In practice, a hyperbola does not collapse to a point, it collapses to a focus. A focus has measurable dimensions. Vertical resolution is easily understood. For a given frequency, higher velocity gives longer vertical wavelength and thus less resolution. When the result of migration is plotted as a function of traveltime depth instead of true depth z , however, enlargement of focus with depth is not visible.
Horizontal resolution works a little differently.
It squeezes a large hyperbola down to a tiny focus. Study the focal widths in Figure 13 . Notice the water-velocity focuses hardly broaden with depth. Right is the same, but with a Gulf of Mexico velocity, i.e. the hyperboloids of Figure 12 migrated back to focuses. Observe focus broadening with depth.