Abstract
The method of constructing a mathematical model of the internal structure of the geological environment is considered for the case, where the function that describes this model has a discontinuity of the first kind. The model is proposed for use in mine seismic tomography. The results of the computing experiment show that even for small orders of Fourier sums, the Fourier coefficients 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 propagation of seismic waves in a given section of the geological environment.
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Translated from Kibernetika i Sistemnyi Analiz, No. 3, May–June, 2019, pp. 80–89.
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Lytvyn, O.M., Lytvyn, Î.O. & Dragun, V.V. Estimating the Structure of a Discontinuous Layer by Tomographic Methods. Cybern Syst Anal 55, 413–421 (2019). https://doi.org/10.1007/s10559-019-00148-1
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DOI: https://doi.org/10.1007/s10559-019-00148-1