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

利用三分量地震信号的盲分离和互相关分析，检测了椭圆极化波的持续时间。假定观测到的三分量信号是椭圆极化波和另一波的线性组合。四阶累积量，峰度，用于测量转换信号的独立性程度。为了实际最小化或最大化峰度，采用了不动点算法。通过分析半pi相移信号与零相移信号之间的互相关函数来检测极化波的持续时间。该算法能较好地检测出具有椭圆质点运动的裂纹波的持续时间。盲分离也采用了由观测信号变换而来的解析信号。该算法利用解析信号减少了结果的模糊性。一个基于归一化四阶累积量的函数，峰度，被用来检测p波到达时间。对87个声发射信号的自动检测误差在6ms以内。

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.