The specific barrier model, which was described in detail by Papageorgiou and Aki (1983), is applied to a set of five moderate to strong Californian earthquakes: Kern County (1952); San Fernando (1971); Borrego Mountain (1968); Long Beach (1933); and Parkfield (1966). Source parameters such as barrier intervals, local stress drops, cohesive zone size, and cohesive stress are inferred. The analysis of the San Fernando earthquake of 1971 revealed a strong frequency dependence of Qβ, suggesting that the high frequencies may not be as strongly attenuated as initially thought. This suggests that the fall-off at high frequencies of observed spectra at a site may not be a propagation path effect but primarily a source effect. The cut-off frequency observed on the source acceleration power spectra of all the events analyzed in this paper, is interpreted in terms of the cohesive zone size and cohesive stress which arrest the localized fractures that occur on the fault plane. It was found that the barrier interval, as inferred by the specific barrier model, increases with the increase in maximum slip. The ratio of the latter to the former represents the local strain drop and was found to increase slightly (factor of 2) with earthquake size. This verifies the relation between barrier interval and maximum slip which has been observed by Aki et al. (1977) who inferred the barrier interval by different methods (i.e., surface measurement of fault slip, seismic measurement of rise time, scaling law of seismic spectrum). Striking similarities with respect to source parameters were found between the Fort Tejon (1857) and Kern County (1952) earthquakes as well as between the Long Beach (1933) and Parkfield (1966) earthquakes. The former are characterized by long barrier intervals and large slips while the latter are characterized by short barrier intervals and small slips. San Fernando (1971) and Borrego Mountain (1968) earthquakes lie in between these two extremes.