Imaging the reflectivity from free-surface reflections

A single impulsive source is located somewhere in depth, and the synthetic data generated in a 4-layer channel model are shown at the top of Figure 9. The interface boundaries are delineated by the dash-dot lines in the bottom figure, including the semi-circle river channel along the third interface. Using the migration operator for ghost reflections given by equation 6, the data are migrated to give the image at the bottom of Figure 9. Note, the source location was unknown, represented by the star symbol in the left bottom part of the migration image. It might be surprising that the single source generates enough data so that the model is almost entirely imaged. Part of the reason for this is that the ghost reflections illuminate a much greater part of the medium (for a fixed recording array) than primary reflections alone. Each point on the free surface acts as a virtual source.

Finally, ten point sources are buried at intermediate depths and their emissions are recorded on the surface. Each source is governed by a distinct random time series. Applying the migration operator for free-surface reflections [equation (6)] to the data shown at the top of Figure 10 yields the result shown in the bottom figure. Fifty one-second records were migrated and stacked with one one another, and show that the sand channel boundary is well imaged.

 

f10
Figure 9 Similar to Figure 7 except now a a 4-layer sand channel model is imaged using one buried source. The source time history is a 30-Hz Ricker wavelet.

 

f12a
Figure 10 Similar to previous figure except there are now ten buried point sources scattered about at intermediate depths. Each source is governed by a distinct random time series.