SPLINE BINARY-MODEL DETERMINATION OF HORIZONTAL DEFORMATION ZONES ON THE EARTH'S SURFACE OF A BLOCK MOUNTAIN GROUP BASING ON GPS NAVIGATION DATA

Abstract

The paper describes the methodology of spline binary-model determination of zones of horizontal deformation on the earth's surface of a block mountain range. A prerequisite for the application of this methodology bases on properties of the studied rock mass as a discrete rigid-elastic medium divided into blocks by disjunctive disturbances. The deformation is formed according to binary models that describe, as follows from GPS navigation data, its contours of areal compression and extension in the contact zone of two adjacent blocks. Since the surface of a structurally mosaic multi-block rock mass contains many inter-block contacts, the total deformation pattern is determined by the weight summation, i.e., the spline of the corresponding binary-model deformations. The paper gives the analytical expressions, with taking into account the applied weight functions. The paper describes the method of calculating the coefficients and parameters of the spline model. Their identification is carried out by the methods of least squares and approximations of the parabolic vertex, implemented in the specified sequence of iterative calculations using the given optimization formulas. Iterative calculations are ruled by the mean-square residual of model and marker displacements, which is reduced to an acceptable small limit determined by the GPS positioning error. The possibility of spline binary-model determination of zones of horizontal deformation of a multi-block earth surface is shown on a practical example of the recorded multidirectional movements of markers in GPS monitoring and the calculation of the corresponding model parameters. The study concluded that the proposed methodology can solve the problem of geospatial detection of geodynamic active zones, within which it may be unsafe to conduct mining operations and to operate maintain man-made objects.