Variable velocity sections

The migration algorithm was adapted to handle variations in migration velocity (which is equivalent to rms velocity) with observed travel times and spatial locations. This was done by defining the velocity as a function of observation time and space, respectively. Illustrations for both cases shall be made on the same dipping reflector model shown in Figure 6.

 

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Figure 6 Dipping reflector (dip, 8 ms/trace).

 

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Figure 7 Zero-offset seismic response of dipping reflector model (velocity function, time-variant).

 

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Figure 8 Output migrated section of Figure 7.

Figure 7 shows the zero-offset seismic response of this model. The velocity function used was taken from a real seismic data record section, and it varies only with observation time. The same velocity function was used to migrate this section, and the output record is shown in Figure 8. The dipping reflector is correctly repositioned, temporally and spatially, to its true subsurface location.

The same results were obtained when spatial variations in velocity were taken into account. The migrated output section (Figure 10) of the zero-offset section shown in Figure 9 is the correct image of the model dipping reflector.

 

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Figure 9 Zero-offset seismic response of dipping reflector model (velocity function, space-variant).

 

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Figure 10 Output migrated section of Figure 9.

Thus it has been shown that if the velocity function is known accurately both in observation time and spatial location, Kirchhoff migration is performed successfully on stacked data. Similar results can be shown for the case of non-zero offset data.