Variations in the migration velocity model directly affect the position of the imaged reflectors in the subsurface, leading to structural imaging uncertainties. These uncertainties are not explicitly addressed when trying to deterministically build an adequate velocity model. This paper presents a new stochastic geology-controlled velocity modeling method handling the possible presence of a salt weld. This permits to generate a large set of geological scenarios and associated velocity models. Each model is used to remigrate the seismic data. Then, a statistical analysis of the resulting seismic images is performed to quantify the local variability of the seismic responses. The approach is applied to the imaging of salt diapirs, in an iterative scheme (migrate, pick and update). The results show that, similarly to stacking common mid-point gathers, the statistical analysis preferentially preserves recurrent features from an image to another. In particular, this analysis permits to distinguish between connected and detached diapirs without prior knowledge about their connectivity, highlighting the potential of the method to resolve important aspects about basin and reservoir architecture. More generally, it provides quantitative information on the parts of the seismic image most sensitive to migration velocity variations, which opens interesting perspective to quantitative interpretation uncertainty assessment. Finally, the presented application also suggests that it is possible to significantly improve the quality of the generated seismic images by sampling many possible geological scenarios.