Determining the optimally smoothed slowness model for ray-tracing based migration using multiple-valued travel-time tables

In complex regions, such as the one that the Marmousi model represents, there can be many ray paths between surface and image points for which amplitudes are significant. Often a ray that traverses the shortest travel-time path does not have a significant amplitude. The success of a Kirchhoffmigration scheme to correctly use multi-valued traveltime tables for such models is dependent on how the velocity/slowness model is smoothed prior to ray tracing. We investigate the relation between model smoothing and the prediction of multi-valued traveltime tables by comparing finite difference modeling of wave propagation through an unsmoothed model with wavefront construction ray tracing through models that have been smoothed in various ways. We show that oversmoothing the model leads to a loss of later arrivals predicted by the wavefront construction algorithm. We show that an optimal smoothing condition can be determined by observing the importance of later arrivals in both the raytracing and finite difference modeling. We investigate the effects of smoothing on later arrivals in a region of the Marmousi model that is not well imaged by most ray-based methods. We show that the choice of an appropriate slowness model for ray tracing leads to a significantly better image than can be obtained from an over smoothed model and that less smoothing does not enhance the image quality, in spite of its added computational cost.