1. MOSRP Multiple Attenuation Review
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MOSRP Multiple Attenuation Review
Ken Matson, BP EPTG, Houston
Nov, 2003
Title slide
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Outline
2D Free-Surface Demultiple (SRME) approximations in practice: what can go wrong?
Internal multiple attenuation
Inverse Scattering
How and why does it work
Wavelet and subtraction issues as compared with SRME
Effect of transmission on amplitudes
Delphi Internal Demultiple
Layer and interface methods
How and why do they work?
Relationship to Inverse Scattering method

3. Some practical approximations made in 2D SRME application
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Some practical approximations made in 2D SRME application
3D Earth (assumes 2D earth shot in dip direction)
3D acquisition geometry (e.g.,feather, multi-cable shooting)
Single term prediction followed by minimum energy adaptive subtraction (e.g., potential damage to primaries, less effective in shallow water).
Minimum energy wavelet estimation (e.g.,corrupted by 3D effects above)
Missing near (and far) offsets and inadequate methods to estimate them
Aliasing
Missing shots (coarse shot interval or gaps in shooting)
Obliquity factor missing
Ghosts not removed
Source and receiver depths not corrected
Air-water interface not a perfect free-surface (sea state?)
Source and receiver arrays not corrected for
3D -> 2D amplitudes not properly corrected for
Direct wave not removed (e.g., water too shallow to mute) …

4. Despite these approximations, the method still works very well …
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Despite these approximations, the method still works very well …
Input
Output
But there is room for
improvement …

5. Some practical approximations made in 2D SRME application
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Some practical approximations made in 2D SRME application
3D Earth (assumes 2D earth shot in dip direction)
3D acquisition geometry (e.g.,feather, multi-cable shooting)
Single term prediction followed by minimum energy adaptive subtraction (e.g., potential damage to primaries, less effective in shallow water).
Minimum energy wavelet estimation (e.g.,corrupted by 3D effects above)
Missing near (and far) offsets and inadequate methods to estimate them
Aliasing
Missing shots (coarse shot interval or gaps in shooting)
Obliquity factor missing
Ghosts not removed
Source and receiver depths not corrected
Air-water interface not a perfect free-surface (sea state?)
Source and receiver arrays not corrected for
3D -> 2D amplitudes not properly corrected for
Direct wave not removed (e.g., water too shallow to mute) …

6. Internal Multiple Attenuation
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Internal Multiple Attenuation
Free-surface multiple
Internal multiple
One or more reflections from
the air-water interface
All downward reflections below the
air-water interface

7. Free-surface multiple prediction (SRME)
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Free-surface multiple prediction (SRME)
Multiples are predicted by the time convolution of subevents
Sub-event 1
Sub-event 2 a b c

8. Inverse Scattering Internal Demultiple
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Inverse Scattering Internal Demultiple
Requires no subsurface information
Predicts the arrival time of all internal multiples exactly
Predicts the amplitudes of internal multiples approximately
(Much) more computationally demanding than free-surface multiple attenuation

9. Inverse Scattering Internal demultiple: 1D version
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Inverse Scattering Internal demultiple: 1D version
For all interfaces:
b1(t1)
b1(t2)
b1(t3)
b1(w) b1(-w) b1(w)

10. Inverse Scattering Internal demultiple: 1D version
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Inverse Scattering Internal demultiple: 1D version
For a selected 3 subevents that satisfy the lower-higher-lower criteria:
Sub-event 2 a b c d
Sub-event 1
Sub-event 3
SE1(w) SE2(-w) SE3(w)

11. Inverse Scattering Internal demultiple: 1D version
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Inverse Scattering Internal demultiple: 1D version
After the convolution and crosscorrelation of these subevents, this gives: a d
Prediction of
internal multiple
with exact kinematics
SE1(w) SE2(-w) SE3(w)

12. Inverse Scattering Internal demultiple: 1D version
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Inverse Scattering Internal demultiple: 1D version
How accurate is the amplitude prediction?
Actual multiple amplitude= (1-r1) *r2 *(-r1) *r3 *(1+r1)
transmission effects r1 r2 r3

13. Inverse Scattering Internal demultiple: 1D version
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Inverse Scattering Internal demultiple: 1D version
Subevent amplitudes
Sub-event 2 r1 a b c d
Sub-event 1
(1-r1) *r2 *(1+r1)
Sub-event 3
(1-r1) *r3 *(1+r1) r1 r2 r3

