Constructing the seismic image in vertical time, as opposed to depth, eliminates the inherent ambiguity of resolving the vertical P-wave velocity from surface seismic data in transversely isotropic media with a vertical axis of symmetry (VTI media). By ray tracing in the space-time (x-)-domain, a traveltime map is built by interpolating the traveltime information along the rays onto a regular grid in space and time. This traveltime map is used by the prestack Kirchhoff time migration to obtain the migration summation trajectories. Since the traveltime map is extracted using ray tracing, the migration can practically handle any lateral velocity variations. Specifically, the prestack time migration yields good images of the isotropic and anisotropic Marmousi models.