Determination of Trends in GPS Time Series Using Complementary Ensemble Empirical Mode Decomposition

Time series of Global Positioning System (GPS) station positions include signals whose characteristics vary over time. Therefore, in detailed analyses, methods dedicated to nonstationary time series should be used. In this study, the Complementary Ensemble Empirical Mode Decomposition (CEEMD) method was used to model trends in time series of GPS station positions and to verify their nonlinearity. As the CEEMD method does not provide equations for assessing the uncertainty of the determined trend, we propose to use the bootstrap method for this purpose. In this study, daily time series of the Up components of 25 GPS stations from seismic regions in Europe and from the Nevada Geodetic Laboratory (NGL) service were used. The determined trends were compared with the trends calculated using the Singular Spectrum Analysis (SSA) method and then interpreted in the context of earthquakes occurring in the vicinity of the station. In turn, the bootstrap method was used to estimate the mean standard deviations of trends determined by the CEEMD as well as SSA method. The conducted studies showed the usefulness of the CEEMD method for modeling trends in time series of GPS station positions, especially for stations where changes may occur on short time scales, visible as the local nonlinearity of the trend, mainly due to earthquake events. The bootstrap-estimated mean standard deviation values for the modeled nonlinear trends are at the level of 1–3 mm, depending on the station. In turn, the root mean square error (RMSE) estimated between the nonlinear trend determined by the CEEMD method and the linear trend fitted to it by the least squares method does not exceed 3 mm. The conducted research indicates that the CEEMD method can be successfully used to model locally nonlinear trends resulting from earthquakes, and the mean standard deviation of the estimated trends is relatively low.