1. Common MidPoint (CMP) Records and Stacking
Environmental and Exploration Geophysics II
Common MidPoint (CMP) Records and Stacking
tom.h.wilson
Department of Geology and Geography
West Virginia University
Morgantown, WV
Tom Wilson, Department of Geology and Geography

2. Note that the stack trace compares quite well with the pure signal.
If we sum all the noisy traces together - sample by sample - we get the trace plotted in the gap at right. This summation of all 16 traces is referred to as a stack trace.
Note that the stack trace compares quite well with the pure signal.
Greenbrier
Huron
Onondaga
Where i is the trace number and j is a specific time
Tom Wilson, Department of Geology and Geography

3. See Feynman Lectures on Physics, Volume 1.
Noise
Noise comes in several forms - both coherent and random. Coherent noise may come in the form of some unwanted signal such as ground roll. A variety of processing and acquisition techniques have been developed to reduce the influence of coherent noise.
Random noise can come in the form of wind, rain, mining activities, local traffic, microseismicity ... +1 -1
The basic nature of random noise can be described in the context of a random walk -
See Feynman Lectures on Physics, Volume 1.
Tom Wilson, Department of Geology and Geography

4. The random walk attempts to follow the progress one achieves by taking steps in the positive or negative direction purely at random - to be determined, for example, by a coin toss. +1 -1
Tom Wilson, Department of Geology and Geography

5. Does the walker get anywhere?
Our intuition tells us that the walker should get nowhere and will simply wonder about their point of origin.
However, lets take a look at the problem form a more quantitative view.
It is easy to keep track of the average distance the walker departs from their starting position by following the behavior of the average of the square of the departure. We write the average of the square of the distance from the starting point after N steps as
The average is taken over several repeated trials.
Tom Wilson, Department of Geology and Geography

6. will always equal 1 ( the average
After 1 step
will always equal 1 ( the average
of +12 or -12 is always 1. After two steps -
which is 0 or 4 so that the average is 2. After N steps
Tom Wilson, Department of Geology and Geography

7. from the starting point.
Averaged over several attempts to get home the wayward wonderer gets on average to a distance squared
from the starting point.
Since
=1, it follows that
and therefore that
Tom Wilson, Department of Geology and Geography

8. See Feynman Lectures on Physics, Volume 1.
The results of three sets of random coin toss experiments
See Feynman Lectures on Physics, Volume 1.
Tom Wilson, Department of Geology and Geography

9. The implications of this simple problem to our study of seismic methods relates to the result obtained through stacking of the traces in the common midpoint gather.
The random noise present in each trace of the gather (plotted at left) has been partly but not entirely eliminated in the stack trace.
Just as in the case of the random walk, the noise appearing in repeated recordings at the same travel time, although random, does not completely cancel out
Tom Wilson, Department of Geology and Geography

10. Hence, the ratio of signal to noise is or just
The relative amplitude of the noise - analogous to the distance traveled by our random walker- does not drop to zero but decreases in amplitude relative to the signal.
If N traces are summed together, the amplitude of the resultant signal will be N times its original value since the signal always arrives at the same time and sums together constructively.
The amplitude of noise on the other hand because it is a random process increases as
Hence, the ratio of signal to noise is
or just
where N is the number of traces summed together or the number of traces in the CMP gather.
Tom Wilson, Department of Geology and Geography

11. In the example at left, the common midpoint gather consists of 16 independent recordings of the same reflection point.
The signal-to-noise ratio in the stack trace has increased by a factor of 16 or 4.
The number of traces that are summed together in the stack trace is referred to as its fold – i.e. 16 fold.
Tom Wilson, Department of Geology and Geography

12. Question -
If you had a 20 fold dataset and wished to improve its signal-to-noise ratio by a factor of 2, what fold data would be required?
Square root of 20 = 4.472
Square root of N(?) = 8.94
What’s N
N=80
To double the signal to noise ratio we must quadruple the fold
Tom Wilson, Department of Geology and Geography

13. The reliability of the output stack trace is critically dependant on the accuracy of the correction velocity.
Tom Wilson, Department of Geology and Geography

