Pre-Stack Wave-Equation Datuming

When the subsurface velocity structure is unknown upward continuation must be performed pre-stack. Pre-stack datuming is done by extrapolating the shots and the geophones separately using equation (2) Berryhill (1984). Once the data have been upward continued to a flat datum, velocity analysis or any other wave based processing algorithm can be applied.

The model used to generate the pre-stack synthetic data is displayed in Figure 10. The subsurface consists of two point diffractors under a topography which is more complicated than for the zero-offset case. The synthetic shot gather is generated using a pre-stack Kirchhoff routine with the shot placed directly above the diffractors at the top of the mountain. The effects of topography are clearly visible as undulations and discontinuities in the nonhyperbolic diffraction curves of Figure 11a.

 

shotmodel Figure 10 Topography and subsurface structure used to generate the pre-stack synthetic data.

Upward continuing the geophones to a planar datum above the mountain results in hyperbolic trajectories (Figure 11b). The moveout along these curves can now be used to determine the subsurface velocity structure. Some of the sharp features in the topography cause artifacts which are visible as diffractions after the main events. These artifacts would not add constructively in the velocity analysis.

 

shotsyn
Figure 11 (a) Synthetic shot gather distorted by the irregular surface topography. (b) Continuing the geophones to a level datum above the topography eliminates the distortions and produces hyperbolic moveout trajectories.