A stable method for using fat-ray tomography to determine a high-resolution velocity model of the subsurface from seismic data (71). The velocity model (72) may be used in migrating the seismic data (76) to image the subsurface. Rays are traced from a subsurface reflection point to surface source and receiver locations (73), using Fresnel zone construction methods (74) that honor correct initial conditions, with the Fresnel radius being a function of velocity.