1. Environmental and Exploration Geophysics II
Amplitude, Frequency and Bandwidth and their relationship to Seismic Resolution
tom.h.wilson
Department of Geology and Geography
West Virginia University
Morgantown, WV
Tom Wilson, Department of Geology and Geography

2. Frequency content of seismic signals
Duration of sound is decreased by adding in lots of frequencies. Having a short duration sound helps you resolve the top and bottom of layers that are close together in time.
Tom Wilson, Department of Geology and Geography

3. The range of frequencies present in the wavelet controls its ability to resolve the top and bottom of a layer of given thickness.
Recall our general introduction to the concept of the wavelet earlier in the semester.
The wavelet or transient mechanical disturbance generated by the source can be thought of as a superposition or summation of sinusoids with varying frequency and amplitude.
Tom Wilson, Department of Geology and Geography
Hilterman, 1985

4. The examples below illustrate the effect of increasing the frequency range or bandwidth of the wavelet.
See sumofcosines.xls
O. Ilmaz, 1987
Tom Wilson, Department of Geology and Geography

5. The following simple example helps illustrate the concept of an amplitude spectrum. Below is a signal consisting of two sinusoids.
Tom Wilson, Department of Geology and Geography

6. Each sinusoid is associated with a specific frequency
Each sinusoid is associated with a specific frequency. There are two frequency components. The 32 sample per cycle component has a frequency of 4 and the 8 samples per cycle component has a frequency of 16. The amplitude of the 32 sample/cycle component is twice that of the 8 sample/cycle component.
The frequency spectrum (above) of the “signal” at the top of the previous slide is an equivalent representation of the signal.
Tom Wilson, Department of Geology and Geography

7. Frequency domain Time domain O. Ilmaz, 1987
Tom Wilson, Department of Geology and Geography

8. Individual frequency components
Amplitude spectrum
Phase spectrum
Individual frequency components
Time-domain wavelets
Zero Phase
Minimum Phase
Tom Wilson, Department of Geology and Geography
Hilterman, 1985

9. Extracting information about wavelet frequency content from an isolated reflection event.
The dominant period (c) of the response corresponds to the time from one peak to the next or from one trough to the next. The reciprocal of this dominant period is a measure of the dominant frequency (fc) of the signal or wavelet spectrum.
The reciprocal of the half-width of the response-envelop (b) provides an estimate of the bandwidth (fb) of the signal spectrum.
Tom Wilson, Department of Geology and Geography
Hilterman, 1985

10. The dominant frequency and bandwidth measured from the time-domain representation of the signal wavelet can be used to provide a sketch of the wavelet spectrum.
Just as importantly these measures can be related directly to the resolution properties of the seismic wavelet.
Hilterman, 1985
Tom Wilson, Department of Geology and Geography

11. Negative reflection coefficient
Review your basic understanding of how the composite seismic signal arises in terms of horizon reflection coefficients and the seismic wavelet. The view below provides a temporal view of reflection shape.
Shape of up-going wave is reversed
Negative reflection coefficient
Tom Wilson, Department of Geology and Geography
Exxon in-house course notes

12. Positive reflection coefficient
These are minimum phase wavelets
Shape of up-going wave is unchanged
Positive reflection coefficient
Exxon in-house course notes
Tom Wilson, Department of Geology and Geography

13. Positive reflection coefficient Negative reflection coefficient
Reflection interference
Positive reflection coefficient
<Lead cycle
positive
<Follow cycle
Negative reflection coefficient
<Lead cycle
negative
<Follow cycle
Tom Wilson, Department of Geology and Geography
Exxon in-house course notes

14. Reflection from the base of the layer
Decrease the two-way travel time between reflection coefficients
<Lead cycle
<Follow cycle
Lead cycle >
Reflection from the base of the layer
If the two layers are located closer together we get to a point where the second cycle in the reflected wavelet from the top of the layer overlaps the lead cycle in the wavelet reflected from the base of the layer. This occurs at two-way time equal to 1/2 the dominant period of the wavelet (or ½ the dominant cycle).
Tom Wilson, Department of Geology and Geography
Exxon in-house course notes

15. Exxon in-house course notes
Sum of reflection amplitudes from overlap in the top and base reflections
At this point there is maximum constructive interference between the reflections from the top and bottom of the layer. The composite reflection event (at right above) reaches maximum negative value in this case.
Tom Wilson, Department of Geology and Geography
Exxon in-house course notes

16. Referred to as 0-phase since all frequency components are in phase
Dominant (or peak) frequency and wavelet phase (shape).
Referred to as 0-phase since all frequency components are in phase
Minimum
Phase
Zero
Phase
The peak period of the wavelet can be determined using peak-to-trough times which correspond to one half the dominant period of the wavelet. Multiply those times by two to get the dominant period.
Tom Wilson, Department of Geology and Geography

17. Reflection Coefficients
trough
Side lobe
peak
Maximum constructive interference illustrated for the zero phase wavelet. The peak-to-trough time equals c/2, which also equals delay time between consecutive reflection events
Tom Wilson, Department of Geology and Geography

18. Tom Wilson, Department of Geology and Geography

19. The Convolutional Model and Seismic Resolution (continued)
Environmental and Exploration Geophysics II
The Convolutional Model and Seismic Resolution (continued)
tom.h.wilson
Department of Geology and Geography
West Virginia University
Morgantown, WV
Tom Wilson, Department of Geology and Geography

