Plate Tectonic Calculator: Stand-Alone Application for Estimating Plate Tectonic Motion over the Earth’s Surface

Abstract

Plate tectonic motion is the displacement of the plates over the earth’s surface. Significant displacements can be detected in regions with high seismic activity. Following Euler’s theorem, continental plates rotate about an axis that runs through the center of the earth’s sphere. Therefore, plate tectonic motion is emphasised, with the rate of movement calculated annually. Hence, this study aims to develop a stand-alone application to calculate plate tectonic motion concerning Euler’s theorem. A plate tectonic calculator (PTC) is designed using optimised parameters and formulations that can calculate motion in any region. Furthermore, the set of formulations from Euler’s theorem that have been revised into a comprehensive form is verified using manual calculation in MATLAB. The formulations are categorized into two stages: the inverse Euler pole problem in the Local Geodetic Coordinate System (LG CS) and the direct Euler pole problem in LG CS. After integrating the PTC in C# using Visual Studio, the sample coordinates and velocities of stations from four case datasets are used to test the PTC’s performance. Moreover, the effectiveness of the PTC is further assessed by comparing its outputs with those of the existing Euler Pole Calculator (EPC). The results show no significant differences in any parameter across all cases. This is because the differences are too small and within uncertainties, and also do not exceed the tolerance range of the standard deviation for each parameter involved. The graph of the velocity differences between PTC and EPC indicates the discrepancies are less than 1×10⁻⁶ meters per year, whereas the velocity residuals and standard deviation show the same discrepancies that are less than 1×10⁻⁹ meters per year. Consequently, it can be concluded that the PTC’s performance has been successfully verified. In addition, it can more effectively detect plate tectonic motion within the given region.