Blind separation of three-component seismic signal with the higher-order statistics

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Duration of an elliptically polarized wave is detected by using the blind signal separation and the cross-correlation analysis in three-component seismic signals. Observed three-component signals are assumed to be linear combinations of the elliptically polarized wave and another wave. The fourth-order cumulant, kurtosis, is used to measure a degree of the independence of the transformed signals. To actually minimize or maximize the kurtosis, a fixed-point algorithm is employed. Duration of the polarized wave is detected by analyzing the cross-correlation functions between the half of pi phase-shifted signal and the zero phase-shifted signal. The duration of crack-waves which have the elliptical particle motion is detected well by using the algorithm. Analytic signal transformed from the observed signal is also used in the blind separation. The algorithm using the analytic signal decreases ambiguity of a result.A function based on the normalized fourth order cumulant, kurtosis, is used to detect the P-wave arrival time. Errors of the automatic detection are within 6 ms in 87 acoustic emission signals.