MULTIVARIATE SIGNAL PROCESSING FOR GPS TIME SERIES IN EARTH SURFACE DYNAMICS

In this study, we demonstrate how multivariate signal processing can be applied to GPS time series to analyze the Earth’s crustal dynamics over different time scales. Although components of displacement are measured and represented separately, each component is still influenced by several processes occurring simultaneously with different frequencies and magnitudes. Unlike univariate signal processing, which analyzes each signal independently, multivariate signal processing considers the interactions and dependencies between all recorded signals. This approach can be applied to multiple GPS stations and analyze them together to better understand the dynamics and magnitude of the process spread across a large region. The Generalized Eigendecomposition (GED) method is used as a tool for multivariate signal processing. It extracts an estimated source signal by taking a linear weighted sum of all recorded data channels. GED achieves this by decomposing a pair of matrices into eigenvalues and eigenvectors, optimizing the weighting of data channels to maximize the signal-to-noise ratio. This method is capable of isolating correlated sources and can be used as a spatial filter, contrast enhancement, and dimension reduction in multi-channel signal processing. In this research, we focus on methodology and demonstrate how multivariate signal processing offers a comprehensive approach for studying GPS time series and provides reliable results for different time scales. To demonstrate the application of GED, we used more than 1,000 GPS stations across California, Oregon, Washington, and Nevada over a period of 10 years, and generated yearly, seasonal, and weekly displacement maps. Seasonal maps reveal phenomena that influence the Earth surface morphology and weekly maps are more relevant for fast processes such as earthquakes. As an example, we show how this method can effectively distinguish and highlight significant dynamics of geological features, such as Mount Shasta on the border of California and Oregon, while traditional approaches using isolated or a small set of GPS stations fail to capture the broader context of the phenomenon.