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. When the velocity increases with depth, wider focuses are found at increasing depth. Consider each hyperbola to be made of many short plane wave segments.
Migration moves all the little segments on top of each other.
The sharpness of a focus cannot be narrower than the width of each of the many plane-wave segments that superpose to make the focus. The narrowest of these plane-wave segments is at the steepest part of a hyperbola asymptote. Thus deeper reflectors with faster RMS velocities have wider focuses so the deeper part of the image is more blurred. Any ray that does this many times is said to be a surface-trapped wave. It cannot sharpen a deep focus.