Affini, 2, 61–73.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Wieczorek, M. A., 2007. Gravity and topography of the terrestrial planets. In Treatise on Geophysics. Oxford, UK: Elsevier-Pergamon, Vol. 10, pp. 165–206.

    Chapter  Google Scholar 

  • Wild-Pfeiffer, F., 2008. A comparison of different mass elements for use in gravity gradiometry. Journal of Geodesy, 82, 637–653.

    Article  Google Scholar 

  • Zuber, M. T., et al., 2013. Gravity field of the Moon from the Gravity Recovery and Interior Laboratory (GRAIL) mission. Science, 339, 668–671.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Spatial Sciences, Curtin University, Perth, WA, Australia

    Christian Hirt

  2. Institute for Advanced Study, TU Munich, Munich, Germany

    Christian Hirt

Authors
  1. Christian Hirt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christian Hirt .

Editor information

Editors and Affiliations

  1. Geodetic Institute, University of Stuttgart, Stuttgart, Germany

    Erik Grafarend

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this entry

Cite this entry

Hirt, C. (2016). Gravity Forward Modeling. In: Grafarend, E. (eds) Encyclopedia of Geodesy. Springer, Cham. https://doi.org/10.1007/978-3-319-02370-0_106-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-02370-0_106-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Cham

  • Online ISBN: 978-3-319-02370-0

  • eBook Packages: Springer Reference Earth and Environm. ScienceReference Module Physical and Materials ScienceReference Module Earth and Environmental Sciences

Publish with us

Policies and ethics

Search

Navigation