Skip to main content
SpringerLink
Log in

Using the Method of S-approximations to Determine Deflections of the Vertical and Geoid Heights

  • Published:
Gyroscopy and Navigation Aims and scope Submit manuscript

Abstract

A modified method for S-approximations of anomalous potential fields is described; its advantages are discussed. Software has been developed to calculate deflections of the vertical (DOV) and geoid heights using the proposed technique. The results of DOV calculations for two regions of the Atlantic Ocean are given.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Balmino, G., Barriot, J.P., and Vales, N., Non-singular formulation of the gravity vector and gravity gradient tensor in spherical harmonics, Manuscripta Geodaetica, 1990, no. 15, pp. 11–16.

  2. Naidu, P., Spectrum of the potential field due to randomly distributed sources, Geophysics, 1968, no. 33, pp. 337–345.

  3. Martyshko, P.S. and Prutkin, I.L., Technology for identification of the sources of the gravitational field by depth, Geofizicheskii zhurnal, 2003, vol. 25, no. 3, pp. 159–168.

    Google Scholar 

  4. Serkerov, S.A., Spektral’nyi analiz v gravirazvedke i magnitorazvedke (Spectral Analysis in Gravimetric Survey and Magnetic Prospecting), Moscow: Nedra, 1991.

    Google Scholar 

  5. Strakhov, V.N., Geofizika i matematika (Geophysics and Mathematics), Moscow: OIFZ RAN, 1999.

    Google Scholar 

  6. Strakhov, V.N. and Stepanova, I.E., S-approximation method and its application to solution of gravimetry problems (regional version), Fizika Zemli, 2002, no. 7, pp. 3–12.

  7. Strakhov, V.N. and Stepanova, I.E., S-approximation method and its application to solution of gravimetry problems (local version), Fizika Zemli, 2002, no. 2, pp. 3–19.

  8. Strakhov, V.N. and Strakhov, A.V., Solving systems of linear algebraic equations with an approximately given right-hand side that occur in the solution of gravimetry and magnetometry problems, Izvestiia sektsii nauk o Zemle RAEN, 1999, vol. 3, November, pp. 20–22.

    Google Scholar 

  9. Strakhov, V.N. and Strakhov, A.V., Osnovnye metody nakhozhdeniya ustoichivykh priblizhennykh reshenii sistem lineinykh algebraicheskikh uravnenii, voznikayushchikh pri reshenii zadach gravimetrii i magnitometrii (Basic Methods for finding Stable Approximate Solutions of Systems of Linear Algebraic Equations in the Solution of Gravimetry and Magnetometry Problems). II, Moscow: OIFZ RAN, 1999.

    Google Scholar 

  10. Strakhov, V.N. and Stepanova, I.E., A Method for finding stable approximate solutions of systems of linear algebraic equations with matrix occurred in the solution of gravimetry and magnetometry problems, Aktual’nye voprosy matematicheskoi geofiziki, vol. 2, part 1, Moscow: OIFZ RAN, 2001, pp. 73–95.

    Google Scholar 

  11. Strakhov, V.N., Stepanova, I.E., Grichuk, L.V., Kerimov, I.A., and Strakhov, A.V., A method of linear integral representations in solving gravimetry and magnetometry problems, Geofizika i matematika: Materialy 1-i Vserossiiskoi konferentsii, Moscow, November 22–26, 1999, Moscow: OIFZ RAN, 1999, pp. 173–183.

    Google Scholar 

  12. Koneshov, V.N., Osika, I.V., and Stepanova, I.E., The method for calculating deflections of the vertical, Fizika Zemli, 2007, no. 6, pp. 16–25.

  13. Pellinen, L.P., Calculation of deflections of the vertical and quasigeoid heights in the mountains, Trudy TSNI-IGAiK, 1969, vol. 176, pp. 99–112.

    Google Scholar 

  14. Stepanova, I.E. and Raevskii, D.N., Solution of inverse problems of gravimetry using the modified method of S-approximations, Fizika Zemli, 2015, no. 2, pp. 44–54.

  15. Stepanova, I.E., Raevskii, D.N, and Shchepetilov A.V., Improving the efficiency of the modified method of S-approximations, Fizika Zemli, 2016, no.1, pp. 149–160.

  16. Shimbirev, B.P., Teoriya figury Zemli (Theory of the Earth’s Figure), Moscow: Nedra, 1975.

    Google Scholar 

  17. Krylov, V.I. and Shul’gina, L.T., Spravochnaya knigapo chislennomu integrirovaniyu (Reference Book on Numerical Integration), Moscow: Nauka, 1966.

    Google Scholar 

  18. Peshekhonov, V.G. and Stepanov O.A. (Eds.), Sovremennye metody i sredstva izmerenya parametrov gravitatsionnogo polya Zemli (Modern Technologies and Methods for Measuring the Earth’s Gravity Field Parameters), St. Petersburg, Concern CSRI Elektropribor, JSC, 2017.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Schmidt Institute of Physics of the Earth (IFZ), Russian Academy of Sciences, Moscow, 123242, Russia

    V. N. Koneshov & I. E. Stepanova

Authors
  1. V. N. Koneshov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. E. Stepanova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. N. Koneshov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Koneshov, V.N., Stepanova, I.E. Using the Method of S-approximations to Determine Deflections of the Vertical and Geoid Heights. Gyroscopy Navig. 10, 21–26 (2019). https://doi.org/10.1134/S2075108719010048

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2075108719010048

Keywords

Search

Navigation