1. Seismic Resolution Lecture 8 * Layer Thickness top 20 ms base 1 10 2030
base
top *
SLIDE 1
Slide introduces topic: Seismic Resolution
This shows a simple sediment wedge model and its seismic expression – we’ll talk about it in this lecture
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L 9 – Seismic Resolution

2. Vertical Resolution Lateral Resolution Outline Resolution vs Detection
Thin Bed Response and Tuning
Lateral Resolution
Fresnel Zone
Migration and Lateral Resolution
SLIDE 2
We need to discuss two components of seismic resolution:
Vertical resolution
Lateral resolution
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L 9 – Seismic Resolution

3. Detection vs. Resolution - Analogy
You are driving at night.
You spot a light in the distance.
Is it a car or a motorcycle???
Aha, it is a car!
SLIDE 3
Here is an analogy that we can all relate to:
You are driving at night
You spot a light in the distance coming towards you
You wonder, I seem to see only 1 light; is it a car or a motorcycle
As the vehicle gets never, we realize it is not a single light but two headlamps – so it is a car
You first detected some light and know there was a vehicle
It was not until the vehicle was closer that we were able to resolve two headlights and realize it was a car
This analogy helps explain the difference between
Detecting something with seismic data, and
Resolving two closely-spaced objects
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L 9 – Seismic Resolution

4. Resolution vs. Detection
Detection: Ability to identify that some feature exists
Resolution: Ability to distinguish two features from one another
Detection limit is always smaller than the resolution limit
Detection limit depends upon Signal-to-Noise
SLIDE 4
Detection is the ability to identify that some feature exists
Resolution is the ability to distinguish two features from one another
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L 9 – Seismic Resolution

5. Vertical Resolution
Gamma Ray
What is the minimum vertical distance between two subsurface features such that we can tell them apart seismically?
Shale
Baseline
Shale
SLIDE 5
As an example of vertical resolution, consider the geology indicated by the gamma ray log
At a gross scale, there is a thick shale unit on top of a thick sand unit
But the sand unit has a thin shale layer interfingered with it near the top
Low resolution seismic data would detect a shaley unit sitting on top of a sandy unit - one interface
Seismic data with high resolution would resolve 3 interfaces, identifying the thin shale unit within the predominantly sandy unit Sd
For Example:
Based on seismic data, could you determine that there is a thin shale layer between the two sands?
Sand
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L 9 – Seismic Resolution

6. Thick Bed Response A Dp B C Question: What is a thick bed?
Wavelet 1 ends before
Wavelet 2 begins
Question: What is a thick bed?
Impedance
R. C.
Wavelet 1
Wavelet 2
Composite A
Top of Bed
Response Dp NO
Interference B
SLIDE 6
To further explain vertical resolution, let’s begin by considering a thick sand (unit B) sandwiched between shales (units A and C)
The RC at the top and base of the sand are shown along with the individual wavelets
Note the pulse duration is less than the thickness of the sand unit
The wavelet associated with the upper RC is fully represented (going down) before the wavelet associated with the lower RC starts
There is no wavelet interference
A thick bed is one in which the bed thickness in units of two-way time is greater than the pulse duration C
Base of Bed
Response
Answer: A thick bed is one that has a TWT > Dp
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L 9 – Seismic Resolution

7. 2nd half-cycle from Wavelet 1 and 1st half-cycle from Wavelet 2
Partial Interference
TWT thickness = 0.9 * Dp
Wavelet 2 starts before
Wavelet 1 ends
Impedance
R. C.
Wavelet 1
Wavelet 2
Composite A
Top of Bed
Response B Dp
Some
Interference C
SLIDE 7
Here the thickness of unit B has been decreased to 0.9 times the pulse duration
The wavelet associated with the upper RC does not complete (going down) before the wavelet associated with the lower RC starts
There is some wavelet interference – the end of the “upper” wavelet overlaps the top of the “lower” wavelet
An interpreter still would be able to distinguish two RCs, but the trough is a “doublet”
Base of Bed
Response
2nd half-cycle from Wavelet 1
and 1st half-cycle from Wavelet 2
form a trough doublet
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L 9 – Seismic Resolution

8. Maximum Interference - Tuning
TWT thickness = ½ Dp
Wavelet 2 starts before
Wavelet 1 ends
Impedance
R. C.
Wavelet 1
Wavelet 2
Composite A
Top of Bed
Response B Dp
Maximum
Interference C
Base of Bed
Response
SLIDE 8
On this slide, the thickness of unit B has been decreased to 1/2 the pulse duration
The second part of the wavelet associated with the upper RC overlaps with the first half of the wavelet associated with the lower RC
Wavelet interference is at a maximum
The trough is larger by about a factor of two than if there was only one RC
It is more difficult for an interpreter to distinguish two RCs
2nd half-cycle from Wavelet 1
and 1st half-cycle from Wavelet 2
are completely in phase
resulting in 2x amplitude
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L 9 – Seismic Resolution

