Non-Parametric Wavelet Functional Analysis for Horizontal and Vertical displacements Derived from GPS Stations in Western Alaska during the Year 2012

In order to analyze the dynamic processes of the Earth interior and the effect of the propagation of the seismic waves to the surface, a comprehensive study of the Earth crust kinematics is necessary. Although the Global Positing System (GPS) is a powerful method to measure ground displacements and velocities both horizontally and vertically as well as to infer the tectonic stress regime generated by the subsurface processes (from local fault systems to huge tectonic plate movements and active volcanoes), the complexity of the deformation pattern generated during such movements is not always easy to be interpreted. Therefore, it is necessary to work on new methodologies and modifying the previous approaches in order to improve the current methods and better understand the crustal movements. In this paper, we focus on western Alaska area, where many complex faults and active volcanoes exist. In particular, we analyze the data acquired each 30 seconds by three GPS stations located in western Alaska (AC31, AB09 and AB11) from January 1, 2012 to December 31, 2012 in order to compute their displacements in horizontal and vertical components by vectorial summation of the average daily and annual velocities components. Furthermore, we design non-parametric DMeyer and Haar wavelets for horizontal and vertical velocities directions in order to identify significant and homogenous displacements during the year 2012. Finally, the non-parametric decomposition of total horizontal and vertical normalized velocities based on level 1 and level 2 coefficients have been applied to compute normal and cumulative probability histograms related to the accuracy and statistical evolution of each applied wavelet. The results present a very good agreement between the designed non-parametric wavelets and their decomposition functions for each of the three above mentioned GPS stations displacements and velocities during the year 2012.