14. Stack = Summation Average Amplitude
Accurate correction ensures that the same part of adjacent waveforms are summed together in phase.
Tom Wilson, Department of Geology and Geography

15. If the stacking velocities are incorrect ….
then the reflection response will be “smeared out” in the stack trace through destructive interference between traces in the sum.
Tom Wilson, Department of Geology and Geography

16. The real world: multilayer reflections
Are they also hyperbolic?
The two-term approximation to the multilayer reflection response is hyperbolic. The velocity in this expression is a root-mean-square velocity.
Tom Wilson, Department of Geology and Geography

17. A series of infinite terms – but we just ignore a bunch of them
The sum of squared velocity is weighted by the two-way interval transit times ti through each layer.
Tom Wilson, Department of Geology and Geography

18. The approximation is hyperbolic, whereas the actual is not
The approximation is hyperbolic, whereas the actual is not. The disagreement becomes significant at longer offsets, where the actual reflection arrivals often come in earlier that those predicted by the hyperbolic approximation.
Tom Wilson, Department of Geology and Geography

19. Refraction into high velocity layers brings the events in along paths that don’t have hyperbolic moveout.
Greenbrier Limestone
Big Injun
The reason for this becomes obvious when you think of the earth as consisting of layers of increasing velocity. At larger and larger incidence angle you are likely to come in at near critical angles and then will travel significant distances at higher than average (or RMS) velocity.
Tom Wilson, Department of Geology and Geography

20. Different kinds of velocity
VRMS VAV and VNMO are different. VNMO does not equal VRMS. Each of these 3 velocities has different geometrical significance.
Tom Wilson, Department of Geology and Geography

21. In actuality the moveout velocity varies with offset.
The VNMO is derived form the slope of the regression line fit to the actual arrivals.
In actuality the moveout velocity varies with offset.
The RMS velocity corresponds to the square root of the reciprocal of the slope of the t2-x2 curve for relatively short offsets.
Tom Wilson, Department of Geology and Geography

22. The general relationship between the average, RMS and NMO velocities is shown at right.
Tom Wilson, Department of Geology and Geography

23. Geometrically the average velocity characterizes travel along the normal incidence path.
The RMS velocity describes travel times through a single layer having the RMS velocity. It ignores refraction across individual layers.
Tom Wilson, Department of Geology and Geography

24. Other benefits derived from Stacking
Seeing double?
Tom Wilson, Department of Geology and Geography

25. Water Bottom Reflection
Normal Incidence Time Section ….
Water Bottom Reflection
Reflection from Geologic interval
Water Bottom Multiple
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26. Interbed Multiples DEPTH
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27. Interbed Multiples
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28. The Power of Stack extends to multiple attenuation
Tom Wilson, Department of Geology and Geography

29. The NMO Corrected CDP gather
Velocities associated with primary reflections are higher than those associated with multiples. The primaries are flattened out while residual moveout remains with the multiple reflection event.
The NMO Corrected CDP gather
Tom Wilson, Department of Geology and Geography

30. Multiple attenuation Primary Reflections Multiple Multiple
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31. Examples of multiples in marine seismic data
Buried graben or multiple
Tom Wilson, Department of Geology and Geography

32. Multiples are considered “coherent” noise or unwanted signal
Tom Wilson, Department of Geology and Geography

33. Interbed multiples or Stacked pay zones
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34. Tom Wilson, Department of Geology and Geography

35. Waterbottom and sub-bottom multiples
Tom Wilson, Department of Geology and Geography

36. Other forms of coherent “noise” will also be attenuated by the stacking process.
The displays at right are passive recordings (no source) of the background noise.
The hyperbolae you see are associated with the movement of an auger along a panel face of a longwall mine.
Tom Wilson, Department of Geology and Geography