9. Determining Vertical Resolution
Input Parameters:
Velocity at the zone of interest
Peak Frequency of the pulse at the zone of interest
Period
(ms)
wavelength =
period X velocity
Pulse
Computations:
Period = 1/Peak Frequency
Wavelength = Period * Velocity
Limit of Vertical Resolution = Wavelength/4
SLIDE 9
To determine seismic resolution, there are two parameters we need to know or estimate
The velocity in the zone we are interested in
The peak frequency of the pulse in the zone of interest
We need to calculate the wavelength of the data
Vertical resolution is ¼ the wavelength
The calculation is shown in the center of the slide
We get the period from 1/peak frequency
We then get the wavelength by multiplying the period by the velocity
If you prefer, wavelength = velocity / peak frequency (simple substitution)
Next we divide the calculated wavelength by 4 to get the vertical resolution
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L 9 – Seismic Resolution

10. A Simple Exercise - 2 Zones
SLIDE 10
Time for an exercise
You will calculate the vertical frequency for:
A shallow zone
A deep zone
The next slide has the ANSWER
Have the students do the exercise before proceeding
Calculating Vertical Resolution
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L 9 – Seismic Resolution

11. Typical Vertical Resolution
Shallow Event
Velocity = 2000 Meters / sec
Pulse:
Center Frequency = 50 Hz
Period = 1 / 50 = sec
Wavelength = .020 x 2000 = 40 Meters
Limit of resolution = 40 /4 = 10 Meters
Deep Event
Velocity = Meters / sec
Pulse:
Center Frequency = 20 Hz
Period = 1 / 20 = sec
Wavelength = x = 150 Meters
Limit of resolution = 150 / 4 = Meters
SLIDE 11
ANSWER
The shallow zone of interest has a wavelength of 40 meters; a vertical resolution of 10 meters
The deep zone of interest has a wavelength of 150 meters; a vertical resolution of 37 meters
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L 9 – Seismic Resolution

12. Summary: Vertical Resolution
Resolution is the ability to distinguish distinct events
Thin bed response occurs below tuning thickness
Short-duration seismic pulses are preferred
Broad bandwidth, zero-phase pulses are best
Pulses with minimal side-lobe energy enhance interpretability
To Improve Resolution
Bandwidth can be increased by deconvolution
Frequencies to be included must have adequate S/N
SLIDE 12
To summarize our discussion of vertical resolution:
Resolution is the ability……
Thin bed response ……
Short-duration …….
To improve ……
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L 9 – Seismic Resolution

13. What Is Lateral Resolution?
Would we image the narrow horst?
Would we image all three channel sands?
SLIDE 13
What do we mean by lateral resolution?
It means how wide does a feature have to be for us to correctly resolve it
For example, in the upper diagram, there is a narrow horst block in the center
If this horst is only 10 meters wide, we probably would not resolve the two edges.
If it was 2 km wide, we would not have any problem resolving the horst
What is the minimum width for which we could resolve both edges?
This is why we want to know the lateral resolution of the seismic data
In the lower diagram, we have three channel deposits of different widths
Would we resolve all three; or only the widest one
Again, this is why we want to know the lateral resolution of the seismic data
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L 9 – Seismic Resolution

14. Lateral Resolution
What is the minimum horizontal distance between two subsurface features such that we can tell them apart seismically?
Neidell & Poggiaglioimi, 1977
SLIDE 14
Here is a ‘classic’ seismic model presented by Neidell & Poggiaglioimi, 1977
In the model there is a reflector (upper black line) that has gaps in it of varying width
On the next slide, we will explain what a Fresnel zone (FZ) is; for now
Accept that the first gap = 2x the FZ
The second gap = 1x the FZ
Etc.
The lower part of the figure shows the modeled seismic response (unmigrated)
Looking at the modeled seismic, we would:
Recognize the first gap
Probably recognize the second gap
Would wonder if the third gap is a break in the reflector
And probably not recognize any break for the fourth gap
Remember, the model is ‘noise-free’
AAPG©1977 reprinted with permission of the AAPG whose permission is required for further use.
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L 9 – Seismic Resolution

15. The Fresnel Zone
An event observed at a detector is reflected from a zone of points
The raypaths from source to detector which differ in length by less than a quarter wavelength can interfere constructively
The portion of the reflector from which they add constructively is the Fresnel zone
SLIDE 15
As promised, we will now explain what a Fresnel zone (FZ) is
The seismic waves “illuminate” an area of a subsurface boundary – like the cone of light from a flashlight shining on a carpet
All the information within this “illuminated” area is “lumped together” or averaged
The size of this “illumination” circle equals the area in which the seismic wave is ¼ the wavelength of the pulse
The diameter of this circle is called the FZ
Shallow in the data the FZ is narrow; it gets progressively broader as we go deeper
Using our flashlight analogy:
If our flash light is close to the carpet, the circle of light is small
If our flash light is far from the carpet, the circle of light is large
Changes that occur within this zone are difficult to resolve
The size of the Fresnel zone depends upon the wavelength of the pulse and the depth of the reflector
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L 9 – Seismic Resolution

