A mathematical model of the acceleration vector by its tracks in seismic prospecting

1Lytvyn, OO
1Ukrainian Engineering Pedagogics Academy, Kharkiv
Dopov. Nac. akad. nauk Ukr. 2016, 11:24-27
Section: Information Science and Cybernetics
Language: Ukrainian
A method of constructing a mathematical model of the $4D$ distribution of the acceleration vector $\overrightarrow{W}(x, y, z,t)$, with which particles of Earth's crust oscillate due to the passage of seismic waves. The method uses both tracks of $\overrightarrow{W}$ in a given system of wells $\mathrm{Γ}_k, k = \overline{1,M}$, and the trace $\overrightarrow{W}(x, y,0,t)$ of the vector $\overrightarrow{W}$ on Earth's. The error of the method and the total error that can occur in a numerical realization of the proposed method are studied. Experimental data used in a mathematical model can be obtained with the use of accelerometers, which are arranged at different depths of both vertical and inclined wells and also at various points on Earth's surface.
Keywords: acceleration vector, approximation error, mathematical model, seismic prospecting, traces of a vector
  1. Seismicheskaya tomografiya. Ed. G. Nolet. Moscow: Mir, 1990 (in Russian).
  2. Sergienko I.V., Deyneka V.S., Lytvyn O.M., Lytvyn O.O. Proceedings of the 7-th World Congress on Industrial Process Tomography (2—5 September 2013). Krakow, Poland, 2013.
  3. Guust Nolet. A breviary of seismic tomography. Cambridge Univ. Press, 2008.
  4. James G. Berryman. Lectures Notes on Nonlinear Inversion and Tomography. I. Borehole seismic tomography. Univ. California, October, 1991.
  5. Antsiferov A.V. Teoriya i praktika shakhtnoy seismorazvedki. Donetsk: OOO "Alan", 2003 (in Russian).
  6. Shearer P.M. Introduction to seismology. Cambridge Univ. Press, 2009. DOI: https://doi.org/10.1017/CBO9780511841552
  7. Stein S. and Wysession M. An introduction to seismology, earthquakes and Earth structure. Blackwell, Malden, USA, 2003.
  8. Towfighi S., Kundu T., Ehsani M. Appl. Mech., 2002, 69: 283—291. DOI: https://doi.org/10.1115/1.1464872
  9. Krasnozhon M.D., Kozachenko V.D. Komplexna interpretatsiya GDS z vykorystannyam komputernoi tehnologii "GEOPOSHUK", Kyiv: UkrDGRI, 2007 (in Ukrainian).
  10. Kaputin Y.E. Gornye komputernye tehnologii i geostatistika. SPb: Nedra. 2002 (in Russian).
  11. Boganik G.N., Gurvich I.I. Seysmorazvedka. Tver': AIS, 2006 (in Russian).
  12. Lisniy G.D. Vykorystannya modeley anizotropnogo seredovyscha dlya analizu seysmichnyh zobrazhen' geologichnyh obyektiv, Kiev: KNU T. Shevchenka, 2002 (in Ukrainian).
  13. Lisniy G.D. Praktychni osnovy pobudovy obyemnyh seismichnyh zobrazhen' za seysmogramamy spil'nyh dzherel, Kiev: Raduga, 2012 (in Ukrainian).