Reconstruction of vertical movements of the earth's crust, according to tide gauge observations

Purpose. The purpose of this study: to reconstruct the vertical movements of the earth crust, crystalline massif of Avalonia is taken as an example, namely in Netherlands according to tide gauge observations during 1900-2012; 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 and averaging the results of tide gauge observations Δt. 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, the azimuth direction of maximum tilt of the block β, the angle of inclination of the velocity field 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 block of Avalonia dependence of change of azimuth of the direction of maximum tilt of the block β and angle of the velocity field α on the average epoch t0 and the averaging period of observation results Δt is estimated. Spatial kinematic model of motion of a tectonic block of Avalonia for Δt=70 years is built. The change in time of the velocity field of the vertical movements of the block is analyzed. Retrospective analysis of changes in kinematic parameters of the study area is performed. Scientific novelty. The dependence of the linear velocity of the tide gauges’ vertical movement VTG and root mean square error mVTG from averaging period observations Δt is determined. The observations revealed that the amplitude of the tide gauges’ speed increases with decreasing of averaging period of observation results Δt. According to tide gauge observations it was found that the speed of lowering of the tectonic block of Avalonia gradually decreases over time. The azimuth direction of maximum tilt of the block β is shifted to the South. The obtained schematic vertical movements of the earth's surface study area according to tide gauge observations are broadly consistent with the results of the repeated leveling. 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 block of Avalonia 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. The proposed method can be used for similar studies in other regions of the world coast. 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.