37. Problem 4.4
Table 1 (right) lists reflection arrival times for three reflection events observed in a common midpoint gather. The offsets range from 3 to 36 meters with a geophone spacing of 3 meters.
Conduct velocity analysis of these three reflection events to determine their NMO velocity. Using that information, determine the interval velocities of each layer and their thickness.
Offset (m)
Reflection1
Reflection2
Reflection3 x
t1 (ms)
t2 (ms)
t3 (ms) 3
21.4
62.3
79.4 6 25
62.4
79.5 9
30.1
62.6
79.6 12
36.1
62.9
79.9 15
42.5
63.2
80.1 18
49.2
63.6
80.5 21
56.2
64.1
80.9 24
63.3
64.7
81.3 27
70.4
65.4
81.8 30
77.6
66.1
82.4 33
84.9
66.9 83 36
92.2
67.7
83.7
Tom Wilson, Department of Geology and Geography

38. Note hyperbolic moveout of the three reflection events.
Tom Wilson, Department of Geology and Geography

39. The variables t2 and x2 are linearly related.
Recall - 2 2
t - x
The variables t2 and x2 are linearly related.
Tom Wilson, Department of Geology and Geography

40. Estimates of RMS velocities can be determined from the slopes of regression lines fitted to the t2-x2 responses.
Keep in mind that the fitted velocity is actually an NMO velocity!
Then what?
Tom Wilson, Department of Geology and Geography

41. Dix Interval Velocity Start with definition of the RMS velocity
The Vis are interval velocities and the tis are the two-way interval transit times.
Tom Wilson, Department of Geology and Geography

42. the two-way travel time of the nth reflector
Let
the two-way travel time of the nth reflector
Tom Wilson, Department of Geology and Geography

43. hence
Tom Wilson, Department of Geology and Geography

44. Vn is the interval velocity of the nth layer
Since
Vn is the interval velocity of the nth layer
tn in this case represents the two-way interval transit time through the nth layer
Tom Wilson, Department of Geology and Geography

45. Hence, the interval velocities of individual layers can be determined from the RMS velocities, the 2-way zero -offset reflection arrival times and interval transit times.
Tom Wilson, Department of Geology and Geography

46. Review: terms in the Dix Equation
See Berger et al. page 173
The
terms represent the velocities obtained from the best fit lines. Remember these velocities are actually NMO velocities.
the two-way travel time to the nth reflector surface
the two-way interval transit time between the n and n-1 reflectors
is the interval velocity for layer n, where layer n is the layer between reflectors n and n-1
Tom Wilson, Department of Geology and Geography

47. You put these ideas into application when solving problems 4.4 and 4.8
Dix Interval Velocity
The interval velocity that’s derived from the RMS velocities of the reflections from the top and base of a layer is referred to as the Dix interval velocity.
However, keep in mind that we really don’t know what the RMS velocity is.
The NMO velocity is estimated from the t2-x2 regression line for each reflection event and that NMO velocity is assumed to “represent” an RMS velocity.
You put these ideas into application when solving problems 4.4 and 4.8
Tom Wilson, Department of Geology and Geography

48. Scattered waves from off line
Coherent Noise
Stacking helps attenuate random and coherent noises
Multiples
Refractions
Air waves
Ground Roll
Streamer cable motion
Scattered waves from off line
Tom Wilson, Department of Geology and Geography

49. Back to your computer projects
Back to your computer projects. Please review the Summary Activities and Report Handout. We are at the mid point in the semester and time will run out quickly.
Questions about gridding and math on two maps topics covered in the last lecture?
Tom Wilson, Department of Geology and Geography

50. Conversion to Depth
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51. Average velocity map
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52. Without Extrapolation
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53. With Extrapolation
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54. Increased projection distance
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55. Time Surface
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56. Tom Wilson, Department of Geology and Geography

57. Wells > Edit > Time Depth Charts
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58. Interval Velocity
Tom Wilson, Department of Geology and Geography

59. Formation top approach (times derived from TD chart and formation top depths from well file)
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60. Time horizon
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61. Conversion to depth
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62. Time vs. Depth
Tom Wilson, Department of Geology and Geography

63. Mark your calendar Problem 4.1 is due today
Problems 4.4 and 4.8 are due 1st Wednesday following Spring Break.
Look over Exercises IV-V. These will be due 1st Monday after Spring Break.
Exercise VI will be due Wednesday after Spring Break
For the remainder of today – Conversion to depth and project work.
Mid Term Reports are due the Monday March 23rd.
Tom Wilson, Department of Geology and Geography