Based on the assumption that directivity effect is mainly a function of the fraction of ruptured area toward the site, I presented a directivity model that generalizes the earlier model of Somerville et al. (1997). The directivity effect is simply defined in terms of one rupture parameter ξ (which depends on fault geometry, a rupture initiation point, and site location), a free coefficient C1, and a directivity coefficient C2 (which is dependent on the period and the soil type). The model is tested extensively using faults of different sizes and geometry, including single-segment strike-slip and dip-slip, and also multisegment strike-slip and dip-slip faults. The NGA data and four attenuation relations were used to compute the two coefficients in the model. Specifically, the directivity coefficients for ground motions in rock and in soil for periods up to 3 s were determined. It is found that rupture directivity effect is present in ground motions at all periods. However, the effect becomes significant at 0.3 s and increases with the period, at least up to a period of 3 s (for which this study was done), and likely beyond that, although with a lower rate. Based on an analysis of the uncertainty, I found that correcting for directivity would result in a decrease of the attenuation standard error term, sigma, by as much as 10%. Based on these results, I conclude that local variations in the near-source ground motions, especially at longer periods, should be partly attributed to rupture directivity. I also investigated the dependence of fault-normal and fault-parallel spectral accelerations in the NGA database on rupture direction. The results showed a strong dependence of FN/FP and FN/AVE acceleration ratios on rupture directivity, especially for long periods. The model can also be used to investigate the effect of rupture heterogeneity on ground motions. Information on fault rupture heterogeneities during earthquakes, such as various features of asperities, distributions of slip, slip-rate, stress drop, etc., can be used to conduct such an investigation. Further study should involve a more detailed analysis of the effects of rupture on near-source ground motions, particularly in terms of fault-parallel and fault-normal components, taking into account the effects of heterogeneities and comparing predicted ground motions with recorded ground motions for various earthquakes.
