10:45 AM - 12:15 PM
[STT44-P07] Polarization analysis based on eigenvalue decomposition of complex spectral matrix and its application to low-SNR event detection
Keywords:Polarization analysis, Particle motion, Spectral matrix analysis, Event detection, Eigenvalue decomposition
Analysis of time-series data of a large number of waveforms is useful for understanding earthquakes and estimating underground structures, and for risk assessment in underground resource development. In particular, if earthquakes with low SNR can be detected and analyzed, the analysis accuracy will improve because of the increase in data. There are methods for event detection such as short-time average/long-time average that use the rapid change of waveform amplitude, match filter that uses the template of earthquake waveform, and methods that use neural networks.
Since the properties of the methods, these methods may not be suitable for detecting low SNR events, or the proper preparation may affect the detection performance. In contrast, there is a method to detect P-wave arrival by analyzing the spectral matrix (SPM) generated from the three-dimensional particle motions generated from three-component waveform data. This method can detect P-wave arrival only by using indices calculated from the eigenvalues and eigenvectors of the SPM, and does not require a template or learning.
In the present study, the spectral matrix analysis was extended to complex numbers. In conventional methods, the spectral matrix is originally a one-rank complex symmetric matrix. Thus, the rank of the SPM is increased by taking the real part of the diagonal component, and the SPM is analyzed as a two-rank real symmetric matrix. Therefore, all information other than the P-wave is included in the second eigenvector at P-wave arrival. In the proposed method, by introducing time delay components and increasing the number of eigenvalues and eigenvectors of the SPM, the noise floor in P-wave detection was reduced. Furthermore, since the eigenvectors can be obtained as complex numbers, the phase information calculated from the real and imaginary parts of the first eigenvector can also be used for the characterization of the waveform. The new evaluation index is proposed by means of the phase information, and the detection accuracy of the low-SNR event is improved by combining it with the previously proposed index.
The proposed method was applied to synthetic and real data, and the performance of the proposed method was evaluated. Synthetic waveforms were generated as a 10 Hz sine wave with two periods, and band-limited noise of 4-10 Hz was superimposed as an additive noise. The results of the sensitivity test for the detection of P-wave arrival by changing the noise level showed that the detection sensitivity of the coherent signal is improved by setting the width of the time delay properly. At an SNR of -5 dB, by taking a time delay of approximately one period of the signal, the noise and signal could be almost separated. Detection experiments using the real data were performed with the waveforms recorded at the Groningen gas field in the Netherlands, and two low SNR events that were not detected by existing methods were newly detected.
Since the properties of the methods, these methods may not be suitable for detecting low SNR events, or the proper preparation may affect the detection performance. In contrast, there is a method to detect P-wave arrival by analyzing the spectral matrix (SPM) generated from the three-dimensional particle motions generated from three-component waveform data. This method can detect P-wave arrival only by using indices calculated from the eigenvalues and eigenvectors of the SPM, and does not require a template or learning.
In the present study, the spectral matrix analysis was extended to complex numbers. In conventional methods, the spectral matrix is originally a one-rank complex symmetric matrix. Thus, the rank of the SPM is increased by taking the real part of the diagonal component, and the SPM is analyzed as a two-rank real symmetric matrix. Therefore, all information other than the P-wave is included in the second eigenvector at P-wave arrival. In the proposed method, by introducing time delay components and increasing the number of eigenvalues and eigenvectors of the SPM, the noise floor in P-wave detection was reduced. Furthermore, since the eigenvectors can be obtained as complex numbers, the phase information calculated from the real and imaginary parts of the first eigenvector can also be used for the characterization of the waveform. The new evaluation index is proposed by means of the phase information, and the detection accuracy of the low-SNR event is improved by combining it with the previously proposed index.
The proposed method was applied to synthetic and real data, and the performance of the proposed method was evaluated. Synthetic waveforms were generated as a 10 Hz sine wave with two periods, and band-limited noise of 4-10 Hz was superimposed as an additive noise. The results of the sensitivity test for the detection of P-wave arrival by changing the noise level showed that the detection sensitivity of the coherent signal is improved by setting the width of the time delay properly. At an SNR of -5 dB, by taking a time delay of approximately one period of the signal, the noise and signal could be almost separated. Detection experiments using the real data were performed with the waveforms recorded at the Groningen gas field in the Netherlands, and two low SNR events that were not detected by existing methods were newly detected.