1. Imaging (and characterisation) of diffractors
A. Bona and R. Pevzner
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2. Example of hard-rock geology
Surface seismic would show only diffractions from the tops of the features
Hillside, South Australia (RexMinerals)

3. Example of sedimentary geology
The terminations of the layers at the fault act as diffractors

4. Huygens principle Huygens 1678: Fresnel 1816: Kirchhoff 1883:
To describe wave scattering at diffractors we use Huygens’ principle
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5. Snapshot of backscattered wavefield from a plate
Note the phase reversal of the diffracted wavefield at its intersection with the reflected wave (red circle indicates the diffracted wavefront).
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6. Huygens’ principle implies that we can decompose a reflected plane wave from an infinite plate as a summation of wavefields scattered from the two halves of the plate.
Babinet’s principle
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7. Backscattered wavefield from one half of the plate
Backscattered wavefield from one half of the plate. The outside part of the diffracted wavefield is as expected; the shadow part of the diffracted wave has opposite polarity to cancel out the diffracted wavefront from the other half of the plate.
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8. Curtin University is a trademark of Curtin University of Technology
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9. Curtin University is a trademark of Curtin University of Technology
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10. Amplitude of diffractor vs. reflector
Since two diffracted wavefronts from the edges of the two halves of the plate have to add up to the reflected wavefield, the amplitudes of the diffracted waves are one half of the amplitude of the reflected wave at the direction of the reflected wave. Away from the reflected wave the amplitudes of the diffracted wavefields decay according to Kirchhoff formula.
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11. Scatterers in 3D plane edge line point line: square prism point: cube
There are four basic types of scatterers in 3D. More subtle types are formed by the combination of these (tips, vertexes, …). We wil explore the responses of these to a point source located at the red X. The response will be investigated at the image point denoted by the red O.
line: square prism
point: cube
with edges of length

12. Diffraction vs. reflection
Diffractors have different kinematic properties compared to reflectors.
common shot gather travel times

13. Slices through common shot gathers along diffraction hyperbola with uniform random noise
plane
SNR =
6dB
edge
To illustrate the radiation patterns of the four scatterer types we plot slices through common shot gathers along the diffraction hypergola corresponding to a point on the scatterer.
line
point

14. Energy
plane
edge
line
point

15. Local semblance plane edge line point
Instead of the energy or waveforms, we visualize the radiation patterns by using local se
line
point

16. Fresnel zones ||imaging ray| - |physical ray|| < wavelength /2
receiver
source
imaging ray
physical ray (Fermat’s principle)
reflector/scatterer
The scattered energy is distributed along the Fresnel zone. The definition of Fresnel zone for diffractors is straightforward genralisation of the definition for reflectors.
image point
trace in the Fresnel zone of the scatterer at the image point if
||imaging ray| - |physical ray|| < wavelength /2

17. Smoothed energy and plane Fresnel zone
edge
Reflected Fresnel zone
line
point

18. Local semblance and line - plane Fresnel zone
edge
Fresnel zones corresponding to Edge diffractors minus the Fresnel zone of reflector. We subtracted reflected energy to separate it from diffracted energy.
line
point

19. Dipping scatterers (20º)
Dip plays an important role when considering Fresnel zones

20. An error in the estimation of the reflected/diffracted energy distribution by using wrong dip of the scatterer.

21. Synthetic example (N/S =2)

22. Synthetic example
Importance of using the right type of Fresnel zone for the imaging.

23. Synthetic example
Searching for the distribution of the diffracted energy along different directions of edges provides not only the orientation of the edges (right), but can help eliminating stacking noise during imaging (by steering the migration only along the proper Fresnel zones).

24. Synthetic example
Standard migration (right) vs. steered migration (left).

25. Kevitsa, Finland (First Quantum)
Field data example. Hard-rock seismic is a good example for its natural use of time imaging (small variations in seismic velocities – reflectivity is mostly caused by contrast in densities).

26. Thanks to Sasha Ziramov for PSTM processing!
Well constrained PSTM
Thanks to Sasha Ziramov for PSTM processing!

27. Edge diffractivity
PSTM vs edge diffractivity
depth ~ 590m

28. Azimuth of diffractors
Diffractivity with direction of edge diffractors
depth ~ 590m

29. Migration of diffractors
Standard PSTM (left) vs steered migration (right). Steered migration picks different features and is less noisy.

30. Conclusions
Compliment to other seismic methods in order to image small objects and edges:
faults, lenses, intrusions, …
Diffractions much weaker than reflections: need to be selective about used data – do not stack noise
Need to carefully consider dipping scatterers

31. Imaging seems to work, now what?
How amplitudes depend on shape of diffractors?
Invert for type of diffractor
For edge/line diffractors try AVO type analysis
Amplitude preserving steered migration
Passive sources - OK in 2D, difficult in 3D

32. Acknowledgements