Migration of one shot record

I illustrate the migration of multiples with one shot. In Figure I display the source function on the left panel, and the recorded wavefield on the right panel. The recorded wavefield is the superposition of primaries and multiples. The migration result for this shot location is shown in Figure a.

Figure displays the source function and the up-going wavefield for the migration of multiples. As proposed in the preceding section, the source function is not impulsive but areal. The recorded wavefield contains the surface-related multiples only. The migration result is shown in Figure b and compares favorably with the output of the migration of primaries.

It is interesting to note that the water-bottom is illuminated with a wider aperture when multiples are used. As illustrated in Figure , for a given receiver R_n, the primary illuminates the reflector in r_a at a closer location to the source in S than does the multiple in r_b. Therefore, for one given shot, the multiples migrate with a wider aperture but with smaller angles.

As a final result, I display in Figures c and d the different illumination patterns for both the impulsive and areal sources (). These maps are obtained by simply computing the amplitude (squared) of the down-going wavefield at each depth and for each frequency. These Figures illustrate the aperture and illumination effects of the multiples.

 

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Figure 4 Shot-profile migration of the primaries. Left: Impulsive source function. Look closely at offset 0. meter and time 0. second to see the impulse. Right: Recorded primaries and multiples.

 

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Figure 5 Shot-profile migration of the multiples. Left: Areal source function. Right: Recorded multiples only. The source function is plotted upside-down to represent the computation involved by the time-reversed process.

 

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Figure 6 Migration results and illumination maps of the down-going wavefields for the imaging of multiples and primaries. (a) Migration of the primaries. (b) Migration of the multiples. (c) An illumination map for the impulsive source. (d) An illumination map for the areal source.