A criterion of reliability for a solution of the resistivity logging inverse problem

1Myrontsov, ML
1Institute of Telecommunications and Global Information Space of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2018, 5:16-21
Section: Information Science and Cybernetics
Language: Russian

The method of numerical solution of the inverse unstable problem of resistivity logging for oil and gas is considered. It is shown that it is possible to introduce a simple physically meaningful criterion of reliability for a solution of the resistivity logging inverse problem. An example of the use of this criterion for four-probe low-frequency induction logging in a nonconducting well is given.

Keywords: criterion of reliability for a solution of the inverse problem, electrometry in wells, inverse problem
  1. Anderson, B. I. (2001). Modeling and inversion methods for the interpretation of resistivity logging tool response. Delft: Delft University Press.
  2. Myrontsov, M. L. (2012). Numerical modeling of electrometry in wells. Kiev: Naukova Dumka (in Russian).
  3. Dovgiy, S. O., Yevdoschuk, M. I., Korjnev, M. M., Kulish, Ye. O., Kurilo, M. M., Malakhov, I. M., Trofimchuk, O. M. & Yakovlev, Ye. O. (2010). Energy resource component of Ukraine's development. Kiev: Nika-Center (in Ukrainian).
  4. Strakhov, V. N. (1967). On the solution of ill-posed problems of magneto- and gravimetry, represented by an integral equation of convolution type. Physics of the Earth. No. 4, pp. 36-54 (in Russian).
  5. Kolosov, A. L. (1985). Direct, mixed and inverse problems of well electrometry. Kiev: Naukova Dumka
  6. (in Russian). 6. Samarskiy, A. A. (1971) Introduction to the theory of difference schemes. Moscow: Nauka (in Russian).
  7. Myrontsov, N. L. (2007). Method of solving the direct and inverse problem of electric logging. Dopov. Nac. akad. nauk. Ukr., No. 2, pp. 128-131 (in Ukrainian).
  8. Gomilko, A. M., Savitsky, O. A. & Trofimchuk, A. N. (2016). Methods of superposition, eigenfunctions and orthogonal polynomials in boundary-value problems in the theory of elasticity and acoustics. Kiev: Naukova Dumka (in Russian).
  9. Epov, M. I., Antonov, Yu. N. (Eds.). (2000). Technology of exploration of oil and gas wells based on VIKIZ. Methodical direction. Novosibirsk: Izd. SO RAN (in Russian).
  10. Myrontsov, M. L. (2010). Pulse lateral logging with high spatial resolution. Dopov. Nac. akad. nauk. Ukr., No. 5, pp. 120-122 (in Russian).
  11. Myrontsov, M.L. (2010). On the method of electromagnetic-pulse logging. Dopov. Nac. akad. nauk. Ukr., No. 7, pp. 110-112 (in Russian).
  12. Myrontsov, M.L. (2012). Hardware-methodical complex for the investigation of collectors with abnormally low resistance. Dopov. Nac. akad. nauk. Ukr., No. 1, pp. 117-122 (in Russian).
  13. Myrontsov, M. L. (2012). Investigation method for “wrong” formations and the relict oil content under the well logging. Dopov. Nac. akad. nauk. Ukr., No. 4, pp. 100-105 (in Russian).
  14. Yegurnova, M. G, Zaikovsky, M. Ya., Zavorotko, Y. M., Tsoha, O. G., Knishman, O. Sh., Mulyr, P.M., Demyanenko, I.I. (2005). Oil and gas prospecting facilities of Ukraine. Oil-gas content and features of li thogeophysical construction of deposits of the lower Carboniferous and Devonian of the Dnipro-Donets depression. Kiev: Naukova Dumka (In Ukrainian).
  15. Myrontsov, N. L. (2007). A quick method of solving the inverse problem of induction logging. Geophys. J., No. 5, pp. 128-131.