## 3 Shallow P-Wave Data Example
We chose line 2, because, of the two lines, it has the lower S/N ratio and is therefore better suited to highlight the benefits of a spatial velocity analysis. The annotated stack section produced by [46], and depicted in Figure 6, shows two dominant reflections. The first, event \(\alpha\), is the deepest coherent reflection in the section and was interpreted as the top of the Paleozoic bedrock, in accordance with the outcrop geology beyond the end of the line. It has an apparent dip to the north-northeast from about 290-165 ms two-way-traveltime (twtt) between CMP locations 10 and 60, before it gently shallows with a dip angle of about 10\({}^{\circ}\), reaching 125 ms twtt at CMP 160. Even though less continuous and with lower amplitudes, event \(\alpha\) can further be identified, from CMP 160 to the end of the line, with its change in reflection character probably caused by a change in reflectivity of the overlying sedimentary sequence. After CMP 160 event \(\alpha\) abruptly starts descending until CMP 200, forming a trough with flat bottom between CDP 200-250, before it gently up-dips from 160 ms to 130 ms twtt at CMP 300. From CMP 300 to the end of the line, it continues to shallow, reaching 66 ms twtt, or a depth of approximately 52 m. The outcrop geology, and the velocity model depicted in Figure 13b, obtained by [46] from combining reflection-derived interval velocities and those derived from first-arrival information using refraction tomography, support the interpretation of event \(\alpha\) as the top of the bedrock. The second of the two dominant reflection events is called event \(\gamma\) and is interpreted as the boundary between Holocene and Pleistocene alluvia. It starts at the beginning of the line and extends at least until CMP 340, where event \(\alpha\) pinches out. It is nearly horizontal, with onset at 50-70 ms twtt. Event \(\gamma\) is overlain by seismic unit A that extends to the surface and consists of Holocene alluvial deposits composed of conglomerates, sands, and clays, according to samples obtained by drilling. Not all events in unit A can be interpreted as genuine reflections, because this very shallow part of the recordings is contaminated by various types of source-generated, high-amplitude coherent noise such as surface and refracted waves. Finally, at the left side of the section, unit B can be found between event \(\gamma\) and event \(\alpha\). Ref. [46] describes this unit as being composed of Pleistocene alluvial deposits. For creating the series of CRS stacking results shown in Figures 7-10, we used the following processing parameters. We chose a laterally constant near-surface velocity of 1600 m/s, consistent with the P-wave velocity of the water saturated sediments close to the ground surface. The total width of the coherence band was set to 33 samples, i.e., 0.0165 s. The offset aperture was 30 m for traveltimes up to 0.03 s and then increased linearly until the full offset range of 245 m was reached at 0.1 s. Roughly, this means that offsets do not become larger than two-times the reflector depth. The midpoint aperture increased linearly from the smallest to the largest traveltimes starting with 5 m half  
Figure 6: Annotated stack section obtained by conventional NMO/DMO-Stack processing, published by [46]. NMO velocities obtained from the cascaded search plus three iterations of event-consistent smoothing, each followed by a local optimization. In Figure 16, the NMO velocities from the hybrid diffraction/reflection search are shown and in Figure 17 the NMO velocities from the full simultaneous three-parameter search. In all the CRS stack examples, the NMO velocities were calculated according to Equation (3) from the estimated CRS parameters. Figure 14: CRS NMO velocities obtained from cascaded search followed by local optimization. Figure 13: CMP stack after NMO/DMO processing (**a**) and the respective stacking velocities after DMO (**b**). Figure modified from [46].