This article presents a new method to estimate S-wave site response relative to a regional layered crustal model. The method is useful for site-specific strong-motion prediction because the estimated site-response functions are referenced to an idealized regional layered model for which we know the ground response exactly. We applied this method to the Northridge earthquake sequence. We determined the site amplifications, from aftershocks with magnitudes 2.6 to 4.3, at 21 stations that were colocated with strong-motion stations. These site-response functions were then used to modify synthetic seismogram calculated for the Northridge mainshock in the same regional layered crustal model and thus obtain site-specific ground-motion estimates. These site-specific synthetic seismograms have higher correlation to observations in comparison to the synthetic seismograms without weak-motion site correction. They have similar amplitude and frequency content to the observations, especially at sites with recorded peak ground accelerations below 0.3 g. At sites with larger ground motions, however, this approach overestimates the strong motion. The differences are made clear when we estimate site-response functions from the strong-motion records and compare them with those from weak-motion records. We express the differences as the average ratio of the weak- to strong-motion site response (AWS ratio). When the ground motion is low, the AWS ratio is near unity, indicating that the weak- and strong-motion site responses agree with each other within the uncertainty. However, the AWS ratio increases as the ground-motion amplitude increses. The difference in weak- and strong-motion site responses becomes significant at stations where peak acceleration was above 0.3 g, peak velocity was above 20 cm/sec, or peak strain was above 0.06% during the mainshock. This result demonstrates directly from the ground-motion observations the relationship between nonlinear site response and peak ground-motion parameters. The nonlinearity is present on soft rock sites as well as on sediment sites.