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The modified method of S-approximations: Regional version

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Abstract

A modified method of S-approximations of the initial field element is described for the regional version of the problem when the sphericity of the Earth should be taken into account. The application of the method is illustrated by the results of the mathematical experiment.

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References

  • Lavrentiev, M.A. and Lyusternik, L.A., Kurs variatsionnogo ischisleniya (A Course in Variational Calculus), Moscow-Leningrad: Gostoptekhizdat, 1950.

    Google Scholar 

  • Stepanova, I.E., Testing the method of S-approximations on the data of detailed gravity and magnetic survey, Geofiz. Zhurn., 2007, vol. 28, no. 1, pp. 97–105.

    Google Scholar 

  • Stepanova, I.E., Constructing the linear transfoirmations of the anomalous potential fields using S-approximations, Geofiz. Zh., 2008, vol. 29, no. 5, pp. 191–201.

    Google Scholar 

  • Stepanova, I.E., On the S-approximations of the Earth’s gravity field. Regional version, Inverse Probl. Sci. Eng., 2009a, vol. 17, no. 8, pp. 1095–1111.

    Article  Google Scholar 

  • Stepanova, I.E., The R-approximation method and its application to the interpretation of detailed gravity and magnetic data, Izv., Phys. Solid Earth, 2009b, vol. 45, no. 4, pp. 287–300.

    Article  Google Scholar 

  • Stepanova, I.E., The R-approximation method in the interpretation of gravity and magnetic data, Geofiz. Zh., 2009c, vol. 31, no. 3, pp. 53–62.

    Google Scholar 

  • Strakhov, V.N., Stepanova, I.E., and Grichuk, L.V., The integral representations method in the solution of the problems of gravimetry and magnetometry in the three-dimensional case, in Voprosy teorii i praktiki geologicheskoi interpretatsii gravitatsionnykh, magnitnykh i elektricheskikh polei (Issues in the Theory and Practice of Geological Interpretation of Gravity, Magnetic, and Electric Fields), Moscow: OIFZ RAN, 1997, pp. 105–108.

    Google Scholar 

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

    Google Scholar 

  • Strakhov, V.N. and Stepanova, I.E., Approximative approach to the solution of some classical problems of gravimetry and magnetometry, in Osnovnye problemy teorii interpretatsii gravitatsionnykh i magnitnykh anomalii (Key Problems in the Interpretation Theory of Gravitational and Magnetic Anomalies), Moscow: OIFZ RAN, 1999, pp. 258–271.

    Google Scholar 

  • Strakhov, V.N. and Strakhov, A.V., O reshenii sistem lineinykh algebraicheskikh uravnenii s priblizhenno zadannoi pravoi chast’yu, voznikayuschikh pri reshenii zadach gravimetrii i magnitometrii (On Solving the Systems of Linear Algebraic Equations with Approximate Right-Hand Side, Which Arise in the Solution of the Problems of Gravimetry and Magnetometry), Moscow: OIFZ RAN, 1999.

    Google Scholar 

  • Strakhov, V.N. and Stepanova, I.E., Analytical extension and separation of three-dimensional potential fields, Dokl. Earth Sci., 2000, vol. 374, no. 7, pp. 1125–1128.

    Google Scholar 

  • Strakhov, V.N. and Stepanova, I.E., The S-approximation method and its application to gravity problems, Izv., Phys. Solid Earth, 2002a, vol. 38, no. 2, pp. 91–107.

    Google Scholar 

  • Strakhov, V.N. and Stepanova, I.E., Solution of gravity problems by the S-approximation method (regional version), Izv., Phys. Solid Earth, 2002b, vol. 38, no. 7, pp. 535–544.

    Google Scholar 

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

    Google Scholar 

  • Tikhonov, A.N., Goncharskii, A.V., Stepanov, V.V., and Yagola, A.G., Chislennye metody resheniya nekorrektnykh zadach (Numerical Methods for Solving Ill-Posed Problems), Moscow: Nauka, 1990.

    Google Scholar 

  • Yagola, A.G., Stepanova, I.E., Van Yanfei, and Titarenko, V.N., Obratnye zadachi i metody ikh resheniya. Prilozheniya k geofizike (Inverse Problems and Methods for Their Solution: Applications to Geophysics), Moscow: Binom. Laboratoriya Znanii, 2014.

    Google Scholar 

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Authors and Affiliations

  1. Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, ul. B. Gruzinskaya 10, Moscow, 123995, Russia

    D. N. Raevskiy & I. E. Stepanova

Authors
  1. D. N. Raevskiy
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  2. I. E. Stepanova
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Correspondence to D. N. Raevskiy.

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Original Russian Text © D.N. Raevskiy, I.E. Stepanova, 2015, published in Fizika Zemli, 2015, No. 2, pp. 44–54.

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Raevskiy, D.N., Stepanova, I.E. The modified method of S-approximations: Regional version. Izv., Phys. Solid Earth 51, 197–206 (2015). https://doi.org/10.1134/S1069351315020093

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  • DOI: https://doi.org/10.1134/S1069351315020093

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