14. Inverse Scattering Internal demultiple: 1D version
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Inverse Scattering Internal demultiple: 1D version
Actual multiple amplitude:
= (1-r1) *r2 *(-r1) *r3 *(1+r1)
Predicted multiple amplitude:
= -1*(1-r1) *(1-r1) *r2 *(-r1) *r3 *(1+r1)* (1+r1)
Excess transmission due to these paths:
Fortunately,
(1-r12) is small,
so the error is
small

15. Inverse Scattering Internal demultiple
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Inverse Scattering Internal demultiple
The algorithm computes this operation for all possible combinations of three subevents in the data that satisfy the lower-higher-lower criteria, thereby predicting all the possible multiples in the data (including converted waves)
2D (and 3D) version contains a more complicated operation across the spatial coordinates, but in pseudo-depth (travel time), it works the same as the 1D code.
Will not predict internal multiples that are sub-wavelet length in scale. Prediction requires events that are resolvable.

16. Wavelet issues with internal multiple attenuation
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Wavelet issues with internal multiple attenuation
Method assumes that the free-surface multiples have already been removed. It has the same data pre-requisites as the free-surface procedure, so the post SRME data should be well suited to internal demultiple
BUT, using the standard SRME flow of estimating the wavelet post-multiple prediction is much more dangerous for internal multiples because minimum energy can easily be violated for internal multiples, even for large data windows. A safer approach is to use the SRME wavelet estimate and remove this wavelet prior to internal multiple prediction.

17. Wavelet issues with internal multiple attenuation
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Wavelet issues with internal multiple attenuation
Data flow:
Free-surface multiple removal (wavelet estimated)
Deconvolve SRME output data with estimated wavelet
Predict internal multiples (single order prediction)
(Mild) adaptive subtraction.
Minimum energy criteria for multiple removal is less valid for internal multiples as compared to free-surface case; therefore, the subtraction has to be carefully constrained.
Even with the source wavelet deconvolved, there is often a residual effective wavelet (finite bandwidth and limited ability of decon to flatten spectrum)

18. Wavelet issues with internal multiple attenuation
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Wavelet issues with internal multiple attenuation
Unlike the free-surface case, the effective wavelet on the internal multiple prediction has the same phase as the input data; the amplitude spectra of this wavelet differs by the autocorrelation of the source wavelet.
Why?
Consider input data with wavelet a = a(w) b1(w)
Internal multiple prediction computed using particular subevents
a(w) SE1(w) a (-w) SE2(-w) a(w) SE3(w)
=a(w) a(-w)a(w) [SE1(w) SE2(-w) SE3(w)]
= a(w) A(w) [SE1(w) SE2(-w) SE3(w)]
Zero phase (autocorrelation of wavelet)

19. Mississippi Canyon Original stack Stack after free-surface demultiple
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Mississippi Canyon
Original stack
Stack after free-surface demultiple
1.6
4.6
Seconds
Water
bottom
Top salt
Base salt
Free-
surface
multiples

20. Mississippi Canyon Stack after free-surface demultiple
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Mississippi Canyon
Stack after free-surface demultiple
& source wavelet deconvolution
Average estimated
source wavelet
1.6
4.6
Seconds
Water
bottom
400 ms
Top salt
Base salt

21. Mississippi Canyon 1-D post-stack internal multiple estimate
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Mississippi Canyon
1-D post-stack internal
multiple estimate
Stack of 2-D pre-stack
internal multiple estimate
Stack of input data
1.6
4.0
Seconds
Water
bottom
Top salt
Base salt

22. Mississippi Canyon Input Predicted multiples Output Input Predicted
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Mississippi Canyon
Input
Predicted
multiples
Output
Input
Predicted
multiples
Output
1.7
3.4
Seconds
Water
bottom
Top salt
Base salt
Internal
multiples
Common Offset Panel (1450 ft)
Common Offset Panel (2350 ft)

23. Mississippi Canyon Water Bottom Top Salt Base Salt Internal multiple
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Mississippi Canyon
Water Bottom
Top Salt
Base Salt
Internal multiple
Water Bottom
Top Salt
Top Salt
Base Salt

24. Post-stack 1-D internal
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Southern Gas Basin
Post-stack 1-D internal
multiple estimate
Stack after Tau-p decon & Radon
Primary
Primary
Primary
Internal
Multiple
Seismic data come from a non-exclusive survey owned by Geco-Prakla. Permission to use this data is gratefully acknowledged.

