UDC 519.6
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2 Ukrainian Engineering Pedagogics Academy, Kharkiv, Ukraine
 loo71@bk.ru
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RESTORATION OF THE STRUCTURE OF THE DISCONTINUITY LAYER
BY TOMOGRAPHIC METHODS
Abstract. The method of constructing a mathematical model of the internal structure of the geological environment is considered, when the function describing this model has a first-order gap. The model is proposed for use in shaft seismic tomography. The results of the computational experiment show that, even with small orders of Fourier sums, the Fourier coefficients, which are found by means of information about the first times of the arrival of the seismic signal from the sources at the observation points, are close to the Fourier coefficients found for the test function, which describes the given terrain image with tectonic damage. The described approaches can be used to improve the mathematical model of the distribution of the slowness of the spread of seismic waves in a given section of the geological environment.
Keywords: computer tomography, mine tomography, Fourier coefficients.
FULL TEXT
REFERENCES
- Litvin O.M., Dragun V.V. The method of searching for the spatial distribution of slowness based on the first approximation in mine shaft seismic tomography. Upravl. Syst. i mash. 2016. No. 6. P. 80–88.
- Litvin O.M. Periodic splines and a new method for solving the plane problem of X-ray computed tomography. System Analysis, Management and Information Technologies: Journal of the Kharkiv State. Polytechnic. un-ty. Kharkiv: KDPU. 2000. No. 125. P. 27–35.
- Kulik S.I. Mathematical modeling in computer tomography using wavelets: Diss. Cand. Phys.-math. Sciences, Kharkiv, 2008.
- Litvin O.M., Litvin O.G. Optimization of the number of experimental data in the method of calculating Fourier coefficients using projections. The Theses of the Conference ISN - PUET (Poltava 16-18.03.2017). Poltava, 2017. P. 175–179.
- Litvin ON, Pershina Yu.I., Sergienko I.V. Restoration of discontinuous functions of two variables when discontinuity lines are unknown (rectangular elements). Kibernetika i sistemnyj analiz. 2014. No. 4. P. 126–134.
- Litvin O.M. Increasing the accuracy of expansion in the Fourier series of discontinuous functions of one and two variables. Herald of the National techn. Un-ty "KhPI".Thematic issue: Mathematical modeling in technology. 2016. No. 6, Iss. 1178. P. 43–46.
- Gottlieb S., Jung J., Kim S. A review of David Gottlieb’s work on the resolution of the Gibbs phenomenon. Commun. Comput. Phys. 2011. N 3. P. 497–519.
- Pereverzev S.V. Optimization of approximate methods for solving operator equations (in Russian). Kiev: Institute of Mathematics NAS of Ukraine, 1996. 251 p.
- Smirnov V.I. The course of higher mathematics (in Russian). Vol. 2. Moscow: Nauka, 1974. 655 p.
- Fichtengolts G.M. Course of differential and integral calculus (in Russian). Vol. 3. Moscow: Fizmatlit, 1966. 656 p.
- Litvin O.M., Litvin O.G. Reconstruction of images using finite Fourier and Feuer sum. Abstracts conf. CCI - PUET (Poltava, 10-12.03.2016). Poltava, 2016. P. 186–189.
- Boganik G.N., Gurvich I.I. Seismic survey (in Russian). Tver: AIS, 2006. 744 p.
- Litvin O.M. Interpolation of functions and some of its applications (in Ukrainian). Kharkiv: Osnova, 2002. 544 p.
- Chapman K. Radon transform and seismic tomography. Seismic tomography (Russian translation). Ed. G. Noletta. Moscow: Mir, 1990. P. 34–60.
