Calculation of Spherical Layer with Variable Density Gravity Field

  • K. M. KuznetsovEmail author
  • A. A. Bulychev
  • I. V. Lygin
Conference paper
Part of the Springer Proceedings in Earth and Environmental Sciences book series (SPEES)


Current article considers efficient algorithm for calculating of gravity effect from a spherical layer with variable density. It is based on using of fast discrete convolution. Features of its software implementation are also considered.


Gravimetry Direct gravity problem Earth’s sphericity accounting Fast discrete convolution Gravitational potential 


  1. Blokh Yu.I. (2009) Interpretation of gravity and magnetic anomalies / M. MGGRU. 2009. pp. 48–58. ( (in Russian).
  2. Bulychev A.A., Gilod D.A., Krivosheya K.V. (2002) Construction of a three-dimensional density model of the ocean’s lithosphere along the geoid heights field. // Bulletin of the Moscow University Vol. 4: Geology. 2002. №2. pp. 40–47. (in Russian).Google Scholar
  3. Bulychev A.A., Krivosheya K.V., Melihov V.R., Zal’cman R.V. (1998) Calculation of the anomalous gravitational potential and its derivatives on the sphere. // Bulletin of the Moscow University Vol. 4: Geology. 1998. Т.4. № 2. pp. 42–46. (in Russian).Google Scholar
  4. Bychkov S.G., Dolgal’ A.S., Simanov A.A. (2015) Calculation of gravity anomalies in high-precision gravimetric surveys. Perm’. UrO RAN. 2015. 142 p.Google Scholar
  5. Kuznetsov K.M., Lygin I.V., Bulychev A.A. (2017) Algorithm of numeric direct gravity calculation of spherical layer with variable density // Geofizika. 2017. №1. pp. 22–27. (in Russian).Google Scholar
  6. Starostenko V.I., Manukyan A.G., Zavorot’ko A.N. (1986) Methods for solving direct problems of gravimetry and magnetometry on spherical planets./ Kiev. Naukova dumka. 1986. 112 p. (in Russian).Google Scholar
  7. Starostenko V.I., Pyatakov Yu.V. (2013) Solution of direct gravimetric problems for spherical approximating bodies. Algorithms. // Izv.Tomsky Polytechnical. Un-ty 2013. Vol. 322. № 1. pp. 28–34 (in Russian).Google Scholar
  8. Strakhov V.N., Lapina M.I. (1986) Direct problems of gravimetry and magnetometry for homogeneous polyhedra. // Geofiz. Journ.1986. Vol. 8. № 6. pp. 20–31. (in Russian).Google Scholar
  9. Hohlova V.V. (2015) Taking into account the sphericity of the Earth when processing gravimetric data. // Geofizika. № 5. 2015. pp. 59–64. (in Russian).Google Scholar
  10. Hellinger S. J (1983). A method for computing the geoid height contribution of three-dimensional bodies within a spherical earth. // Geophysics. 1983. Vol. 48 № 12. p. 1664–1670.CrossRefGoogle Scholar
  11. Johnson L. R., Litehiser J. J. (1972) A Method for Computing the Gravitational Attraction of Three-Dimensional Bodies in a Spherical or Ellipsoidal Earth. // Geophysics. 1972. Vol. 77 № 35. p. 6999–7009.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • K. M. Kuznetsov
    • 1
    Email author
  • A. A. Bulychev
    • 1
  • I. V. Lygin
    • 1
  1. 1.Department of Geophysical Methods of Earth Crust Study, Faculty of GeologyLomonosov Moscow State UniversityMoscowRussian Federation

Personalised recommendations