16. Migration Reduces Lateral Smearing
Ideal / Model
Response
800 m
Stack
No Migration
SLIDE 16
Fortunately for us, the data processing step called migration:
Not only better positions the reflections in 3D space, but
Also greatly improves lateral resolution
This slide shows a reflection indicating a strong decrease in impedance (zero phase central trough) on the left and a abrupt change to a moderate increase in impedance (zero phase central peak) on the right
The ideal response is in the upper figure
The real-world response is shown in the central figure – a stacked section without migration
The bottom shows what happens when seismic migration is applied to the data in the central figure
Note how the abrupt change in the center is “smeared” in the central figure
The FZ for this example is on the order of 800 m (red arrow)
Also note how the migration process has “cleaned up” the image and the abrupt change is much better imaged
Image After
Migration
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L 9 – Seismic Resolution

17. Good Migration Enhances Resolution
SLIDE 17
Here is a seismic line with two types of migration:
On the left a standard (fast,cheap) migration algorithm was used
On the right, a more sophisticated (more time, money, people-hours) algorithm was used
Note the fault on each image
The termination of reflections are much sharper on the right; the fault can be more precisely drawn
On the left the reflection terminations are more “smeared” since the lateral resolution is much lower
Standard Migration
High-end Migration
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L 9 – Seismic Resolution

18. Fresnel Zone Equations
Pre-Migration
Post-Migration
Fd = Vavg T/F
Fd = λ /4 = Vavg /4 F
where:
Fd = Fresnel Diameter
Vavg = Average Velocity
T = Time
F = Frequency of Pulse
λ = Wavelength
SLIDE 18
Here are the equations that we use to calculate the Fresnel diameter
The equation on the left is for data that have not been migrated
The parameters are the average velocity down to the zone of interest, the time down to the zone of interest, and the frequency at the zone of interest
The equation on the right is for data that has had a seismic migration process applied to it
The parameters are the wavelength of the pulse at the zone of interest; or by substitution the average velocity and the frequency
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L 9 – Seismic Resolution

19. Another Simple Exercise - 2 Zones
SLIDE 19
Let’s do another exercise
You will be given the necessary parameters for:
A shallow zone
A deep zone
The ANSWER is on the next slide
Give the students some time to work the exercise
Calculating Fresnel Zone Diameters
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L 9 – Seismic Resolution

20. Typical Lateral Resolution
Shallow Event
Time = 1.0 s
Vint = Vavg = 2000 m/s
Pulse = 50 Hz
PreMig Fresnel Diameter = 282 m
PostMig Fresnel Diameter = 10 m
Deep Event
Time = 5.0 s
Vint = 4600 m/s
Vavg = 3800 m/s
Pulse = 20 Hz
PreMig Fresnel Diameter = 1900 m
PostMig Fresnel Diameter = 47.5 m
SLIDE 20
ANSWER to the exercise
For the shallow zone – pre-migration, the FD is 282 m; after migration it is reduced to 10 meters – what an improvement
For the deep zone – pre-migration, the FD is 1900 m – almost 2 km; after migration it is reduced to 48 meters – another substantial improvement
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L 9 – Seismic Resolution

21. Graphical Answers Fresnel Zone Circles Shallow Window Deep Window
282 m pre-migration
10 m post-migration
SLIDE 21
This shows the area over which the seismic “smears” the geologic information from our last exercise
Note the 1 km scale bar
The small green circle in the upper left is the FD for the shallow zone before migration
There is a white circle in the center which is the FD after migration
The large circle on the right is the FD for the deep zone
The white circle in the center is the FD after migration
Even if the seismic reflections are fairly flat lying (horizontal), this shows the benefit of migrating the data – even though the reflctions are not repositioned very much since dips are very low
Deep Window
1900 m pre-migration
47.5 m post-migration
1 km
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L 9 – Seismic Resolution

22. Summary: Lateral Resolution
Migration enhances lateral resolution
Large aperture (receiver cable length) is needed for high lateral resolution
Fine spatial sampling is needed for high lateral resolution
Prestack migration provides better lateral resolution than poststack migration
Depth migration provides better resolution than time migration
SLIDE 22
In summary for lateral resolution:
Migration ……
Large aperture ….
Fine …..
Prestack ……
Depth migration …..
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L 9 – Seismic Resolution