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Information × Registration Number 0217U004374, 0115U002498 , R & D reports Title Development and research of a new method for constructing the accelerometric interwell 4D mathematical model of the Earth's crust by the seismic sounding data. popup.stage_title Head Lytvyn Oleg Mikolayovich, Доктор фізико-математичних наук Registration Date 02-02-2017 Organization Ukrainian Engineering-Pedagogic Academy popup.description2 The object of research is the process of mathematical modeling of the Earth's crust content seismic tomography. The subject of research is mathematical modeling of the Earth's crust 4D structure using interlination vector functions, which are the acceleration of soil vibrations. The aim is to develop, research and apply of a new method of constructing interwell accelerometric 4D mathematical model of the Earth's crust, according to seismic sensing. To achieve this goal it was a created general theory of spline interlination of vector functions that can be speed or acceleration, information of which is known only at the specified system points or holes on the surface of the studied region. At this stage, this interwell mathematical model was constructed using spline interlination of vector functions if support functions are splines of two variables first or third degree on a triangular grid nodes. In the first part of the report the analytical review methods of constructing splines of one and two variables, examination of the construction spline interlination for scalar functions of three variables and identified opportunities generalization of these results to the case interlination ofvector functions of four variables (x,y,z,t) are drawn. In the second section it is proposed to build the spline interlination operators using the general theory of polynomial interpolation on a system of points which is the intersection of system non-parallel lines. This method is practically implemented when building spline interlination of vector functions operators on a triangular grid nodes. It is constructed explicit formulas for operators of spline interlination functions using splines of the first and third degrees as support functions. In the case where information about partial derivatives in the wells is not known, the method of these derivatives by known values approximated function W (x,y,z,t) is proposed. The examples are considered. In the third section it is provided packages for building the spline interlination of vector functions operators using their tracks in the set of wells. The software package designed to SCM MathCAD. The numerical tests were made by the software package. In particular it is shown that when the function is linear investigated the amount of auxiliary spline functions multiplied by traces of vector functions and it is given only in the wells, the mathematical models accurately restore these approximated functions. Product Description popup.authors Лісний Георгій Дмитрович Литвин Олег Миколайович Сергієнко Іван Васильович Славік Олексій Валерійович Хурдей Євгенія Леонідівна Черняк Оксана Олександрівна Чорна Тетяна Іванівна Ярмош Олена Віталіївна popup.nrat_date 2020-04-02 Close