Model detection and prediction of horizontal deformation of the earth’s surface based on the movement of its markes

Relevance of the topic. To identify areas of increased deformation of the earth’s surface of rock blocks containing a mineral Deposit, GPS monitoring measurements of horizontal movements of markes installed at different points are carried out. An actual problem that arises here is the creation of a methodology that reliably describes and predicts the formation and location of deformation zones based on the movements of labels. The aim of the research is to create a methodology for forming, calculating and applying a binary mathematical model that describes and predicts the location and contours of the resulting areal deformations of the earth’s surface of two neighboring rock blocks based on placemark movements. Research methods include mathematical modeling of areal deformation, functional and numerical optimization of the parameters of the created model, experimental calculations and analysis of the distribution of the resulting and predicted deformation in a practical example of placemark movements. Research result. The model is based on the idea of blocks based on the spatial constraints of their horizontal dimensions and elastic properties in the hierarchical mosaic structure of composing rocks. Assuming that the size of a block of the earth’s surface does not exceed 5 km within the limits of a mineral Deposit, the movements of its points are considered in the plane. The resulting areal deformation is represented by the sum of linear and angular deformations. The model parameters were identified using the methods of least squares and parabolic vertex approximations implemented in the specified sequence of iterative calculations using the given optimization formulas. Calculations are regulated by the standard deviation of model and labels displacements. It boils down to the permissible small limit determined by the GPS positioning error. A practical example of interpreting placemark offsets shows the properties of model invariance in a multidirectional spatial coordinate system, as well as the detection of areal deformation zones and the forecast of its contour development. Conclusions. The applicability of the presented methodology for the deformation interpretation of multidirectional movements of the earth’s surface markes registered by the monitoring system is noted. The model’s conclusions about the areal location of deformation zones and its level can be used in predictive estimates and criteria that determine the possibility of safe mining operations in the detected zone and the content of man-made objects in it.

FUNCTIONAL FACTOR MODEL OF HORIZONTAL MOVEMENT OF LOCAL EARTH BLOCKS

The formation, analysis and practical application of the functional factor model of horizontal displacement of local blocks of the earth’s surface located in the area of anthropogenic influence of mine workings are considered. In the movement of its points, the influence of rotation factors and translational displacement is taken into account. The model parameters are calculated by the approximation methods of a parabolic vertex and the smallest sum of squares of its residuals with experimentally determined motion vectors of markers. According to the results of the analysis of the model, the relationships between the kinematic parameters of rotation and translational displacement are revealed. Examples of practical application of the model are given.