Математична модель просторового розподілу вмісту деякої сукупності корисних копалин в корі за даними з кернів свердловин методом інтерлінації функцій

Abstract

The problem of recovering a finite set of elements of the periodic table or their combinations distributed with linear density at a given depth at each point between a given set of oblique boreholes is studied. We do not consider all the elements of the periodic table but restrict ourselves to a set of n chosen elements and their combinations. A method for constructing a matrix function interlineation operator is proposed. Each component of the interleanation matrix function depends on three variables on a system of curves. The interleanation matrix function coincides with the approximated matrix function at the given depth in each of the boreholes and allows to determine the approximated matrix function values at the given depth at each point between the boreholes. The method of constructing mathematical models of spatial distribution of the minerals between the oblique boreholes proposed in the paper allows creating mathematical models of the Earth crust using all mineral compositions present in the cores of the oblique boreholes which will contribute to the development of efficient methods of mineral prospecting and mining. The prospects of further research are also discussed.