The characteristics of a vector wavefield can be investigated through the polarization method. This study presents an alternate polarization method to separate (or isolate) the longitudinal and the transverse waves in the elastic case. Besides, this method can be used to reduce nonlinear elliptical waves. First, the vector wavefield with vertical and the radial components is selected and the analytic signals are obtained through a Hilbert treansform. Then, their polarization parameters, including phase difference, ellipticity and the strength of linear polarization, are calculated in the time domain. According to these parameters, the filter function of linear longitudinal and transverse waves are defined. Finally, the synthetic data are analyzed, therby showing that it is very effective to remove unwanted wave types even when the S/N ratio is as low as 1.667.