Using the Method of S-approximations to Determine Deflections of the Vertical and Geoid Heights
https://doi.org/10.17285/0869-7035.2018.26.4.014-022
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.
About the Authors
V. N. KoneshovRussian Federation
I. E. Stepanova
Russian Federation
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.
4. Serkerov, S.A., Spektral’nyi analiz v gravirazvedke i magnitorazvedke (Spectral Analysis in Gravimetric Survey and Magnetic Prospecting), Moscow: Nedra, 1991.
5. Strakhov, V.N., Geofizika i matematika (Geophysics and Mathematics), Moscow: OIFZ RAN, 1999.
6. Strakhov, V.N. and Stepanova, I.Е., 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.Е., 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.
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: ОIFZ RAN, 1999.
10. Strakhov, V.N. and Stepanova, I.Е., 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: ОIFZ RAN, 2001, pp. 73–95.
11. Strakhov, V.N., Stepanova, I.Е., Grichuk, L.V., Kerimov, I.А., and Strakhov, А.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: ОIFZ RAN, 1999, pp. 173–183.
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 TSNIIGAiK, 1969, vol. 176, pp. 99–112.
14. Stepanova, I.Е. 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.Е., Raevskii, D.N, and Shchepetilov А.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.
17. Krylov, V.I. and Shul’gina, L.T., Spravochnaya kniga po chislennomu integrirovaniyu (Reference Book on Numerical Integration), Moscow: Nauka, 1966.
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.
Review
For citations:
Koneshov V.N., Stepanova I.E. Using the Method of S-approximations to Determine Deflections of the Vertical and Geoid Heights. Giroskopiya i Navigatsiya. 2018;26(4):14-22. (In Russ.) https://doi.org/10.17285/0869-7035.2018.26.4.014-022



