# Migration exercises

Series Investigations in Geophysics Öz Yilmaz http://dx.doi.org/10.1190/1.9781560801580 ISBN 978-1-56080-094-1 SEG Online Store

## Exercises

Exercise 4-1. Consider the special case of a 90-degree dipping reflector in Figure 4.1-1a. Sketch the corresponding zero-offset time section.

Exercise 4-2. Consider Huygens’ secondary sources along a dipping reflector. Sketch the zero-offset section by superimposing the individual responses from these sources. Remember, to do zero-offset modeling, you must map a point in the x − z plane to a hyperbola in the x − t plane with its apex as the input point.

Exercise 4-3. For which case is spatial aliasing a more serious problem, the low-velocity or high-velocity medium?

Exercise 4-4. Locate the dipping event AA′ on the migrated section in Figure 4.E-1.

Exercise 4-5. A point in the x − t plane is mapped onto a semicircle in the x − z plane. Where does it map on the x − τ plane, where τ = 2z/v.

Exercise 4-6. Refer to Figure 4.1-14. It suggests that if the subsurface consisted of a semicircular reflector (b), then the zero-offset response would be as in (a). What would the subsurface be like if you obtained (a) using a source-receiver pair with a finite separation between them? (See Figures D-5 and D-6.)

Exercise 4-7. Suppose you specified the wrong trace spacing in your migration. What effect does it have, overmigration or undermigration? Assume that you supplied the wrong sampling rate in time. What effect does it have on migration output?

Exercise 4-8. Suppose you want to do zero-offset recording of the steep flank of a salt dome. Which case would require a longer line length when the medium velocity along the raypath is (a) constant or (b) vertically increasing?

Exercise 4-9. How would Figure 4.3-6 look if you used a 15-degree phase-shift migration algorithm?

## Figures and equations

 ${\displaystyle k_{z}={\frac {\omega }{v}}DSR(Y,H).}$ (D-23)

 ${\displaystyle k_{z}={\frac {2\omega }{v}}{\sqrt {1-Y^{2}}}.}$ (D-29)

## References

1. Chun and Jacewitz, 1981, Chun, J.H. and Jacewitz, C., 1981, Fundamentals of frequency-domain migration: Geophysics, 46, 717–732.
2. Yilmaz, 1979, Yilmaz, O., 1979, Prestack partial migration: Ph.D. thesis, Stanford University.
3. Clayton, 1978, Clayton, R., 1978, Common midpoint migration: Stanford Expl. Proj., Rep. No. 14, Stanford University.