1. Stacked sections are zero offset sections
Because of the distortions due to structure, and diffractions, stack sections only approximate the true subsurface
Distortion can be extreme in structurally complex areas
Solution is “seismic migration” (topic of the next lecture(s))
Model
Events on stack section

2. Introduction to seismic migration
Even for a simple, dipping reflector the reflection appears in the wrong place on the stack section
Examination of the figure shows that
Events on the stack section appear vertically below midpoints; true reflection points are further updip
The reflection has a gentler dip on the stack section than in reality
The reflection points are further apart on the stack section than they are in reality

3. Introduction to seismic migration
You should be able to derive the “migration equation” from an examination of the Figure:

4. Introduction to seismic migration

5. Introduction to seismic migration
Which of the two sections below is the original stack, and which is the migrated section?

6. Introduction to seismic migration
The Figure points to a method for manual migration:
Use a compass to draw constant traveltime circles from several points on the reflection surface
Use a ruler to find a tangent plane to all such circles

7. Introduction to seismic migration
Manual migration:
Use a compass to draw constant traveltime circles from several points on the reflection surface
Use a ruler to find a tangent plane to all such circles
The strategy works equally well for migrating diffractions
Constant traveltime circles all intersect at a point, corresponding to the true location of the discontinuity

8. Introduction to seismic migration
Any successful migration algorithm will therefore:
Move events updip
Steepen dips
Shorten events
Collapse diffractions onto points

9. Introduction to seismic migration
Any successful migration algorithm will
Move events updip
Steepen dips
Shorten events
Collapse diffractions onto points
Any algorithm that meets condition 4 automatically satisfies conditions 1-3.
Why?
any reflector can be imagined to be made up of a series of point diffractors
if we succesfully migrate each diffraction, the final result will be a successful migration of the whole reflector

10. Introduction to seismic migration
The “wavefront” method for seismic migration:
every pixel on the section defines a traveltime
the computer can generate a constant traveltime circle on the section
constant traveltime curves are known as “wavefronts”
the energy found at each pixel is distributed over the wavefront
result is a coherent superposition where these wavefronts are tangent, or where they intersect

11. Introduction to seismic migration
The wavefront method corresponds to moving (“migrating”) energy along constant traveltime curves (“wavefronts”)

12. Introduction to seismic migration
The “diffraction stack” method for seismic migration:
every subsurface point corresponds to a diffraction curve on the stack
the computer can generate the diffraction curves automatically
energy is collected on the stack from pixels that are intersected by the diffraction curve
the total energy found for each diffraction curve is mapped to the corresponding pixel on the migrated result
result is that all diffractions are “stacked” into the correct location

13. Introduction to seismic migration
The diffraction stack method corresponds to moving (“migrating”) energy from diffraction curves onto corresponding diffractor locations

14. Introduction to seismic migration
Both the wavefront method and the diffraction stack method are equivalent: both produce the same migrated section

15. Examples of seismic migration
Model with diffractions, anticlines, synclines

16. Examples of seismic migration
Example of “bowtie” associated with syncline

17. Examples of seismic migration
Example of “bowtie” associated with syncline

18. Examples of seismic migration
Example of diffractions associated with faulting

19. Examples of seismic migration
Example of diffractions associated with faulting

20. Examples of seismic migration
A, B are multiples

21. Examples of seismic migration
Example of multiples: incorrect positioning of multipes after migration