Skip to main content
Log in

Spectral Analysis of Profile Topographic Data Using Modified F-Approximations

  • DISCUSSIONS
  • Published:
Izvestiya, Physics of the Solid Earth Aims and scope Submit manuscript

Abstract—Analytical approximations are constructed and spectral analysis carried out for the profile data on terrain elevations obtained from global navigation satellite systems (GNSS). The results of calculations using the developed computer technologies within structural-parametric approach of the method of linear integral representations are presented.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.

Similar content being viewed by others

REFERENCES

  1. Bolotin, Yu.V. and Vyazmin, V.S., Spectral analysis of the airborne vector gravimetry problem, Fundam. Prikl. Mat., 2018, vol. 22, no. 2, pp. 33–57.

    Google Scholar 

  2. Kerimov, I.A., Stepanova, I.E., and Raevskii, D.N., Combined approximation methods for solving of gravity and magnetic problems, Geol. Geofiz. Yuga Rossii, 2018, no. 3, pp. 37–50.

  3. Koneshov, V.N. and Protsenko, S.V., Korrelyatsionnye svyazi geofizicheskikh polei (Correlations of Geophysical Fields), Moscow, 1984.

  4. Koneshov, V.N. and Stepanova, I.E., Analytical approximations of Arctic basin depths and their spectral analysis, Izv. Phys. Solid Earth, 2008, vol. 44, no. 5, pp. 381–387.

    Article  Google Scholar 

  5. Osipov, O.V., Spectral analysis of discrete signals with high frequency resolution, Vychisl. Metody Program., 2019, vol. 20, no. 3, pp. 270–282.

    Google Scholar 

  6. Oskolkov, K.I., Ridge approximation, Chebyshev–Fourier analysis and optimal quadrature formulas, Proc. Steklov Inst. Math., 1997, vol. 219, pp. 265–280.

    Google Scholar 

  7. Perederin, F.V., Aleshin, I.M., Ivanov, S.D., Mikhailov, P.S., Pogorelov, V.V., and Kholodkov, K.I., Portable GNSS signal registration system: field trials and application prospects, Nauka Tekhnol. Razrab., 2018, vol. 97, no. 4, pp. 28–40.

    Google Scholar 

  8. Showstack, R., Map provides high-resolution look at nearly entire Arctic region, Eos, 2017, vol. 98. https://doi.org/10.1029/2017EO085451

  9. Stepanova, I.E., Kerimov, I.A., Raevskiy, D.N., and Shchepetilov, A.V., Combined method of F-, S-, and R-approximations in solving the problems of geophysics and geomorphology, Izv. Phys. Solid Earth, 2018a, vol. 54, no. 1, pp. 91–105.

    Article  Google Scholar 

  10. Stepanova, I.E., Raevskiy, D.N., and Shchepetilov, A.V., Effective technology for building digital relief models and analytical approximations of the Earth’s potential fields, Nauka Tekhnol. Razrab., 2018b, vol. 97, no. 3, pp. 5–14. https://doi.org/10.21455/std2018.3-1

    Article  Google Scholar 

  11. Stepanova, I.E., Kerimov, I.A., and Yagola, A.G., Approximation approach in various modifications of the method of linear integral representations, Izv. Phys. Solid Earth, 2019, vol. 55, no. 2, pp. 218–231.

    Article  Google Scholar 

  12. Stepanova, I.E., Kerimov, I.A., Raevskiy, D.N., and Shchepetilov, A.V., Improving the methods for processing large data in geophysics and geomorphology based on the modified S- and F-approximations, Izv. Phys. Solid Earth, 2020a, vol. 56, no. 3, pp. 364–378. https://doi.org/10.31857/S0002333720030114

    Article  Google Scholar 

  13. Stepanova, I.E., Raevskiy, D.N., and Shchepetilov, A.V., Separation of potential fields generated by different sources based on modified S-approximations, Izv. Phys. Solid Earth, 2020b, vol. 56, no. 3, pp. 379–391.

    Article  Google Scholar 

  14. Stepanova, I.E., Shchepetilov, A.V., Pogorelov, V.V., and Mikhailov, P.S., Structural-parametric approach for building digital models of the relief and the Earth’s gravity field using analytical S-approximations, Geofiz. Protsessy Biosfera, 2020c, vol. 19, no. 2, pp. 107–116. https://doi.org/10.21455/gpb2020.2-8

    Article  Google Scholar 

  15. Strakhov, V.N. and Kerimov, I.A., Approximation implementation of spectral analysis in gravimetry and magnetometry, in Osnovnye problemy teorii interpretatsii gravitatsionnykh i magnitnykh polei (Basic Problems of the Theory of Interpretation of Gravitaty and Magnetic Fields) Strakhov, V.N., Ed., Moscow: OIFZ RAN, 1999a, pp. 183–206.

  16. Strakhov, V.N. and Strakhov, A.V., On the solution of the systems of linear equations with the approximate right-hand side arising in the problems of gravimetry and magnetometry, Izv. Sekts. Nauk Zemle RAEN, 1999b, no. 3, pp. 20–49.

  17. Strakhov, V.N. and Strakhov, A.V., The central computational problem within the third paradigm in the theory and practice of potential field interpretation: 1. Fundamentals of theory and numerical methods, in O nekotorykh voprosakh teorii interpretatsii potentsial’nykh polei (On Some Questions of the Theory of Interpretation of Potential Fields), Moscow: OIFZ RAN, 1999c, pp. 128–191.

  18. Strakhov, V.N., Kerimov, I.A., and Stepanova, I.E., Razrabotka teorii i komp’yuternoi tekhnologii postroeniya lineinykh analiticheskikh approksimatsii gravitatsionnykh i magnitnykh polei (Development of the Theory and Computer Technology for Constructing Linear Analytical Approximations of Gravitational and Magnetic Fields), Moscow: IFZ RAN, 2009.

  19. Zorich, V.A., Matematicheskii analiz (Mathematical Analysis), Part 2, Moscow: Nauka, 1984.

Download references

Funding

The study was carried under the state contract of IPE RAS and supported by the Russian Foundation for Basic Research (projects nos. 19-35-51014 and 19-35-90092).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to I. E. Stepanova.

Additional information

Translated by M. Nazarenko

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Stepanova, I.E., Kerimov, I.A., Spesivtsev, A.A. et al. Spectral Analysis of Profile Topographic Data Using Modified F-Approximations. Izv., Phys. Solid Earth 57, 573–581 (2021). https://doi.org/10.1134/S1069351321040091

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1069351321040091

Keywords:

Navigation