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Modified Method S-, F- and R-Approximations in Solving Inverse Problems of Geophysics and Geomorphology

  • I. E. StepanovaEmail author
  • I. A. Kerimov
  • D. N. Raevsky
  • A. V. Shchepetilov
Conference paper
Part of the Springer Proceedings in Earth and Environmental Sciences book series (SPEES)

Abstract

The connection of different modifications of the linear integral representation method is studied. Solutions of the related inverse problems based upon a «gibrid version of three approximations» of the topography and geopotential fields enable more refined tuning of the method in solving the inverse problems of geophysics and geomorphology and more complete interpretation for the a priori information about the surface elevation data and elements of anomalous fields. The technique for finding a stable approximate solution for the inverse problem of determining the mass distributions equivalent to the external gravitational (or any other potential) field is presented. The results of the mathematical experiment are discussed.

Keywords

Regularization Integral Representation Modified Optimal 

References

  1. Stepanova, I. (2008). On the S-approximation of the Earth’s gravity field, Inverse Problems in Science and Engineering. (16)5,. 547–566.CrossRefGoogle Scholar
  2. Stepanova, I. (2009). On the S-approximation of the Earth’s gravity field. Regional version, Inverse Problems in Science and Engineering. (17)8, 1095–1111.CrossRefGoogle Scholar
  3. Stepanova, I. and D. Raevsky. (2014). On solving reverse problems of geophysics applying the methods of the theory of dynamic systems. Geophysical Journal. (36) 3, 118–131.CrossRefGoogle Scholar
  4. Stepanova, I. and D. Raevsky (2015). On the solution of inverse Problems of gravimetry. Izvestiya Physics of the Solid Earth. (51)2, 207–218.CrossRefGoogle Scholar
  5. Stepanova, I. and D. Raevsky (2015). The modified method of S-approximation. Regional version. Izvestiya Physics of the Solid Earth. (51)2, 197–206.CrossRefGoogle Scholar
  6. Strakhov, V.N and I.E. Stepanova (2002). The S-Approximation Method and Its Application to Gravity Problems. Izvestiya, Physics of the Solid Earth. (38)2, 91–107.Google Scholar
  7. Strakhov, V.N. and I.E. Stepanova (2002). Solution of Gravity Problems by the S-Approximation Method (Regional Version). Izvestiya, Physics of the Solid Earth. (38)7, 535–544.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • I. E. Stepanova
    • 1
    Email author
  • I. A. Kerimov
    • 1
  • D. N. Raevsky
    • 1
  • A. V. Shchepetilov
    • 2
  1. 1.Schmidt Institute of Physics of the Earth, Russian Academy of SciencesMoscowRussia
  2. 2.Faculty of PhysicsMoscow State UniversityMoscowRussia

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