Determination of the horizontal strain rates tensor in Western Ukraine

Doppler Orbitography and Radio-positioning Integrated by Satellite (CORS) observations from 37 Global Navigation Satellite System (GNSS) stations located in the Western Ukraine area were processed using Bernese Processing Engine module (BPE) of Bernese GNSS Software version 5.2 for a time span of about 2.5 years. To get a better agreement for constrains, the IGS stations closest to the surrounding area of study were chosen with fixed coordinates of ITRF2008 at epoch 2005.0. Eastern and Northern components of velocities of GNSS observations from these 37 permanent stations, calculated from GNSS measurements, were used to construct a 2D model of horizontal strain rates field for the area. This study is presented in three parts. Firstly, two exact solutions for the components of the 2D strain rate tensor derived on the geosphere based on solving the eigenvalues – eigenvectors problem were analyzed, including skew symmetric rotational rate tensor. Secondly, based on the most simple and useful formulas from the first stage, a rigorous estimation of the accuracy of components of the 2D strain rate tensor were obtained based on the covariance propagation rule. Finally, the components of the 2D strain rate tensor, dilatation rate and components of the sheer rate tensor in the region were computed. A model of the rotation rate tensor was constructed for the described area, which led to the conclusion that the region of study should be interpreted as a deformed territory. Based on the computations from the GNSS-data model of components of horizontal deformations, the rates of principal values and rates of principal axes of the Earth’s crust deformation were found. To be consistent, the main tectonic formations are shown as the background intensity of different components of velocities, the rotation rate and strain rate tensors. Topographic features of the region were based on the SRTM-3 model (Shuttle Radar Topography Mission) with resolution 3²´3². At the first sight, the maximum sheer rates have greatest values in the areas located around the Ukrainian Carpathians. The dilatation rate has also a similar distribution.  Nevertheless, because in the paper only eigenvalue – eigenvector problem without accuracy estimation has been considered, which possibly leads to doubtful conclusions regarding interpretation and requires an additional solution of a purely mathematical problem. The full covariance matrix of the strain rate tensor should be found based on given full covariance matrix of the velocity components obtained by Bernese software. As a matter of fact, the study region is very complex in terms of crustal movements, which, according to the results obtained, require further densification of permanent GNSS stations.