Reflection seismograms from a simple model

Figure  describes the model parameters. Figure  shows the horizontal and vertical components of the wavefield generated by the dual-operator modeling scheme using the model of Figure . The reflections with zero-offset traveltime equal to 0.8, 1.1, and 1.55 seconds correspond, respectively, to the water-bottom reflection, the reflection in the interface between the second and third layers, and the first multiple of the water-bottom reflection. The two other visible reflections correspond to the PS and SS reflections at the interface between the second and third layers.

 

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Figure 1 Model used to compare the results obtained with three different modeling schemes. Elastic constants are given in $\mbox{N}/\mbox{m}^2$, and densities in $\mbox{g}/\mbox{cm}^3$.

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.

 

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Figure 2 Surface wavefield generated by the dual-operator scheme. (a) Vertical component. (b) Horizontal component.

 

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Figure 3 Surface wavefield generated by the propagator-matrix scheme. (a) Vertical component. (b) Horizontal component.

 

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Figure 4 Surface wavefield generated by the traditional finite-difference scheme. (a) Vertical component. (b) Horizontal component.

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.