Time migration differs from depth migration in how it uses velocity models. The key distinction is that time migration takes its velocity model and creates local one-dimensional models for each image trace in the output. Then each image trace is processed independently in its own local 1D world. Depth migration takes its velocity model and uses it as a single physical space. Obviously what time migration does with the velocity model is unphysical except in a horizontally stratified (1D) Earth, which would seem to be a big disadvantage. Time migration is still used because this unphysical approximation can lessen the burden on velocity model construction (at least if one is not being very fastidious about velocity model accuracy). Furthermore, in Kirchhoff implementations, it is more straightforward to construct continuous diffraction summation curves in the Time migration case, which often leads to cleaner images.