To the problem of elimination of invariance loss effects in the evaluation of deformation fields of the earth using GNSS-data

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To the problem of elimination of invariance loss effects in the evaluation of deformation fields of the earth using GNSS-data

Journal Title: Геодинаміка - Year 2017, Vol 23, Issue 2

Abstract

Aim. Solving the problem associated in using GNSS monitoring data in the ITRS to evaluate deformation of fields of the Earth in terms of elimination of invariance loss errors. Methodology and results. The problem is considered in the context of the geophysical nature of the ITRS in conjunction with the global deformation field of the Earth. The attention is focused on the consequences of deformation of the ITRS system, which manifests itself as invariance loss effects in the interpretation of deformation fields. It is proposed to solve the problem on the basis of the theory of differential presentation of transformations of Riemannian space images in the form of its complicated diffeomorphic manifold such as the tangent Euclidean space, which is parameterized by a rectangular Cartesian coordinate system. As a geometric system, ITRS is a partial case of rectangular Cartesian. On this basis, and with the hypothesis that the transformation of space has a geophysical origin, a method of evaluating deformation fields has been developed. It is foreseen that the direct use of coordinates are obtained by the GNSS-method. Due to this, the evaluation of the topographic surface on which deformation processes are manifested, has been achieved. As a component part of this method, there are working formulas for determining angular and scale distortions of the ITRS at an arbitrary time point relative to the ITRF-realization. Considering the homeomorphism potential of diffeomorphic manifolds, the formulas have taken into account the perspective of the transfer of nonlinear deformation effects. Scientific novelty and practical significance. This used basis has a generalizational character compared to the mathematical theory of elasticity in the framework of its linearly homogeneous model of the infinitely small deformation, which is traditionally used for deformation analysis in geodynamics. Solutions on a generalizational basis have a higher informative resource and provide estimates of deformation fields that are adequate to GNSS data. Given current distortions of the coordinate system, the developed method is able to eliminate the invariance loss effects. Practical recommendations for the formulation and performing deformation analysis tasks by GNSS data in arbitrary observation epochs, which do not coincide with ITRF-realizations of the ITRS, are formulated.

Authors and Affiliations

O. А. Tadyeyev

Keywords

ITRS ITRF GNSS-method deformation analysis invariance space mapping space metric form space metric tensor

EP ID EP455731
DOI 10.23939/jgd2017.02.034
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