Lytvyn O. Mathematical modeling by interlineation functions methods in mineral exploration and the construction of the surface

The dissertation is devoted to the development and investigation of a general method for constructing the Hermitian interpolation operators for functions of two variables on a system of points of intersection of nonparallel lines, none three of which intersect at one point. The application of this method to the construction of spline interpolation operators of Zlamal-Zheniszek 3 and 5 degrees on a triangular grid. Methods for constructing the operators of the interlineation of functions of 3 variables and vector functions of 4 variables that allow us to compute these functions or vector functions at arbitrary points between the indicated system of disjoint lines are created and investigated if they are specified only by their tracks on the indicated lines. The theory of constructing operators of Hermitian interlination of functions of two and three variables with automatic preservation of the class of differentiability is created and studied. Based on the developed methods, mathematical models of the spatial distribution of minerals and the acceleration vector using interlineation with auxiliary functions in the form of polynomials, splines and global auxiliary functions were created and investigated on the basis of data on the distribution of minerals in a system of inclined wells and data on the distribution of the acceleration vector measured Accelerometers in the system of inclined wells and on the surface of the geological environment.