25. Southern Gas Basin Primary Primary Primary Internal Multiple
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Southern Gas Basin
Primary
Primary
Primary
Internal
Multiple

26. Southern Gas Basin Stack after Tau-p decon & Radon
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Southern Gas Basin
Stack after Tau-p decon
& Radon
1-D post-stack internal
multiple prediction
After internal multiple
adaptive subtraction
Internal multiples
Seismic data come from a non-exclusive survey owned by Geco-Prakla. Permission to use this data is gratefully acknowledged.

27. Common offset gathers (1000 ft)
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Southern Gas Basin
Data after WEMS,
Tau-p decon & Radon
2-D pre-stack internal
multiple prediction
Data after adaptive
subtraction
Common offset gathers (1000 ft)
Seismic data come from a non-exclusive survey owned by Geco-Prakla. Permission to use this data is gratefully acknowledged.

28. Southern Gas Basin Raw shot gather after NMO After Tau-P decon,
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Southern Gas Basin
Raw shot gather
after NMO
After Tau-P decon,
WEMS, Radon
After internal
multiple subtraction
Predicted 2-D internal
multiple
Offset
Seismic data come from a non-exclusive survey owned by Geco-Prakla. Permission to use this data is gratefully acknowledged.

29. Southern Gas Basin Raw shot gather after NMO After Tau-P decon,
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Southern Gas Basin
Raw shot gather
after NMO
After Tau-P decon,
WEMS, Radon
After internal
multiple subtraction
Predicted 2-D internal
multiple
Offset
Seismic data come from a non-exclusive survey owned by Geco-Prakla. Permission to use this data is gratefully acknowledged.

30. Southern Gas Basin AVO ‘A’ Section
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Southern Gas Basin
AVO ‘A’ Section
Before internal multiple attenuation
After internal multiple attenuation
Seismic data come from a non-exclusive survey owned by Geco-Prakla. Permission to use this data is gratefully acknowledged.

31. Southern Gas Basin AVO ‘B’ Section
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Southern Gas Basin
AVO ‘B’ Section
Before internal multiple attenuation
After internal multiple attenuation
Seismic data come from a non-exclusive survey owned by Geco-Prakla. Permission to use this data is gratefully acknowledged.

32. Inverse-scattering internal multiple attenuation conclusions
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Inverse-scattering internal multiple attenuation conclusions
Effectively attenuates internal multiples on synthetic and field data
Subsurface independent; applicable to data with simple or complex geology (no a-priori information required)
Requires accurate source wavelet removal
Highlights need for improved subtraction processes
In conclusion, the point scatterer method attenuates all internal multiples in the seismic record, it does not require any a-priori subsurface information, and it is therefore specifically designed to be effective in areas with complex geology which are increasingly the focus of our exploration efforts.

33. Delphi Internal Demultiple Methods
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Delphi Internal Demultiple Methods
Interface Based
Layer Based
Relation to Inverse Scattering Method

34. Delphi Interface Method
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Delphi Interface Method a b c d
Sub-event 2
Sub-event 1
Internal multiple
generating interface

35. Delphi Interface Method
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Delphi Interface Method
Downward continue these paths
to the interface where the internal
multiple is generated a b c d
Sub-event 2
Sub-event 1

36. Delphi Interface Method
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Delphi Interface Method
Now convolve these two subevents
as in SRME to obtain a kinematic
prediction of the internal multiple. a
SE1(w) SE2(w) d
Sub-event 2
Sub-event 1
In principle, the interface
reflectivity must be provided.

37. Delphi Interface Method
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Delphi Interface Method
Essentially the free-surface multiple prediction concept applied to a subsurface reflector
Requires:
Proper downward continuation to the interface of interest. Needs explicit velocity model or CFP operators (model dependent).
Source wavelet
Effective wavelet on the prediction has the same amplitude and phase error as the SRME prediction. Estimating this wavelet by matching the prediction to the multiples in the input data is much more hazardous than in the free-surface case. Probably better to remove the source wavelet prior to multiple prediction (as in the Inverse Scattering flow)
Estimate of interface reflectivity
Often this unknown is bundled into an adaptive subtraction. Similar to the source wavelet estimation, this has to be done very conservatively to preserve primaries.

