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Neural Network Algorithm for Solving 3d Inverse Problem of Geoelectrics

  • M. I. Shimelevich
  • E. A. Obornev
  • I. E. ObornevEmail author
  • E. A. Rodionov
  • S. A. Dolenko
Conference paper
Part of the Springer Proceedings in Earth and Environmental Sciences book series (SPEES)

Abstract

The approximating neural network algorithm for solving the inverse problems of geoelectrics in the class of grid (block) models of the medium is presented. The algorithm is based on constructing an approximate inverse operator using neural networks and makes it possible to formally obtain the solutions of the geoelectrics inverse problem with a total number of the sought parameters of the medium \( \sim n\, \times \, 10^{ 3} \). The questions concerning the correctness of the problem of constructing the inverse neural network operators are considered. The a posteriori estimates of the degree of ambiguity in the inverse problem solutions are calculated. The work of the algorithm is illustrated by the examples of 2D and 3D inversions of the synthesized data and the real magnetotelluric sounding data.

Keywords

Geoelectrics Inverse problem Approximation A priori and a posteriori estimates Neural networks 

Notes

Acknowledgements

The research was carried out using supercomputers at Joint Supercomputer Center of the Russian Academy of Sciences (JSCC RAS). This study was supported by the Russian Science Foundation (project no. 14-11-00579).

References

  1. Cybenko, G. (1989) Approximation by superpositions of a Sigmoidal Function // Mathematics of Control, Signals, and Systems, V.2, pp. 303-314, 1989.Google Scholar
  2. Dmitriev V.I. (2012) Obratnye zadachi geofiziki [Inverse Problems o f Geophysics]. Moscow, MAKS Press Publ., 340 p., 2012.Google Scholar
  3. Dolenko S., Guzhva A., Persiantsev I., Obornev E. and Shimelevich M. (2009) Comparison of adaptive algorithms for significant feature selection in neural network based solution of the inverse problem of electrical prospecting// In: C. Alippi et al (Eds.): ICANN 2009, Part II. Lecture Notes in Computer Science, 2009 - V. 5709 - pp. 397405.-Springer-VerlagBerlinHeidelberg.CrossRefGoogle Scholar
  4. Feldman I.S., Okulesky B.A., Suleimanov A.K. (2008) Elektrorazvedka metodom MTZ v komplekse regionalnyh neftegazopoiskovyh rabot v evropejskoj chasti Rossii [Electrical exploration by MTS method in a complex of regional oil and gas prospecting works in the European part of Russia // Journal of Mining Institute, St. Petersburg, 176: 125–131, 2008.Google Scholar
  5. Glasko V.B., Gushhin G.V. and Starostenko V.I. (1976) O primenenii metoda reguljarizacii A.N. Tihonova k resheniju nelinejnyh sistem uravnenij[On the application of the method of regularization of A.N. Tikhonov to the solution of nonlinear systems of equations] // ZhVM and MF, 16 (2): 283–292, 1976.Google Scholar
  6. Haykin S. (1999) Neural networks: A Comprehensive Foundation. 2nd ed. Pearson Education, 823 p., 1999.Google Scholar
  7. Hidalgo H., Gómez-Treviño E. and Swiniarski R. (1994) Neural Network Approximation of a Inverse Functional // IEEE International Conference on Neural Networks, V. 5, pp. 3387–3392, 1994.Google Scholar
  8. Lönnblad L., Peterson C., and Rögnvalsson T. (1992) Pattern recognition in high energy physics with artificial neural networks—JETNET 2.0 // Computer Physics Communications, Vol. 70, 1, pp. 167–182, 1992.Google Scholar
  9. Mackie R.L., Smith J.T. and Madden T.R. (1994) Three-dimensional electromagnetic modeling using finite difference equations: the magnetotelluric example // Radio Science, 29, pp. 923–935, 1994.CrossRefGoogle Scholar
  10. Poulton M., Sternberg B., and Glass C. (1992) Neural network pattern recognition of subsurface EM images // Journal of Applied Geophysics, V.29, Is.1, pp. 21–36, 1992.CrossRefGoogle Scholar
  11. Raiche A. (1991) A pattern recognition approach to geophysical inversion using neural nets // Geophysics J. Int., 105, pp. 629–648, 1991.CrossRefGoogle Scholar
  12. Shimelevitch, M. and Obornev, E., The Method of Neuron Network in Inverse Problems MTZ, Abstr. of the 14th Workshop on Electromagnetic Induction in the Earth, Sinaia, Romania, 1998.Google Scholar
  13. Shimelevich M.I. and Obornev E.A. (2009) An approximation method for solving the inverse mts problem with the use of neural networks. Izvestiya - Physics of the Solid Earth 45(12), 1055–1071, 2009.CrossRefGoogle Scholar
  14. Shimelevich M.I., Obornev E.A., Obornev I.E., and Rodionov E.A. (2017) The neural network approximation method for solving multidimensional nonlinear inverse problems of geophysics. Izvestiya - Physics of the Solid Earth 53(4): 588–597, 2017.CrossRefGoogle Scholar
  15. Shimelevich M.I., Obornev E.A., Obornev I.E., and Rodionov E.A. (2013) Numerical methods for estimating the degree of practical stability of inverse problems in geoelectrics. Izvestiya - Physics of the Solid Earth 49(3): 356–362, 2013.CrossRefGoogle Scholar
  16. Spichak, V.V., and Popova, I.V. (1998) Application of the neural network approach to the reconstruction of a three-dimensional geoelectric structure. Izvestiya - Physics of the Solid Earth 34(1): 33–39, 1998.Google Scholar
  17. Werbos P.J. (1974) Beyond regression: New tools for prediction and analysis in the behavioral sciences. Ph.D. thesis, Harvard University, Cambridge, MA, 1974.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • M. I. Shimelevich
    • 1
  • E. A. Obornev
    • 1
  • I. E. Obornev
    • 2
    Email author
  • E. A. Rodionov
    • 1
  • S. A. Dolenko
    • 2
  1. 1.Russian State Geological Prospecting University MGRI-RSGPUMoscowRussia
  2. 2.Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics (MSU SINP)MoscowRussia

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