Recent ground-motion observations suggest that surface-rupturing earthquakes generate weaker near-fault ground motion than buried earthquakes. This difference is significant in the period range of 0.3-3 sec. Contributing factors to this phenomenon may include the effect of fault zone weakness at shallow depth on rupture dynamics and rupture directivity during earthquakes. We present results from numerical experiments of spontaneous dynamic rupture and near-source ground-motion simulations of surface rupturing and buried earthquakes and discuss mechanisms for the observed ground-motion differences. The surface-rupturing earthquake is modeled with a shallow zone of 5 km thickness containing areas of negative stress drop (within the framework of the slip-weakening friction model) and lower rigidity. Surface-rupturing models with this weak zone generate lower amplitude ground velocity than do models without this modification. Observed ground-motion differences between surface and buried events are qualitatively reproduced by imposing higher stress drop in the buried earthquakes than in the surface earthquakes, combined with introducing a deeper rupture initiation for buried rupture, enhancing upward rupture-directivity effects for the latter events. In the context of our simplified model parameterization, then, the observed differences in ground motion could arise from combined effects of relative weakness of the shallow layer of faults, the relatively larger stress drops of buried ruptures, and a tendency of near-fault sites to record strong upward directivity from buried ruptures.