38. Delphi Layer Method Sub-event 2 a b c d Sub-event 1 Sub-event 3
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Delphi Layer Method
Downward continue these paths
to a point below the interface where the internal
multiple is generated
Sub-event 2 a b c d
Sub-event 1
Sub-event 3
Internal multiple
generating interface
Target depth (time)
for downward
continuation

39. Delphi Layer Method Sub-event 2’ a b c d Sub-event 1’ Sub-event 3’
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Delphi Layer Method
Downward continue these paths
to a point below the interface where the internal
multiple is generated
Sub-event 2’ a b c d
Sub-event 1’
Sub-event 3’
Internal multiple
generating interface
Target depth (time)
for downward
continuation

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Delphi Layer Method
To predict the internal multiple, perform the operation
SE’1(w) SE’2(w) SE’3(w) a d
Sub-event 2’
Sub-event 1’
Sub-event 3’
Internal multiple
generating interface
Target depth (time)
for downward
continuation

41. Delphi Layer Method Giving the prediction of the internal multiple: a
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Delphi Layer Method
Giving the prediction of the internal multiple: a d

42. Delphi Layer Method How does this work?
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Delphi Layer Method
How does this work?
Apply downward continuation operator to subevents:
T = time to
target depth
Sub-event 2’=
exp(iwT) SE2 (w) exp(iwT)
Sub-event 3’=
exp(iwT) SE3 (w)
Sub-event 1’=
SE1(w) exp(iwT)

43. Delphi Layer Method SE’1(w) SE’2(-w) SE’3(w)
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Delphi Layer Method
Apply the operation
to obtain:
SE’1(w) SE’2(-w) SE’3(w)
SE1(w) exp(iwT) exp(-iwT) SE2 (-w) exp(-iwT) exp(iwT) SE3 (w)
= SE1(w) SE2 (-w) SE3 (w)
The downward continuation operators cancel, and you obtain the proper prediction
Why do the downward continuation at all? Delphi claims that the event separation (muting) is best done in the downward continued domain.
The subevents carry the amplitude information similar to the Inverse Scattering Method

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Delphi Layer Method
This works for a single interface as shown, how does the method work for a series of reflectors, i.e., a layer?
Multiple Prediction
Interface 1
A B1* C
Interface 2
A B2* C
A B3* C
Interface 3

45. Delphi Layer Method Sum these: A (B1 + B2 + B3) * C A (BN) * C
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Delphi Layer Method
Sum these:
Multiple Prediction
Interfaces
1,2 and 3
A (B1 + B2 + B3) * C
and by extension
A (BN) * C
where BN represents the series of reflectors above the
target separation depth. This approach predicts all internal multiples
that contain a downward reflection above the target depth and upward
reflections below the target depth.

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Delphi Layer Method
This approach is efficient and effective but does not predict multiples that look like:
To predict these events, you would have to iteratively define a
separation time that separates the top reflector from the rest
of the reflectors, predict the internal multiples, remove this top reflector,
and then continue doing this for all the reflectors from the top down.
This would then emulate the Inverse Scattering algorithm which does
all this automatically without all the user interaction.

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Delphi Layer Method
First
Second
Third

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Delphi Layer Method
Efficient way to predict a selected subset of multiples.
Requires:
Downward continuation to an interface that separates the upward from downward reflectors. CFP operators used, does not need to be accurate (in that way, it is subsurface independence).
Source wavelet
Has the same characteristics as the Inverse Scattering Method as far as the wavelet is concerned.
Adaptive subtraction
Must be careful, as subtraction can easily damage primaries.
May have advantage in terms of correcting for the depth dependent transmission effects by stepwise generating different predictions for different depths.

49. Internal Multiple Attenuation Comparison
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Internal Multiple Attenuation Comparison
Delphi method(s) are well suited when you have small number of strong internal multiple generators that are easily separable. These methods will efficiently and effectively predict the most important internal multiples in this situation.
The Inverse Scattering Method is useful when you have a large number of internal multiple generators that are not easily separable. This method will predict everything at once without user interaction, but at increased computation time/cost.
In this way, the two types of methods are complementary and both should be included in your processing toolbox.

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Conclusions
There are plenty of approximations made in applying 2D SRME in practice. Improving the most egregious of these will further improve our ability to remove multiples in complex situations.
Inverse Scattering and Delphi layer based method are different but complementary methods that are useful for different situations
Both are subsurface independent
Both suffer from lack of accurate wavelet information
Both require a more fit for purpose set of subtraction tools
Both require adequate removal of free-surface multiples to reach their full potential (or very deep water).

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Acknowledgements
Arthur Weglein, Fernanda Araujo Gasparotto, Robert Stolt, Richard Coates, Paulo Carvalho, Dennis Corrigan, Eric Verschuur, A.J. Berkhout, Nurul Kabir, Jim O’Connell, Andre Romanelli, Phil Christie, Steve Moore, Bill McLain, Simon Shaw
BP, Western Geophysical, Geco-Prakla