Abstract
Presented in the article information is of a scientific and methodical character. Accumulation of coordinate monitoring data in networks of permanent GNSS stations made it possible to increase the efficiency of solving of many problems of moderngeodynamics. At the same time, their use made it necessary to rethink traditional theoretical approaches to solving of the problem, in particular, in terms of developing methods for evaluation of three-dimensional deformations.The analysis of the used theoretical approaches and methods for evaluation of three-dimensional deformations of the Earth in this article are presented. The insufficient degree of their correspondence to the potential information resource of GNSS data is substantiated.The method for evaluation of deformations of the Earth from the standpoint of the theory of transformations of Riemannian space imagesin the form of complex diffeomorphic manifolds is proposed. Properties of complex manifolds in the form of a tangent Euclidean space, which is parameterized by a rectangular Cartesian coordinate system, are used. This choice is justi-fied by its identity with the ITRS system, which is used to monitoring of coordinates by the GNSS method. The algorithm for constructing a functional model of deformation based on the homeomorphism of transformations is formulated. The method involves the direct use of coordinates in the ITRS system and modeling of deformations of the curvilinear topographic surfaceof the Earth in three-dimensional space. The method provides evaluation of three-dimensional deformation tensors and related invariants, which belong to the topographic surface. Working formulas for evaluation of main linear deformations, dilatation and rigid rotation of the Earth have been obtained. The method is generalized for evaluation of nonlinear deformations
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
