Methodology to detect and predict horizontal deformation at the Earth’s surface of adjacent rock mass blocks by GPS data

The main provisions of the methodology for detecting and predicting horizontal deformation at the Earth’s surface of adjacent rock mass blocks based on GPS monitoring data are presented. The scope of the methodology is disclosed, including the mathematical modeling of block displacements and the resultant deformation in the interblock contact zone, methods for identifying parameters of the model and the aspects of its application. The model is created with regard to the recorded multidirectional trend movements of reference points within the geodetic observation network (markers), based on the representations of the blocks by the spatial constraints of their horizontal dimensions and their elastic properties in the hierarchical mosaic structure of the enclosing rock mass. Assuming that the size of a block of the Earth’s surface is not larger than 5 km within a mineral deposit, the displacements and strains are considered in plan view. The distributions of the linear and angular strains in the blocks and in the zone of interblock contact are calculated as derivatives of the displacement functions of their points. The resultant areal deformation is represented by the sum of the linear and angular strains. The model parameters are identified using the methods of least squares and parabolic vertex approximations implemented in the specified sequence of iterative calculations from the given optimization formulas. In case of rotation of the blocks, it is sufficient to identify the coordinates of their conditional centers from the marker vectors, assuming that there is no translational movement. The iterative calculations are controlled by the standard deviation of the model and marker movements, which is reduced to an acceptable small limit determined by the GPS positioning error. The capacity of the model to detect the zones of horizontal deformation of different value and sign is demonstrated as a case-study of recorded displacements of markers and by the calculation of the corresponding model parameters.

Antonov V. A. Methodology to detect and predict horizontal deformation at the Earth’s surface of adjacent rock mass blocks by GPS data. MIAB. Mining Inf. Anal. Bull. 2021;(5— 2):16—29. [In Russ]. DOI: 10.25018/0236_1493_2021_52_0_16.

The work was implemented within the framework of the State Contract with the Institute of Mining, Ural Brunch of the Russian Academy of Sciences in Ekaterinburg, Topic No. AAAA-A19-119020790024-7.

Antonov V. A., Dr. Sci. (Eng.), Institute of Mining, Ural Branch, Russian Academy of Sciences, Ekaterinburg, Russia, Antonov@igduran.ru.

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