Abstract: 165 distinct pulse records are quantitatively indentified by considering the uncertainty of pulse orientation and using wavelet method from 3661 groups of strong motion records in 175 earthquake events from Wenchuan and Ludian earthquake in China and the NGA (Next Generation Attenuation) database of the US to form a database for this study. The long-period pulses are extracted from the original pulse record. We compare the response spectra of the original records with the residual ground motion after the pulse extraction. The results show that the response spectra at the period rang near the pulse period, T_p, are highly amplified due to the presence of large velocity pulses, and shown as a narrow-band effect. Based on a quantitative analysis of the epsilon parameter, we find that median amplification curves vary with period and show distinct peak values near the pulse period, T_p, with strongest amplification of approximately 3.5, and decrease when departing from T_p. The most significant period range with amplification effects is from 0.5T_p to 2T_p. Quantitative empirical models of amplification factor A_f and pulse period T_p are proposed based on least-squared fitting of the results. We further investigate the effects of earthquake magnitude and site shear wave velocity on the amplification factor curves. With the increase of the magnitude, the affected period band due to pulse amplification becomes broader, and the peak period moves towards the long period direction. Both the affected period band and the peak period moves towards the short period direction with the increasing of shear wave velocity. The empirical model of pulse amplification factor obtained in this study can be used as a modification of the response spectra for a specific earthquake and site condition in near-fault cases.