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-correlations between the $pi /2 $ phase-shifted signal andthe zero phase-shifted signal. The duration of crack-waves which have the elliptical particle motion is detected well by using the algorithm.