###### Abstract
If we go one step further and assume a circularly shaped reflector segment with a finite curvature and a dip relative to the surface, we obtain a traveltime surface tilted with respect to the midpoint axis by an angle corresponding to the reflector dip, and with a curvature in midpoint direction proportional to the reflector curvature. For an infinite curvature of the reflector, i.e., for a diffraction point, we would obtain a bell-shaped traveltime surface, which is hyperbolic both in offset and midpoint direction. Let us now assume that our records not only contain the reflected signal energy of the source pulse but also noise energy from ambient sources, like nearby street traffic or construction activities. These uncorrelated noises can be reduced by stacking amplitudes of traces with (a) different offsets and (b) different reflection points, located on the same reflector within a certain neighborhood, which translates in practice into a range of midpoints. To facilitate structural interpretation, the stack amplitude is placed at the extrapolated traveltime that would be registered by a notional experiment with coincident source and receiver positions. The corresponding Zero-Offset (ZO) ray hits the reflector normally. It ascends on the same trajectory towards the receiver on which it descended from the source down to the reflector. If the projected midpoint stacking aperture on the reflector, which is an area around the Normal-Incidence Point (NIP) of the ZO ray, does not exceed the size of the first interface Fresnel zone of the reflected wavefield, stacking can be expected to increase the Signal-to-Noise (S/N) ratio without harming resolution [1]. Obviously, only a smaller part of the amplitudes stemming from a laterally extensive continuous reflector can be stacked into a single ZO traveltime. This is different for a diffraction where in principle the entire traveltime surface can be collapsed to a point. In real applications, the structure of the subsurface is unknown. Therefore, scanning for reflection and diffraction events, so-called velocity analysis, must precede each stacking process. Velocity analysis and stacking need to be conducted for all traveltimes before a simulated ZO trace is obtained, and for all midpoints before the final ZO section is completed. While stacking creates a simulated ZO section of high S/N ratio, velocity analysis delivers geometrical information regarding the reflecting interface and the wave propagation velocities within the strata set above it, blended into one or more parameters. The simplistic two-layer scenarios discussed previously in this section illustrated that for 2D seismic reflection events are surfaces in a 3D multi-coverage dataspace. This makes clear that both velocity analysis and stacking should be performed along these surfaces in midpoint and offset direction. In the pre-digital age of seismic prospecting, it was impracticable, if not unthinkable, to search for spatial reflection events in 3D pre-stack data volumes. After the introduction of multi-coverage data, Common-Midpoint (CMP) stacking [2] was considered a breakthrough and maintained large popularity for a long time. The method limits both stack and velocity analysis to single CMP gathers, where one parameter, the Normal-Moveout (NMO) velocity, is enough to parameterize the moveout hyperbola along which the recorded amplitudesare shifted to ZO traveltime and summed up. The difference between the traveltime of a real finite-offset ray and the traveltime of the notional ZO ray is called normal-moveout. For a planar surface and a parallel reflector separating two homogeneous layers, the midpoint of the ZO trace coincides with the lateral location of the reflection point, while the reflection traveltime multiplied by the NMO velocity is equal to the length of the ray path or twice the depth of the reflector.