20. Exxon in-house course notes
Once the separation in time drops to less than half the dominant period of the wavelet destructive interference in the reflections from the top and bottom of the layer will occur.
However, as the layer continues to thin, the dominant period of the composite reflection event does not drop below 1/c. The amplitude of the composite continues to drop. But not the period.
Tom Wilson, Department of Geology and Geography
Exxon in-house course notes

21. Seismic Wavelet trough Side lobe peak
Maximum Constructive Interference
Seismic Wavelet
trough
Side lobe
peak
Two-way interval time separating reflection coefficients is c/2
The peak-to-trough time equals c/2.
Tom Wilson, Department of Geology and Geography

22. Model of a thinning layer
15,000 fps
11,300 fps
Low velocity sand
19,000 fps
Tom Wilson, Department of Geology and Geography

23. These amplitude relationships are summarized below in the model seismic response of a thinning layer similar to that shown in the preceding slides.
Zero phase wavelet
Tom Wilson, Department of Geology and Geography

24. The amplitude difference - trough-to-peak remains constant for two-way travel times much greater than half the dominant period.
As the top and bottom of the layers merge closer and closer together, the lead cycle in the reflection from the base of the layer overlaps with the follow-cycle in the reflection from the top and the amplitude of the composite reflection event begins to increase.
Destructive interference
Thickness =Vt/2
Tom Wilson, Department of Geology and Geography

25. Layer thickness is simply Vt/2, where t is the two-way interval transit time. Tuning occurs at two-way times equal to one-half the dominant period (c/2). If the interval velocity of the layer in question is known, the dominant period can be converted into the tuning thickness.
In this plot the conversion to thickness has already been made. Compute c.
Let layer thickness = d; then
d=?
Destructive interference
Tom Wilson, Department of Geology and Geography

26. Difference of arrival time between the reflections from the top and bottom of the layer decreases abruptly at about 8 milliseconds.
8 milliseconds represents the two-way travel time through the layer; it is also the time at which tuning occurs and is half the dominant period of the seismic wavelet.
8 milliseconds is c/2 and the two way time through the layer. Thus, c/4 is the one-way time through the layer.
Tom Wilson, Department of Geology and Geography

27. 11,300 f/s * 0.004s = 45.2 feet
c/4, the one-way time through the layer, equals 4 milliseconds. The interval velocity in the layer is 11,300 f/s. Hence, the thickness of the layer at this point is ~45 feet. This is the tuning thickness or minimum resolvable thickness of the layer obtainable with the given seismic wavelet.
Tom Wilson, Department of Geology and Geography

28. Broader spectra produce sharper, shorter duration wavelets
Amplitude spectra and wavelets
What is the amplitude spectrum of wavelet #5?
Broader spectra produce sharper, shorter duration wavelets
Ilmaz, 1987
Tom Wilson, Department of Geology and Geography

29. Spectral bandwidth, wavelet duration in the time domain and resolution
Spectral bandwidth, wavelet duration in the time domain and resolution. C is only one parameter that affects resolution. b is also an important parameter.
Greatest Bandwidth
Smallest Bandwidth
Tom Wilson, Department of Geology and Geography
Hilterman, 1985

30. The Convolutional Model
Hilterman, 1985
Physical nature of the seismic response
Tom Wilson, Department of Geology and Geography

31. Exxon in-house course notes1 1
The seismic response is dominated by reflections from layers 1 and 2. We see two prominent events. They are delayed because the wavelet phase is minimum. 2a 2a 2b 2b
The output is a superposition of reflections from all acoustic interfaces
Tom Wilson, Department of Geology and Geography
Exxon in-house course notes

32. The wavelet in this case is also minimum phase
Tom Wilson, Department of Geology and Geography

33. Subsurface structure - North Sea
One additional topic to consider is the process of wavelet deconvolution. As you’ve seen already, wavelet shape can affect geologic interpretations …. Consider the following structural model
Subsurface structure - North Sea
Tom Wilson, Department of Geology and Geography
Neidel, 1991

34. Potential hydrocarbon trap?
Below is the synthetic seismic response computed for the North Sea model.
Potential hydrocarbon trap?
Consider part 2 of the handout
Tom Wilson, Department of Geology and Geography
Neidel, 1991

35. Consider the effect of wavelet shape on the geologic interpretation of seismic response. In the case shown below, the primary reflection from the base of the Jurassic shale crosses a side-lobe in the wavelet reflected from the overlying basal Cretaceous interval.
Tom Wilson, Department of Geology and Geography
Neidel, 1991

36. wavelet compression
Deconvolution is a filter operation which compresses and simplifies the shape of the seismic wavelet. Deconvolution improves seismic resolution and simplifies interpretation.
Tom Wilson, Department of Geology and Geography

37. Neidel, 1991
North Sea Seismic display after deconvolution. The geometrical interrelationships between reflectors are clearly portrayed.
Tom Wilson, Department of Geology and Geography

38. Any questions about today’s exercises?
Using the estimation procedure discussed in class today measure the appropriate feature on the above seismic wavelet and answer the following questions:
What is the minimum resolvable thickness of a layer having an interval velocity of 10,000fps? Show work on your handout
What is the phase of the wavelet? Why do you say that?
Tom Wilson, Department of Geology and Geography

39. Phase and resolution footnote:
The zero-phase wavelet is also considered to have higher resolving power. It is generally more compact than the equivalent minimum phase wavelet and is, overall, easier to interpret.
The exploration data is in a zero phase format.
Tom Wilson, Department of Geology and Geography
Hilterman, 1985

40. Zero versus minimum Hilterman, 1985
Tom Wilson, Department of Geology and Geography
Hilterman, 1985

41. Questions? If you haven’t already … finish reading chapter 4!
Tom Wilson, Department of Geology and Geography