The Marmousi velocity model (Figure ) generates complex propagation paths in which late energetic arrivals are not fit well by first-arrival finite-difference traveltimes. In Figures through , a modeling program written by Martin Karrenbach (1995) is used to generate snapshots of the acoustic wavefield from two surface locations in the Marmousi model. The corresponding contours of first-arrival traveltime have been overlaid. These contours are from the first-arrival traveltime tables used for Kirchhoff datuming and migration later in this chapter.
At the early-time snapshots displayed in Figure , the first-arrival contours overlay the energetic portions of the wavefield nicely. This is because there has not been enough time for adverse propagation effects to develop fully. Since the first-arrival traveltime matches the high energy portions of the wavefield, using these traveltimes for Kirchhoff migration will result in good imaging at these early times.
In contrast, snapshots for the same source locations at later times of 0.9 s and 1.05 s (Figure ) show that the first-arrival traveltimes do not always correspond to energetic portions of the wavefield. If these traveltimes were used for migration, the resulting image would suffer because parts of the summation trajectories would not correspond to energetic arrivals. This last sequence of two figures demonstrates that as the wavefield evolves, complex propagation effects begin to manifest themselves, and the first-arrival traveltimes no longer match the most energetic wavefront.
Figure is generated by starting the acoustic modeling and the first-arrival traveltime calculation from a depth of 1500 m. The 0.2 s and 0.3 s contours correspond nicely to the high energy portions of the wavefields. There is some deviation in the shallow part of the lower left 0.3 s panel, but for the most part, the first-arrival traveltime contour fits the bulk of the acoustic energy very well. The pulling away of the first-arrival traveltime contour represents a headwave propagating along the thin high velocity layer that starts under the fault at lateral position of about 5500 m and a depth of 1500 m in Figure .
Overall, the contours in Figure and have not pulled away from the energetic wavefront as they have in Figure . This shows that if traveltime calculation is limited to early times, the first-arrival traveltimes accurately parameterize the most energetic portions of the acoustic wavefield.