Geodetic measurements provide important and statistically estimated information about the coordinates of geodetic points and their changes over time. This geodesic information can be used to study geodynamic processes and their manifestations, primarily on the earth’s surface. Particularly intense such geodynamic phenomena occur in areas of active development of minerals due to the intense man-made effects on the near-surface layer of the Earth. It is logical to perform the description of surface motions using mathematical field theory. According to the changes of geodetic elements (coordinates, heights, directions) after repeated measurements it is possible to imagine the field of displacement vector of geodetic points. When studying the stress-strain state of the earth’s surface, the vectors obtained can be used not only to calculate the earth’s deformation tensor in the area under study, but also the differential characteristics of the vector field. One of them is called divergence. The authors of the article propose to determine the divergence of the vector field of surface displacements by discrete geodesic observations of displacement vectors made only on the surface of the study area. The model of the vector displacement field can be chosen taking into account the set of source data and the density of placement of geodetic points, the carriers of spatial coordinates.
Geodetic data and their subsequent statistical analysis enable mathematical modeling and identifying the stress-deformed state of geodynamic systems in concern to the aspect of natural and man-made disasters prediction. Geodetic monitoring geodynamic processes is necessary for solving a number of scientific and practical tasks of geodesy i.e. expanding and maintaining the national geodetic network, studying changes in gravity field in time, using GNSS technology. Most important extension of research is mathematical modelling of geodynamic systems in a predictive order. To study the complex (nonlinear) geodynamic processes the appropriate mathematical framework should be selected. Here are theoretical foundations for studying rotation movements of the earth’s surface. A mathematical model of rotary circular structures of the Earth was mentioned. There are mathematical models explaining the nature of sudden global, regional and some local geodynamic processes. They are based on differences in temporal and spatial scales, of geodynamic systems. Theoretical bases of description rotational motions on a plane by a system of differential equations were considered. Some examples of integral curves were given. They can be qualitative characteristics of geodynamic systems. In many cases, a similar trajectory corresponds to the rotational horizontal movements of the earth’s surface.
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