Across a single vertical fault in the earth the velocity will be a simple step function of the horizontal coordinate. Rays traveling across such a fault suffer in amplitude because of reflection and transmission coefficients, depending on the angle. Since near-vertical rays are common, only small velocity contrasts are required to generate strong internal reflections. By this reasoning, steep faults should be more distorted, and hence more recognizable, on small-offset sections than on wide-offset sections or stacks.
This phenomenon is somewhat more confusing when seen in (x,t)-space. Figure 24 was computed by Kjartansson and used in a quiz. Study this figure and answer the questions in the caption. Here is a hint: A reflected ray beyond critical angle undergoes a phase shift. This will turn a pulse into a doublet that might easily be mistaken for two rays.
Figure 24 exhibits a geometry in which the exploding-reflector model fails to produce all the rays seen on a zero-offset section.
The exploding-reflector model produces two types of rays: the ray that goes directly to the surface, and the ray that reflects from the fault plane before going to the surface. A zero-offset section has three rays: the two rays just mentioned, but moving at double travel time, once up, once down; and in addition the ray not present in Figure 24, which hits the fault plane going one way but not the other way.
There is a simple way to make constant-offset sections in laterally variable media when the reflector is just a point. The exploding-reflector seismogram recorded at x=s is simply time convolved with the one recorded at x=g. Convolution causes the travel times to add. Even the non-exploding-reflector rays are generated. Too bad this technique doesn't work for reflector models that are more complicated than a simple reflecting point.