Eigenvalue decomposition polarization analysis: A regularized sparsity-based approach

Polarization analysis is a signal processing tool for decomposing multi-component seismic signals to a set of rectilinearly or elliptically polarized elements. Theoretically, time-frequency polarization methods are the most compatible tool to analyze the intrinsically non-stationary seismic signals. They decompose the signal to a superposition of well-defined polarized elements, localized in the time and frequency domains. However, in practice, they suffer from instability and limited resolution for discriminating between interfering seismic phases in time and frequency, as the time-frequency decomposition methods are generally an underdetermined mapping from the time to the time-frequency domain. Our contribution is threefold: Firstly we obtain the frequency-dependent polarization properties in terms of the eigenvalue decomposition of the Fourier spectra of three-components of the signal. Secondly, by extending from the frequency to the time-frequency domain and using the regularized sparsity-based time-frequency decomposition (Portniaguine and Castagna, 2004) we are able to increase resolution and reduce instability in the presence of noise. Finally, by combining directivity, rectilineary, and amplitude attributes in the time-frequency domain, we extend the time-frequency polarization analysis to extract and filter different seismic phases. By applying this method on synthetic and real seismograms we demonstrate the efficacy of the method in discriminating between the interfering seismic phases in time and frequency, including the body, Rayleigh, Love, and coda waves. This research contributes to the FCT-funded SHAZAM (Ref. PTDC/CTA-GEO/31475/2017) project.

REFERENCES
Portniaguine, O., and J. Castagna, 2004, Inverse spectral decomposition, in SEG Technical Program Expanded Abstracts 2004: Society of Exploration Geophysicists, 1786–1789.