Important Dates Rest of Term

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. Two-way time for central ray: Two-way time for any other ray, distance l/2 from the central ray: Separation in time is a half-cycle, thus: Therefore: or 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

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.