<p>In seismic imaging, understanding the relationship between wavefront-propagation velocity and time-interval velocity is crucial for achieving optimal resolution. However, this task becomes even more challenging when considering anisotropic situations. Over the past century, numerous seismic processing techniques have been developed and applied for practical purposes. However, the majority of these methods are specifically tailored for use in heterogeneous and isotropic models. The advancement of seismic technologies capable of effectively addressing media with anisotropic properties remains a significant technological challenge. To accurately account for the influence of anisotropy on wavefronts, it is essential to have a solid grasp of the underlying physics. Unfortunately, the anisotropy model that best describes the medium is often unknown. To address this issue, we utilize paraxial-ray theory in a ray-centered coordinate system to study the wavefront phenomenon. This approach allows us to develop explicit expressions that describe the physics of the problem. Using this theoretical framework, we can accurately generalize the relationship between time-migration rays and Dix velocity by incorporating the velocity-spreading factor for general anisotropic media. Moreover, the velocity-spreading factor provides valuable information for various applications, including model building, time-imaging, and time-to-depth conversion. In summary, the results presented here provide new tools to develop advanced seismic imaging technologies, which are fundamental to the oil and gas industry.</p>