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Kirchhoff versus phase-shift migration

In chapter , we were introduced to the Kirchhoff migration and modeling method by means of subroutines kirchslow() and kirchfast() . From chapter  we know that these routines should be supplemented by a filter such as subroutine halfdifa() . Here, however, we will compare results of the unadorned subroutine kirchfast() with our new programs, phasemig() and phasemod() . Figure 7 shows the result of modeling data and then migrating it. Kirchhoff and phase-shift migration methods both work well. As expected, the Kirchhoff method lacks some of the higher frequencies that could be restored by .Another problem is the irregularity of the shallow bedding. This is an operator aliasing problem addressed in chapter .

comrecon
Figure 7
Reconstruction after modeling. Left is by the nearest-neighbor Kirchhoff method. Right is by the phase shift method.

Figure 8 shows the temporal spectrum of the original sigmoid model, along with the spectrum of the reconstruction via phase-shift methods. We see the spectra are essentially identical with little growth of high frequencies as we noticed with the Kirchhoff method in Figure .

 phaspec Figure 8 Top is the temporal spectrum of the model. Bottom is the spectrum of the reconstructed model.

Figure 9 shows the effect of coarsening the space axis. Synthetic data is generated from an increasingly subsampled model. Again we notice that the phase-shift method of this chapter produces more plausible results than the simple Kirchhoff programs of chapter .

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Figure 9
Modeling with increasing amounts of lateral subsampling. Left is the nearest-neighbor Kirchhoff method. Right is the phase-shift method. Top has 200 channels, middle has 100 channels, and bottom has 50 channels.

Next: Damped square root Up: PHASE-SHIFT MIGRATION Previous: Pseudocode to working code
Stanford Exploration Project
12/26/2000