Polarization Analysis in Time-Frequency Domain by Complex Spectral Matrix: Application to Various Phases of Seismogram

The detection and analysis of low signal-to-noise-ratio (SNR) events are valuable for a better understanding of various physical processes in underground reservoirs. The spectral matrix (SPM) analysis for detecting low-SNR P-wave arrivals, which is a previously proposed templateless detection method, is extended. The introduction of time-delay components increases the rank of SPM and makes it possible to characterize various polarized waves and detect further low-SNR events by a complex SPM analysis. In a P-wave detection problem, a new weighting function based on the phase information of the first eigenvector was proposed, and the polarization evaluation of the P-wave arrival was further improved. The results with the synthetic waveform showed that the separation of signal and noise is improved by the proposed method. In addition, detection experiments were performed with the waveforms recorded at the Groningen gas field in the Netherlands, and the proposed method newly detected two low-SNR events that were not detected by existing methods. The proposed method is robust to noise and shows the potential to detect low-SNR coherent signals and to characterize comprehensive polarized waves efficiently. Furthermore, we tested the proposed method on the whole seismogram of microseismicity and intermediate-depth earthquakes. We could identify the different phase arrivals by combining the magnitude of the first eigenvector. The contribution of the present work is an extension of the SPM analysis itself. Users can design appropriate indices based on three complex eigenvectors and eigenvalues.