1. Important Dates Rest of Term
Friday, Nov 30th – last day of term
Monday, Dec 3rd – only possible day for review session
Monday, Dec 10th – Final exam, 7 pm

2. Seismic resolution
Potential resolution of seismic data is very high (higher than any other geophysical method – except georadar)
Nevertheless, resolution is limited by the physics of the measurement
It is important to understand the physical limitations when interpreting seismic data

3. Seismic resolution
Most significant limitation is that caused by frequency content
Highest frequencies in the data are controlled by geology (remember the seismic Q factor?)
Recall the relationships:

4. Seismic resolution
Loss of frequency content can change the geological interpretation

5. Seismic resolution
Loss of frequency content can change the geological interpretation

6. Seismic resolution
Loss of frequency content can change the geological interpretation

7. Seismic resolution
Rayleigh’s criterion is a standard measure of resolution
Applied to astronomy it defines the angular separation two stars must have to be resolved by a given light frequency:
Two objects are said to be “resolved” if the maximum of the diffraction pattern for one source, falls on the first minimum of the diffraction pattern for the other source

8. Seismic resolution: vertical resolution
Rayleigh’s criterion can be applied to seismic reflections
In seismic terms, two reflection events (in time) must be separated by a half-cycle of the dominant frequency in the data
If the reflectors are too close together, they merge into a single reflector (the two beds are no longer resolved)

9. Seismic resolution: vertical resolution
For two events reflected from the top and bottom of a layer of thickness Δh, the time difference between reflections is
Rayleigh’s criterion is the two events should be separated by half-cycle, hence
Solving for the thickness (and using λ=v/f):
For example, if f=40 Hz, v= 4000 m/s, then λ=v/f=100 m: Rayleigh’s criterion predicts we could not resolve beds closer together than 25 m

10. Seismic resolution: vertical resolution
In this example, a thickness of λ/4 corresponds to 12 ms

11. Seismic resolution: vertical resolution
20 Hz
In this example, a pinch out is probed with a 20 Hz seismic signal. Position A is the location of the pinch out, B is the thickness given by the Rayleigh criterion, C is the location beyond which the true thickness can be measured.

12. Seismic resolution: vertical resolution
30 Hz
In this example, a pinch out is probed with a 30 Hz seismic signal. Position A is the location of the pinch out, B is the thickness given by the Rayleigh criterion, C is the location beyond which the true thickness can be measured.

13. Seismic resolution: vertical resolution
30 Hz, Reverse polarity
In this example, a pinch out is probed with a 30 Hz seismic signal. Position A is the location of the pinch out, B is the thickness given by the Rayleigh criterion, C is the location beyond which the true thickness can be measured.

14. Seismic resolution: vertical resolution
40 Hz
In this example, a pinch out is probed with a 40 Hz seismic signal. Position A is the location of the pinch out, B is the thickness given by the Rayleigh criterion, C is the location beyond which the true thickness can be measured.

15. Seismic resolution: vertical resolution
In this example, a series of faults with differing amounts of vertical throw (measured in wavelengths) are probed with a zero offset seismic section

16. Seismic resolution: lateral resolution
Lateral resolution is poorer than vertical resolution
This is because the wavelength limitation combines with the poor focussing issue of the zero-offset section
Contrary to intuition, energy does not return from a single subsurface point
A finite region of points on the reflector contributes to the reflected signal

17. Seismic resolution: lateral resolution
A finite region of points on the reflector contributes to the reflected signal
“Fresnel Zone”: that part of the reflector from which energy is returned within a half-wavelength of the central ray
All such energy contributes constructively to the reflection pulse
The pulse is thus a mixture of contributions from this zone

18. Seismic resolution: lateral resolution
“Fresnel Zone”: that part of the reflector from which energy is returned within a half-wavelength of the central ray d
Two-way time for central ray:
, l
Two-way time for any other ray, distance l/2 from the central ray:
Separation in time is a half-cycle, thus:
Therefore: or

19. Seismic resolution: lateral resolution
“Fresnel Zone”: that part of the reflector from which energy is returned within a half-wavelength of the central ray d
, l
Using the previous example, if f=40 Hz, v= 4000 m/s, then λ=v/f=100 m:
Rayleigh’s criterion predicts we could not resolve beds closer together than 25 m
The Fresnel zone at 3 km depth is

20. Seismic resolution: lateral resolution
“Fresnel Zone”: that part of the reflector from which energy is returned within a half-wavelength of the central ray d
, l
Note that the formula predicts the Fresnel zone gets bigger with depth – the deeper a structural feature is, the poorer is the lateral resolution of the seismic data!

21. Seismic resolution: lateral resolution
Note that the formula predicts the Fresnel zone gets bigger with depth – the deeper a structural feature is, the poorer is the lateral resolution of the seismic data!
In the example, the four gaps in the reflector are less resolved the deeper the reflector is in the section.
Note: the diffractions are causing this poor resolution – migration will collapse the diffractions and restore resolution.