Exploring the Manifold of Seismic Waves: Application to the Estimation of Arrival-Times

We propose a new method to analyze seismic time series and estimate the arrival-times of seismic waves. Our approach combines two ingredients: the times series are first lifted into a high-dimensional space using time-delay embedding; the resulting phase space is then parametrized using a nonlinear method based on the eigenvectors of the graph Laplacian. We validate our approach using a dataset of seismic events that occurred in Idaho, Montana, Wyoming, and Utah, between 2005 and 2006. Our approach outperforms methods based on singular-spectrum analysis, waveleta nalysis, and STA/LTA.