Ground motion with strong‐velocity pulses can cause significant damage to buildings and structures at certain periods; hence, knowing the period and velocity amplitude of such pulses is critical for earthquake structural engineering. However, the physical factors relating the scaling of pulse periods with magnitude are poorly understood. In this study, we investigate moderate but damaging earthquakes ( 6–7) and characterize ground‐motion pulses using the method of Shahi and Baker (2014) while considering the potential static‐offset effects. We confirm that the within‐event variability of the pulses is large. The identified pulses in this study are mostly from strike‐slip‐like earthquakes. We further perform simulations using the frequency–wavenumber algorithm to investigate the causes of the variability of the pulse periods within and between events for moderate strike‐slip earthquakes. We test the effect of fault dips, and the impact of the asperity locations and sizes. The simulations reveal that the asperity properties have a high impact on the pulse periods and amplitudes at nearby stations. Our results emphasize the importance of asperity characteristics, in addition to earthquake magnitudes for the occurrence and properties of pulses produced by the forward directivity effect. We finally quantify and discuss within‐ and between‐event variabilities of pulse properties at short distances.