Common shot gathers constructed using the synthetic experiments described above are shown in Figures 6 to 9.
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Figures 6 and 7 shows common shot gathers over Models 1 and 2, a single horizontal reflector and a single dipping reflector. The left panels were generated by a conventional finite difference experiment, while the middle and right panels were generated by cross-correlating waves from below. The difference between the middle and left panel is that the sources of the incoming waves were at infinity for the middle panel, giving planar waves; and within the zone of interest for the right panel, giving curved wavefronts.
The reflection events visible in the cross-correlation seismograms seem to be consistent with the conventional shot gathers to within the resolution of the modeling; this true for both sources located within the zone of interest as well as at infinity. The direct waves, however, are not consistent with the conventional seismograms. This is due to the factors discussed in the introduction and the lack of incident waves with an apparent slowness equal to the slowness of the near surface layer.
Common shot gathers modeled over Model 3 are shown in Figure 8. Again the kinematics of the two reflections appear correct to within the resolution of the modeling, for both plane wave and point sources of ambient noise. However, in the point source case (right panel), an extra event appears at 0.15 s travel-time. This is a corresponds to the primary reflection from the event below the sources (see Figure 10). This event is coherent in this example because the point source were all situated at the same depth of 0.3 km. If the point source had been located at random depths then this event would not have been coherent.
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belowref
Figure 10 Reflection from below source that causes extra event in common shot gather created by cross-correlation. |  |
The shot gathers for the fault block model are shown in Figure 9; and zero-offset sections of this model, created by auto-correlating noise traces, are shown in Figure 11. Again the kinematics are consistent to within the resolution of the experiment. Diffractions can even be seen from the edge of the fault.
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zsec.block
Figure 11 Zero-offset sections of fault block model generated by cross-correlation method. Left panel: sources of ambient noise at infinity. Right panel: sources of ambient noise within zone of interest. |  |
Another point that can be seen in the Figures is that the bandwidth of the cross-correlation seismograms is comparable to the bandwidth of the conventional seismograms. This implies that the resolution we may expect from field data is governed by the bandwidth of the ambient noise, not by the length of the time series that are cross-correlated.