Figure 1

Figure shows the vertical and horizontal components of the wavefield generated with the Haskell-Thomson scheme, and Figure shows the vertical and horizontal components of the wavefield generated with the traditional finite-difference scheme.

Figure 2

Figure 3

Figure 4

The wavelet is clearly broader in both finite-difference-based methods because they require that the source extends over more than one grid-point. That is also the reason for the small precursor lobe in the wavelet generated by these two methods. Although both finite-difference schemes have operators with the same number of points (of same order in time and space), the traditional method is more dispersive, as indicated by the high-frequency ringing that contaminates the near traces of the vertical component. This higher dispersion is noticeable mainly when a liquid layer is present. Other differences are: the phase change of the sea bottom reflection near the offset 1300 meters in the vertical component of the traditional finite-difference scheme, the much weaker amplitude of the PSSP mode (the third event from the bottom) in the traditional finite-difference scheme, and the weaker near-offset amplitude of the PSPP mode (the fourth event from the bottom) in both finite-difference schemes relative to the propagator-matrix scheme.

11/18/1997