What happens is that as the waves get deeper into the earth, their spatial wavelengths get longer because of the increasing velocity. The case of horizontal resolution is similar, but the horizontal wavelength is directly measurable at the earth's surface. Observable lateral wavelengths get longer with increasing depth. Thus lateral resolving power decreases with depth. Hyperboloids from shallow and deep scatterers are shown.
Shallow hyperbolas have early tops and steep asymptotes.
Deep scatterers have late tops and less steep asymptotes. The less steep asymptotes have longer horizontal wavelength. Horizontal wavelengths measured at the surface are unchanged at depth, even though velocity increases with depth. Thus, lateral spatial resolution gets worse with depth. Compounding the above reason for decreasing resolution is the loss of high-frequency energy at late travel time.