Polarization Analysis in the Discrete Wavelet Domain: An Application to Volcano Seismology

Abstract

We propose a method for analyzing the polarization of three-component digital recordings using the discrete wavelet transform (DWT). This method allows for the automatic detection and separation of seismic phases that have a coherent linear or elliptical polarization. It can be correctly used in the analysis of seismic signals relating to volcanic activity because they arise from a complex wave field that consists of near-field and far-field components that have frequency-dependent polarization. First, the analytic extension of the signal is decomposed using DWT, then each single component is used to determine a local complex polarization vector in the timescale domain. This analysis reveals the presence of seismic phases with coherent polarization over a range of DWT scales and finite temporal intervals. Using the orthogonality property of the DWT, it is possible to isolate a single coherent component, reconstructing it in the time domain and computing the full polarization tensor. This procedure can be fully automated, introducing a quantitative definition of wavelet polarization coherence on the DWT dyadic grid. A recursive algorithm (called POLWAV) starts from the wavelet coefficient with the highest modulus, and then selects all of the neighbors that show coherence with it above a given threshold. We show how the POLWAValgorithm can be used for separating wave-field components and for detecting coherent seismic phases on continuous recordings. Example applications to actual seismic recordings at Stromboli Volcano (Tyrrhenian Sea) are presented.