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
https://doi.org/10.15407/dopovidi2016.11.024
Section: Information Science and Cybernetics
Language: Ukrainian
Abstract: 
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
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