Coherent‐subspace array processing based on wavelet covariance: an application to broad‐band, seismo‐volcanic signals

SUMMARY Long‐Period (LP) and Very‐Long‐Period (VLP) signals are the most characteristic seismic signature of volcano dynamics, and provide important information about the physical processes occurring in magmatic and hydrothermal systems. These events are usually characterized by sharp spectral peaks, which may span several frequency decades, by emergent onsets, and by a lack of clear S ‐wave arrivals. These two latter features make both signal detection and location a challenging task. In this paper, we propose a processing procedure based on Continuous Wavelet Transform of multichannel, broad‐band data to simultaneously solve the signal detection and location problems. Our method consists of two steps. First, we apply a frequency‐dependent threshold to the estimates of the array‐averaged WCO in order to locate the time‐frequency regions spanned by coherent arrivals. For these data, we then use the time‐series of the complex wavelet coefficients for deriving the elements of the spatial Cross‐Spectral Matrix. From the eigenstructure of this matrix, we eventually estimate the kinematic signals' parameters using the MUltiple SIgnal Characterization (MUSIC) algorithm. The whole procedure greatly facilitates the detection and location of weak, broad‐band signals, in turn avoiding the time‐frequency resolution trade‐off and frequency leakage effects which affect conventional covariance estimates based upon Windowed Fourier Transform. The method is applied to explosion signals recorded at Stromboli volcano by either a short‐period, small aperture antenna, or a large‐aperture, broad‐band network. The LP (0.2 < T < 2 s) components of the explosive signals are analysed using data from the small‐aperture array and under the plane‐wave assumption. In this manner, we obtain a precise time‐ and frequency‐localization of the directional properties for waves impinging at the array. We then extend the wavefield decomposition method using a spherical wave front model, and analyse the VLP components ( T > 2 s) of the explosion recordings from the broad‐band network. Source locations obtained this way are fully compatible with those retrieved from application of more traditional (and computationally expensive) time‐domain techniques, such as the Radial Semblance method.