Modeling of vertical movements of tectonic blocks, according to tide gauge observations

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Department of Higher Geodesy and Astronomy of Lviv Polytechnic National University
Department of Higher Geodesy and Astronomy, Lviv Polytechnic National University

Purpose. The purpose of this study: to reconstruct the vertical movements of the earth crust in northern parts of Europe, according to long-term tide gauge observations; to investigate the change of kinematic parameters of the crystalline massif, where the tide gauges, selected for the study, are situated, depending on the average epoch of the observation period t0=1958, 1963, 1968, 1973 та 1978 years and averaging the results of tide gauge observations Δt=60 years. Priori assumed that the crystalline massife is a hard tectonic block with linear field of vertical velocity. Methodology. To perform the reconstruction of the vertical movements of the earth's crust a method of determining the necessary length of tide gauge observations to determine the vertical movements with given precision is developed. In addition, an algorithm for determining kinematic  parameters of the tectonic block, which characterize the position of the line of zero velocity vertical motion, directional azimuth of changing maximum inclination angle of tectonic block β, the velocity of changing maximum inclination angle of tectonic block α is developed. The definition of these parameters was performed by the method of iterations in several stages. Zero approximation determines the approximate values of unknown parameters that serve as input data to perform the first approximation. The first approach is the method of exact solutions, which involves finding the optimal spatial position of the tectonic blocks in relation to tide gauges and their velocities. During this approximation a search for the minimum of a function of the deviation of the motion models of the block relative to the actual measurements of tide gauges is also performed. The solution to this problem, namely the search of the minimum of the objective function, was made by a gradient method of Fletcher-Reeves. The second iteration checks the convergence of the results desired parameters and executes them to evaluate the accuracy using the least squares method. Results. The results of this study are: the speed change of tide gauges depending on changes in the average epoch t0 and the averaging period of observation results Δt is determined. For tectonic blocks of northen Europe territory dependence of change of directional azimuth of changing maximum inclination angle of tectonic block β and the velocity of changing maximum inclination angle of tectonic block α on the average epoch t0=1958, 1963, 1968, 1973 та 1978 and the averaging period of observation results Δt=60 years is estimated. Spatial kinematic model of motion of a tectonic blocks of northen Europe territory for Δt=60 years is built. The change in time of the velocity field of the vertical movements of the blocks is analyzed. Retrospective analysis of changes in kinematic parameters of the study area is performed. Scientific novelty. The obtained results almost completely are confirmed with results of high accuracy levellings and systematic differences obtained according to GNSS observations are related with changes of geoid height over time on the set territories. In general, tectonic block kinematics is correlated with neo-tectonic movements depicted in geological sections. Practical significance. According to the study a theoretical framework and method of determining kinematic parameters of the velocity field of the vertical movements of the crust of tectonic blocks according to long tide gauge observations are developed. Kinematic model of the velocity field of the tectonic blocks of northen Europe territory is built. The dependence of the kinematic parameters of the block will serve for further in-depth study of the vertical movements of the European crust in general, and if necessary of its individual parts. Execution of the research may allow to carry out vertical crust movement reconstruction. It helps to study the historical development of isostatic processes and changes in the Earth gravitational field and to study the position of changing altitude geodetic network and sustainability of its systems. It also allows us to predict changes in position of the coastline, has a significant influence in the design and construction of hydrotechnic structures in coastal areas. In addition, this technique provides the ability to perform the reconstruction of the vertical movements of the crust in the past.

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