Method of interlineation of the vector functions on a system of boreholes and its application in cross-hole seismic tomography

I.V. Sergienkoa, V.S. Dejnekaa, Oleg M. Lytvynb, Oleg O. Lytvyn b

aInstitute of Cybernetics of NASUkraine, Kyiv, Ukraine

bDepartment of High and Applied Mathematics/Ukrainian Engineering-Pedagogical Academy, Kharkiv, Ukraine

Abstract

The authors propose a method of constructing operators of interlineation of vector functions for four variables, defined by means of a system of components on a system of vertical well boreholes.These operators can calculate an approximate vector at a point between the well boreholes for any moment of time. It is proposed to be used for the constructing cross-hole seismic accelerometer 4D mathematical model of the structure of the Earth's crust on the basis of the mentioned system of components of the acceleration vector of the planet's crust at the points of each well borehole. These data can be obtained by means of accelerometers in seismic sounding the planet's crust.

Keywords: seismic waveform tomography, accelerometer, interlineation, 4D vector - acceleration mathematical model